sphères d'or ont été nucléées sur chaque coin des plaquettes. Nous avons montré comment la taille des sphères peut être ajustée en modifiant la quantité de précurseur d'or, ainsi que ses effets sur le spectre d'absorption. Par des images HR-STEM, nous avons aussi montré l'orientation des cristaux, bien que comme déjà éprouvé par d'autres groupes, il soit difficile d'explorer l'interface de tels systèmes utilisant la microscopie électronique. Nous avons montré qu'aucun alignement n'est présent entre la structure de l'or et du CdSe. Cette étude est toujours en cours et peut potentiellement fournir un système très intéressant et unique.

thank you to both Michel Goldmann and Bertrand Donnio for having taken their time to so thoroughly read and report my work. My next thanks goes to the RIX ODEMC MATRIX group in general, for welcoming me within their group and making me feel at home me throughout doctorate. There are however a few people I must thank in particular: first and foremost I would like to thank Benjamin Abécassis, who followed and guided me through this experience which lasted for three and a half years. He taught me how to set up a project, proceed through the inevitable difficult moments and follow through. Throughout all this he gave me the freedom to act and to pursue the research in the direction I deemed more interesting, as well as the means to do so by making both his knowledge and competences available to me. He showed me ways to advance with my work even when it looked to me as though most all possibilities were blocked, allowing me to move forward in the intricate path that is the scientific research. Knowing the many important obligations he had during this time, such as twins to come home to every night, makes me doubly thankful for always having had time to spare to listen and help me. I would also like to thank Patrick Davidson, who helped co-direct me during my doctorate.

He always made sure to be informed on the progress of my work, the results, and the difficulties I was facing, offering advice on how to proceed. His input was always precious, i and often provided a refreshing view of the situation. Doru Constantin also played an important role in my three years and in the writing of this thesis. He provided great help with all that required mathematical interpretation. He was always available for lengthy discussions, which usually ended in explanations, and would always made sure to follow on my development of the problem. He was fundamental for the analysis of the light absorption data, as well as for the study of the folded platelets.

I also extend my thanks to Wiebke Drenckhan. I am sorry we didn't actually get a chance to work on a combined project of Janus particles and emulsions, as I believe I would have enjoyed the experience. Nevertheless I am thankful to her for having given me the possibility of finishing my work in a more timely manner, without rushing through the final steps.

My gratitude also goes to Mathieu Kociak, who accepted the role of godfather for these years. Most of all however, I have to thank him for all the assistance he provided in all that was electron microscopy. Whether it was a simple calibration of the instrument, or a full on surgical operation, in order to prolong the life of an old but oh so necessary electron microscope, he was always ready to lend me a hand. He also lent his time to help me take some wonderful high resolution images of a very difficult sample, giving us some very valuable information On a similar note, my thanks go to Jéril Degrouard and Raphaël Weil for helping me, during the last months, to obtain the microscopy images necessary to adequately respond to the referee's reports for my paper. I am certain that without their help I would not have had such a positive response, and am therefore very grateful. I would also like to mention Alberto Zobelli, who helped me set-up my code on the cluster of the LPS in order to run some long calculations. Without his help I would literally still be here waiting for my poor laptop to finish the calculating the scattering of bent platelets.

Next in my thanks must obviously come Santanu Jana, with whom I spent most of my time both in and out of the labs. In one way or another he helped me in almost all that was chemical in nature, listening to the set-backs in the reactions, and proposing ideas to work around them. His ability in understanding the synthesis of all the particles we were preparing in the lab meant that he was always able to provide insightful help when it was in need. It also resulted in the common understanding among those who worked besides him that he did not "mess up" when doing a reaction, he simply found a better, more efficient way of obtaining a better product.

To Claire Goldmann, who joined the lab during my last year and who has been by office mate ever since, thank you for teaching me all those necessary french expressions, useful in iii my day to day life, most of which have not place on a thesis. Also a great thanks for the huge effort and will needed to make everyone come together for the greater good of actually performing the much needed task of cleaning the labs. Your daily work undoubtedly makes the labs a better place to work, I just wish I had had more time to actually make use of it.

A big thank you also to Elise with whom I shared many of the daily struggles of the PhD.

It was always helpful to have someone remind me of all the important things to do, such as registering to all the PhD activities, which I would promptly forget to do until she reminded me.

Finally I would like to thank all the people outside of the lab who have been close to me in these last years, despite my geographical distance. It is always touching to return home and see how some relationships do not suffer the distance. So a big thank you to my Coach, whom, for some strange time distortion reason, I appear to reaching in age; and to all my track and field team. I would not dream of forgetting Carlo, whom I am still waiting for to come and visit during one of his bike trips, but who I will surely meet before, at the annual Christmas reunion. And a big thank you to the tight group of AISG '89 friends. It is warming to see how all these years have done nothing to our friendship and comradery.

A huge thank you to my family, which over all these years have always been supportive, which has allowed me to be here today, at the end of this long learning cycle. I know I would not be here today without your help, just as much as I know you would not be using computers without mine.

In conclusion i would like to thank Simona, with whom I embarked on our adventure 789 many years ago. Thank you for your support and help over all this time: travelling a road is always easier when you have company and I know I couldn't have found better company than you. During these last three years you have made the darker times less scary, and the lighter days so much brighter, allowing me to go on with a smile on my face and with the serenity that everything would work out.

CONTENTS

Résumé en français

Il est difficile de commencer une dissertation concernant les nanoparticules sans mentionner la présentation de 1959 de Feynman "Il y a beaucoup de place au fond" [START_REF] Feynman | There's Plenty of Room at the Bottom[END_REF] où il a prévu la possibilité de contrôler la matière à une échelle atomique pour stocker et récupérer des informations, aussi bien que créer des nano-machines. Il a proposé ces idées presque trente ans avant 1985, quand un étudiant de Stanford a finalement réussi à graver la première page deTale of Two Cities -et le relire -dans une police de caractères suffisamment petite pour "mettre toute Encyclopédie Britannica sur une tête d'épingle". Avec l'avancement des nanotechnologies des années 90, il est devenu possible de produire des objets à l'échelle nanometrique d'une façon contrôlée, tandis qu'avant 2004 des entreprises étaient capables de produire industriellement des circuits dans lesquels la taille typique était au-dessous de100 nm [START_REF]IBM PowerPC®970FX RISC Microprocessor[END_REF].

De même que Feynman doit être reconnu quand on parle des nanoparticules, de Gennes doit être mentionné quand on parle des particules Janus. Il a le mérite d'avoir popularisé le terme Janus pour faire référence aux particules qui ont deux moitiés qui diffèrent dans la composition et-ou dans les propriétés physiques [START_REF] De | Soft Matter (Nobel Lecture)[END_REF]. Ces particules, contrairement aux machines de Feynman, avaient déjà été synthétisées, mais étaient initialement de taille micrométrique. De Gennes avait prévu comment elles pourraient être utilisées pour stabiliser des émulsions de la même façon que des tensio-actifs, en maintenant une perméabilité entre l'intérieur et l'extérieur. Nous pouvons maintenant synthétiser ces particules à l'échelle de nanométrique utilisant une large variété de matériaux et ouvrant une variété de possibilités.

Tandis qu'ils possèdent des propriétés uniques, comme être des bons catalyseurs [START_REF] Wei | Janus Au-TiO 2 Photocatalysts with Strong Localization of Plasmonic Near-Fields for Efficient Visible-Light Hydrogen Generation[END_REF][START_REF] Wei | Anisotropic Growth of Titania onto Various Gold Nanostructures: Synthesis, Theoretical Understanding, and Optimization for Catalysis[END_REF], ils sont aussi étudiés pour leur comportement collectif, en particulier en ce qui concerne les ressemblances qu'ils offrent comparé aux molécules et aux tensio-actifs [START_REF] Jiang | Janus Particle Synthesis and Assembly[END_REF][START_REF] Glotzer | Anisotropy of building blocks and their assembly into complex structures[END_REF][START_REF] Bernard | Particles as surfactants-similarities and differences[END_REF]. La possibilité d'introduire des interactions directionnelles dans des structures qui sont à une échelle xi xii RÉSUMÉ EN FRANÇAIS mésoscopique pourrait aboutir à la possibilité de créer des structures ressemblant à des molécules ou à des cristaux, dans lesquelles les composants sont un ou deux ordres de grandeur plus grands que des atomes, ouvrant probablement de nouvelles possibilités en ce qui concerne la science des matériaux. Beaucoup d'études théoriques ont été concentrées sur l'auto-assemblage de ces particules en solution [START_REF] Sciortino | Phase Diagram of Janus Particles[END_REF][START_REF] Munaó | Cluster formation and phase separation in heteronuclear Janus dumbbells[END_REF][START_REF] Preisler | Equilibrium phases of one-patch colloids with short-range attractions[END_REF][START_REF] Munaó | Phase separation and self-assembly of colloidal dimers with tunable attractive strength: from symmetrical square-wells to Janus dumbbells[END_REF]. Tous ces articles montrent des structures qui peuvent théoriquement être obtenues en utilisant des nanoparticules de Janus avec des formes différentes et des propriétés théoriques. Cependant, un des points communs entre ces articles est que, pour produire des clusters organisés, les forces d'interaction doivent avoir une portée qui est comparable avec la taille des particules. Ceci n'a pas été le cas pour la plupart des études d'auto-assemblage faites sur des particules Janus jusqu'à maintenant [START_REF] Hong | Clusters of Amphiphilic Colloidal Spheres[END_REF][START_REF] Chen | Directed self-assembly of a colloidal kagome lattice[END_REF][START_REF] Chaudhary | Janus Colloidal Matchsticks[END_REF][START_REF] Nie | Janus and Ternary Particles Generated by Microfluidic Synthesis: Design, Synthesis, and Self-Assembly[END_REF] vu que la taille des particules utilisées est de l'ordre du micromètre, et dans lesquelles les interactions ont une portée d'une dizaine de nanomètres. Le développement, dans les dernières années, de procédures pour la synthèse de nanoparticules de Janus avec des tailles nanométriques ( [START_REF] Chen | Scalable Routes to Janus Au-SiO 2 and Ternary Ag-Au-SiO 2 Nanoparticles[END_REF][START_REF] Read | Au-Ge and Ag-Ge Heterodimers with Tunable Domain Sizes: A Supersaturation-Precipitation Route to Colloidal Hybrid Nanoparticles[END_REF][START_REF] Yu | Dumbbell-like Bifunctional Au-Fe 3 O 4 Nanoparticles[END_REF]) a permis de préparer des particules assez petites pour être comparables en taille avec des interactions comme celles de Van der Waals ou l'attraction hydrophobe. Néanmoins, la plupart des systèmes produits par les procédures publiées sont stables en solution et ne présentent pas d'interactions attractives, il est donc nécessaire de modifier les systèmes pour introduire les interactions nécessaires.

Nous commençons ce manuscrit en décrivant les principes physiques et mathématiques de la diffusion des rayons X aux petits angles (SAXS, de l'anglais : small angle X-ray scattering). Ceci est un technique en-situ, non destructive utilisée au cours de notre étude.

Elle est généralement utilisée dans la science colloïdale pour caractériser des particules en suspension. Le signal est sensible aux changements de taille et de polydispersité des enchantillons, permettant de mesurer avec haute précision ces paramètres. Nous montrons la précision de cette technique dans le cadre d'une étude sur les nanoparticules des PbS, PbSe. Ce travail a été fait en collaboration avec le groupe du Professeur Hens Zeger "Physics and Chemistry of Nanostructures" à l'Université du Gand, pour une étude sur la croissance des nanoparticules de semiconducteurs. Les données obtenues par SAXS ont été utilisées pour obtenir une courbe d'étalonnage plus précise pour la détermination de la taille des particules à partir des spectres d'absorption. Les données seront aussi utilisées pour mieux comprendre le mécanisme de formation de ces particules. Le fait que les mesures soient faites in-situ constitue un avantage pour l'analyse des systèmes colloïdaux, et permet d'étudier les particules en uspension sans ajouter d'artefacts. Ceci est encore plus important pour l'étude des assemblages de particules en suspension car cela apporte la certitude que xiii les structures n'ont été ni formées ni modifiées pendant la préparation type. Tandis que la taille des particules les situe vers la limite de détection de petit q pour des équipements de laboratoire, rendant les mesures des assemblages impossibles, des angles de dispersion plus petits sont accessibles sur les lignes de synchrotron. Il est donc possible d'obtenir des informations sur des clusters ayant une taille de l'ordre de centaines de nanomètres en faisant les mesures sur de telles installations.

La suite de la thèse est divisée en deux parties. Dans la première partie de cette thèse, nous décrirons le travail fait dans les trois dernières années sur un système Janus particulier, en essayant d'accéder au diagramme de phase décrit par Sciortinoet d'autres. [START_REF] Sciortino | Phase Diagram of Janus Particles[END_REF]. Parmi les nombreuses synthèses disponibles, nous avons décidé de nous approcher de l'assemblage utilisant des hétérostructures "dumbbell-like" d'or et silice. Les particules d'or possèdent plusieurs caractéristiques qui en font des candidats idéaux pour une des deux moitiés.

Premièrement, les synthèses disponibles pour l'or colloïdal sont abondantes, bien étudiées et leurs mécanismes de formation sont connus. Deuxièmement, les particules d'or ont des propriétés optiques très intéressantes. Ils présentent un spectre d'absorption particulier avec une résonance dans la gamme verte, qui explique la couleur rouge des leurs suspensions.

De plus, le spectre d'absorption est sensible aux changements environnementaux, comme un changement de solvant [START_REF] Mie | Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen[END_REF] ou des molécules en surface [START_REF] Goldmann | Charge Transfer at Hybrid Interfaces: Plasmonics of Aromatic Thiol-Capped Gold Nanoparticles[END_REF], aussi bien que l'interaction entre les particules [START_REF] Prodan | A Hybridization Model for the Plasmon Response of Complex Nanostructures[END_REF]. Les structures préparées utilisant ces particules pourraient donc être étudiées par absorbance de lumière, tout en produisant des effets optiques intéressants.

Finalement, la chimie or-thiol a été étudiée en détail, faisant de la modification des surfaces d'or un sujet connu en littérature et facilitant le réglage de l'interaction entre les particules.

La silice est aussi un matériel communément utilisé pour la synthèse des nanoparticules.

Ceci est en grande mesure en raison de la facilité avec lesquelles elles peuvent être synthétisées par la méthode St "o ber, la réaction utilisant seulement le tetraethylortosilicate (TEOS), l'ammoniaque, l'eau et l'alcool. Les hétérodimères obtenus par la combinaison de ces deux systèmes sont des particules hydrophiles, avec une absorption forte autour de 550 nm, donné par la particule d'or. La silice fonctionne comme protecteur d'un partie de la surface d'or, nous permettant d'introduire une interaction attractive sur seulement la moitié d'une particule.

Le deuxième chapitre est donc consacré à l'état de l'art de la synthèse des nanoparticules d'or, en particulier par la réduction de tétrachlorure d'or (III) (HAuCl 4 ) en solution aqueuse. Ceci est historiquement une des premières techniques décrites pour la préparation de xiv RÉSUMÉ EN FRANÇAIS colloïdes d'or. Bien que des améliorations soient toujours faites tant sur la compréhension du mécanisme que sur la procédure de synthèse, les méthodes actuelles permettent d'obtenir des particules avec une taille bien définie et une bonne monodispersité . Nous décrirons la méthode Turkevich, qui est la norme(le standard) pour la réduction de citrate de sel d'or, aussi bien que deux modifications de la synthèse qui permettent de mieux contrôler les colloïdes résultants. En particulier nous avons suivi une synthèse multi-étapes, ou les réactifs sont introduits en ordre inverse par rapport à la synthèse Turkevich traditionnelle.

Ceci nous a permis d'obtenir des particules sphériques et de choisir la taille avec précision.

Les particules produites sont le point de départ pour la préparation des particules Au -SiO 2 .

Dans le chapitre trois, nous présentons les hétérodimères utilisés pour l'assemblage. La synthèse originale provient d'un article publié en 2010 par Chen et al. [START_REF] Chen | Scalable Routes to Janus Au-SiO 2 and Ternary Ag-Au-SiO 2 Nanoparticles[END_REF], nous avons continué cependant à optimiser les paramètres pour notre cas utilisant de nouvelles particules et conditions. Nous avons constaté que la synthèse originale abouti à une grande quantité de nanoparticules d'or et de silice individuelles dans la suspension avec les colloïdes Janus. Nous avons donc étudié l'effet de la quantité d'or et TEOS utilisés afin de réduire le nombre de particules indésirables, nos échantillons en conservent toutefois une petite quantité. La diminution de la quantité de précurseur de silice a abouti à un plus grand nombre de particules d'or nues en suspension. La modification de la quantité de particules d'or en suspension nous a permis d'augmenter la proportion de particules de Janus. Nous avons constaté qu'il était possible de doubler la concentration de la suspension initiale d'or tout en conservant la même proportion de particules Janus en fin de synthèse. Nous avons également utilisé une synthèse différente pour les colloïdes d'or (celle décrite dans le chapitre d'avant). Ceci a abouti à un meilleur produit final, les particules obtenues étant davantage sphériques comparées aux particules allongées utilisées dans l'article original.

Les hétérodimères résultants sont donc plus homogènes, une caractéristique recherchée pour l'auto-assemblage.

Le quatrième chapitre -le dernier de cette première partie -explique la procédure que nous avons mise au point pour déclencher l'auto-assemblage des colloïdes ainsi que les techniques utilisées pour étudier les clusters. Pour introduire une interaction attractive entre les particules, nous avons exploité la forte interaction entre les thiols et les surfaces d'or pour échanger le ligand sur les moitiés d'or avec un alcanethiol. Le thiol a rendu la surface d'or hydrophobe, ce qui a conduit à la formation des clusters auto-assemblés dans xv l'environnement aqueux. La présence d'une coque de silice sur un des deux hémisphères a joué un double rôle : définir la taille de la surface attractive et fournir l'interaction stérique. L'effet combiné est d'empêcher une croissance incontrôlée des clusters. La formation des groupes a été caractérisée par un changement de couleur de la solution. Ceci a été étudié dans le temps par spectroscopie d'absorption et a montré l'apparition et la croissance d'un couplage plasmonique, confirmant que les particules d'or étaient proches les unes des autres (quelques nanomètres). En utilisant la décomposition en valeur singulière, nous avons divisé la formation des colloïdes en trois phases, celles initiales et finales étant caractérisées par le fait de n'avoir que deux espèces dans la solution. Cette interprétation est corroborée par la présence de deux points isobestiques, un visible pendant les dix premières heures et un second après la quarantième heure. Nous avons étendu l'analyse en préparant des échantillons avec des thiols de différentes longueurs. La position de la bande plasmon de couplage et son intensité a montré que des chaînes plus courtes mettent plus de temps à initier l'assemblage et induisent une distance interparticulaire plus faible. L'analyse de spectres d'absorbance a été complétée par l'étude du facteur de structure obtenu par mesure de SAXS. Les résultats obtenus en faisant le "fitting" du signal utilisant une approche de Monte-Carlo nous ont donné la taille moyenne des clusters aussi bien que la distance interparticulaire moyenne. Nous avons montré que la taille de groupe avait une limite supérieure de 5 particules Janus, confirmant que la silice fournit la protection nécessaire pour arrêter la croissance des clusters. Nous avons aussi trouvé une relation linéaire entre la longueur de la chaîne de thiol et la distance moyenne entre particules, dont la pente indique qu'il-y-a de l'inter-digitation entre les ligands.

A partir du sixième chapitre nous avons consacré notre étude à un système différent : les nanoplaquettes de CdSe. Nous avons analysé en détail la nucléation et la croissance des plaquettes minces de 3 monocouches (3ML), ainsi que l'enroulement des plaquettes qui forment des cylindres. La déformation est documentée, à la fin de la synthèse, par des images de microscopie électroniques. Nous avons utilisé des mesures de SAXS et de WAXS pour suivre l'évolution des plaquettes pendant leur formation. Une première étude à 200 • C a montré que les plaquettes 3ML ont une tendance à s'enrouler en cylindres d'un rayon moyen de ≈13 nm dès le début de la synthèse. Ceci se déduit de la présence d'oscillations en SAXS et de la position et la forme des sommets dans le régime de WAXS. Une étude des effets de la température de réaction sur le produit final a montré que la vitesse de la réaction est directement liée à la température à laquelle la réaction est conduite. Nous xvi RÉSUMÉ EN FRANÇAIS avons aussi remarqué qu'à hautes températures (220 • C et 240 • C) la fraction volumique des plaquettes subit une diminution courte mais significative dans l'intensité quand la solution est gardée à la température de réaction longtemps après la formation des particules. Cette diminution est seulement provisoire et est visible tant en SAXS qu'en WAXS. L'origine de ce comportement est toujours en cours d'interprétation.

Les plaquettes de CdSe ont été aussi étudiées comme point de départ pour la synthèse des hétérodimères. Dans ce cas, des plaquettes 5ML (5 monocouches) ont été utilisées et des Chapter 1

Introduction

It is hard to start a dissertation focused on nanoparticles without mentioning Feynman's 1959 talk "There's plenty of room at the bottom" [START_REF] Feynman | There's Plenty of Room at the Bottom[END_REF] where he envisioned the possibility of controlling matter at an atomic scale in order to store and retrieve information, as well as creating nano-machines. He proposed these ideas almost thirty years before 1985, when a Stanford student was able to etch the first page of Tale of Two Cities -and read it back -in a font small enough to "fit the whole Encyclopedia Britannica on the head of a pin". With the advancement of nanotechnologies in the 90's, it became possible to produce objects at the nanometric scale in a controlled way, while by 2004 companies where able to mass produce circuits in which the linewidth was below 100 nm [START_REF]IBM PowerPC®970FX RISC Microprocessor[END_REF].

Just as Feynman has to be acknowledged when referring to nanoparticles, de Gennes must be mentioned whenever Janus particles are concerned. He has the merit of popularizing the term Janus when referring to particles which have two moieties different in composition and/or properties [START_REF] De | Soft Matter (Nobel Lecture)[END_REF]. These particles, unlike Feynman's machines, had already been synthesised but were initially micrometric in size. De Gennes envisioned how they could be used to stabilize emulsions in much the same way as surfactants, while maintaining some permeability between the inside and the outside. We can now synthesize these particles at the nanometric scale using a wide variety of materials and opening up a variety of possibilities. While they own unique properties, such as good catalysists [START_REF] Wei | Janus Au-TiO 2 Photocatalysts with Strong Localization of Plasmonic Near-Fields for Efficient Visible-Light Hydrogen Generation[END_REF][START_REF] Wei | Anisotropic Growth of Titania onto Various Gold Nanostructures: Synthesis, Theoretical Understanding, and Optimization for Catalysis[END_REF], they are also studied for their collective behaviour, in particular with respect to the similarities they offer compared to molecules and surfactants [START_REF] Jiang | Janus Particle Synthesis and Assembly[END_REF][START_REF] Glotzer | Anisotropy of building blocks and their assembly into complex structures[END_REF][START_REF] Bernard | Particles as surfactants-similarities and differences[END_REF]. The possibility of introducing directional interaction in structures which are at a mesoscopic scale could result in the possibility of creating molecule or crystal-like structures in which the building blocks are one or two orders of magnitude larger than atoms, possibly unlocking new possibilities with regards to material sciences.

A lot of theoretical studies have been focused on the self-assembly of these particles in solution [START_REF] Sciortino | Phase Diagram of Janus Particles[END_REF][START_REF] Munaó | Cluster formation and phase separation in heteronuclear Janus dumbbells[END_REF][START_REF] Preisler | Equilibrium phases of one-patch colloids with short-range attractions[END_REF][START_REF] Munaó | Phase separation and self-assembly of colloidal dimers with tunable attractive strength: from symmetrical square-wells to Janus dumbbells[END_REF]. All of these articles show the theoretical structures which can be obtained using Janus nanoparticles with different shapes and properties. However, one of the common points between these works is that, in order for the self assembly to produce organized clusters, the interaction forces have to have a range which is comparable to the size of the particles. This has not been the case for most of the self-assembly studies done on Janus particles up until now [START_REF] Hong | Clusters of Amphiphilic Colloidal Spheres[END_REF][START_REF] Chen | Directed self-assembly of a colloidal kagome lattice[END_REF][START_REF] Chaudhary | Janus Colloidal Matchsticks[END_REF][START_REF] Nie | Janus and Ternary Particles Generated by Microfluidic Synthesis: Design, Synthesis, and Self-Assembly[END_REF] which use micrometre sized particles, in which the interactions have a range of tens of nanometres. The development, in the last years, of procedures for the synthesis of Janus nanoparticles with nanometric sizes ( [START_REF] Chen | Scalable Routes to Janus Au-SiO 2 and Ternary Ag-Au-SiO 2 Nanoparticles[END_REF][START_REF] Read | Au-Ge and Ag-Ge Heterodimers with Tunable Domain Sizes: A Supersaturation-Precipitation Route to Colloidal Hybrid Nanoparticles[END_REF][START_REF] Yu | Dumbbell-like Bifunctional Au-Fe 3 O 4 Nanoparticles[END_REF]) has made it possible to prepare particles small enough to be comparable in size to interactions such as the van der Waals or hydrophobic attraction. Nevertheless, most of the systems produced through published procedures are stable in solution and do not present any attractive interactions, it is therefore necessary to modify the system in order to introduce the necessary interactions. We start this manuscript by describing the physical principle and mathematical description of small angle X-ray scattering. This is a non-destructive, in-situ technique used throughout our study. It is a commonly used technique in colloidal sciences to characterize particles in solution. The signal is sensitive to changes in the size and polydispersity, allowing one to measure with high precision and accuracy these parameters. We show the precision of this technique in the framework of a study on the PbS, PbSe nanoparticles. This work was done in collaboration with the group of Prof.

Zeger Hens "Physics and Chemistry of Nanostructures" at Ghent University as a study on the growth of semiconducting nanoparticles. The data obtained from the small angle scattering was used to obtain a more precise calibration curve for the determination of the particle size starting from the absorption spectra. The data is also being used to better understand the mechanism of formation of these particles.

The fact that the measurements are done in-situ provides further benefit to the analysis of colloidal systems, as it allows to probe the particles within the solution without introducing artefacts. This is of even greater importance when studying organized assemblies of particles in solution as it ensures that the structures where not formed or modified during the sample preparation. While the size of the particles places them towards the small q detection limit for in-lab machines, making measurements of the assemblies impossible, smaller scattering angles are accessible on synchrotron lines. Therefore, it is possible to obtain information from clusters which are of the order of hundreds of nanometres by doing the measurements at such facilities.

In the following chapters, we will describe the work done in the last three years on a particular janus system, striving to access the phase system diagram by Sciortino et al. [START_REF] Sciortino | Phase Diagram of Janus Particles[END_REF]. Between the many available syntheses, we decided to approach the assembly using dumbbell-like heterostructures of gold and silica. Gold particles possess several characteristics which make them ideal candidates as one of the two moieties. Firstly, the syntheses available for colloidal gold are abundant, well studied, and their formation mechanisms are known. Secondly, gold particles have very interesting optical properties. They present a particular absorption spectrum with a resonance in the green range, resulting in brightly colored solutions. The absorption spectrum is sensitive to environmental changes, such as a change in the solvent [START_REF] Mie | Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen[END_REF] or the surface ligands [START_REF] Goldmann | Charge Transfer at Hybrid Interfaces: Plasmonics of Aromatic Thiol-Capped Gold Nanoparticles[END_REF], as well as the interaction between particles [START_REF] Prodan | A Hybridization Model for the Plasmon Response of Complex Nanostructures[END_REF]. The structures prepared using these particles could therefore be studied through light absorption technique, as well as produce interesting optical effects. Finally, gold thiol chemistry has been thoroughly studied, making the modification of gold surfaces a known subject in literature, and facilitating the tuning of the interaction between the moieties. Silica is also a common material when working with nanoparticles. This is in large part due to the ease with which it can be synthesized through the Stöber reaction using only tetraethylortosilicate (TEOS), ammonia, water and an alcohol. The heterodimers obtained from the combination of these two systems are hydrophilic particles, with a strong absorption at around 550 nm, provided by the gold particle. The silica serves as a protector of part of the gold surface, allowing us to introduce an attractive interaction between only half of the particles.

The second chapter is dedicated to the state of the art of gold nanoparticle synthesis, in particular through the reduction of gold(III) tetrachloride (HAuCl 4 ) in aqueous solution. This is historically one of the first techniques described for the preparation of gold colloids.

Even though improvements are still made on both the understanding of the mechanism and the synthesis procedure, the current methods allow for the preparation of finely tuned and monodisperse particles. We will describe the Turkevich method, which is the standard for citrate reduction of gold salt, as well as two modifications of the synthesis which allow to better control the resulting colloids. The particles produced will be the starting point for the preparation of the Au -SiO 2 particles.

In the third chapter we will introduce the heterodimers published in 2010 by Chen et al. [START_REF] Chen | Scalable Routes to Janus Au-SiO 2 and Ternary Ag-Au-SiO 2 Nanoparticles[END_REF]. The particles obtained from this procedure are gold spheres with a silica sphere covering roughly half of the gold. We varied some of the parameters of the synthesis in order to find the conditions required to have as many janus particles in solution, while minimizing the number of bare gold and silica particles. In particular, we studied the effect of the concentration of the initial gold solution and the role of the amount of silica precursor (TEOS).

The fourth chapter is dedicated to the self-assembly of the heterodimers produced in chapter three. We explain how we induce the assembly by using the strong affinity of thiols for gold surfaces. We then proceed with an in-depth analysis of the clusters obtained. The analysis is done using two different techniques: light absorption and small angle X-ray scattering. The first relies on the dependence of the absorption spectrum on the interaction between gold particles. The properties of this technique allowed us to gather time-resolved data on the solution, thus providing information on the kinetics of the assembly. The SAXS analysis provides more detailed information on the structure of the clusters themselves such as the size and the inter-particle distance. Due to experimental constraints though, we could only obtain a snapshot of the system at a single time during the evolution. It was therefore important to use information from both sources to provide a complete picture of the evolution of the clusters.

The last two chapters are dedicated to a different system, namely that of CdSe platelets. These are quasi 2D semiconductor particles whose unique optical-electronic properties derive from the reduced size in one of the three dimensions. They produce very sharp emission peaks at different wavelengths depending on their thickness. The possibility of preparing samples in which the particles all have the same thickness [START_REF] Ithurria | Quasi 2D Colloidal CdSe Platelets with Thicknesses Controlled at the Atomic Level[END_REF] means they are ideal candidates for the production of both solar cells as well as light-emitting products, such as computer screens.

In the first of the two chapters, we study the nucleation and growth of thin platelets which have a tendency to fold and roll up. The nucleation and growth mechanisms of these particles are of great interest, particularly with regards to the reasons behind such anisotropic growth. Unlike CdSe particles with wurtzite, whose anisotropic growth can be attributed to preferential growth along the c-axis [START_REF] Alivisatos | No Title[END_REF] or ligand adsorption along preferential crystalline faces [START_REF] Manna | Synthesis of Solube Rod-, Arrow-, Teardrop-, and Tetrapod-Shaped CdSeNanocrystals[END_REF], the platelets synthesised by Dubertret et al. have an isotropic zinc-blend structure, which cannot easily explain the formation of platelets. Furthermore, the thin CdSe nanoplatelets have been found to bend over themselves and form cylinders, a behaviour which can be reversed by changing the surface ligands on the particle [START_REF] Bouet | Two-Dimensional Growth of CdSe Nanocrystals, from Nanoplatelets to Nanosheets[END_REF].

By probing the growth of the platelets using X-ray scattering we are able to gain more insight on the evolution of these platelets during their synthesis. A first analysis is done by electron microscopy to confirm the folding of the particles. SAXS and wide-angle X-ray scattering (WAXS), are then used to study how the platelets form and bend. The analysis is done both by simulating the scattering pattern of the platelets, using analytical and numerical methods, as well as by looking at the general behaviour of the signal at small q for the SAXS, and of the evolution of one of the scattering peaks in the WAXS region. In the second part of the chapter, the signals obtained from synthesis performed at different temperatures are also analysed. This allowed us to assess the role of the temperature on the nucleation and growth of the particles.

In the seventh chapter, we introduce a new heterostructure starting from the CdSe platelets, onto which we grow gold beads. The noble metal/semiconductor interaction is a very interesting one. It can, for example, result in enhanced catalytic properties. The procedure for the preparation of the colloids is simple and reliable, it produces regular structures where the rectangular semiconductor colloids are decorated with golden beads on the corners. The final size of the beads can be easily tuned by varying the amount of gold precursor used, obtaining spheres with a radius from 1 nm to 2.5 nm. The system is still being studied, in particular to try and determine how and where the nucleation occurs, and to see how these beads can modify the interaction between platelets.

A concluding chapter is dedicated to summarising the results of this work, as well as offering prospectives for both the Au -SiO 2 heterodimers, as well as the CdSe -Au structures.

Chapter 2

Sizing of Nanoparticles by SAXS

Characterizing synthetic nanoparticles

The characterization of a synthesis batch of nanoparticles is a non-trivial but fundamental question to consider. The size of nanoparticles affects many of the properties of the colloids: below a certain radius colloids can exhibit anomalous magnetic behaviour [START_REF] Kodama | Finite Size Effects in Antiferromagnetic NiO Nanoparticles[END_REF], in biological studies the size of the particle can change the uptake in mammals [START_REF] He | Effects of particle size and surface charge on cellular uptake and biodistribution of polymeric nanoparticles[END_REF], while for plasmonic particles the size determines the wavelength of maximum absorbance [START_REF] Haiss | Determination of Size and Concentration of Gold Nanoparticles from UV-Vis Spectra[END_REF]. the shape can also change how the ligands on the surface of the particles behave, influencing things such as the structure of the molecules [START_REF] Himadri | Effect of the Surface Curvature on the Secondary Structure of Peptides Adsorbed on Nanoparticles[END_REF], or the apparent pKa of the coating [START_REF] Wang | How and Why Nanoparticle's Curvature Regulates the Apparent pKa of the Coating Ligands[END_REF]. The distribution of the particles is another important parameter, in particular when the system is used for self assembly as this process is sensity to the size distribution of its building blocks [START_REF] Peter | Monte Carlo study of freezing of polydisperse hard spheres[END_REF][START_REF] Pusey | The effect of polydispersity on the crystallization of hard spherical colloids[END_REF][START_REF] Pusey | Liquids, Freezing, and the Glass Transition[END_REF]. Many different methods are available to determine the size of nanoparticles, among the most common methods are: electron microscopy and light scattering.

TEM

Transmission electron microscopy (TEM) allows the user to have an image in the direct space of the object being observed. As such it is often the most straightforward way of characterizing particles, and will be often used throughout the manuscript. It has however some inherent limitations such as the relatively small sample size which can be analyzed.

When characterizing the size of particles by microscopy, several thousands are usually measured at most, with the precision of these measurements usually dependent on the resolution of the camera and the measurement procedure. Most of the time, the analysis can be automatized using an image analysis software such as ImageJ [START_REF] Schneider | NIH Image to ImageJ: 25 years of image analysis[END_REF]. Human intervention is often needed though, in order to fix possible mistakes made by the computer. Besides the issue of analyzing the images, the preparation of the grids used for electron microscopy also poses a problem. The grids are usually prepared by either drop casting -placing a drop of the sample on the grid and allowing it to dry -or by immersing the grid directly in the solution and then allowing it do dry in air. The drying process can introduce artifacts in the grid, in particular if there are supra-structures in the sample held together by weak forces. Furthermore the colloids tend to aggregate during the evaporation of the solvent, forming large structures which make it impossible to discern individual particles.

Small-Angle X-ray Scattering

While somewhat less intuitive to interpret, light scattering is a convenient alternative to electron microscopy which addresses the issues present in TEM. Though the basic formalism for the scattering of electromagnetic waves is not dependent on the type of light used, we will refer to X-ray scattering, more precisely small-angle x-ray scattering (SAXS), throughout the manuscript, as that is the technique used to do the characterization of the nanoparticles. The measurement is based on the elastic , or quasi-elastic, single scattering of x-rays by particles in an non-homogeneous medium. When an incoming photon interacts with a volume element it induces a dipole moment whose strength depends on the dielectric constant of the volume. As a result radiation is emitted at the same wavelength (hence the elastic scattering) over the whole solid angle. If the whole sample were homogeneous, with no differences in the dielectric constant, destructive interference between the scattered waves would impede the formation of a scattering pattern. The presence of variations in the dielectric constant of the sample results in the formation of variations in the intensity of the scattered radiation. The scattering signal is therefore a measurement of the variation of the dielectric constant in the sample made in the reciprocal space. Small angle X-ray scattering measurements deal, in particular, with x-rays scattered within a solid angle θ <10°, therefore they allow the probing of structures which range from nanometre size to several tens or sometimes hundreds of nanometres depending on the smallest accessible angle.

Unlike electron microscopy, SAXS measurements provide very statistically significant sample size. The signal is averaged over the whole cylinder of interaction between the beam and the sample, for the duration of the exposure. This means that a beam measuring 0.45 µm x 0.06 µm interacting with a 1 mm capillary containing a solution of Au nanoparticles with a concentration of 10 × 10 15 nanoparticles•L -1 will average the signal from 10 × 10 7 nanoparticles. Using these estimates the sample size is at least several orders of magnitude larger with respect to electron microscopy, where sample sizes are rarely above 10 × 10 4 nanoparticles. SAXS is also well suited for measurements of samples in solution, thus avoiding to interfere with the nanoparticles and allowing one to study the interaction between the particles without introducing external disturbance. If particularly intense light sources are used, such as at synchrotrons, multiple measurements can be made at short intervals, effectively allowing one to closely follow the evolution of a reaction. The resulting pattern from a scattering measurement is also sensitive to anisotropies in the sample, it is thus possible to efficiently study systems with long range orientation such as liquid crystals.

All of these possibilities make small angle x-ray scattering a very appealing technique in soft matter and colloidal sciences. On the other hand, unlike electron microscopy, the data obtained from x-ray scattering is in the reciprocal space. As such, recovering the statistical characteristics of the sample from the scattering pattern is an inverse problem, which can be solved if the direct solution is known. Because of this, the result of a SAXS experiment is often less intuitive to interpret compared to electron microscopy. Furthermore, care has to be taken in the setup of the experiment in order to correctly remove the background and normalize the intensity if information such as the concentration of the particles is to be calculated. Finally, even though SAXS is, per se, a non destructive analysis method, x-rays can cause radiation damage, especially during long exposures or when high energy/flux sources are used. It is thus always important to ensure that the sample is not damaged by the measurement; this is usually done by repeating the measurement several times and comparing the result, checking that the pattern has not changed between the first and last exposures.

Theory

In order to interpret a scattering pattern, it is necessary to understand how the pattern is formed by the scattering from an assembly of particles.

Absolute scattering intensity

In a typical SAXS experiment, a coherent light beam with a flux N 0 (photons/s) interacts with a sample of volume V and thickness d. The sample causes a fraction of the flux (∆N ) to be scattered elastically in direction k d within a solid angle ∆Ω. The flux fraction which is scattered to a given direction is given by [START_REF] Spalla | Neutrons, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter[END_REF]:

∆N = N 0 T d V δσ δΩ ( k d )∆Ω, (2.1)
with T being the transmission of the sample which depends on the sample thickness (d)

and its linear attenuation coefficient (µ): T = e -µd . δσ/δΩ( k d ) is the differential scattering cross section, which depends on the specific interaction between the sample and the beam.

From eq.(2.1) it is possible to define the intensity I scattered by a unit volume as:

I(m -1 ) = 1 V δσ δΩ ( k d ) = ∆N N 0 1 T d∆Ω . (2.2)
This quantity is experimentally accessible, provided the sample thickness (d), its transmission, as well as the setup properties, such as the beam flux (N 0 ) are known. When treated in order to take into account these parameters, the data is said to be in absolute scale. Two signals normalized to absolute scale can be effectively compared, regardless of the characteristics of the set-up, such as: the flux of the incident beam, the thickness of the sample, the distance between the sample and the detector, etc.

When analyzing scattering patterns it is customary to refer to the scattering vector modulus (q) rather than the wave vector of the scattered beam. The scattering vector is defined as the difference between the incident and scattered beam wave vectors ( k dk i ), the amplitude is then defined by:

q = 4π λ sin(Θ) (2.3)
where λ is the wavelength of the beam and 2Θ is the angle between the incident and the scattered beams. The intensity at a given scattering vector q thus gives information on the sample structure in the scale of 2π/q (Fig. 2.1). In a typical SAXS experiment, the measured scattering vector is between 0.006 nm -1 and 6 nm -1 , which in direct space converts to a scale between 1 µm and 1 nm

Wave-matter interaction

While the equations presented up to now are generally valid for all light sources, provided the correct wave-matter interaction is known, the interaction itself strongly depends on the wavelength used, and can be characterized by the contrast of the sample. When analysing colloidal sample the contrast is the difference in scattering length density between the colloids and the solution (∆ρ = ρ colρ sol ). In the case of x-rays, the beam has enough energy to interact with all the electrons in the sample, the sample can then be described by the local density of electrons ρ e . Elements with a higher electron density will be prevalent in the scattering pattern while elements with a lower weight will not scatter as much.

With visible light on the other hand, only the most external electron shell can interact with the incoming wave, and the scattering length density is then proportional to the polarisability of the atom. Finally, when using yet another type of wave, neutrons, the scattering length density depends on the atomic nucleus, making it possible to differentiate between isotopes, for example between Hydrogen and Deuterium, which have a scattering length of -0.3742 × 10 -12 cm and 0.6671 × 10 -12 cm respectively. The x-ray scattering length for a particular atom can easily be calculated using Thomson's scattering length b = e 2 /(4π 0 mc 2 ) which is equal to 0.282 × 10 -14 m, the atomic number of the atom (Z), its atomic mass (M ) and density(d) using the following equation:

ρ = ZdN a M b (2.4)
where N a is Avogadro's number.

When working with x-rays, it is also possible to approximate the interaction of the beam with the sample by arguing that the interaction of the beam with one of the scatterers does not depend on that of the other scatterers present. This approximation, called Born's approximation in the case of x-rays, allows us to define the amplitude of the scattered wave at a given q vector by a volume V as:

A(q) = V ρ r e -i q• r d r. (2.5)
Using eq.(2.5), the scattered intensity per unit volume is thus described by:

I( q) = A( q)A * ( q) V . (2.6)
Combining eq.(2.6) and eq.(2.5), the intensity can be defined as:

I( q) = V γ( r)e -i q• r d r (2.7)
where the function γ is the correlation function and is defined by:

γ( r) = 1 V V ρ( r)ρ( r )e -i q•( r-r ) d rd r = 1 V P ( r) (2.8)
where P ( r) is called Patterson function. Eq.(2.7) shows that the scattered intensity is in fact the Fourier transform of the spatial correlation function of the scattered length density.

From 3D to 2D and 1D

The process of recording a scattering pattern is a transformation from a 3-dimensional space (the cylinder of interaction between the beam and the sample) to a 2-dimensional space (the surface of the detector). In the case of isotropic samples (in which there is no preferred orientation), the pattern on the detector is radially symmetrical -in polar coordinate, pixels with the same r have the same intensity save for random noise. In this case, and only in this case, the dimensionality of the data can be further reduced by doing a radial average (averaging over a given r for 0 ≤ Φ ≤ 2π), thus producing a 1-dimensional pattern, without losing information (Fig. 2.2). During the first transformation though, information is lost due to the reduction of the dimensionality. Passing from R 3 → R 2 , the measured information is obtained by averaging over all possible orientations. As a result, it is impossible to recover the original structure solely from the diffraction pattern without any further information. This is known as the inverse scattering problem, and presents no unique solution. On the other hand the direct problem can be solved exactly, giving a basis from which to start for the fitting of the data, provided a minimal amount of information is known about the sample a priori. The direct problem can then produce an initial spectra, adjustments are made to the supposed structure, and the process is repeated until a pattern is found which fits the data within the statistical accuracy.

Scattering by a single particle

If the system is dilute enough that no correlation exists between the particles, the total scattering signal is the sum of the signals coming from all the particles. It is then sufficient to know the scattering of one particle to obtain the total signal. Given a particle of scattering density ρ( r), the normalized scattered amplitude is:

a( q) = V ρ re -i q• r d r = f ( q), (2.9)
which gives a scattered intensity of:

I P art = a( q)a * ( q) = V 2 P art P ( q), (2.10)
where:

P ( q) = 1 V 2 P art V P art ρ( u)ρ( v)e -1 q•( u-v) d ud v, (2.11)
and is also known as the form factor of the particle. It is important to note here that the scattering intensity of a single particle depends on the square of its volume (eq.(2.10)). The signal coming from a sphere with radius 2R will be 64 times more intense compared to that coming from a spherical particle with radius R. As a result of this, SAXS patterns will be strongly skewed by a relatively small population of large particles. Using eq.(2.10)

along with the fact that the total intensity is the sum of the single scattering intensities, the absolute scattering intensity of a sample is:

I( q) = N V V 2 P art P ( q) = ΦV P art P ( q) (2.12)
where Φ is the volume fraction of the particles in solution. It is then clear that, if the form factor is known, it is possible to resolve the inverse problem of characterizing the particles in solution from their scattering pattern. In the most general case, the form factor can be calculated by averaging the form factor of the particle over all possible orientations with respect the direction of the incident beam. In the case of spherical particles though, this is not necessary, and if the scattering density is homogeneous within the particle the form factor is known and given by:

P ( q) = ∆ρ 2 V P art P art e iqr dr = ∆ρ 2 3 sin(qR) -qRcos(qR) (qR) 3 2 (2.13)
Along with the form factor of spheres, analytical functions for many different shapes are known, such as for hollow spheres, cylinders, platelets [START_REF] Skov Pedersen | Neutrons, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter[END_REF]; more complex structures may not have an analytical function to describe them.

Scattering by an assembly of dilute polydisperse spherical particles

Eq.(2.12) described the scattering intensity by a solution containing identical spheres.

If the size of the spheres is not monodisperse, but follows a distribution, the final pattern will be a weighed average of the single particles [START_REF] Skov Pedersen | Neutrons, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter[END_REF]:

I(q) = c ∞ 0 D(R)V (R) 2 P (q, R)dR (2.14) I(q) = c∆ρ 2 (4π) 2 ∞ 0 D(R)R 6 sin(qR) -qRcos(qR) (qR) 3 2 dR, (2.15)
where c is the concentration of particles in solution, ∆ρ is the difference in scattering length density between the particles and the solution and D(R) is the distribution function of the radius of the particles. The distribution has to be normalized such that its integral has a value of 1. The two distributions which will be used in this manuscript are the normal distribution:

D(R, R 0 , σ) = 1 √ 2πσ e -(R-R 0 ) 2 2σ 2 , (2.16)
which has an average of R 0 and a full-width at half-maximum 2 2ln(2)σ, and the Schultz-Flory distribution, defined as:

D(R, R 0 , Z) = 1 R 0 R R 0 Z-1 Z Z e -Z R R 0 Γ Z , (2.17)
were R 0 is the maximum of the distribution, Z a parameter which is related to the variance by Z = 1/σ 2 and:

Γ(n) = ∞ o = (n -1)!. (2.18)
For both of these equations, an analytical solution exists when they are inserted in eq. (2.14) which enables to calculate the exact scattering intensity at a given q value. For the normal distribution :

I(q) = c∆ρ 2 4π 3q 2 1 + q 2 (R 2 0 + σ 2 ) 2 + q 2 R 2 0 -1 2 - 3 2 q 2 σ 2 -2q 4 σ 4 cos(2qR 0 )- qR 0 (1 + 2q 2 σ 2 ) sin(2qR 0 ) e -2q 2 σ 2 (2.19)
while using Shultz's distribution:

I(q) = 8π 2 × R 0 Z -1 6 × Z + 1 qR 0 (Z+7) × Z + 1 qR 0 -(Z+1) - 4 + Z + 1 qR 0 2 -Z+1 2 cos Z + 1 arctan 2 Z+1 qR 0 -2(Z + 1) 4 + Z + 1 qR 0 2 -Z+2 2 sin Z + 2) arctan 2 Z+1 qR 0 (2.20)
As can be seen from Fig. 2.3A) the position of the first minimum (q min ) in the plot is inversely proportional to the mean radius of the nanoparticles, following the equation q min × R = 4.5. On the other hand, as the polydispersity of the sample increases, the oscillations dampen. The form of the function is thus strongly dependent on both parameters of the distribution, with each parameter affecting the curve in a different way. As a result of this, as seen in 2.2.3, if the sample is known to be a dilute solution of spherical or quasispherical particles, it is possible to precisely determine the properties of the nanoparticles from their scattering pattern.

Asymptotic behavior

If the form factor of the particles is not known, as is the case for more complex particles, important information can still be obtained from the scattering pattern by studying its behaviour at both the small q range limit and the large q limit.

Scattering intensity for q → 0 The scattering intensity in the limit of very small q values is of particular interest for very dilute systems with no interaction between the particles. If the system is too concentrated, the interactions will affect the scattered intensity for q → 0, with a higher intensity indicating attractive interaction between the particles, and a decreasing intensity characterizing particles with repulsive interaction. More in-depth analysis is thus impossible as the signal from the interaction will blur any other information, but in dilute systems the form factor can be studied and can be seen to follow a general form described by the following expansion:

P (q) = 1 V P art D 0 4πγ P art(r) r q qr - (qr) 3 6 + . . . dr, (2.21)
which can be transformed to:

P (q) = 1 V P art D 0 4πr 2 γ P art(r) dr 1 - (qR G ) 2 3 + . . . , (2.22) if:
R 2 G = 1 2

V P art r 2 γ(r)dr

V P art γ(r)dr , (2.23)
which is the definition of the gyration radius. For the limit of very small q, the intensity scattered by a solution of dilute particles can be approximated by:

I(q) ≈ ΦV P art e -(qR G ) 2 3
(2.24)

CHAPTER 2. SIZING OF NANOPARTICLES BY SAXS

This is known as the Guinier approximation [START_REF] Guinier | Small angle scattering of X-rays[END_REF], and it allows to determine the radius of gyration of particles in solution by fitting the small q regime of the scattering pattern.

It is important to note that the approximation considers "small q", those values of wave vector modulus for which the relationship qR G < 1 holds true. The radius of gyration is thus often obtained by iterating a fitting of the curve followed by confirmation of the above relationship.

Scattering intensity for large q

In the case of a biphasic system, with two phases of density ρ 1 ,ρ 2 and volume fraction Φ and 1 -Φ respectively, the scattered intensity can be defined by [START_REF] Spalla | Neutrons, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter[END_REF]:

I m(q) = 4πΦ(1 -Φ)(∆ρ) 2 ∞ 0 r 2 γ 0(r) sin(qr) qr dr, (2.25)
the equation can then be rearranged to give:

Q = ∞ 0 I m(q) q 2 = 2π 2 Φ(1 -Φ)(∆ρ) 2 , (2.26)
with ∆ρ equal to ρ 1ρ 2 within Φ and 0 elsewhere. Q is called the Porod invariant, and, as it does not depend on the shape of the two phases, it allows to determine the relative volume fraction of each in the sample. The only information required, besides the measured and normalized spectra, is the scattering density of both phases and the behaviour of the scattering pattern for q → ∞ (for spherical particles I ∼ q -4 ). It is important to note that for the integral to have a finite value, I must decrease with order O(q -3 ) or greater.

Scattering from an assembly of nanoparticles

The calculations done up to this point assumed that the solution was sufficiently dilute that no correlation was present between the particles. It was thus possible to base all the calculations on the scattering signal of a single particle and the fact that the total scattering was simply the sum of the signals from different scatterers, giving rise to eq.(2.10). In the case of a more concentrated sample, or of larger structures, formed by assemblies of the primitive ones, the problem has to be approached differently. Starting from Eq. (2.6), which was introduced before the assumption of non-interacting colloids, an average over time has to be done in order to take into account the brownian dynamics of the system.

For an ergodic system, the intensity then becomes [START_REF] Spalla | Neutrons, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter[END_REF]:

I( q) = A( q)A * ( q) V = 1 V ρ( r)e -i q• r d r ρ( r )e i q• r d r (2.27)
If the center position of a particle r i is introduced and r = r i + u, the intensity then becomes:

I( q) = 1 V N i=1 e -i q• r i V P art ρ( u)e -i q• u d u N j=1 e -i q• r j V P art ρ( v)e i q• v d v (2.28)
equation (2.28) can be rearranged to:

I( q) = N V V P art ρ( u)ρ( v)e -i q•( u-v) d ud v 1 N N i=1 N j=1 e -i q•( r j -r i ) (2.29)
Supposing the particles are spherical in shape and monodisperse, then the average can be commuted with the product, as a result the first term simplifies to the form factor V 2 P art P (q) defined in eq (2.11). The second term is called the structure factor S( q):

S( q) = 1 + N -1 V N i=1 N j =1 e i q•( r j -r i ) d r (2.30)
when going to the continuous limit:

S( q) = 1 + N -1 V V g( r)e i q• r d r (2.31)
with g( r) being the pair correlation function of the particle center of mass. By joining eq.(2.31) and eq.(2.29), a fundamental equation is obtained:

I( q) = ΦV P art P ( q)S( q). (2.32)
This equation shows that the total signal from an assembly of scatterers is the product of the signal obtained by the individual particles (the form factor P ( (q))) and the structure factor arising from the correlation between particles. As the structure factor describes interactions between the particles, the typical distances involved are greater than those of the form factor; thus the effect of S( q) are visible at shorter wave vectors, and the function tends to 1 for larger values of q. The result of introducing the structure factor in a system is shown in Fig. 2.4. In the case where there are no correlations between the position of the colloids, the second term in both Eq.(2.30) and Eq.(2.31) is 1 and S(q) = 1, Eq.(2.32) becomes Eq.(2.12).

The structure factor of a particular assembly of nanoparticles can be simulated using Debye's formula [START_REF] Debye | Zerstreuung von Röntgenstrahlen[END_REF]. The formula was originally derived to calculate the scattering of atoms within a crystal lattice, but, as it does not depend on the size of the objects but only on the relative positions of the scatterers, the formula can be used to simulate the structure factor of any assembly as long as the particles can be approximated as spheres of equal size.

S(q) = 1 + 2 N -1 i=0 N j=i+1 sin(qr ij ) qr ij (2.33)
where i and j are the indices of different particles within the assembly.

Experimental setup

The SAXS patterns presented throughout this thesis were recorded either on the ID02 line at the ESRF in Grenoble or on the SWING beamline at the SOLEIL synchrotron in Gif-sur-Yvette. Both of these facilities are synchrotrons dedicated to the study of matter through its interaction with X-rays.

Synchrotron radiation

The working principle of a synchrotron is to use rapidly accelerating charged particles (electrons) as a source of radiation for experiments which require the use of intense light beams. The emission of radiation was at first detected as a secondary (and unwanted) effect of the acceleration of electrons in an electron gun [START_REF] Elder | Radiation from Electrons in a Synchrotron[END_REF]. In order to obtain beams with high intensity, electrons are made to travel in a large torus under vacuum. The change in direction causes the electrons to emit radiation tangentially to their trajectory. As the speed of the electrons approaches relativistic speeds, the cone of emission of the radiation becomes more and more focused. At the same time though, the emitted radiation spectra widens. As a result monochromators are used as well as collimators to prepare the beam.

Third-generation synchrotrons, such as ESRF and SOLEIL, use a primary linear accelerator (LINAC) to give an initial boost to the particles. The electron beam is then accelerated in a first loop called a booster, until it reaches the correct speed. The electron beam is then injected into the storage ring. There, the electrons are kept at speed through electromagnetic elements. Multiple beamlines are inserted tangentially along the storage ring. The beam first passes through a series of optical elements (monocromator, mirror,. . . ) which produce a well-collimated monocromatic beam. The beam then travels to another room where the sample can be placed. The whole path of the beam, up to the sample, takes place in a vacuum. The beam then passes through an x-ray transparent window (e.g. beryllium) in order to make the positioning of the sample easier. The scattered x-rays, enter a vacuum chamber through the same sort of window, in order to form the pattern on the detector. The distance of the detector from the sample, which can vary from about 1 m to several tens of meters, as well as the size of the detector, determine the q-range which is recorded on the detector. The detector is often placed on a movable support in order to increase the q-range of the beamline. The importance of minimizing the length of the path in atmosphere is to maintain the highest possible intensity of the scattered beam, as well as to avoid noise due to air scattering, and thus maximize the signal-to-noise ratio.

The intensity of the incoming beam is characterized by its brilliance, expressed in photons s -1 mm -2 mrad -2 . On synchrotron beamlines, the brilliance is in the order of 10 21 photons s -1 mm -2 mrad -2 , which, compared to traditional x-ray tubes which have a brillance of

Sample preparation

The samples are analyzed in solution and thus require very little preparation before the experiment. It is important to make sure that the solutions are dilute enough that no large aggregates are present. As mentioned earlier, the scattering intensity of a particle scales like the square of its volume, meaning that information from smaller particles is quickly overshadowed by that of larger ones. The solutions are usually placed in quartz or glass capillaries with a diameter which varies from 0.5 to 2 mm. The capillaries are then inserted in holders which have multiple holes; the holder is then placed in position between the incoming x-ray beam and the detector chamber. Flow cells can also be used when precise measurements are needed. In such cases, both the blanks and the samples can be measured in the same capillary, allowing the user to directly compare the patterns as both the thickness of the sample and the signal coming from the capillary remain the same.

Obtaining intensities in absolute scale

In eq.2.2 the absolute scattering intensity was introduced as an important measure to derive information such as the concentration of nanoparticles in solution. The equation is presented again here for convenience:

I(m -1 ) = ∆N N 0 1 T e S ∆Ω
While not always necessary, this information can sometimes be useful, and appropriate steps need to be taken during the experiment in order to derive the absolute scale from the raw data. The equation presented earlier includes the thickness of the sample, the transmission as well as a series of experimental values which vary from setup to setup. This part of the manuscript will thus show how the absolute measurement was obtained for some of the samples studied.

In order to obtain information regarding the experimental parameters, characteristic of the line and setup, a primary reference sample is used. The sample can be a variety of different materials, as long as the scattering diagram is known, as well as the thickness. During our experiments, we used a glassy carbon sample, with a thickness of 1 mm, whose normalized spectrum was supplied by the producer [START_REF] Zhang | Glassy Carbon as an Absolute Intensity Calibration Standard for Small-Angle Scattering[END_REF]. Comparing the intensities of the supplied curve with the experimental data provided with a multiplicative factor which could be applied to all the data as a means of normalizing the setup parameters. In order to have constant thickness for all measurements, a flow cell was used; this is fundamental, as the to the pattern provided with the sample. A multiplicative factor of 5.197 × 10 -2 m -1 is found and will be used to multiply all the other spectra. B) The spectra of toluene (minus the one of the capillary) is first multiplied by the multiplicative factor found with the glassy carbon, and then divided by the thickness of the capillary. In this case, the value found was 0.9976 mm. capillary thicknesses are only nominal and can vary greatly. The pattern from the empty capillary along with patterns for pure water and toluene were recorded to extrapolate the thickness of the flow cell capillary. The two solvents were used both as blanks and because their scattered intensities can be easily calculated using the following formula:

I = ρ 2 b 2 kT χ T , (2.34)
where ρ is the density of the solvent, b the scattering length (number of electrons times

Thompson's length), k is Boltzmann's constant, T the temperature in absolute scale and χ T the isothermal compressibility. The two plots showing both the glassy carbon curve and the scattering by the toluene, used as a reference, are shown in Fig. 2.6 The pattern of the capillary was subtracted from that of the two solvents and then multiplied by the multiplicative factor found by normalizing with the glassy carbon. A linear region of the spectra was then used to fit to the tabulated value of scattered intensity for both toluene (2.36 m -1 )and water (1.632 m -1 ). In both cases, the thickness of the capillary was found to be very close to 1 mm, the two values were averaged and the thickness was set to 0.9976 mm.

All subsequent samples of the run were thus normalized using the multiplicative factor and the thickness to yield absolute intensities.When using capillaries in place of flow cells, it is not possible to proceed with the same method, as the thickness of the capillaries varies, as well as the signal from the capillary, and it is not possible to measure either precisely. As a result, it is impossible to derive the absolute intensities from those measurements. It is nonetheless important to subtract both the capillary and the solvent from the raw data. This is done by comparing the high q-range of the blank capillary to the sample. In this range, the intensity scattered by the nanoparticles decreases quickly (O(-2)) while the solvent has a strong signal. It is then possible to align the two sets of data and correctly subtract the blank from the sample. In this case, the absolute value of the intensity will not be used, but the average radius, and the polydispersity (which influence the position and the amplitude of the oscillations respectively) will still be measured correctly.

Fitting the data to the models

After normalizing the data and retrieving either the absolute intensity or the intensity in arbitrary units, the experimental curve has to be fitted to the theoretical models. The handling of the data was done using python and the Jupyter Notebook interface. This allowed the creation of easy to write and interactive code ideal for the treatment of data.

In particular, the fitting was done using the LMFIT module, which provides a high level interface to the scipy.optimize algorithms, used for non-linear optimization and curve fitting [START_REF] Newville | LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python[END_REF]. The two functions presented earlier for the analytical description of a normal and a Schultz distribution of spheres eq.(2.19) and eq.(2.20) were implemented as lmfit models.

Along with these two models, bi-modal distributions of both were implemented as a sum of two mono-modal (D 1(R) and D 2(R) ) distributions multiplied by a normalizing factor. This can be done as long as they are both positive, the sum of the two factors is 1. If both these requisites are true, then the bimodal distribution function is in fact normalized. Thus, given a parameter p ∈ [0, 1], a distribution D(R) is defined by:

D(R) = pD 1(R) + (1 -p)D 2(R) .
The normalization of this distribution can then be calculated:

∞ 0 D(R)dR = p ∞ 0 D 1(R) + (1 -p) ∞ 0 D 2(R) = 1 D(R)
is thus proven to be in fact normalized and can be inserted in eq.(2.14), one then obtains:

I(q) = c pI 1(q) + (1 -p)I 2(q)
which shows that the total intensity of a bi-modal distribution of particles is the sum of the two mono-modal intensities normalized.

PbS nanoparticle sizing and concentration

This set of particles were measured using a flow cell, which allowed for correct normalization of the signal and the extraction of the absolute scattering intensity. The samples were prepared by the group of "Physics and Chemistry of Nanostructures" at Ghent University under the supervision of Prof. Zeger Hens. The scope of the measurements is to study the growth of quantum dots in order to better study the mechanism of formation. In some of the samples two different size populations are visible, possibly indicating the formation of smaller clusters which come together to form larger particles. The samples had already been studied using fluorimetric techniques. The SAXS measurements allowed us to confirm the data obtained from those measurements (e.g. the presence of two populations), as well as improve the calibration curve used for determining the size of the particles based on their emission peak. Fig. 2.7 shows the scattering curves of seven different suspensions of PbS nanospheres along with their fits. For clarity, the data is presented shifted along the vertical axis by an order of magnitude each. As can be seen, for the most part, the fitted curves follow the experimental data very well, with at most a vertical shift between the experimental and fitted cuves. This discrepancy can be attributed to a population of small particles, whose form factor is not discernible, but which provides a positive baseline. The smaller graphs on the right show the shape of the distribution of the various fits respectively.

As can be seen by comparing the figure and the recapitulative Tab.2.1, the SAXS pattern is very sensitive to the average size of the nanoparticles. The patterns present a visible shift in the position of the oscillation even when the difference between the radius is of the order of only a few Å. Because the data was scaled to absolute scale, the concentration of sample was calculated from the scattering curve. The data confirmed the particle size calculated starting from the excitation peak, and were also able to detect the two populations of particles in the first sample.

PbSe particle characterization

As the previous particles, these quantum dots were also prepared by Prof. Zeger Hens' group within the framework of the same project. The measurements on PbSe particles were done using 1.5 mm capillaries, so the intensities are not in absolute scale and the particle concentrations were not calculated. The fitting of the data provides nonetheless accurate information regarding the size and polydispersity of the nanoparticles. It is possible to deduce from the fact that quite a few oscillations are visible in the patterns that the samples have a low polydispersity. This hypothesis is then confirmed by the graphs on the side, which show sharp peaks (Fig. 2.8, and the Tab.2.2 recap which shows polydispersities between 5.5% and 7.9% for all but one sample.

Small Au nanoparticle characterization

Gold nanoparticles in water, with a diameter between 5 and 30 nm were synthesised using a procedure published by Bastus et al [START_REF] Piella | Size-Controlled Synthesis of Sub-10nanometer Citrate-Stabilized Gold Nanoparticles and Related Optical Properties[END_REF]. This procedure is a step-wise synthesis in which small gold seeds are used to grow larger particles. The seeds are prepared in a solution of Na -Citrate (150 mL of 2.2 mm solution), along with 5 mL of 150 mm K 2 CO 3 and 2 mL of 2.5 mm tannic acid, kept at 70 • C, to which 1 mL of 25 mm HAuCl 4 is added.

Each successive growth step was done over a period of 20 min during which two aliquots of 0.5 mL each were added at 10 min intervals. At the end of the 20 min the solution was diluted by removing 55 mL of colloidal solution and adding the same amount of 2.2 mm

Na -citrate solution. The main reducing agent in this synthesis is the Na -citrate, while the K 2 CO 3 serves to maintain the particles spherical and the tannic acid is used in the first step to control the fast nucleation of the particles. Eleven subsequent growth steps are shown in Fig. 2.9. The different patterns clearly show how, as the size of the nanoparticles increases, the positions of the oscillations are shifted towards smaller values of q.

Large Au nanoparticles characterization

Larger nanoparticles (up to around 50 nm) were prepared using a synthesis similar to that for smaller particles, publisched by Bastus et al. [START_REF] Neus | Kinetically Controlled Seeded Growth Synthesis of Citrate-Stabilized Gold Nanoparticles of up to 200 nm: Size Focusing versus Ostwald Ripening[END_REF], the details of the synthesis will be explained in the next chapter. The reaction is based, as the previous one, on the reduction of gold tetrachloride by sodium citrate. This synthesis takes place at 90 • C, without the aid of tannic acid. As with the smaller nanospheres, the increase in size can be easily detected by just looking at the SAXS patterns and noticing the shift towards the left of the oscillations.

Alternative fitting models

All of the fitting done until now on the experimental data was done starting from an analytical formula. The equation was obtained by merging the formula for the form factor of a sphere and a distribution function for the size of the particles. This method of analysing SAXS data is extremely rapid and easy to implement, especially considering the number of fitting algorithms which exist and the availability of pre-written libraries for different programming languages. It is furthermore applicable to any system, as long as an analytical expression exists for describing the scattering of a polydisperse population of the specific colloid; this is the case, for example, for spheres, rods, polymer coils, etc. [START_REF] Skov Pedersen | Neutrons, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter[END_REF]. Nonetheless, least-squares minimization imposes a strict distribution on the particles, requiring the user to chose between the available functions, and forcing the results to follow it. This supposes that the user knows beforehand how the size distribution of the particles is shaped, and that the shape follows a known distribution. In the case of solutions of colloids such as the first curve of the PbS spheres (Fig. 2.7), where the distribution is bimodal, this results in having to try multiple distributions, both monomodal and multi-modal, in order to find the best one. Even once a good fit is found, the result is always confined with the rules imposed by the chosen function. There are other approaches which can be used to avoid this problem, two of which will be presented here. Both of these methods remove the constraint on the shape of the distribution, requiring only the form factor of the particle to be known, but present other limitations, which have to be kept in mind.

Monte Carlo simulations

One possible approach is to use a Monte Carlo simulation. In this case, instead of calculating the total scattering pattern by integrating the product of the form factor and a size distribution (as done in eq.2.14), a set of randomly selected particles is created.

The total scattering pattern is then calculated as a weighed sum of the scattering pattern for each available size. The goodness of the fit between the experimental and simulated curves can then be summarized using a "value of merit" (χ 2 ). At each subsequent step, one particle in the set is replaced by another with the same shape but different size, and the new scattering pattern is calculated. If the χ 2 value shows an increase in the goodness of the fit the change is accepted, if not it is rejected. A stopping criteria has to be implemented, which takes into consideration the uncertainty of the measurement, and which ensures that the iterations will come to a stop. Such an approach is implements in the python package MCSAS [START_REF] Pauw | Improvements and considerations for size distribution retrieval from small-angle scattering data by Monte Carlo methods[END_REF], which allows the user to fit the SAXS data, also providing information such as the minimum visibility threshold for all different sized particles. If the data is normalized, and the correct electron density contrast is provided, the algorithm can also calculate the concentration of particles in solution. Nevertheless, as explained by the authors of the library, this is a brute-force approach to the analysis of the data, and as such may require considerable amounts of time to converge to a solution. The calculation time can be reduced by using realistic error bars for the data and by providing a fitting range for the colloid size which is within the q-range (π/q max < R < π/q min ). A final concern with regards to this method is linked to the scattering intensity of small particles. As seen previously the signal strongly depends on the volume (I(q) ∝ V 2 ), therefore number distributions obtained by Monte Carlo fitting may have unreasonably large values for small particles, in particular when the size distribution of the particles is broad [START_REF] Pauw | Improvements and considerations for size distribution retrieval from small-angle scattering data by Monte Carlo methods[END_REF].

Expectation maximization approach

As with the Monte Carlo approach, this method does not impose a distribution, but only uses the form factor of the particles. A mathematically exhaustive demonstration of how the problem is posed, as well as it's convergence and stopping criteria, can be found in [START_REF] Benvenuto | A Robust Inversion Method According to a New Notion of Regularization for Poisson Data with an Application to Nanoparticle Volume Determination[END_REF][START_REF] Benvenuto | Expectation maximization for hard X-ray count modulation profiles[END_REF]. In general terms, the process is based on the probability of obtaining the experimental (noisy) data (y δ ) from a given size distribution vector x, supposing the data is affected by

Poisson noise. Here we will show how the algorithm can be implemented and the results obtained from it, as well as a brief explenation of how the algorithm was derived. For a more in-depth explanation, as well as a rigorous mathematical proof we direct the readers to [START_REF] Benvenuto | A Robust Inversion Method According to a New Notion of Regularization for Poisson Data with an Application to Nanoparticle Volume Determination[END_REF][START_REF] Benvenuto | Expectation maximization for hard X-ray count modulation profiles[END_REF]. The authors start by defining the scattered intensity as the sum of the scattered intensity of each particle. The sum can then be rearranged by sampling the whole range of radii, giving the equation:

I(q) = γ(∆ρ) 2 N j=1 n j |V R j | 2 )|F R j (q)| 2 (2.35)
Where N is the number of samples used to divide the range of radii (R 1 , R 2 , . . . , R N ) and n j is the number of particles with that particular radius. The experimental scattering intensity can then be defined in matricial form as:

y = Hx (2.36)
where matrices H and x are:

H =     |V R 1 ||F R 1 (q 1 ) 2 • • • |V R N ||F R N (q 1 )| 2 . . . . . . . . . |V R 1 ||F R 1 (q M ) 2 • • • |V R N ||F R N (q M )| 2    
and:

x = x 1 , • • • x N T .
F Rn (q m ) is the value of the form factor for a sphere of radius R n at a q value of (q m ) and,

x is the random distribution vector. V, used in the definition of H, is the volume vector, defined as:

V = |V R 1 |, • • • |V R N | T .
V Rn is the volume of a sphere with radius R n . By imposing that the noise on the signal is mainly Poisson, the probability of of obtaining the noisy data (y δ ) given a set of particles (x) is given by:

p(y δ |x) = M i=1 e -Hx i y δ i ! HX y δ i i .
(2.37)

The problem then becomes finding the x vector which maximized the probability of obtaining y δ , with x ≥ 0. By manipulating this equation, and using [START_REF] Dempster | Maximum Likelihood from Incomplete Data via the EM Algorithm[END_REF], the authors arrive at the formula for calculating each successive iteration: .38) Multiplications and divisions between vectors are intended as element wise, and 1 is used in place of a vector whose entries are all 1. The first x vector is initialized with all of its elements equal to 1 (any positive initialization is valid), and the authors show that the algorithm converges to a meaningful result. The final problem with iterative methods is to determine the stopping criteria. The authors argue that a valid method is to use the following equation:

x k+1 = x k H T 1 H T y Hx k . ( 2
k e = inf k ∈ N|(A k ) j ≤ κ 2 (B k ) j , (x k ) j > , j = 1, . . . , N (2.39)
which is to say the last iterate is the first for which all the elements of A are inferior to the respective element of B multiplied by κ 2 , without considering those elements for which the number of particles (x j ) in inferior to . κ and are both greater than zero; the first one filters only those components whose intensity is above a certain threshold, while κ gives the minimum distance between each component of successive iterates as number of standard deviations. A j and B j are the elements of:

A = H T y Hx k - 1 2 (2.40)
B = H T 2 1 Hx k . (2.41)
Unlike the Monte Carlo approach, this is not a brute-force attack on the data, and as such is much faster, it can also rely on fast matrix operations available on most programming languages (e.g. on python the numpy library implements many of these operations in C, a much faster language). As the previous technique though, the user has to provide a reliable range of radii value, the article proposes using:

R max = 1 4∆q (2.42)
based on the Shannon-Nyquist theorem [START_REF] Shannon | Communication In The Presence Of Noise[END_REF]. Furthermore, the two parameters and κ have to be chosen in such a way as to not over-fit the data, for example by trying to obtain a better fit than the experimental error allows. For a more rigorous development of the algorithm, as well as of the mathematics behind it, we again invite the reader to reference the original oarticle, along with the previous version [START_REF] Benvenuto | A Robust Inversion Method According to a New Notion of Regularization for Poisson Data with an Application to Nanoparticle Volume Determination[END_REF][START_REF] Benvenuto | Expectation maximization for hard X-ray count modulation profiles[END_REF], an all references therein.

Comparison between the three approaches

After discussing the mechanisms for all three techniques, and analysing the advantages and drawbacks for each we will now present how the same data set (the first curve from Fig. q all the curves follow the experimental data well all the way up to, and including, the fist oscillation. After that, the red curve (obtained by fitting using least squares minimization) decreases at a faster rate compared to the signal, while the other two curves closely follow the experimental data up to the end. If we look at the distributions obtained using the three methods we see that for all three there is a peak positioned between 20 Å and 30 Å.

The least-squares fitting though, has another peak at 6 Å, while the other two fits have the second, less intense peak, at 11 Å. It is also important to reiterate that while for the least-squares approach we had to initially try a monomodal distribution, and then impose a bi-modal one. The other two methods are not limited in the shape of the distributions; this can be seen in the blue curve (Monte Carlo approach), which clearly shows variations from a smooth distribution, as well as the green curve (expectation maximization approach), in which an even smaller peak can be seen at very small radii. Another difference in the codes is that both the least-squares fitting and the Monte Carlo approach both integrate the possibility of adding/subtracting a background to the curve, while this is not possible using the third method. We could nonetheless envision the possibility of adding a constant form factor the the H matrix, to work as a background.

Conclusion

This introduction to small-angle X-ray scattering provides the basic notions necessary to understand the physical phenomena behind this technique, as well as the steps necessary to analysis the results. It is clear how SAXS is a valuable technique for the analysis of colloidal particles: it provides information on both the size and polydispersity of the sample in-situ and, as long as the necessary precautions are taken, does not interfere with the system. It is thus a non destructive method that can be applied to small volumes of solutions (≈100 µL).

Provided the correct normalisations are done, it is also possible to obtain quantitative information on the sample, namely the concentration of particles in solution. Furthermore, the probed population is much larger compared to direct observation techniques such as electron microscopy. As seen in this chapter the number of particles analysed with the former is orders of magnitude larger than when using the latter, even for dilute systems.

The average size and polydispersity of the particles obtained by SAXS is then much more statistically reliable, and less prone to biases. Also, the preparation of the samples and the measurements themselves are easy to conduct and rapid. If the normalization of the signal is not required (there is no interest in the concentration of the particles in solution)

the samples are prepared by simply filling glass capillaries with the colloidal solution and can be analysed in series, making the measurement efficient and automated. When using flow cells the process is more laborious as the capillary needs to be accurately washed after each measurement, but the acquisition is nonetheless rapid, especially when working at synchrotron facilities, and precise concentrations can be obtained.

This method does present some drawbacks which need to be taken into account. Notably, care has to be taken to insure that the sample is not being affected by the x-rays. This is particularly important when working on organic samples, but must be taken into consideration in all experiments, e.g. when observing the synthesis of colloidal particles the high energy photons could influence the nucleation. Another difficulty when dealing with scattering phenomena is the analysis of the results. In the chapter we explain the need of having some a-priori information with regards to the system in order to correctly fit the scattering curve. If, for example, the shape of the colloids is known, along with the analytical form of it's scattering profile, the experimental data can be fitted to the form factor. Because of the importance of SAXS in the colloidal community the form factors for many of the basic, and not-so-basic, shapes have already been calculated [START_REF] Skov Pedersen | Neutrons, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter[END_REF], but when analysing very specific systems the form factor has to be derived. An example of how a form factor can be calculated starting from the shape of the colloid is presented in Ch.6.

In order for the form factor to be useful in real-life analysis it is also necessary to be able to consider the parameters as a distribution rather than as a single value. This can be done, as was shown here, by multiplying the form factor by a distribution function and integrating the signal over the size parameters. The equation obtained in such a way can be fit to the data and determin both the mean value and the polydispersity. While efficient to do, this supposes that the product of the two functions can be analytically integrated and that the particles are distributed along a simple and known distribution curve. As for the form factor, many equations are analytically known and can be used [START_REF] Skov Pedersen | Neutrons, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter[END_REF], but this is not always the case. Different methods can be used, such as the Monte Carlo approach used in the MCSAS package [START_REF] Pauw | Improvements and considerations for size distribution retrieval from small-angle scattering data by Monte Carlo methods[END_REF], or an expectation maximization iterative algorithm [START_REF] Benvenuto | A Robust Inversion Method According to a New Notion of Regularization for Poisson Data with an Application to Nanoparticle Volume Determination[END_REF],

which return histograms of the size distribution, but which risk to over-fit the data if the stopping criteria is not well posed.

When dealing with spherical particles we will only consider the fitting of algebraic expressions for monomodal distributions throughout most of the manuscript. A different approach will be used in Ch.6, where no algebraic equation exists for a distribution of those specific colloids.

Chapter 3

Synthesis of Gold Nanoparticles

History of gold nanoparticles

The first reported synthesis of colloidal gold particles, starting from a chloroaurate (AuCl 4 -) aqueous solution, belongs to Faraday [START_REF] Faraday | The Bakerian Lecture: Experimental Relations of Gold (and Other Metals) to Light[END_REF]. In 1857 he published a paper on the optical properties of thin gold -and other metal -films, under different conditions of temperature and pressure. In this same paper, he also describes how, by pouring a dilute solution of gold tetrachloride over a piece of phosphorus, one can obtain a ruby fluid of dispersed particles of gold. He then proceeds to describe how, by dissolving the phosphorus in carbon disulfide, the production of the ruby formation is favoured. In his lecture, he also highlights how sensitive the reaction is to the initial conditions; noting that the ratio between the volume of the solutions has to be exact. If not, the solution either forms a more violet product, or the particles aggregate and fall to the bottom of the beaker. Following Faraday's procedure, several different synthesis routes were proposed for the preparation of colloidal gold solutions. In 1928, Rinde prepared a ruby red solution of gold colloids by adding acetone to a boiling solution of chloroauric acid [START_REF] Rinde | The distribution of the sizes of particles in gold sols: prepared according to the nuclear method[END_REF]. The same procedure was reproduced by many different authors who used different reducing agents to obtain gold sols.

Among the reducing agents used are: acetone [START_REF] Davies | The Kinetics of the Coagulation of Gold Sols. An Investigation of the "Thermo-Senescence Effect" exhibited at Elevated Temperatures[END_REF], tannine [START_REF] Garbowski | No Title[END_REF], oxalic acid (

H 2 C 2 O 4 ) [54],
hydroxyle amine-hydrochloride (NH 2 OH• HCl) in neutral or basic conditions [START_REF] Thiessen | Spontane Keimbildung in verdünnten, hochübersuttigten Goldlösungen[END_REF], carbon monoxide gas (CO) [START_REF] Donau | Über eine rote, mittels Kohlenoxyd erhaltene kolloidale Goldlösung[END_REF] of the then known syntheses [START_REF] Turkevich | Electron Microscopy of Colloidal Systems[END_REF]. He found that using sodium citrate as reducing agent results in mono-disperse and spherical nanoparticles, while most of the other reductors produce elongated particles, often the result of aggregation between two or more colloidal particles [START_REF] Turkevich | A Study of the Nucleation and Growth Processes in the Synthesis of Colloidal Gold[END_REF]. Building on Turkevich's results, Frens published a paper in which he studied the role of the ratio of gold salt to reducing agent in the final size and size distribution of the sol [START_REF] Frens | Controlled Nucleation for the Regulation of the Particle Size in Monodisperse Gold Suspensions[END_REF]. The gold nanoparticles were prepared by heating to boiling a 0.254 mm aqueous solution of gold tetrachloride and injecting varying amounts of a 34 mm solution of trisodium citrate (Table 3.1). The paper showed that the final diameter of the gold sols can be tuned from 16 nm to 150 nm by playing with the HAuCl 4 :Na 3 -Citrate ratio. When very small quantities of reducing agent are used, the reaction becomes less reproducible and the particles tend to be more elliptical in shape.

Optical properties of gold nanoparticles

Gold is a metal whose bulk color is a well known yellow; nevertheless, the colloidal solution prepared by Faraday in his dissertation is a ruby red color. Faraday also notes that in some situations the colloidal solution acquires a blue color, and attributes it to the aggregation of the gold nanoparticles [START_REF] Faraday | The Bakerian Lecture: Experimental Relations of Gold (and Other Metals) to Light[END_REF], indicating that people at the time were aware of the chromatic properties of gold colloids. The use of gold particles for the preparation of red solutions actually dates back to ancient times. Gold has been used since ancient Roman times to tint, in various hues of red and blue, glass and ceramics, though it is still not clear how much of the technique was understood/controlled by the craftsmen of the time. The most commonly known example of such use is in the Lycurgus cup. A study of the glass shows that when seen in transmitted light, the glass appears red, while when seen with reflected light, the cup is green. It was only in 1908, though, that Gustav Mie found a mathematical description of the chromatic properties of gold colloids by solving Maxwell's equations in spherical coordinates [START_REF] Mie | Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen[END_REF]. Mie was able to derive an equation which describes the absorption cross section σ ext for a metallic sphere with radius R as a function of the wavevector κ.

σ ext (κ) = 2π κ 2 ∞ L=0 (2L + 1) (a L(R,κ) + b L(R,κ) ) (3.1)
where κ is the wavevector of the incoming light, a L and b L are the scattering coefficients in terms of the Riccati Bessel functions of order L (ν L and φ L ), and are defined by:

a L(R,κ) = mψ L(mx) ψ L(x) -ψ L(mx) ψ L(x) mψ L(mx) η L(x) -ψ L(mx) η L(x) (3.2) b L(R,κ) = ψ L(mx) ψ L(x) -mψ L(mx) ψ L(x) ψ L(mx) η L(x) -mψ L(mx) η L(x) (3.3) (3.4)
where x = κR is the sizing parameter and m = n/n m is the ratio between the complex refractive index of the particle and the real refractive index of the medium. The summation limit in eq(3.1) determines up to which electric dipole the interaction is calculated (L = 1 for a dipole moment, L = 2 corresponds to a quadrupole and so on). For small particles -where the ratio between the radius and the wavelength is 1 -an approximation to a simpole dipole is sufficient. In this case the formula simplifies to:

σ ext (ω) = 9ω 3/2 m c V 2 ( 1 + 2 m ) 2 + 2 2 (3.5)
where V is the volume of the nanoparticle, m is the dielectric constant of the medium, while the dielectric constant of the spherical particle is defined as

= 1 + i 2 .
While the dielectric constant of the medium can often be considered constant throughout the visible spectrum, for the metallic particle this is not the case, especially with regards to the real part. By setting the imaginary part as a constant, it is then possible to determine the value of ω for which the cross section has a maximum: This frequency is a first approximation of what is called the surface plasmon resonance (SPR) frequency, and it is situated around 550 nm in the case of gold nanoparticles in water.

1(ωp) = -2 m (3.6)
When an electromagnetic wave with a wavelength much larger than the particle interacts with metallic nanoparticles, the cloud of free electrons located on the surface creates an oscillating dipole Fig. 3.1. The electronic properties of the metal determine the intrinsic resonating frequency of the dipole, which in turn determines the frequency at which the interaction is most effective. In order to obtain a more precise position of the SPR higer order moments can be calculated (L=2,3,• • • ). Nevertheless this model still fails to perfectly describe metallic spheres in solution, as it does not take into account all of the relevant parameters, such as the ligands bound to the surface of the sphere, which inevitably affect the electronic properties of the colloid [START_REF] Kumar | Solvent and Ligand Effects on the Localized Surface Plasmon Resonance (LSPR) of Gold Colloids[END_REF][START_REF] Duval | Chain Length Dependence and Sensing Capabilities of the Localized Surface Plasmon Resonance of Silver Nanoparticles Chemically Modified with Alkanethiol Self-Assembled Monolayers[END_REF]. Furthermore, while many different studies have been done on the dependence of the dielectric constant on the wavelength, the results are not always in agreement with each other, especially as regards the imaginary part. Mie's model model furthermore is only valid under the condition that the particles are perfectly spherical. As the particles become oblong, the resonant frequency splits in two frequencies, corresponding to the oscillation modes along the major and minor axes. The absorption spectrum of metallic rods thus has two absorption peaks (Fig. 3.2). As the shape becomes more complex, the final spectrum becomes harder to describe using analytical methods.

Despite the difficulties in finding a direct correlation between the absorption spectra and the shape and size of the colloids, many different models have been developed and are often used with profitable results, in particular when dealing with simple shapes. The absorption spectrum of a sphere is independent of the incident angle between the incoming radiation and the particle due to the isotropic shape of the particle. When light interacts with an anisotropic particle, such as a rod, on the other hand, the absorption spectrum depends on the relative orientations of the wave and the particle.

Stateof the art gold nanoparticles synthesis by salt reduction

Growth reaction

The apparently simple procedure of the preparation of gold nanoparticles using chloroauric acid and sodium citrate actually hides a more complex reaction, whose various steps and roles of the two precursors are still not completely clear. Nonetheless, the reaction proves to be reproducible, and various improvements have been made in the last years. The first step in the formation of gold nanoparticles by citrate reduction is the red-ox reaction, which yields dicarboxyl acetonate and gold(I) chloride. The two half-reactions are: Oxidation:

COO - COO - OH COO - citrate COO - O COO - acetonedicarboxylic acid + H + + 2 e -+ CO 2
Reduction:

AuCl 3 + 2 e - AuCl + 2 Cl -
The next step is the disproportionation reaction of three gold(I) chloride complexes to two gold atoms and one gold(III) chloride complex:

3 AuCl 2 Au + AuCl 3 This step is facilitated by the presence of the acetonedicarboxylic acid, which complexes and helps bring together the gold atoms [START_REF] Turkevich | A Study of the Nucleation and Growth Processes in the Synthesis of Colloidal Gold[END_REF][START_REF] Abid | Laser induced synthesis and nonlinear optical properties of metal nanoparticles[END_REF]:

3.3. STATEOF THE ART GOLD NANOPARTICLES SYNTHESIS BY SALT REDUCTION47 AuCl O - C O Ac C O O - AuCl O - C O Ac C O O - AuCl O - C O Ac C O O - Ac CH 2 - C O CH 2 -
Once stable nuclei are formed, the disproportionation can directly occur on the surface of the nanoparticles, thus increasing the size of the particle rather than creating new nuclei.

The citrate molecules then loosely bind to the surface of nanoparticles, providing colloidal stability through electrostatic repulsion. The citrate serves the double role of reducing agent and stabilizing agent of the nanoparticles. In 2007 Xiaohui et al. [START_REF] Xiaohui | Size Control of Gold Nanocrystals in Citrate Reduction: The Third Role of Citrate[END_REF] also showed that citrate also plays a third role, that of buffer to the acidic gold salt. Sodium citrate is a weak base, with three known pK a points at 3.2, 4.8 and 6.4. Gold(III) chloride on the other hand is an acid, whose reactivity as a function of pH has been shown to change based on the dissociation state [START_REF] Goia | Tailoring the particle size of monodispersed colloidal gold[END_REF]. Notably, when moving from a pH above 7.1 to a more acidic environment, and again, when descending below pH 6.2, the gold salt changes from AuCl(OH) 3 to AuCl 2 (OH) 2 and AuCl 3 (OH) respectively, increasing in reactivity.

Improvements of the Turkevich method

Due to their optical, electronic, catalytic and biological properties, gold nanoparticles are now almost ubiquitous in all areas of science [START_REF] Kühn | Enhancement of Single-Molecule Fluorescence Using a Gold Nanoparticle as an Optical Nanoantenna[END_REF][START_REF] Brust | Self-Assembled Gold Nanoparticle Thin Films with Nonmetallic Optical and Electronic Properties[END_REF][START_REF] Huang | Plastic-Compatible Low Resistance Printable Gold Nanoparticle Conductors for Flexible Electronics[END_REF][START_REF] Tseng | Polyaniline Nanofiber/Gold Nanoparticle Nonvolatile Memory[END_REF][START_REF] Lopez | Catalytic CO Oxidation by a Gold Nanoparticle: A Density Functional Study[END_REF][START_REF] Chen | Visible Light Driven Oxidation of Organic Contaminants in Air with Gold Nanoparticle Catalysts on Oxide Supports[END_REF][START_REF] Giljohann | Gold Nanoparticles for Biology and Medicine[END_REF]. The need for mono-disperse particles of finely tuned size, dispersed in various solvents -both aqueous and organic -has brought a plethora of original syntheses, and modifications of already existing ones, to suit the needs of particular applications [START_REF] Neus | Kinetically Controlled Seeded Growth Synthesis of Citrate-Stabilized Gold Nanoparticles of up to 200 nm: Size Focusing versus Ostwald Ripening[END_REF][START_REF] Liu | A Study on Gold Nanoparticle Synthesis Using Oleylamine as Both Reducing Agent and Protecting Ligand[END_REF][START_REF] Schulz | Little Adjustments Significantly Improve the Turkevich Synthesis of Gold Nanoparticles[END_REF][START_REF] Xia | Synthesis of Monodisperse Quasi-Spherical Gold Nanoparticles in Water via Silver(I)-Assisted Citrate Reduction[END_REF][START_REF] Sun | Shape-Controlled Synthesis of Gold and Silver Nanoparticles[END_REF][START_REF] Brust | Synthesis of thiol-derivatised gold nanoparticles in a two-phase Liquid-Liquid system[END_REF]. Though many different paths are now available for the synthesis of gold nanoparticles in aqueous solution, reduction through sodium citrate is still a preferred method, especially when further functionalization is envisioned [START_REF] Leonov | Detoxification of Gold Nanorods by Treatment with Polystyrenesulfonate[END_REF].

This is due to the fact that, while citrate is effective in stabilizing gold nanoparticles by electrostatic repulsion, it is at the same time weakly bound to the gold surface allowing for an exchange with a ligand with higher affinity (e.g. a thiol). Furthermore, as shown by

Frens' study (Table 3.1), citrate reduction can be used to produce nanoparticles with a wide range of sizes, a characteristics which is hard to reproduce using other reducing agents.

On the other hand, the basic one-step synthesis proposed by Turkevich and Frens does not allow for the synthesis of highly mono-disperse particles. Furthermore, when preparing larger colloids, the final shape is often elongated and spurious triangles are present along with the ellipsoids. Because of these shortcomings and the great interests shown by the scientific community, modifications of the citrate reduction synthesis have been proposed which result in nanoparticles with higher mono-dispersity and shape definition.

Seed-mediated growth

One very efficient method to control both the final size and the monodispersity of the nano-spheres is through the use of a seed-mediated synthesis. An initial batch of small and highly mono-disperse nanoparticles is used as a seed solution. Aliquots of precursor are then added to the solution and made to reduce on the surface of the seeds. If the reduction rate on the surface of the existing particles is higher than the rate of nucleation, the final solution will have a mono-disperse population of nano-spheres with a larger diameter with respect to the starting solution. If, on the other hand, nucleation is favoured, the final batch will have two populations of nanoparticles. In the case of the reduction of AuCl 4 -, the tendency of the gold ion to reduce on a surface of impurities is very high, making it necessary to filter and scrupulously clean all glassware prior to use [START_REF] Kenneth | Seeding of Colloidal Au Nanoparticle Solutions. 2. Improved Control of Particle Size and Shape[END_REF]. As such, the growth on already existing spheres is greatly favoured compared to the nucleation of new particles.

The first presentation of such a method for gold nanoparticles in a scientific paper was done by Natan et al. [START_REF] Kenneth | Seeding of Colloidal Au Nanoparticle Solutions. 2. Improved Control of Particle Size and Shape[END_REF]. In their article, the group noted how very large particles (up to 200 nm) could be synthesized, while maintaining an ellipticity close to 1 (the ellipticity of a sphere). The research also showed that the size distribution does not widen during the growth. This observation had already been theoretically predicted by Howard Reiss in 1951 [START_REF] Reiss | The Growth of Uniform Colloidal Dispersions[END_REF]. In his paper on the Growth of uniform colloidal dispersions, Reiss had noted that, provided the free space around a particle is a sphere with a radius at least ten times that of the particle, if one were to start with a distributions of particles, a diffusion-dominated growth process would sharpen the distribution by favouring the growth of the smaller particles.

Step-growth mechanism thus provides a size-focusing regime for the nanoparticles.

Care has to be taken though to insure that the growth process is in fact dominated by diffusion. If, for example, the concentration of free monomers in solution is too low, the reaction is then driven by the surface energy of the particles. Because smaller particles have a higher surface to volume ratio, this induces a reduction in size of the smaller particles to the advantage of the larger ones [80]. This phenomenon is called Ostwald ripening after the Russian-German chemist who first described it, and leads to a widening of the size distribution of colloidal particles.

Inverse Turkevich method

A second improvement of Frens' synthesis was provided by Bastus et al. in 2011 [START_REF] Ojea-Jimeénez | Influence of the Sequence of the Reagents Addition in the Citrate-Mediated Synthesis of Gold Nanoparticles[END_REF].

The paper proposes to invert the order in which the precursors are added: an aqueous solution of gold tetrachloride is rapidly injected in a boiling solution of sodium citrate in water. As seen in the formation mechanism, the active molecule in the reduction of the gold salt to gold nanoparticles is acetonedicarboxylic acid whose formation, through the oxidation of sodium citrate, allows for the reduction of gold(III) chloride to gold(I) chloride, and which then complexes with the AuCl to allow the gold atoms to form the initial clusters. Inverting the order in which the precursors are added ensures that all of the citrate is effectively oxidized to acetonedicarboxylic acid before reacting with the gold salt.

This reduces the induction time and increases the reaction rate. The smaller induction time and fast nucleation prevent the nucleation and growth stages from overlapping, resulting in a single, mono-disperse population of seeds.

Characterization techniques used for gold colloids

As mentioned in the previous chapter, SAXS measurements were used, when possible, as they provide accurate, fast and in situ information regarding the colloids. Unfortunately, due to the size of the colloids (∼45 nm), the information is contained at q-values around 3 × 10 -2 Å -1 , which is below the limit of available laboratory SAXS setup. Scattering measurements of the particles could then only be performed on synchrotron lines, where ultra-small scattering angles are available. Furthermore, as previously seen, scattering measurements provide information in the reciprocal space, making it less intuitive to understand. Therefore, different methods were used to obtain information on the synthesized particles, in particular light absorption spectroscopy proves to be very practical in the analysis of gold colloids, and electron microscopy, which provides the user with direct imaging of a sample, though it holds less statistical significance and is more time consuming.

Light absorption spectroscopy for gold nanoparticles

As seen at the beginning of the chapter, gold nanoparticles present a very particular interaction with the visible range of the electromagnetic spectrum. Because of the correlation between the absorption spectrum and the shape of the particle, UV-Visible-IR spectroscopy is often used to obtain preliminary information on the colloidal solution. Light absorption spectroscopy is a technique which measures the absorbance/reflectance of a sample in the ultraviolet-visible range of the electromagnetic spectrum. In a typical experiment, a quartz or plastic cuvette is filled with the solution to analyse and is placed within the instrument. A light beam is shone on the sample and a detector placed on the other side of the sample records the intensity of the transmitted beam. The final data is often presented as the logarithm of the ratio between the recorded intensity and that of the original beam (A = log I 0 I ). In order to study the absorption as a function of wavelength, either a fixed or scanning monochromator can be used, coupled with either an array or a single detector respectively. Furthermore the incident beam can be split in two before reaching the sample, giving the possibility to measure a reference at the same time as the sample. As with SAXS, this technique enables the user to measure the particles in situ and to average the result over a huge number of particles.

Because of the relationship between the size and shape of the particle to the absorption spectrum -described earlier in the chapter -the shape of the absorption peak can be used to extract the size of the particles. This analysis can be done using several different methods such as by fitting the analytic formula of the absorption spectra to the data [START_REF] Slyusarenko | Morphology of gold nanoparticles determined by full-curve fitting of the light absorption spectrum. Comparison with X-ray scattering and electron microscopy data[END_REF], by finding a relationship between the position of the peak and the size of the particle [START_REF] Haiss | Determination of Size and Concentration of Gold Nanoparticles from UV-Vis Spectra[END_REF],

or by simulating the spectra using boundary elements method [START_REF] Rockstuhl | Application of the boundaryelement method to the interaction of light with single and coupled metallic nanoparticles[END_REF][START_REF] Hohenester | MNPBEM -A Matlab toolbox for the simulation of plasmonic nanoparticles[END_REF]. The latter, while too demanding for simple shapes such as spheres or rods, proves to be very useful for more complex shapes or in case of interacting particles. For the most part, unless interactions had to be taken into account, we used the paper by Haiss et al. [START_REF] Haiss | Determination of Size and Concentration of Gold Nanoparticles from UV-Vis Spectra[END_REF] to calculate the size of the particles from the absorption spectra. The model is based on eq.(3.1) and uses as functions for the refractive index a spline fitting of the values found by Johnson and Christy in 1972 [START_REF] Johnson | Optical Constants of the Noble Metals[END_REF]. The extended Drude model is used as a framework to correct the values by incorporating the effects due to the reduced free mean path of the electrons in small nanoparticles. The authors then give an empirical equation to determine the size of the particles based on either the position of the absorption peak -for particles larger than 35 nm -or on the ratio between the absorption at 450 nm and that of the plasmon peak. In both cases, empirical coefficients found based on electron microscopy images are given.

Transmission electron microscopy

The third technique, which is extensively used throughout the manuscript, is transmission electron microscopy (TEM). This is the only technique of the three presented which produces a direct image of the sample. The images obtained from TEM can be analysed using image treatment software such as ImageJ [START_REF] Schneider | NIH Image to ImageJ: 25 years of image analysis[END_REF], which allows one to measure the size of the particles present in the image and calculate an average. TEM, however, is the technique which provides the smallest statistical sample of the three, with the number of particles analysed being orders of magnitude lower than SAXS and UV-Visible. Furthermore, as the technique is not in situ, the procedure used to prepare the sample can introduce artefacts in the sample due, for example, to the drying of the solvent.

TEM samples are usually prepared on carbon grids covered by a polymer, the samples in the images presented in this manuscript were prepared using 300 mesh carbon grids with a film of Formvar. If the sample is dispersed in aqueous solution, the blank grids can be placed in a plasma for several seconds in order to enhance the wetting of the grid. A drop of solution is then placed on the grid and allowed to dry; care has to be taken to ensure a correct concentration of the solution, so as to obtain well dispersed particles on the surface.

All of the images presented in the manuscript were taken at 120 keV either on the electron microscope available in the Lab (a JEOL 1400) or on one of the microscopes available on the imaging platform Imagif [START_REF]I2BC Imaging Platform -Imagif[END_REF]. The images are analysed using ImageJ's plug-in for the detection of spherical particles. A threshold is applied to the image in order for the software to easily discriminate between background and particles. ImageJ then finds all connected black pixels and groups them as a single particle. The area of the particle is easily calculated by counting the number of pixels and knowing the scale of the image. A rough approximation of the shape is also done by finding the best fitting ellipse, the major and minor axes are then recorded along with the area to a file.

Comparison between SAXS, UV-Visible absorption and TEM

The three characterization techniques presented SAXS, UV-Visible and TEM, are used throughout the manuscript. Because of their characteristics, not all techniques are used on all the samples. While statistically accurate and fast, SAXS measurements on such big colloids require the measurements to be done at a synchrotron and, because of the difference in scattering power, SiO 2 is less visible to X-rays when mixed with gold. TEM gives easy to analyse information and both Au and SiO 2 are visible. It is a slow technique however, with a small sample size, and which requires the drying of the sample prior to analysing.

Finally, UV-Visible absorption is an extremely fast in situ technique but it does not provide accurate information on the structure of the sample. It is therefore important to be able to assert that the results from all three techniques are comparable, and that, for example, using UV-Visible absorption at the end of the Au synthesis is sufficient to insure that the particles are round and of the right size without necessarily analysing them by electron microscopy or using X-ray scattering. In order to do that, gold nanoparticles ranging from ∼6 nm in diameter up to ∼30 nm, which were presented at the end of Chapter 2 to show the fitting of SAXS data, were also analysed by UV-Visible absorption and TEM. This particular synthesis was chosen as it passed through eleven different growth steps, thus producing many different samples to analyse covering a wide range of sizes. For TEM analysis, at least 600 nanoparticles were analysed for each growth step. The radius was calculated by measuring the area of the nanoparticles and considering the nanoparticles as perfect spheres. In the case of elliptical particles, the calculated radius is then a geometrical mean of the major and minor axes. UV-Visible absorption spectra were taken immediately after each growth step and the diameter of the nanoparticles was calculated based on the ratio between the absorbance at the plasmon peak and at 450 nm, as specified in Haiss' paper [START_REF] Haiss | Determination of Size and Concentration of Gold Nanoparticles from UV-Vis Spectra[END_REF]. This could be due to several factor, among which the fact that plasmon depends on many parameters, such as the solvent, the surface, adding more variability to the measurement. Furthermore, in both the TEM and SAXS analysis the particles were presupposed to be

Sample

UV-Vis spherical (for the electron microscopy the size was deduced from the area, while for the SAXS the fitting curve was that of a Gaussian distributions of spheres), in the case of light absorption the plasmon properties cannot be separated from it's shape, adding further discrepancy between the results. Light absorption also differes from the other two, as it is the only one which does not provide a size dispersion. Nonetheless, from Fig. 3.3, we can see that the difference between the particles is at most of only a few nanometers. Light absorption then proves to be a very useful tool to control the system during the synthesis.

R(nm) SAXS R(nm) TEM R(nm) Au1
3.5 Two-step synthesis of 44 nm Au nanoparticles

Experimental method

The initial procedure we used for the synthesis of the gold nanoparticles with an average diameter of 44 nm was a two-step procedure: the synthesis began with the preparation of 17 nm seeds which were subsequently grown to the required size [START_REF] Chen | Scalable Routes to Janus Au-SiO 2 and Ternary Ag-Au-SiO 2 Nanoparticles[END_REF][START_REF] Krpetić | High-Resolution Sizing of Monolayer-Protected Gold Clusters by Differential Centrifugal Sedimentation[END_REF].

Considerations on the reaction

The reaction is particularly sensitive to the initial conditions. The fast nucleation ensures the production of the seeds, but a variation in the initial concentration of seeds can have a strong influence on the growth procedure. A higher initial concentration will result in a slower growth, while fewer nanoparticles will grow at a faster rate. Because of this, it is important to control the concentration of the nanoparticles early on and make sure that the initial concentration is always constant.

The dilution after each third growth step serves the double purpose of reducing the concentration of nanoparticles in solution and of restoring the concentration of sodium citrate in solution. The reduction in concentration is necessary because the amount of material needed to increase the radius of a sphere (R 1 ) by a fixed quantity (δR) depends on the cube of the amount by which the radius is increased ((δR) 3 ) and the square of the starting radius (R 2 1 ). If the concentration of nanoparticles were kept constant, the growth rate would rapidly decrease. It is also true that as chloroauric acid is added to the flask, it decreases the pH of the solution. As a result, the citrate is protonated, reducing its charge and ability to stabilize the colloids. If the pH of the solution drops below 3.2 -the third pK a point of the citrate -the molecule is completely protonated, causing the particle in solution to aggregate. The addition of fresh citrate keeps the pH of the solution above 6.4the first pK a of sodium citrate -ensuring colloidal stability.

Comparison between two-step and multi-step synthesis

The two syntheses presented both produce citrate-stabilized Au nanoparticles in water with roughly the same size -the second reaction can be adjusted to obtain a wide variety of sizes. It is then important to note the differences between the two, in order to choose the one best suited as a starting point for the heterodimers. In particular, we wish to assess if the extra steps necessary for the production of nanoparticles following the multi-step synthesis are justified by the advantages provided by the synthesis. The parameters to take into account for determining the quality of the particles are the monodispersity and the roundness of the particles. The final concentration of the colloids, while easy to correct for, is also a parameter to take into account.

UV-Visible absorption spectra

As shown previously in the chapter, UV-Visible spectroscopy is a very useful and practical tool to characterize gold colloids. While not necessarily as precise as TEM or SAXS, it is by far easier and faster to use. Also, it provides an easy way to compare the concentration of nanoparticles in solution, provided the two solutions have colloids of comparable sizes (The absorbance is dependent on both the concentration and size of the particles). Fig. 3.4 shows three UV-Visible spectra: the two-step synthesis, the multi-step synthesis and the multi-step synthesis after dilution to match the absorbance at 450 nm of the two-step synthesis. Comparing the two spectra of the solution without adjusting the concentration clearly shows that the multi-step synthesis produces a solution with a much higher concentration compared to the two-step one. Comparing the two solutions with similar concentrations the position of the plasmon peak of the multi-step solution can be seen to be shifted to shorter wavelength. This indicates that the particles are slightly smaller, this difference could also be due, in part, to the two-step particles being more oval

TEM

Electron microscopy gives the possibility of obtaining more direct information regarding the shape of the nanoparticles. Fig. 3.5 shows two TEM images taken of Au colloids prepared using the two-step synthesis (Fig. 3.5A)) and the multi-step synthesis (Fig. 3 The particles are faceted rather than round, but are similar in size and present fewer elongated particles. In order to quantify the shape of the particles, the eccentricity for both syntheses was measured. The eccentricity, given by 1 -b 2 a 2 , where a and b are the semi-major axis and the semi-minor axis respectively, is equal to 0 for a circle and reaches 1 for a parabola. The major and minor axes were found using the ImageJ particle detection algorithm. Because ImageJ fits all the particles with an ellipse, this value of eccentricity is only a measure of how elongated the particle is, but does not give a measure of the shape regularity, i.e. it will give the same value of eccentricity for regular triangles and circles.

The results of the eccentricity measurements are shown in Fig. 3.6. From the histogram, it appears that the multi-step process does in fact produce rounder particles compared to the two-step procedure.

Comparison conclusions

Both syntheses produce Au nanoparticles in water stabilized by citrate with comparable sizes. The two-step synthesis is faster as it consists in the formation of the seeds which are then directly grown to the final size in a single step. In order to do so, only a small amount of the seeds are used for the growth step. This results in a more uneven growth, with elongated particles forming (as had been noticed by Frens in his one-step growth of large particles) and in the formation of a second population of smaller particles as the nucleation cannot be inhibited. The multi-step procedure proposed by Bastús on the other hand combines two alterations to the original Turkevich method to produce more spherical particles. Firstly, the number of steps is increased, which results in smaller growth at each step, a more concentrated solution and rounder particles. The decrease in temperature after the first step ensures that further nucleation is inhibited so as not to have multiple populations in solution. Furthermore the inversion of the order of addition of the precursors -a hot citrate solution in which a small amount of concentrated gold salt solution is addedensures a faster nucleation rate and more mono-disperse colloids. Finally, the possibility of stopping the reaction at any step, along with the possibility of monitoring the nanoparticles through UV-Visible spectroscopy throughout the reaction, allows for the possibility of better tuning the final size of the particles.

Conclusion

This chapter served as an introduction to colloidal gold nanoparticles, in order to gain insight on the system which will the the basis for the preparation of the heterodimers. We provided an overview of the synthetic procedures as well as a historical context for these particle. The relative ease of the preparation of gold sols starting from a gold salt solution has resulted in an early discovery of such systems, though a more thorough analysis was done only more recently (19 th century). With the development of the synthetic procedures gold colloids have proven useful in many areas, such as optics, self-assembly, catalysis, bio-imaging, etc., thanks to their interesting physical properties. The range of available synthesis for the preparation of colloids with different size and stability is now extremely wide. This allows researchers to work with particles ranging from small clusters of Au atoms to particles of several hundred nanometers in diameter, dispersed in both acqueous and organic solvents. We saw, in particular, that the Turkevich method, and later the synthesis proposed by Frens, allow for the preparation of particles of varying size, stabilized in aqueous solutions by the charge provided by the adsorbed citrate. The particular interest in such particles being that the citrate is only weakly bound to the surface of the gold and can be easily displaced by stronger bonds, such as the thiol-gold bond [START_REF] Sellers | Structure and binding of alkanethiolates on gold and silver surfaces: implications for self-assembled monolayers[END_REF][START_REF] Park | Structural Study of Citrate Layers on Gold Nanoparticles: Role of Intermolecular Interactions in Stabilizing Nanoparticles[END_REF]. More recent studies have provided better insight into the synthesis procedure, such as the role of the citrate in the reaction [START_REF] Xiaohui | Size Control of Gold Nanocrystals in Citrate Reduction: The Third Role of Citrate[END_REF]. This has allowed for a perfecting of the procedure by applying two important modifications: the inversion of the addition order of the precursors (a concentrated HAuCl 4 solution is added to a boiling Na -Citrate solution), and using a seed mediated growth. As explained the first modification results in a more homogeneous nucleation, as the citrate molecules are all activated by the heat, while the second ensures a constant growth of all the particles, by separating the nucleation, growth and Ostwald ripening phases. The growth process, followed by SAXS Fig. 2.10, shows a steady increase in the size of the colloids, while the polydispersity found by fitting the data (Tab.2.4) shows signes of actually decreasing with each step.

We also explored the electronic/optical properties of metallic colloids. The dependence of the extinction cross section on the frequency of the incident light was first described, for spherical particles, by Mie (eq.3.5). This description is able to explain the appearance of the plasmon peak in the spectrum of colloidal particles. Since then, more refined models have been proposed to take into account other parameters besides the dielectric constant, such as the effect of the particle size on the cross section. Such models allow to use light absorption, which is a fast and volumetric measurement, for the sizing of the particles in solution. While many parameter come into play when dealing with plasmon position, we have seen that there is good agreement between SAXS, TEM and spectroscopy measurements (Fig. 3.3).

Both electron microscopy and absorption spectroscopy were used for a rapid comparison between the Frens synthesis and a stepwise procedure using the inverted Turkevich method.

This was done in order to find a procedure which allows us to reproducibly prepare spherical gold particles The combination of the two techniques showed that the modified procedure results in more spherical particles, as well as a higher concentration of colloids in solution.

Because of both these properties it was chosen as the favoured synthesis for the preparation of the aqueous gold nano-spheres.

The particles prepared in this fashion were then used as the starting block for the preparation of the heterodimers which were the subject of our study. This initial characterization was necessary as it allowed us to ensure that the particles were homogeneous and spherical, as well as having a reproducible procedure for the preparation of citrate stabilized gold colloids. This gave us a standard starting point for the following steps.

Chapter 4

Synthesis of Janus Nanoparticles

Introduction

Ever since de Gennes popularized the term "Janus beads" -a term coined by Casagrande et al. [START_REF] Casagrande | Janus Beads": Realization and Behaviour at Water/Oil Interfaces[END_REF] -in his Nobel Prize lecture in 1992 [START_REF] De | Soft Matter (Nobel Lecture)[END_REF], the word has appeared more and more often, alongside the similarly used heterodimer. All these terms refer to a subset of nanoparticles composed of two moieties, which differ in composition and/or physical properties. It is in light of these opposing characteristics that the name of the two-faced Roman god of doors and change was bestowed upon them. The introduction of these particles coincided with the boost of nano-technologies at the beginning of the 90s, which, inspired by Feynman's 1959 speech: "There's Plenty of Room at the Bottom", aimed at producing building blocks for the engineering of new materials. Heterodimers provide a unique tool for the bottom-up approach, as they can encompass multiple properties, often conflicting ones, on the same particle, and provide an anisotropy which can be hard to achieve on other nanoparticles.

The synthesis of such nanoparticles, though, has proved challenging. While microfluidics can be used to produce a wide range of well controlled janus particles, with complex structures [START_REF] Nie | Janus and Ternary Particles Generated by Microfluidic Synthesis: Design, Synthesis, and Self-Assembly[END_REF][START_REF] Serra | Microfluidic-Assisted Synthesis of Polymer Particles[END_REF][START_REF] Dendukuri | Continuous-flow lithography for high-throughput microparticle synthesis[END_REF][START_REF] Eun | Programmable Fluidic Production of Microparticles with Configurable Anisotropy[END_REF], the size achievable through such production techniques remains limited to the micrometric range. In order to further decrease the size of the particles and reach nanometric properties, many different procedures have been proposed, which can usually be categorized as either surface or volume approaches. The first type relies on masking part of the particles and proceeding to modify the exposed part, before removing the masking and obtaining the heterodimers. Under this category fall a number of techniques, often more "physical" in nature. This was also the first approach taken by researchers for the 63 preparation of janus beads, as it often proves to be the simplest. The particles can be masked in many different ways, such as by embedding them in film, leaving only part of the surface exposed [START_REF] Casagrande | Janus Beads": Realization and Behaviour at Water/Oil Interfaces[END_REF][START_REF] Ondarçuhu | Specific properties of amphiphilic particles at fluid interfaces[END_REF] (Fig. 4.1B)). The necessity of positioning the particles on a surface, though, limits the production volume of these techniques. In order to increase the available surface, the particles can be adsorbed at the interface of droplets in emulsion [START_REF] Rossmy | From polyurethane foam stabilization to amphiphilic particles -An example of industrial R & D in colloid chemistry[END_REF][START_REF] Gu | Heterodimers of Nanoparticles: Formation at a Liquid-Liquid Interface and Particle-Specific Surface Modification by Functional Molecules[END_REF] as shown in Fig. 4.1C). The droplets can also be made using wax above its melting temperature, and later cooled in order to lock the particles at the surface [START_REF] Reculusa | Synthèse de matériaux d'architecture contrôlée à base de silice colloïdale[END_REF]. In either case, the exposed surface can then be modified, e.g by washing with a solution containing ligands which bind to the particle and change the surface properties. It is not always necessary to actively mask the particles, for example, when using evaporation techniques, the particles themselves act as masks (Fig. gold on latex spheres placed on a substrate, the lower part of the particles is not covered by the gold, resulting in Au-latex heterodimers which can easily be functionalized through thiol chemistry [START_REF] Takei | Gradient Sensitive Microscopic Probes Prepared by Gold Evaporation and Chemisorption on Latex Spheres[END_REF].

The second category of techniques relies on a more chemical approach and allows for the production of a much higher number of particles, as a result of an easier scale-up. Some examples of such an approach are processed based on the dewetting, epitaxial growth, or ligand segregation. FePt -CdS heterodimers can be prepared starting from core-shell nanoparticles. By heating them up, the mis-match between the lattice parameters and the dewetting lead to the formation of snow-man like nanoparticles [START_REF] Gu | Facile One-Pot Synthesis of Bifunctional Heterodimers of Nanoparticles: A Conjugate of Quantum Dot and Magnetic Nanoparticles[END_REF], a scheme of the process is presented in Fig. 4.1D). By using materials with compatible lattices, and particular electronic properties, it is possible to use nanoparticles as seeds to epitaxially grow a second sphere of a different material. This was the approach used for the preparation of dumbbell

Symmetry breaking of Au nanoparticles

In 2008 Chen et al. published an article in which they showed a procedure for the preparation of patchy particles using gold nanoparticles as a core and two different ligands, a hydrophobic long-chained thiol and a smaller hydrophilic ligand [START_REF] Chen | Controlled Assembly of Eccentrically Encapsulated Gold Nanoparticles[END_REF]. In the article, they show how, by adjusting the relative amounts of the different ligands, the nanoparticle-ligand system can be made to vary between two configurations they call homocentric and eccentric.

The first configuration, obtained by using a hydrophobic thiol and an amphiphilic diblock copolymer as stabilizer, resulted in gold nanoparticles encapsulated in a polymeric ligand, forming what are commonly called core-shell nanoparticles. The second configuration, which was obtained by adding the small hydrophilic ligand to the solution, consisted in a gold core around which the hydrophobic ligand had formed an eccentric shell, leaving part of the colloids covered by the hydrophilic molecule. By using a contrasting agent they were able to increase the scattering power of the overall background. As a result, the polymer shell, which has a lower scattering power, appears brighter than the background. When imaging the homocentric particles, a lighter crown is clearly visible around the nanoparticles, indicating that the diblock copolymer is uniformly distributed on the nanoparticle surface. When, on the other hand, the eccentric particles were imaged, the lighter shape of the polymer forms a circle off-centred with respect to the darker gold circle Fig. This separation is used to selectively grow silica on only one of the two sides.

the surface of the nanoparticles. This initial result was then built upon in a following paper by the same group, in which a new synthesis for the preparation of Au-silica heterodimers is presented [START_REF] Chen | Scalable Routes to Janus Au-SiO 2 and Ternary Ag-Au-SiO 2 Nanoparticles[END_REF]. The molecules used for the creation of the heterodimers were then chosen in such a way as to favour/inhibit the growth of a further particle on the surface of the existing gold colloid. This growth results in the formation of geometrically asymmetric particles which are then used in the next chapter as building blocks for the self assembly.

Ligand segregation

The segregation of the ligands on the surface of the gold nanoparticles is the first symmetry breaking in what are, otherwise, isotropic particles. According to the authors, in both cases, this separation is driven by the different natures of the molecules, which favours an interaction between similar ligands and inhibits the formation of interfaces between the two. In particular, the difference in hydrophilicity between the two molecules, as well as other possible interactions such as the π-stacking in the case of phenyl bearing molecules, 50 nm across, rather than patchy particles with multiple smaller domains. Furthermore, because of the difficulties involved in precisely mapping the disposition of ligands on a round surface, Chen et al do not perform an in-depth analysis of the segregation, but rather assume a ligand segregation from the more large-scale effect of the disposition of the diblock copolymer/silica on the surface. Both the TEM images of the encapsulated Au nanoparticles and those taken of the Au -SiO 2 heterodimers clearly indicate that there is an asymmetry in the colloids whose effect is comparable to the size of the particles and which can be linked to the presence of the two different ligands on the surface of the gold nanoparticles. The correlation between the ligands and the janus properties of the colloids is explored in both articles by varying the ratio of the two ligands. In the two cases, the system goes from a core-shell to a janus configuration passing through an eccentric phase.

This evolution is clearly visible in the six panels of Fig. 4.3, which presents images taken from the two articles published by Chen et al. [START_REF] Chen | Scalable Routes to Janus Au-SiO 2 and Ternary Ag-Au-SiO 2 Nanoparticles[END_REF][START_REF] Chen | Controlled Assembly of Eccentrically Encapsulated Gold Nanoparticles[END_REF] The first row of TEM images refers to the first article in which the segregation of the ligands is visualized using a staining resin and a diblock copolymer. The second row on the other hand is taken from the later paper, in which the asymmetry is used to grow silica on one of the colloid hemispheres. In this case, the asymmetry is visible without the need of a resin due to the electron contrast between Au, SiO 2 , and the carbon grid. In both cases, the image in the first column (Fig. 4.3A) and Fig. 4.3D)) shows the colloids when only one of the two ligands is added; moving from left to right, increasing amounts of the second ligand are added. It is clear that as more of the second ligand is added, the core-shell system becomes more eccentric and janus-like. As a result of this, even though nothing can be said with regards to the exact disposition of the ligands on the surface of the gold nanoparticles, it becomes very clear that the overall effect of the two ligands on the surface is to break the symmetry of the particle and induce a long range segregation.

Selective SiO 2 growth

Following the segregation of the ligands on the surface of the Au nanoparticles, the colloids are further modified by growing a SiO 2 sphere on one of the hemispheres. The actual growth of the second part of the heterodimers is made through a classic Stöber reaction, whose nucleation is driven by the ligands on the Au surface. The two ligands are chosen in such a way as to render one moiety of the colloid vitreophilic (4-mercaptophenylacetic acid MPAA) [START_REF] Wallace | Kinetics of Silica Nucleation on Carboxyl-and Amine-Terminated Surfaces: Insights for Biomineralization[END_REF][START_REF] Xue | Self-Assembled Monolayer Mediated Silica Coating of Silver Triangular Nanoprisms[END_REF], and the other vitreophobic (poly-(acrilic acid) PAA). Much of the selective mineralization of surfaces derives from studies on bio-mineralization, as it is the basis for the formation of mineralized tissues and skeletal components for living organisms, and several papers have been dedicated to understanding the role of the surface molecules in the mineralization of the surface [START_REF] Mann | Biomineralization and biomimetic materials chemistry[END_REF][START_REF] Mann | Biomineralization: the form(id)able part of bioinorganic chemistry! *[END_REF][START_REF] Mann | Biomineralization-Principles and Concepts in Bioinorganic Materials Chemistry[END_REF]. In particular, the silica coating of surfaces has been shown to be favoured by carboxylic functional groups [START_REF] Wallace | Kinetics of Silica Nucleation on Carboxyl-and Amine-Terminated Surfaces: Insights for Biomineralization[END_REF][START_REF] Xue | Self-Assembled Monolayer Mediated Silica Coating of Silver Triangular Nanoprisms[END_REF]. This, along with the high interfacial energy between the MPAA and the solvent, make the part of the colloid covered by the shorter molecule more favourable to the growth of the SiO 2 [START_REF] Chen | Scalable Routes to Janus Au-SiO 2 and Ternary Ag-Au-SiO 2 Nanoparticles[END_REF][START_REF] Mann | Biomineralization-Principles and Concepts in Bioinorganic Materials Chemistry[END_REF].

The effect of the PAA, on the other hand, has to be explained by taking into account the polymeric nature of the molecule. As is the case of MPAA, PAA also contains carboxylate groups, which should favour the mineralization of the surface. The length of the chain though could prevent the diffusion of the silica precursor to the surface of the colloid [START_REF] Mann | Biomineralization-Principles and Concepts in Bioinorganic Materials Chemistry[END_REF].

Furthermore, the high solubility of the molecule in solution results in low interfacial energy and makes the heterogeneous nucleation of the silica unfavourable [START_REF] Chen | Scalable Routes to Janus Au-SiO 2 and Ternary Ag-Au-SiO 2 Nanoparticles[END_REF].

Experimental Methods

The synthesis for the Au-silica heterodimers requires, as starting point, citrate stabilized Au nanoparticles of ∼40 nm in diameter in aqueous solution (first image of the scheme in Fig. 4.2). Initially, these nanoparticles were prepared using a modified Frens' protocol used by the authors, which has been detailed in the previous chapter. Subsequently, we decided to prepare the starting nanoparticles using a multi-step synthesis developed by N.G. Bastús et al. [START_REF] Neus | Kinetically Controlled Seeded Growth Synthesis of Citrate-Stabilized Gold Nanoparticles of up to 200 nm: Size Focusing versus Ostwald Ripening[END_REF], also detailed in the previous chapter. This new synthesis gave us a starting solution of more spherical nanoparticles and with a higher concentration.

The nanoparticles are concentrated by centrifuging two 1.5 mL Eppendorf vials at 2900 g for 10 min. The supernatant is then removed using a micro-pipette, leaving a dark red solution behind containing the concentrated nanoparticles. The two sediments are combined together and topped to 500 µL using millipore water. The solution is then sonicated in order to ensure the full re-dispersion of the nanoparticles. It is then added dropwise to

Characterization of the janus nanoparticles

Light absorption spectrometry

As with the pure gold nanoparticles, light absorption spectra were recorded throughout the synthesis. The final spectrum of the colloidal solution is red shifted compared to the starting point with a shift of the absorption peak from ∼530 nm to ∼540 nm. This shift in the plasmon resonance, however, cannot be solely attributed to the growth of silica, but also to the change in the environment and the exchange of ligands, in particular the presence of the thiol binding on the surface of the nanoparticle [START_REF] Goldmann | Charge Transfer at Hybrid Interfaces: Plasmonics of Aromatic Thiol-Capped Gold Nanoparticles[END_REF]. This can be seen from the evolution of the UV-Visible spectra of the gold nanoparticles in water compared to the system in iso-propanol and ligands which shows that the plasmon shift begins before the addition of the silica precursor (Figure 4.4). The absorption spectra then, while instructive when trying to determine the size and concentration of gold spheres, is of very little help in determining the morphology of these new heterodimers or the presence of free silica particles. As a result, this technique was used to ensure that particles had not aggregated during the transfer from an aqueous to all alcohol environment -which would have shown up as an increase in the absorption at longer wavelength -but the morphology of the final heterodimers was assessed though TEM.

Transmission Electron Microscopy (TEM)

TEM was used on all samples as a means of obtaining direct information on the system.

The samples were prepared by drop-casting the colloidal solution on the grids. 500 µL of solution were diluted with 1 mL of millipore water and centrifuged at 2900 g for 15 min.

The transparent supernatant was removed and the remaining concentrated nanoparticle solution was diluted to ∼200 µL with millipore water. This allowed us to concentrate the nanoparticles to an adequate concentration for electron microscopy and to remove from the solution any unreacted ligands, as well as part of the spurious silica which might have formed during the polymerization of the TEOS. The hydrophilicity of the TEM grids was enhanced by placing them for 20 s in a plasma with a current of 5 mA. A drop (5 µL) of washed and concentrated nanoparticle solution was then placed on the copper grids, the sample was then allowed to dry in air for several hours. The images were taken of a JOEL 1400 electron microscope at 120 kV. The TEM images of the heterodimers showed that the gold particles have very diverse shapes, from spherical to very elongated or triangular.

The analysis of the images was done with the ImageJ software. Th particles were detected by hand due to the difficulty of implementing an algorithm capable of accurately discerning between gold, silica and janus nanoparticles. In particular, as a result of the particles coming together during the drying, it was hard to determin whether a two adjacent gold-silica particles should be considered as a single janus or not. In order to simplify the task, a plug-in called MiToBo [START_REF] Glaß | MiToBo -A microscope image analysis toolbox[END_REF] , developed for bio-imaging research, was used. The plug-in allows the user to create different color markers and count the occurrences of different populations in the image. The results can be saved as either a text file, in which the total number of occurrences for each element type is displayed or as an xml file, which stores the position of each marker.

SAXS

SAXS measurements do not provide useful information in the case of the Au -SiO 2 heterodimers because of the difference in scattering length density between gold and silica.

As seen in eq.(2.5), the amplitude of scattered wave is directly proportional to the scattering length density of the material. In the case of Au, the scattering length density using X-rays with a wavelength of 1.033 Å is 1.088 × 10 -4 Å -2 , while in the case of SiO 2 the value is

0.226 × 10 -4 Å -2
. As the intensity of the signal is a function of the square of the amplitude, in the final SAXS pattern the contribution of the gold will be roughly 30-40 times that of the silica. The SAXS signal of the heterodimers can thus be approximated to that of the pure gold nanoparticles. Fig. 4.5 shows the two SAXS curves of the Au nanoparticles and the Au -SiO 2 heterodimers on the same graph. Both curves can be seen to overlap perfectly with just a slight difference at very small q values. This difference is outside of the q range affected by the shape and can be better attributed to the change in solvent as well as the ligands, which alter the interaction between the particles. The presence of PAA on the surface, as well as the iso-propanol used as solvent, induces a slightly more attractive interaction between the particles.

Adjustments to the synthesis parameters

Throughout our work, different modifications were done on the original synthesis in order to address some of the shortcomings that we encountered. Some of the modifications resulted in an improved version of the reaction, while others proved to be not as effective and we thus reverted to the original conditions.

Original synthesis

We started our synthesis of heterodimers following Chen's paper, in particular we used the two-step gold nanoparticle synthesis described in section 3.5, which produced elongated gold particles at a relatively low concentration. The TEM images of the heterodimers showed that the gold particles have very diverse shapes, from spherical to very elongated or triangular (figure 4.6). This polydispersity, both in size and shape, is a significant hurdle to the self assembly of nanoparticles. A polydispersity of more than 5% already provides enough difference between the particles to inhibit the spontaneous self-assembly of spherical particles [START_REF] Nikhil | Shape Effect in Nanoparticle Self-Assembly[END_REF]. Furthermore, some of the reactions showed a very high excess of silica nanoparticles which formed along with the heterodimers. This can be attributed to the fact that the reagents used for the synthesis of the silica part of the heterodimer are also used in the Stöber reaction for the preparation of silica nanoparticles. of silica beads. Even though the interfacial energy between the MPAA and the solvent produces preferential nucleation sites, some homonucleation cannot be avoided. As a result, modifying the amount of added silica precursor does not increase the ratio of heterodimers but only reduces the total amount of silica in the final product.

Effects of the amount of Gold Nanoparticles

An analysis of Fig. 4.7F) shows that in the standard reaction the amount of free gold nanoparticles in solution is extremely small, almost zero, while free silica particles are present in abundance. This suggests that the problem could be due to a low availability of free gold surface on which the silica can heterogeneously grow, inducing a homogeneous nucleation.

We thus proceeded to study the effect of varying the amount of gold nanoparticles present in solution on the total outcome. Three different concentrations of gold were studied besides that described by the original article: 1.5, 2, and 2.5 times the original concentration. The different reactions were prepared by varying the number of eppendorf tubes centrifuged.

While in the original reaction two 1.5 mL eppendorfs were centrifuged, three where used for the reaction labelled 1.5x Au NP, while four and five where used for the 2x and 2.5x reactions respectively. Apart from this, no other alteration was applied to the protocol. As

Effects of changing the synthesis of the gold nanoparticles

A further change on the original synthesis dealt the starting gold nanoparticles. As seen in the previous chapter, the two step synthesis procedure used by Chen in his article produces irregularly shaped nanoparticles which are not well suited for auto-assembly. In contrast, the synthesis, also presented in the previous chapter, taken from Bastús et al.

[44] produces monodisperse nanoparticles with spherical shape. Because of the higher concentration of nanoparticles in the latter reaction, the protocol was kept the same, with two 1.5 mL eppendorfs roughly corresponding to twice the concentration of the original synthesis. Apart from this difference, the only other adjustment made to the reaction was the amount of ligand solution added to the flask. While the original synthesis called for 20 µL for both ligands, having doubled the number of nanoparticles meant that 40 µL of ligand solution were used. The result were heterodimers with a more regular shape and a higher concentration. Though bare gold and silica nanoparticles were still present in the overall solution, we decided to proceed with our studies using this colloidal system as no other higher throughput reaction for the preparation of gold silica heterodimers was available.

Reproducibility of the synthesis

The final study done on the system investigated its reproducibility. In order for the heterodimers to form, the two ligands have to bind to the gold surface and self assemble on the Söber reaction occurred -there are very few janus or silica nanoparticles at all -the others all show a high amount of both janus and silica nanoparticles, but also a random ratio between the three populations. For the most part, bare gold nanoparticles are the least represented in the successful synthesis but the presence of gold and silica is balanced out over all the reactions. This suggests that while the separation of the ligands on the surface of the gold nanoparticles does induce a separation in the vitreophilic property of the particles, the presence of MPAA is not sufficient to inhibit the homonucleation of silica in solution. It is also important to note once more that electron microscopy can be subject to sampling bias. While more than 1000 particles were counted in all six reaction, the number varied between one sample and another. This could have lead to some unbalanced sampling effect in the final toll. These are important considerations to take into account whenever microscopy measurements are done, but are difficult to quantify. Unfortunately, due to the characteristics of the system, the other measurement techniques could not be applied to quantify the number of janus particles in solution (namely the low contrast of the silica to

x-rays, and the undefined effect of the silica on the gold's plasmon).

Consequently, while all of the batches of janus nanoparticles have to be analysed through electron microscopy in order to determine the state of the system before proceeding, the limitations of this technique have to be always kept present.

Conclusions

In this chapter we introduced the synthesis of Au -SiO 2 heterodimers taken from [START_REF] Chen | Scalable Routes to Janus Au-SiO 2 and Ternary Ag-Au-SiO 2 Nanoparticles[END_REF].

It is a chemical synthesis done in solution which relies on the segregation of two different ligands on the surface of gold particles. The segregation is probably driven by the difference in nature of the ligands, one a short thiol with a phenyl group, while the other is a long polymer with repeating -OH groups. The chemical characteristics of the two ligands also serve the purpose of either facilitating or hindering the growth of silica on the gold surface.

On the one hand the MPAA provides a good nucleation site, as a result of carboxylic groups which favour the growth of SiO 2 [START_REF] Wallace | Kinetics of Silica Nucleation on Carboxyl-and Amine-Terminated Surfaces: Insights for Biomineralization[END_REF][START_REF] Xue | Self-Assembled Monolayer Mediated Silica Coating of Silver Triangular Nanoprisms[END_REF], as well as having a high interfacial energy with the water/iso-propanol mixture [START_REF] Chen | Scalable Routes to Janus Au-SiO 2 and Ternary Ag-Au-SiO 2 Nanoparticles[END_REF][START_REF] Mann | Biomineralization-Principles and Concepts in Bioinorganic Materials Chemistry[END_REF]. At the same time the PAA has a high affinity for the solvent [START_REF] Chen | Scalable Routes to Janus Au-SiO 2 and Ternary Ag-Au-SiO 2 Nanoparticles[END_REF], and the long polymer hinders the arrival of the precursor molecules on the surface of the particle [START_REF] Mann | Biomineralization-Principles and Concepts in Bioinorganic Materials Chemistry[END_REF] making it harder for the particles to nucleate there.

Different parameters of the synthesis were tested to find the optimal conditions for the preparation of the particles. While we were never able to obtain a solution containing only Au -SiO 2 particles we were nonetheless able to maximize the percentage of heterodimers in solution, while minimizing the free gold particles. This was initially done by increasing the starting amount of colloidal gold solution used, and at a later time by changing the synthesis of the gold particles to produce a solution with a higher concentration of nanospheres. This second synthesis -which was presented in the previous chapter -also provided the added benefit of producing rounder particles with lower polydispersity. We also tested the effect of changing the amount of silica precursor used in the synthesis (namely TEOS) in order to reduce the number of free silica particles in solution. What we found was that the number of janus particles decreased along with silica particles. This lead us to the conclusion that the homogeneous nucleation of silica cannot be completely suppressed regardless of the ratio between the TEOS used and the gold nanoparticles in solution.

Finally we tested the reproducibility of the synthesis, by repeating it six times in parallel.

the analysis showed an important variation in the relative amounts of the different species.

Though the measurements can suffer from some bias, due to the analysis being done by electron microscopy, it brought us to the conclusion that a microscopic analysis was necessary on all batches before further works, in order to assure the reproducibility of the results.

Chapter 5

Self-assembly of Janus nanoparticles

The particles obtained after the growth of the silica present a breaking in symmetry, both with regards to the shape and to the constituent material. They are also colloidally stable due to the absence of any net attractive interaction between them. The gold moiety is stabilized by the carboxylic groups in the PAA chain, while the silica one is covered by OH groups which provide electrostatic repulsion. Under such conditions, the heterodimers are stable for long periods of time, with only minor sedimentation occurring over several weeks.

In order to obtain self assembly, a driving force has to be provided to the system, which induces the colloids to come together in an ordered way. In the case of nanoparticles with spherical symmetry this driving force can only be isotropic and can lead to the formation of ordered 2D layers or super-crystalline structures [START_REF] Courty | Supra Crystals" Made of Nanocrystals[END_REF][START_REF] Bentzon | Ordered aggregates of ultrafine iron oxide particles: 'Super crystals[END_REF][START_REF] Motte | Self-Organization into 2D and 3D Superlattices of Nanosized Particles Differing by Their Size[END_REF][START_REF] Motte | Self-Assembled Monolayer of Nanosized Particles Differing by Their Sizes[END_REF]. A simple example of organized 2D structures which can be obtained from isotropic nanoparticles is readily available when TEM grids are prepared by drying a drop of solution containing highly monodisperse colloids.

If the particles are sufficiently monodisperse, they will tend to form 2D hexagonal lattices or sometimes stacks of multiple layers. Fig. 5.1A) and Fig. 5.1B) show one and two ordered layers respectively, prepared by drying a solution of small mono-disperse gold nanoparticles on a TEM grid. Shown beside each TEM image is the Fast Fourier Transform of the image which helps to visualize the periodicity of the lattices. Such systems have been, and are, extensively studied [START_REF] Lin | Constructing Two-Dimensional Nanoparticle Arrays on Layered Materials Inspired by Atomic Epitaxial Growth[END_REF][START_REF] Rabani | Drying-mediated self-assembly of nanoparticles[END_REF][START_REF] Terry | Kinetically driven self assembly of highly ordered nanoparticle monolayers[END_REF], along with others which produce large supra-crystalline structures with regular lattices [START_REF] Courty | Supra Crystals" Made of Nanocrystals[END_REF][START_REF] Goubet | Which Forces Control Supracrystal Nucleation in Organic Media?[END_REF]. The building blocks of all these structures, though, are nanoparticles with isotropic interaction and limited or no directionality (in some cases, such as with prismlike particles, rods, or platelets, some directionality is present in the system, but with no overall preferential orientation), resulting, for the most part, in standard structures such as hexagonal tiling or stacking. While more complex shapes can be achieved through other means such as templating [START_REF] Xia | Template-Assisted Self-Assembly of Spherical Colloids into Complex and Controllable Structures[END_REF] or by designing special linkers [START_REF] Yong | DNA-programmable nanoparticle crystallization[END_REF], they are still limited and require precise programming.

On the other hand, because of their similarity with surfactants, heterodimers have attracted much attention due to the possibility of self assembling into complex structures. Theoretical studies of patchy particles in solution have already predicted the formation of diverse structures such as micelles, vesicles [START_REF] Sciortino | Phase Diagram of Janus Particles[END_REF], helices [START_REF] Sobrino Fernández | Self-assembly of Janus particles into helices with tunable pitch[END_REF], chains or rings [START_REF] Rovigatti | Self-Assembly in Chains, Rings, and Branches: A Single Component System with Two Critical Points[END_REF], which can be obtained by varying the position and intensity of the attractive and repulsive forces on the particles as well as the confinement of the particles. Similar simulations conducted on 2D surfaces, such as at the interface between two solvents or at a liquid-air interface, have also shown the appearance of interesting and unique patterns for the crystallization of heterodimers in 2 dimensions [START_REF] Shin | Theory of two-dimensional self-assembly of Janus colloids: crystallization and orientational ordering[END_REF]. Experimental studies on janus systems have also shown the possibility of achieving a wide range of outcomes, but have for the most part dealt with microscopic particles. Fluorescent zwitterionic colloids, treated in such a way as to have a positively and a negatively charged hemisphere gather to form complex clusters of varying size [START_REF] Hong | Clusters of Charged Janus Spheres[END_REF]. Similarly, Kraft et al. have produced colloidal micelles using smooth and rough particles [START_REF] Kraft | Surface roughness directed self-assembly of patchy particles into colloidal micelles[END_REF]. The formation of Kagome lattices, an interesting structure both from a mathematical and a mechanical point of view, was obtained by Granick et al., using triblock particles placed on a surface [START_REF] Chen | Directed self-assembly of a colloidal kagome lattice[END_REF].

Even though these interesting structures have already been achieved using microparticles, the theoretical simulations cited seem to propose that a wider phase diagram exists for particles in solution. In particular, the 2009 article written by Sciortino et al. [START_REF] Sciortino | Phase Diagram of Janus Particles[END_REF] explores the interactions of simple spherical janus particles made of two hemispheres with different interacting potentials, showing the existence of a complex phase diagram. The interaction is simplified as being either a square well attraction with a range comparable to the radius of the colloids, or as a hard sphere interaction. The authors study the effect of both the temperature of the system and the concentration of the particles, focusing in particular on how the system moves from the gas to the liquid phase. They note that as the temperature is lowered the particles tend to form either single-layer or double-layer micelles in which the attractive hemispheres are in contact. This results in stable structures, as they present a hard sphere surface to the other particles in solution and therefore avoid aggregation. A most peculiar characteristic of the system is that the gas-liquid coexistence has a negative slope, similar to the liquid-solid curve for water. This is a result of the gas phase (where the micelles form) being more ordered than the liquid phase. The article was later built upon by introducing modifications of the basic spherical, evenly divided particle. The ratio between the attractive and the hard-sphere hemisphere was varied between 30% and 60%, while maintaining the particle spherical in reference [START_REF] Preisler | Equilibrium phases of one-patch colloids with short-range attractions[END_REF]. What they found was that perfect spheres where 60% of the surface has an attractive interaction, for example, will tend to form bilayers. When the attractive surface was reduced to 30% the particles would actually form "open" crystals made up of connected pentagonal structures. In a different study, the perfectly spherical particles where substituded by dumbbell-like structures made of two spheres of equal size, but with varying interaction. In this case, the authors found a rich phase diagram which presents regions where small micelle-like clusters are stable, as well as others characterized by the presence of larger lamellar structures [START_REF] Munaó | Phase separation and self-assembly of colloidal dimers with tunable attractive strength: from symmetrical square-wells to Janus dumbbells[END_REF]. By varying the size ratio between the two spheres, they were instead able to show that the formation of micelles is favoured when the attractive spheres are smaller with respect to the hard-sphere half, but is completely inhibited when the interacting sphere is just 10% larger than the hard-sphere moiety. [START_REF] Munaó | Cluster formation and phase separation in heteronuclear Janus dumbbells[END_REF]. Through all these studies, we can paint an interesting picture of the richness of the phase diagram, which depends on multiple factors. One of the critical parameters that the authors note, especially in the first article [START_REF] Sciortino | Phase Diagram of Janus Particles[END_REF], is the range of the interaction forces.

In simulations, the range can be tuned to any value, but in real systems we are bound by the characteristics of the particles and the force being used. In the articles, the square well is set to have a range equal to a fraction of the radius, usually between 5-50% of the radius. In most of the janus systems for which self-assembly has been studied and which we presented earlier, the particles are micrometric in size while the interaction forces are of the order of tens of nanometres. In order to experimentally probe all the areas of the phase diagram explored in the simulations, it is therefore necessary to either reduce the size of the particles to the nanometre range or increase the range of the attractions. The new procedures mentioned above make it possible to prepare particles small enough to be comparable in size to interactions such as the van der Waals or hydrophobic attraction.

The decrease in size of the particles also opens up the possibility of accessing the unique physical properties which arise when dealing with such length scales, such as plasmonic effects [START_REF] Eustis | Why gold nanoparticles are more precious than pretty gold: Noble metal surface plasmon resonance and its enhancement of the radiative and nonradiative properties of nanocrystals of different shapes[END_REF], quantum confinement [START_REF] Alivisatos | Perspectives on the Physical Chemistry of Semiconductor Nanocrystals[END_REF], enhanced catalytic properties [START_REF] Buonsanti | Architectural Control of Seeded-Grown Magnetic-Semicondutor Iron Oxide-TiO 2 Nanorod Heterostructures: The Role of Seeds in Topology Selection[END_REF], etc., resulting in the appearance of new collective properties as they are brought together and assembled [START_REF] Taleb | Collective optical properties of silver nanoparticles organized in twodimensional superlattices[END_REF][START_REF] Russier | Optical absorption spectra of arrays of metal particles from cluster calculations: cluster size and shape effects[END_REF][START_REF] Russier | Collective magnetic properties of cobalt nanocrystals self-assembled in a hexagonal network: Theoretical model supported by experiments[END_REF][START_REF] Ngo | Nanoparticles of Cobalt Ferrite: Influence of the Applied Field on the Organization of the Nanocrystals on a Substrate and on Their Magnetic Properties[END_REF][START_REF] Ngo | Assemblies of Ferrite Nanocrystals: Partial Orientation of the Easy Magnetic Axes[END_REF]. Surface plasmons have, for example, been shown to hybridize when brought close enough to each other, resulting is a red shift of the absorption spectra [START_REF] Prodan | A Hybridization Model for the Plasmon Response of Complex Nanostructures[END_REF].

Hydrophilic/hydrophobic heterodimers provide further interest due to their similarity with surfactants, and have for this reason also been called "solid surfactants". Casagrande's et al.

initial studies had already showed the tendency of janus beads to remain anchored at the interface between oil and water, unlike uniform beads which preferentially locate themselves completely within either one, or the other, solvent [START_REF] Casagrande | Janus Beads": Realization and Behaviour at Water/Oil Interfaces[END_REF]. As a result of this tendency, janus nanoparticles had been predicted to greatly stabilize emulsions, by reaching the interface between the two liquids [START_REF] Binks | Particles Adsorbed at the Oil-Water Interface: A Theoretical Comparison between Spheres of Uniform Wettability and "Janus" Particles[END_REF]. Pendent drop measurements later showed that the interface tension is indeed reduced by more than a third when Au -Fe 3 O 4 nanoparticles are added to the oil solution prior to the insertion of the water droplet [START_REF] Glaser | Janus Particles at Liquid-Liquid Interfaces[END_REF].

Because of these possibilities we proceeded to induce an asymmetry in the surface properties of the Au -SiO 2 nanoparticles. Our approach was to use the gold surface chemistry to selectively modify the solvophilicity of the gold moiety in order to introduce in the system a directional and selective attractive force. As a result, we were able to induce the formation of finite-size clusters in which the particles have a particular orientation.

Self-assembly strategy

We decided to intervene on the gold hemisphere, as gold surface chemistry is well studied, in particular with regards to its affinity with thiols [START_REF] Häkkinen | The gold-sulfur interface at the nanoscale[END_REF][START_REF] Richard | The Chemistry of Gold[END_REF][START_REF] Thompson | Gold: Progress in chemistry, biochemistry and technology[END_REF][START_REF] Laguna | Modern Supramolecular Gold Chemistry: Gold-Metal interactions and Applications[END_REF]. Thiols are known to form strong covalent bonds with the gold surface, ensuring a complete replacement of the existing ligand, adsorbed on the surface through weaker carboxylic bonds [START_REF] Kunze | Electrochemical evaluation of citrate adsorption on Au(111) and the stability of citrate-reduced gold colloids[END_REF][START_REF] Sandroff | Kinetics of displacement and charge transfer reactions probed by SERS: evidence for distinct donor and acceptor sites on colloidal gold surfaces[END_REF], while at the same time being unreactive with SiO 2 . Furthermore, a wide variety of thiols are commercially available, allowing us to explore the effect of varying the bound ligand. In particular, we decided to use alkanethiols as they provide all the properties needed for inducing the self assembly, while not introducing too much complexity in the system. They are relatively simple molecules with a single SH group and a carbon chain.

The carbon tail changes the hydrophilicity of the gold, making it hydrophobic, further breaking the solvophilic symmetry of the particle, and providing the driving force for the assembly. Furthermore, the possibility of varying the length of the thiol chain allows for the variation of some of the parameters in play, such as the affinity of the thiol for gold and the hydrophobicity of the thiol-covered surface [START_REF] Laibinis | Comparison of the structures and wetting properties of self-assembled monolayers of n-alkanethiols on the coinage metal surfaces, copper, silver, and gold[END_REF][START_REF] Abbott | Active Control of Wetting Using Applied Electrical Potentials and Self-Assembled Monolayers[END_REF][START_REF] Walczak | Reductive desorption of alkanethiolate monolayers at gold: a measure of surface coverage[END_REF][START_REF] Widrig | The electrochemical desorption of n-alkanethiol monolayers from polycrystalline Au and Ag electrodes[END_REF]. Once the ligand exchange is complete, the particles present a hydrophilic moiety, stabilized by electrostatic repulsion, and a hydrophobic side, which provides an attractive force through what is known as the hydrophobic effect [START_REF] Chandler | Interfaces and the driving force of hydrophobic assembly[END_REF]. This phenomenon is present in many aspects of science, from the creation of emulsions to the folding of proteins [START_REF] Nicholls | Protein folding and association: Insights from the interfacial and thermodynamic properties of hydrocarbons[END_REF][START_REF] Spolar | Hydrophobic effect in protein folding and other noncovalent processes involving proteins[END_REF][START_REF] Tanford | The hydrophobic effect and the organization of living matter[END_REF], and is responsible for the attraction between hydrophobic entities in aqueous solution. Though a complete theoretical model is still not available, in the case of particles in solution, the attractive force between them can be explained by considering the solvation free energy of the particles. If n hydrophobic particles are well dispersed in an aqueous solution, the total solvation energy will be equal to the solvation energy for one particle multiplied by n. As such, if more particles are added to the solution, the total energy will increase linearly with the number of particles. On the other hand, if the particles come in close contact with one another, the total solvation energy will decrease, as only the exterior surface of the micell will contribute to the solvation energy. Unlike purely hydrophobic particles which will tend to form larger and larger clusters if placed in a poor solvent, heterodimers behave as amphiphilic molecules, resulting in micelle-like structures. Furthermore, the steric hindrance provided by the large SiO 2 moiety, also contributes to regulating the size of the clusters. A simple representation of the predicted process is shown in Fig. 5.2. A similar situation was presented by Steve Granick in 2008 [START_REF] Hong | Clusters of Amphiphilic Colloidal Spheres[END_REF], where micron-sized particles at the bottom of a glass container were initially treated to produce a hydrophobic side and a negatively charged side through gold coating and the use of octadecanethiol. The structures resulting from the hydrophobic attraction were clusters of dimers, trimers, up to groups of nine particles. If the electrostatic repulsion between the hydrophilic hemispheres was screened by adding salt, then further aggregation was favoured, with larger, worm-like aggregates forming.

Experimental Methods

To induce the self assembly of the heterodimers, a volume (3.6 mL) of the solution resulting from the janus synthesis is placed in a small glass vial. 40 µL of a solution of an alkanethiol is added to the vial. The concentration of the alkanethiol solution is set so that the final concentration in the sample will be 50 times the concentration of the PAA used for the synthesis (32.25 mm). After the addition of the new ligand, the vial is agitated using a vortex and placed to sonicate for 30 min. After making sure that the solution is well mixed, the vial is left to rest. The solution then slowly changes color passing from the reddish pink, characteristic of Au nanoparticles, to a more blue and finally purple color. The exact final color of the solution depends on the thiol used. The intensity of the solution's color also varies as the assembly proceeds. As the particles come together, some larger assemblies form. These objects lose colloidal stability and fall to the bottom of the vial, the absorption of the solution thus decreases over time. Nonetheless, smaller assemblies remain stable for several weeks after the addition of the thiol.

Spectroscopic analysis

The most evident variation in the solution after the addition of the thiol is the change of color which occurs over a period of several hours -the systems can be seen evolving for 2-3 days. Because of this, following the absorption spectra of the solution over time can provide useful information regarding the process of self assembly which takes place.

Plasmon coupling

The variation in color of the solution observed after the addition of the thiol is due to an effect called plasmon coupling. As described in Chapter 3, the presence of a peak in the absorption spectra of gold nanoparticles is due to the particle's electron cloud which interacts with the incoming electromagnetic wave. When the interparticle distance is large, no interaction can occur between the electron clouds of neighbouring particles. As the nanoparticles are brought together however, their electron clouds start to interact giving rise to multiple oscillation modes. This phenomenon has been, compared to the hybridization of atomic orbitals, which form when two or more atoms are placed close enough together [START_REF] Prodan | A Hybridization Model for the Plasmon Response of Complex Nanostructures[END_REF][START_REF] Myroshnychenko | Modelling the optical response of gold nanoparticles[END_REF]. As with orbital hybridization, when two plasmons interact, they form two hybridized plasmons, called, by similitude with orbital theory, bonding and anti-bonding plasmons. The bonding plasmon has lower energy and is localised between the two particles. The antibonding plasmon, instead, is located at the extremities of the dimer and has a higher energy compared to the parent plasmons. A schematic representation of the energy for the new bonding and antibonding modes is shown in Fig. 5.3. The presence of these different plasmon levels is evidenced by the appearance of other resonance peaks in the absorption spectra, corresponding to the energy of the new plasmon levels. While for two particles the system can be described rather easily, as the number of particles increases, taking into account all the interactions becomes more complex, especially when trying to describe the system analytically.

Evolution of the light absorption spectra

The absorption spectra of the solution after the addition of the thiol were recorded over time in order to obtain insight on the evolution of the system. The thiol used was dodecanethiol, a chain of twelve carbon atoms ending with an SH group. Fig. 5.4 shows the evolution of the absorption spectra over a period of 80 h. The coupling plasmon initially appears as a hump on the side of the main peak. It then shifts to longer wavelengths increasing in intensity at the expense of the main peak. Because the shape of the spectra at lower wavelength remains unaffected by the plasmon coupling, the absorption at 450 nm can be used to follow the concentration of the nanoparticles in solution. In this region, the intensity of the curve decreases with time, indicating that part of the particles fall out of the solution and sediment at the bottom of the cuvette. In order to have a clearer view of the evolution of the system without the influence of the change of concentration, all the spectra can be normalized to the first one, using the absorption value at 450 nm as a reference. The resulting graph is shown in Fig. 5.5A).

During the first few hours, the system does not evolve; the plasmon peak intensity then starts to decrease as the coupling peak appears on the side of the main peak. The coupling peak shifts to longer wavelengths and increases in intensity, finally becoming stronger than the original peak. The red-shift of the plasmon resonance frequency can be attributed to the particles packing closer together over time [START_REF] Quinten | Absorption and elastic scattering of light by particle aggregates[END_REF][START_REF] Shipway | Investigations into the Electrostatically Induced Aggregation of Au Nanoparticles[END_REF]. The change in the peak could also be seen as an evolution of the system, with more particles coming together to form more complex structures. The progress of the intensity of the coupling plasmon is an indicator that the relative number of clusters in solution increases.

Another interesting feature of the graph is highlighted in the inset, which is a zoom of the curves between 600 nm and 680 nm. The inset shows, that after the first few curves, all of the spectra tend to pass through a particular point (λ ∼ 630 nm and absorption ∼ 2 ). Such a point is called "isosbestic point" in spectroscopy, and is an indication that one specie in the sample transforms into another specie, the two species having different absorption (∆λ ∼100 nm). The peak quickly shifts to longer wavelengths and tends to 760 nm. C) The relative intensity of the coupling plasmon compared to that of the primary plasmon peak. The coupling plasmon is initially weak compared to the primary peak. As the system evolves, the primary peak decreases in intensity, while the coupling peak rises.

spectra. The absorbance at the intersection point between the two spectra will then remain invariant throughout the transformation. The detail in the inset shows that the curves do not perfectly intersect in one point, but the intersection is slightly distributed over a few different wavelengths. This "de-focusing" of the isosbestic point can be attributed to an intermediate species which forms and which causes the shift of the curves, but it could also be due to the normalization which does not perfectly compensate for the variations in concentration of the nanoparticles. Fig. 5.5B) shows the position of the coupling plasmon as the system evolves. The peak first appears after ∼ 20 h at 620 nm, it then rapidly shifts to higher wavelengths, finally reaching a stable position around 760 nm. The shape of the curve indicates that while the distance between the colloids varies during the first 20-30 h, the clusters eventually reach a final configuration. Fig5.5C) similarly follows the intensity of the peak through the experiment.

The intensity is given as the ratio between the intensity of the coupling plasmon peak to that of the single nanoparticle plasmon; it is thus independent of the normalization process. The coupling peak starts off at around half the intensity of the main peak and rapidly increases before settling just below 1.3 times that of the main peak. The study of the coupling plasmon provides insightful information regarding the system: the onset of the assembly and the qualitative evolution of the clusters. Because of the complexity in the theoretical model behind the coupling of plasmons, the data cannot be fitted to an analytical function to obtain the corresponding particle structure, and because of the high computational cost, fitting with simulations is not a feasible approach. Hence, we conducted a singular value decomposition of the measurements to simplify the data with minimal loss. U and V are unitary matrices and their columns are called the left and right singular vectors respectively, while Σ is the singular value matrix, and has non-zero values only on the diagonal. One of the advantages of this technique is that it can be used to reduce the dimensionality of a signal, as it not only provides the principal components which make up the information (the column vectors in U and V), but also the relative importance of each (stored in the diagonal elements of Σ). As a result, a user can decide to discard the components containing less information, reducing the dimensionality of the signal and sacrificing only the finer details. As the components are placed in order of importance, this can be done by using only the first p components, the resulting matrix will then be said to be of rank p. The result of this resizing can be easily seen by doing a SVD on an image and trying to reconstruct it using a varying number of components. The image shown in The mechanism behind the SVD can be intuitively understood if examined on a lower dimensionality, such as, for example, on a set of points on a Cartesian plane. The points plotted in Fig. 5.7A) lay on the line y = x to which Gaussian noise has been added on both the x and y coordinates. The distributions along the two axes look fairly even, and as a result both of the axes can be seen as containing the same amount of information. If a SVD is applied to the set of data it is possible to extract from the V matrix the two principal axes (which will be orthogonal, due to the matrix being unitary), and the singular values from the Σ matrix, the first of which is larger than the second (4.72 vs 1.47). The first axis defined in the V matrix is the one which maximizes the dispersion of the data, the second is the axis, orthogonal to the first, which defines the second most dispersive direction. In 2 dimensions, the direction of the second axis is fixed by the first but in more dimensions multiple axes can be found, each pointing towards the direction of maximum information dispersion. If the axes are plotted on the Cartesian plane and the projection of the points on the axes are also marked, it is clear that the dispersions along the new two axes are different. The first one (plotted in red) contains most of the information whereas the projection of the points on the second axis (in green) are mostly gathered around the centre. As a result, if only the information from the first axis is taken (only the first component), the data can be plotted using less information, but without loosing the overall trend.

Singular Value Decomposition (SVD)

SVD on time resolved the light absorption data

The great advantage of the SVD is then to reduce the dimensionality of a data set, whether to reduce the total memory occupied or to extract the most prominent components from a signal. In particular, with regards to this last approach, SVD can be used to analyse absorption spectra composed of multiple spectra linearly combined and separate them [START_REF] Shrager | Chemical transitions measured by spectra and resolved using singular value decomposition[END_REF][START_REF] Hofrichter | Nanosecond absorption spectroscopy of hemoglobin: elementary processes in kinetic cooperativity[END_REF]. This technique can then be applied to the evolution of the absorption spectra after the addition of the thiol, in order to study the species present in solution. When this is done, M is a 800 × 72 matrix (800 wavelengths recorded once an hour over a period of 72 h), while U is 800 × 800, V 72 × 72 and Σ is 800 × 72. We can interpret the column vectors of U as the base spectra, whose linear combination can produce the signal at any instant during the measurement, while the row vectors of V are the temporal coefficients which indicate the intensity of each specific signal at each time interval. It is then possible to reconstruct the sequence using a lower rank matrix by only selecting some of the components of U and their respective temporal coefficient vectors. In the case of the thiol-induced evolution, a minimum of three components are necessary to adequately reconstruct the signal. The whole data can then be seen as the linear combination of three species which are present in different ratios at different times. The downside of this approach is that SVD is a purely mathematical operation whose results are restricted only by mathematical rules, while physical principles place further conditions on the output. In particular, all of the components of U and V must be always positive, as in this case there can be no "negative absorption". In order to ensure that all the output respected this further constraint, a new matrix is introduced: R along with its inverse R -1 . The purpose of this new matrix is to apply a transformation to the original U and V (truncated after their third component) in order to obtain signals which are always positive. The equation for the modified SVD then becomes:

M = URR -1 ΣV (5.2)
where we use the fact that RR -1 = 1. The equation can then be re-written as:

M = U V (5.3)
where U = UR and V = R -1 ΣV. The new matrices are respectively the principal absorption spectra and the evolution of their relative importance over the period of the measurement. The result of the operation is show in Fig. 5.8. The first row of the figure

shows the three components separately. The red signal has only one peak and is the absorbance measured at the beginning of the observation. The blue one exhibits a second peak, the position of which is well aligned with that of simulated dimers with a surface to surface distance of 2.2 nm. The simulated spectrum was obtained using a Matlab toolbax [START_REF] Hohenester | MNPBEM -A Matlab toolbox for the simulation of plasmonic nanoparticles[END_REF] for the calculation of the extinction cross section of metallic nanoparticles. The specifics of the simulations will be delineated later in the chapter (Sec.5.5) The final curve, in green, has the peak further red-shifted, and is representative of larger clusters with particles closer together. The evolution of the different curves can be seen in the second row, where the coefficient for each spectrum is plotted as a function of time elapsed since the addition of the thiol. The curve relative to the monomers starts at a maximum before decreasing rapidly after a few hours, and reaching zero between 30 -40 h. The blue spectrum of the dimers has an initial value of zero and then increases in a reversed fashion compared to the monomers. At 20 h, it reaches a maximum and then decreases at a slower rate. Finally, the green curve of the multimers has a longer induction time and becoming relevant after 10 h. It then rapidly gains importance before slowing down. The overall interpretation is that the monomers quickly start to assemble into dimers, an operation which begins soon after the addition of the thiol and goes on for about 30 h. Once the dimers are formed, they tend to assemble into larger clusters. This second step starts later compared to the formation of dimers, and is generally slower, since it did not reach completion even after 72 h of observation.

Isosbestic points

The application of SVD to the evolution with time of the absorption spectra allowed us to extract an overview of the mechanism behind the formation of the small clusters which come together after the thiol addition to the solution of heterodimers. According to the picture drawn from the analysis of the SVD, the whole reaction can be divided in three The absorption of the sample at 680 nm over the whole measurement shows that, somewhere between 30 h and 40 h, the absorption reached a stable level which stays constant to the end of the measurement.

top graph of both images shows a detail of the absorption spectra around the time interval during which the point is visible (the first 25 h for the first and the last 30 h for the second).

The bottom part of the images on the other hand shows the intensity of the curve at a specific wavelength (566 nm and 680 nm respectively). From these graphs it is clear that in the first case -Fig. 5.9A) -the intensity is constant over the first 10 h, and then slowly declines. In Fig. 5.9B) instead, the absorbance at 680 nm reaches a stable value somewhere in between the 30 th and the 40 th hour. This second analysis further confirms the presence of only two species during the first hours after the addition of the thiol, whose absorbance spectra intersect at 566 nm, as well as later on during the process, with an intersection point which is more red-shifted at 680 nm.

SAXS

The structure factor

As shown in the chapter on small-angle X-ray scattering (Chapter 2), the scattering of X-rays can be used not only to obtain information regarding the shape and concentration of colloids, but also to extract information regarding the structure of clusters through analysis of the structure factor. For reference, the intensity of the scattered signal from an assembly of particles as a function of the wave vector is: I( q) = ΦV P art P ( q)S( q).

(5.4)

While the first part of the equation depends on the shape of the particle and the concentration of particles in solution, the last term (S( q)) depends on the correlation between particles through the pair correlation function, and is called the structure factor. Because the total scattered intensity is a product of these two components, if one of the two is known, the contributions can be separated. In particular, the first part of the equation, concerning the shape of the particles, their concentration, and parameters which depend on the experimental set-up, does not change before and after the self-assembly of the particles, as long as the measurements are done with the same setup. If the form factor of the particles is measured before the addition of the thiol and if the system is dilute enough, there is no spatial correlation between the particles, the cross term in eq.(2.30) then vanishes and S( q) = 1. Then the scattering pattern of the assembled particles differs from the pure solution only by the value of the structure factor. This is true provided that the particles have not been modified by the assembly process, a reasonable assumption considering that the only change to the system is the addition of a thiol. The structure factor of the assembled system is then given by the ratio of the initial pattern to the final one: S(q) = I(q) thiol I(q) pure N pure N thiol (5.5)

Experimental setup

Because of the size of the particles an the assemblies SAXS measurements had to be done on a synchrotron line, which allows measurements to small enough angles to appreciate the differences between the individual particles and the clusters. Moreover, due to the tame span of the assembly -several days as seen by light absorption measurements -we were not able to follow the evolution of the assembly process.We therefore prepared the samples beforehand and froze then in liquid nitrogen to pause the assembly process. The exact time between the addition of the thiol and the freezing varied as the reaction speed of the different thiols is not the same, the 16C thiol for example was frozen 24 h after the addition of the thiol. The samples where kept immersed in liquid nitrogen until right before the measurements, at which point they were removed, the sample rapidly melted and was injected into the glass capillaries.

Data treatment

Eq.(5.5) highlights the dependence of the scattering on the concentration of the two solutions (N pure and N thiol are the number of particles in the solution of heterodimers before and after the addition of the thiol respectively). In order to obtain the correct structure factor, the incoming beam has to interact with the same number of nanoparticles, a condition which is naturally verified if the two solutions have the same concentration and if the capillaries have the same size, but which is not the case in our measurements.

As the measurements were done in standard glass capillaries which can present important variations in diameter, the interacting volume was not only variable but also unknown.

Furthermore, because of some sedimentation which occurred following the assembly, the concentrations of the two samples are not the same. In order to obtain the structure factor the two signals had to be normalised. This was done by matching the curves at high q values because in the limit of large q values, the structure factor tends to 1 for any assembly.

This in our case was done in a q-range between 3.5 × 10 -1 nm -1 and 4.5 × 10 -1 nm -1 , which approximately results in comparing features between 10 nm and 20 nm, so below the characteristic size of the heterodimer assemblies. Fig. 5.10 shows the SAXS patterns for both the solution containing the heterodimers and the solution of assemblies formed after the addition of the dodecanethiol. For large values of q (>3 × 10 -1 nm -1 ), the two curves superpose, in accordance with the fact that lim q→∞ S(q) = 1. For smaller values of the wave-vector, the two patterns start to diverge. The curve of the pure heterodimers tends to level off, following the general shape of the form factor for spherical particles. The pattern obtained from the solution containing the assemblies on the other hand keeps a more constant slope increasing in intensity with decreasing q throughout the whole range of available q-values. Following the general rule of thumb that the sizes inspected by scattering are related to the q-vector modulus though the relationship d = 2π q , the maximum sizes investigated are of the order of two hundred nanometres. This agrees with the idea of several janus nanoparticles coming together. Fig. 5.11 shows the result of the division of the two signals, the one of the pure heterodimers and the one after their assembly. As detailed previously, the structure factor tends to 1 for larger values of q, with the amplitude of the oscillations decreasing and almost disappearing at around 3.5 × 10 -1 nm -1 . At small values of q, on the other hand, the signal can be seen to grow rapidly, indicating an attractive interaction between the particles. The position of the first maximum can be used to evaluate the distance between first neighbours, in the same way as the position of the first oscillation Figure 5.10: SAXS patterns for the solution of heterodimers both before and after the addition of dodecanethiol. The two curves from the dispersed and assembled heterodimers overlap for high values of q (>3 × 10 -1 nm -1 ) but then differ at smaller values of q. The curve from the dispersed heterodimers levels for small values of q, while the scattering profile of the assemblies continues to grow with decreasing q in the q-range available, indicating an attractive interaction between the particles. of the form factor can be used to estimate the size of nano-spheres. The first maximum is located at around 1.6 × 10 -9 nm -1 , which means that the center to center distance between particles is around 40 nm. This is again in agreement with the available data, which sets the average diameter of the gold nanoparticles to 43 nm.

Fitting the structure factor

Although some information has already been deduced by a first glance at the SAXS curve, a more in depth analysis can be done to obtain further information. As mentioned in chapter 2, Debye's formula can be used to calculate the structure factor of an assembly of particles given the relative distances between the centres of the particles. Provided all the scatterers are identical and spherical in shape, the formula can be simplified and reduces to:

S(q) = 1 + 2 N -1 i=0 N j=i+1 sin(qr ij ) qr ij . (5.6)
In this equation, r ij is the center-to-center distance between the i th and j th particle and is the only relation of the structure factor to the cluster. Because of this, the structure factor not only does not depend on the orientation, but it is also invariant with respect to the absolute positions of the particles within the assembly. As long as the set of relative distances between the particles centres does not change, the structure factor resulting from different clusters will be the same. Distributions of points in space which have the same point-to-point distances are called isospectral point sets. Examples of isospectral arrangements, both in the 2D and 3D cases can be seen in Fig. 5.12A) and Fig. 5.12B) respectively. Isospectral distributions are called like this because their distance spectra are identical, i.e. if the frequency of the distances were to be plotted in a histogram, the two graphs would be indistinguishable. This limitation in the derivation of the configuration from the scattering pattern is a direct result of the fact that obtaining the structure from a SAXS pattern is an ill-posed inverse problem which does not have a unique solution.

Obtaining the exact spatial disposition of the particles in each cluster is then both unrealistic -while anisotropy and specificity are present in the system, each cluster will have a different configuration, and the resulting pattern is an average of all the clusters and all orientations -and impossible because the information necessary for perfect reconstruction is lost in the scattering process. Studying the structure factor can, nonetheless, give important information regarding both the average distance between particles in the cluster and the average number of particles within the clusters. The inter-particle distance has an effect on the position of the maxima and minima of the structure factor while the number of particles within the cluster influences the slope at small values of q.

Iterative fitting algorithm

In order to find a configuration whose structure factor fits the one obtained experimentally, we implemented an iterative algorithm, based on the simplified Debye formula assuming that all the particles are both perfectly spherical and mono-disperse. While this is a simplification of the actual system, it is necessary for an analysis of the structure factor.

Both assumptions can, furthermore, be justified. As explained and proven in the previous chapter, the heterodimers can in fact be considered as simple gold nanoparticles, due to the difference in scattering length density between Au and SiO 2 . Furthermore, according to the SAXS data the polydispersity of the particles is only 12%. While not perfectly monodisperse they can be considered, at first approximation, to be so. The aim of the algorithm is to place the centres of the particles in a 3D space in such a way as to create a configuration whose structure factor fits the experimental one within a set error. Because Debye's formula does not take it into account, the algorithm also needs to check for excluded volume effect: the distance between any two centres has to be greater than 2R where R is the average radius of the particles. The iterative algorithm starts with a single particle and keeps adding particles to the conformation as long as they minimize the difference between the experimental and the simulated structure factors. The algorithm first places a particle

(1) at the origin of the Cartesian system (0,0,0). Starting from this origin particle, a random distance d is chosen such that d > 2R and d < d max where d max is set in order to place an upper limit for the random selection -at the end of the run, the distances are analysed in order to ensure that d max did not impose a bias in the result. Once the distance is selected, two more random variables are created: θ and φ: the azimuthal and elevation angle. In this first step, no interpenetration is possible as the distance d is always greater than 2R, so the second particle's center is placed, in spherical coordinates, in position (d,θ,φ). Once the second particle ( 2) is positioned, the structure factor for the cluster is simulated and the error compared to the experimental data is calculated. The configuration is stored along with its error in an array. The process is repeated until N configurations of two particles are found. The typical value of N used is 1000. The configuration with the lowest error is selected and stored while the others are discarded. At this point, one of the two particles (e.g. 2) is chosen at random and a third particle ( 3) is added to it following the same method explained above, in order to obtain a trimer. This time, an excluded volume check is done to make sure that the added particle (3) does not intersect with the remaining particles (e.g. 1). Again, the configuration is temporarily stored. This time though the error is compared to that of the dimer configuration, and must be smaller in order for the new configuration to be stored. Once N acceptable configurations are found, the one with the lowest error is kept and the process goes on. The algorithm stops either when the error of the structure factor is below a set threshold or if no acceptable configurations have been found after trying M different ones. M is taken larger than N, and is typically equal to 10000. The error is calculated as a percentage, by taking the absolute value of the difference between the experimental and the simulated data, dividing it by the experimental data and taking the average over all the wavevectors. The algorithm returns a configuration compatible with the available structure factor, but it also relies on the assumptions that the minimization of the error is a strictly decreasing function of the number of particles added. That is to say, it supposes that no intermediate configuration with a higher error can eventually lead to a lower error configuration.

Fitting an experimental structure factor

An example of the various steps of the algorithm is given in Fig. 5.13. The structure factor is the one already presented, obtained from the SAXS pattern of the heterodimers assembled using dodecanethiol. The fist step shown is that of a dimer -the structure factor of a single sphere, by definition is S(q) = 1. As more spheres are added to the cluster, the simulated structure factor can be seen to approximate the oscillations better.

Each successive addition also induces a change in the small q limit. While the slope of the structure factor of the dimer does not vary fast enough at small q values, with each subsequent step, the absolute value of the slope increases. The slope of the curve at low q is related to the gyration radius of the cluster. By comparing the slopes at each step, we can deduce that the clusters in solution are made up of no more than 4-5 heterodimers. It is important to note that while adding more particles to the cluster would undoubtedly result in a better fit at larger wavevector values, though marginally, it would also reduce the quality of the fit at smaller q. As discussed earlier, the information obtained from the structure factor is not unique. As a result, even if the structure factor were perfectly fit, we

would not obtain exact information on the cluster conformation. Then, the data obtained through this analysis, has to be interpreted with the understanding that it represents an averaged information over the whole sample. In the case of the example shown in Fig. 5.13, the average center-to-center distance between neighbouring particles is 45.5 nm. This is consistent with an average size of the particle of 43.2 nm and an average surface to surface distance of 2.3 nm

Comparing SAXS analysis to spectroscopic data

As already mentioned, the computational cost of simulating the absorption spectra of coupled plasmonic structures is too high to be effectively used for fitting the data from the the values is provided with the toolbox and is based on the experimental study by Johnson

and Christy [START_REF] Johnson | Optical Constants of the Noble Metals[END_REF]. Once the system is set-up, it is probed using multiple planar waves. This is necessary because the coupling plasmon is sensitive both to the direction of the incoming wave and to its polarization. Two plasmonic nanoparticles placed sufficiently close along the x-axis, interacting with two electromagnetic waves moving in the y direction, one polarized along the z-axis and the other along the x-axis, will exhibit plasmon coupling with the latter but not with the former [START_REF] Gudjonson | Accounting for inhomogeneous broadening in nano-optics by electromagnetic modeling based on Monte Carlo methods[END_REF]. The extinction spectra for the system is calculated for wavelengths ranging from 400 nm to 1000 nm. The final value for each wavelength is the average over all wave directions and polarizations. Fig. 5.14 shows both an experimental spectrum as well as a simulated one obtained from a configuration calculated to fit the structure factor. Because the SAXS curve was acquired from a solution which had rested for 24 h after the addition of the thiol, the absorption curve shown here also corresponds to that of the solution 24 h after the addition of the thiol. While the two spectra do differ, the position of the coupling peak of the simulated spectrum is in very good agreement with that of the experimental spectrum. The most noticeable difference is the shape of the coupling peak, which is sharp in the simulated spectrum while being wide in the experimental data.

As was the case for the structure factor, this discrepancy can be explained by taking into account that the experimental data is a result of an average of multiple assemblies. Since the assembly process does not impose exact distances between particles, the position of the absorption peak of the coupling plasmon is not unique, causing a widening of the peak in the measured spectrum. The width of the coupling peak also explains why the hump, present in the simulated curve around 580 nm and which can be attributed to the coupling of particles which are not first neighbours, is not visible in the experimental spectrum.

Influence of the thiol on the self-assembly

The self-assembly procedure delineated in the previous sections was done by adding a solution of dodecanethiol in toluene to the colloidal solution of heterodimers. As the driving force of the assembly is provided by the alkanethiol, which exchanges with the poly-acrylic acid on the Au surface, a study on the effect of the chain length on the self-assembly was done. Different thiols were chosen with different carbon chain lengths and will be referred to using the number of carbons in the tail followed by a 'C'. Using such notation, the dodecanethiol used up until this point is denoted as 12C. Because of their extensive use in gold surface chemistry, much is already known with regards to thiols, in particular alkanethiols, and gold surfaces like their affinity for gold, their kinetics of adsorption and the hydrophobicity they induce. Longer alkanethiols have, for example, been shown to adsorb at a faster rate than shorter ones on gold surfaces [START_REF] Rowe | Chain Length and Solvent Effects on Competitive Self-Assembly of Ferrocenylhexanethiol and 1-Alkanethiols onto Gold[END_REF][START_REF] Kim | Adsorption kinetics of alkanethiols studied by quartz crystal microbalance[END_REF][START_REF] Jung | Sticking Probabilities in Adsorption of Alkanethiols from Liquid Ethanol Solution onto Gold[END_REF], as well as to bind with higher energy to gold [START_REF] Qu | 1,n-Alkanedithiol (n=2,4,6,8,10) Self-Assembled Monolayers on Au(111): Electrochemical and Theoretical Approach[END_REF]. Furthermore, the hydrophobicity of gold surfaces covered by a thiol mono-layer increases with the chain length, though this effect is more noticeable with shorter chains and tends to wane as the chain has more than 10 carbon atoms [START_REF] Laibinis | Comparison of the structures and wetting properties of self-assembled monolayers of n-alkanethiols on the coinage metal surfaces, copper, silver, and gold[END_REF][START_REF] Bain | Formation of monolayer films by the spontaneous assembly of organic thiols from solution onto gold[END_REF]. Because of the difference in these properties, along with the size of the molecule itself, we can expect a change in the evolution of the system due to the thiol used to induce the assembly.

As with the dodecanethiol the effect of the thiol on the kinetics of the system was studied by taking time-resolved absorption spectra. A similar study is not possible for synchrotron SAXS measurements, as this technique is not adapted to the study of systems over such a long period of time. As seen for 12C, the system keeps evolving for several days after addition of the thiol solution. The samples for SAXS were thus prepared in advance in order to make the measurements once the systems had stabilized. The scattering patterns were then used to compare the average distance between nanoparticles as a function of the carbon tail length.

Absorption spectroscopy

As seen with the dodecanethiol, the formation of clusters of heterodimers causes the appearance of a second absorption peak. The interesting properties of the peak are its position along with its intensity. Due to the total decrease of intensity of the solution, arising from the formation of some larger aggregates, the intensity of the coupling peak is normalized by the intensity of the primary peak. The graphs shown in Fig. 5.15 show the analysis done on the temporal evolution of the coupling plasmon of samples prepared using three different thiols.

For all three samples, the coupling plasmon appears some time after the addition of the thiol, and continues to red-shift up till end of the measurements. The evolution of the coupling plasmon's shift strongly depends on the length of the chain. While the longest thiol is the one with the shortest induction time (the plasmon first appears in less then 10 h), it is also the one which takes the longest to reach a stable position. The curve reaches a stable point more than 60 h after the appearance of the peak. On the other hand, the peak in the sample prepared with the 12C thiol takes longer to appear, roughly 20 h, but then evolves at a faster rate, with the curve stabilizing about 40 h after the peak appearance. Finally, the sample prepared with the shortest thiol (10C) is the one with the longest induction time, with a rather small peak appearing between 20 h and 30 h. Furthermore, the peak does not evolve much for another 10 h, before rapidly shifting to longer wavelengths in a very short period of time.

This last sample also exhibits a more anomalous behaviour with regards to the intensity of the peak. While the first two show a constant increase in the relative intensity, the sample prepared with the 10C thiol exhibits a very rapid increase followed by a steady decline.

This leads us to think that the clusters prepared using the shorter thiol are not as stable as the others.

A comparison can also be made regarding the final position of the coupling plasmon resonance. As the distance between the Au nanoparticles decreases, the splitting between the plasmon levels increases, resulting in a larger red-shift for particles that are closer together. We can see this when comparing the position of the coupling plasmon. For the assemblies prepared with 16C the peak is located at 700 nm, while for the 12C the peak is shifted further, to 740 nm, and finally in the case of the shortest chains (10C), the peak shifts all the way to 870 nm.

A final consideration can be made by comparing the curve of the peak position to that of its intensity. In all cases (though this is harder to see for the 10C), the intensity of the peak varies at a faster rate than the position of the peak, indicating that after their initial formation the clusters continue evolving.

SAXS structure factor

Similarly to the analysis on the absorption spectra, a comparative study of the effect of the thiol length was done on the structure factor. The same starting solution of heterodimers was divided in multiple vials and a different thiol was added to each. This was done in advance in order to allow the system to evolve to a stable state. The SAXS pattern for each sample was recorded, and divided by that of the original heterodimers in order to obtain the structure factor for the different samples. The structure factors were then fitted multiple times using the iterative algorithm described above. The distance between first

Conclusion

The self assembly of nanoscale heterodimers is a complex and interesting subject, which has theoretically been shown to be a very wide and interesting subject [START_REF] Sciortino | Phase Diagram of Janus Particles[END_REF]. Here we show a first attempt at creating structures using Au -SiO 2 janus particles as building blocks. The assembly of the particles was driven by a change in the hydrophilicity of the gold moiety.

We used alkanethiols as our hydrophobic ligands as they have a simple structure (a carbon chain with a thiol group at one end), are hydrophobic, and the thiol group provides a strong binding with the gold surface. The exchange with the existing ligand is done by simply adding a dilute solution of the thiol to the solution containing the heterodimers, and mixing the sample through sonication or vortex mixing. The high affinity for gold surfaces of the thiol results in an exchange of the surface ligand on the gold hemisphere, where the PAA is substituted by the thiol. The gold surfaces are then brought together by hydrophobic interactions, as they try to minimize the thiol surface exposed to the solvent. Complete and rapid aggregation of the sample is prevented by the presence of the silica moiety, which provides steric repulsion, therefore hindering the particles from becoming too large.

The formation of the clusters was characterized by a variation in the absorption spectra of the solution, which can be observed by a change in color of the sample. As with plain gold particles the heterodimer solution is a bright red color, but as the clusters form it becomes a deep violet. This is the result of what is called plasmon coupling: an interaction between the vibrating modes of two or more plasmons in close proximity with each other. On the absorption spectrum this effect is translated as the appearance of a second peak situated at higher wavelengths. The formation of the clusters can therefore be followed through spectrometric measurements. This allows us to record information regarding the evolution of the system in a semi-continuous fashion without interfering with the process.

An analysis of the light absorption measurements was done through singular value decomposition (SVD) to find the basic spectra which can be used to reconstruct the total signal.

From this analysis we were able to find three signals which, when linearly combined, can be used to create the spectrum at any moment during the measurements. The behaviour of the temporal coefficients for the three signals suggested that the process can be divided in three phases based on the species present in solution. An initial phase is characterized by the heterodimers forming dimers, the intermediate phase has some of the janus particles still in form of monomers, the dimers, and more complex structures all in solution at the same time, while during the final stage the monomers have completely disappeared, and the balance between the dimers and multimers is shifting towards of the latter. This division is three stages can also be found by looking at the isosbestic points present in the spectra.

The presence of these points is an indication of the transformation of only one specie into another, and they can be found during the initial and final hours of the measurement, further supporting our interpretation of the SVD analysis.

SAXS was also used to probe the samples, in particular to study the structure of the clusters. Unlike light absorption we were not able to follow the evolution of the system but took a single shot of the system during it's evolution. By comparing the signal from the assembly solution to that of the free heterodimers we obtained the structure factor of the assemblies. Because of the properties of the scattering phenomena described in Ch 2 the structure factor cannot be traced to a unique solution, but it can be used to obtain more general information. In order to do so we implemented an algorithm to create clusters whose structure factor approaches the experimental one using a Monte Carlo like approach. By running the algorithm multiple times we produced a population of assemblies with a compatible structure factor, from these we obtain average values of the total size of the clusters in number of particles and average distance between the heterodimers. By repeating the analysis on several different samples we were able to draw a relationship between the average distance between first neighbours and the length of the thiol chain.

The surface to surface distance scales linearly with the number of carbons in alkanethiol chain, but the slope of the curve -less then twice the C -C bond length -indicates some level of inter-digitation between the ligands. This trend can also be seen in the position of the coupling plasmon peak. When shorter thiols are used the position of the coupling peak is shifted to longer wavelength which can be attributed to a shorter distance between particles.

Through the analysis of both the light absorption spectrum and the structure factor from the SAXS we were able to show that the addition of a hydrophobic thiol to a solution of Au -SiO 2 heterodimers in a water/iso-propanol solution induces the formation of clusters.

The size of the clusters is limited to a few particles, this can be seen by the slope of the structure factor at small q. Furthermore the intra-particle distance is dependent on the carbon tail of the thiol. This is corroborated by both the position of the coupling plasmon peak and the analysis of the structure factor.

Chapter 6

CdSe Platelet Synthesis Kinetics

Introduction

Passing from bulk to the nanometric world often leads to the appearance of surprising properties, such as plasmons in metallic nanoparticles. These new properties arise when the size of the particles becomes comparable to the characteristic length of particular physical phenomena. In the case of semi-conducting particles, this happens as the size of the particle approaches Bohr's exciton radius. The exciton is then in a confined state and the system can be approximated to a particle in a well. Due to Heisenberg's uncertainty principle, when a particle is confined in space the uncertainty on its momentum increases as the size of the spatial confinement decreases. The principle can be expressed in the form of an inequality as:

∆p∆x ≥ 2 (6.1)
where ∆p and ∆x are the uncertainties in the momentum and spacial position respectively.

We can then assign a confinement energy (E c ) based on the size of the confinement:

E c = ∆p 2 2m ≈ 2 2m * ∆x 2 (6.2)
where m * is the effective mass of the confined particle. However, the confinement energy will only be appreciable when comparable to the thermal energy of the system (≈ 1 2 k B T ). This results in a maximum size, above which this effect is not visible, given by: For free electrons, this confinement space is below 2 nm, but as the effective mass of the electrons in semi-conductors is typically 0.1m 0 (where m 0 is the mass of a free electron), the effects of quantum confinement become visible for particles of the order of 5 nm. Because of the confinement in all three dimensions, these objects are often treated as 0-dimensional objects, and are referred to as quantum dots. Other objects, with different dimensionality can also be produced. Thin wires for example, have two confined dimensions, while thin platelets, also known as quantum wells, are confined in only one dimension. In all three systems, the confinement of the electrons in one or more directions results in a complete change in the density of states function. In bulk, the density of states is a continuous

∆x ≤ 2 m * k B T . ( 6
function proportional to (E -E g ) 1 2
, where E g is the gap energy. In quantum dots, where all three dimensions are confined, the particle behaves in much the same way as an atom, resulting in all energy levels being discrete, with no bands available. The density of states is then a series of Dirac δ-functions. If only one of the dimensions is reduced below the confinement limit though, the density of states still exhibits bands, but becomes independent of the energy. As a result, the density of states vs. energy curve is a step function. The energy of the n th level can be found by solving Schrödinger's equation for an infinite potential well:

E n = 2 2m * nπ d 2 (6.4)
where d is the thickness of the platelet. A qualitative representation of the density of states for all four systems (bulk, quantum well, wire and dot) is shown in Fig. 6.1. One of the consequences of the quantization of the energy levels is the appearance of particularly fine peaks in the absorption and emission peaks of the particles. As with bulk semi-conductors, incoming photons can interact with electrons forming electron/hole pairs (excitons), provided their energy is larger than the band gap. Low energy photons will not be able to create any excitons, resulting in an absorption close to zero at long wavelength. As the energy of the photons increases, they are absorbed with increasing probability, in particular when the energy is close to that of the band gaps. This results in peaks superposed to a constantly increasing absorption. As the electron/hole pairs recombine, they may do so through a radiative process, re-emitting a photon with an energy close to that of the band-gap. This process can be detected by measuring the emission spectra of a colloidal solution of dots. The width of the emission peak is determined by the polydispersity of the particle -the band-gap depends on the size of the confinement -and the thermal energy of the system, as it provides additional energy levels besides the ground state.

Since the band-gap energy is closely related to the size of the particle, it is possible to fine tune the the emission peak by adjusting the size of the particles. Thus, even though the band-gap of CdSe in bulk is 1.74 eV, or 712 nm, colloidal CdSe quantum dots can be made to emit a wide range of wavelengths which span the visible spectrum. This results in quite spectacular photographs such as the one shown in Fig. 6.2A), where vials illuminated by UV light show the fluorescence of quantum dots varying between 2 nm to 5 nm. The graph to the right (B) shows examples of the emission spectra of nanoparticles in the same range. Because of their precise emission, along with the high efficiency which has been achieved, quantum dots are becoming the main focus both for light-emitting devices -where they allow for high contrast, faithful color reproduction and low consumption - [START_REF] Kim | White Electroluminescent Lighting Device Based on a Single Quantum Dot Emitter[END_REF][START_REF] Mashford | High-efficiency quantum-dot light-emitting devices with enhanced charge injection[END_REF][START_REF] Zhao | Efficient CdSe/CdS Quantum Dot Light-Emitting Diodes Using a Thermally Polymerized Hole Transport Layer[END_REF] and solar-cells, which greatly benefit from the high efficiency of these particles [START_REF] Semonin | Peak External Photocurrent Quantum Efficiency Exceeding 100% via MEG in a Quantum Dot Solar Cell[END_REF][START_REF] Lan | 10.6{%} Certified Colloidal Quantum Dot Solar Cells via Solvent-Polarity-Engineered Halide Passivation[END_REF][START_REF] Chia-Hao | Improved performance and stability in quantum dot solar cells through band alignment engineering[END_REF].

6.2 Semi-conducting nanoplatelets

Description of the system

While the synthesis of monodisperse colloidal dots has been studied for more than twenty years now [START_REF] Murray | Synthesis and characterization of nearly monodisperse CdE (E = sulfur, selenium, tellurium) semiconductor nanocrystallites[END_REF], it is only recently that a chemical procedure for the preparation of 2D nano-platelets has been published by Dubertret and Ithurria [START_REF] Ithurria | Quasi 2D Colloidal CdSe Platelets with Thicknesses Controlled at the Atomic Level[END_REF]. The synthesis produces CdSe platelets with a zinc-blende structure and a thickness tunable between 0.6 nm and 1.5 nm. The platelets are often differentiated by their number of monolayers, where one monolayer is composed of a cadmium and a selenium layer. All the platelets are atomically flat, therefore the thickness is the same anywhere along the particles. As both the top and bottom exposed faces of the platelets are cadmium, the platelet can have between 2.5 and 5.5 monolayers, and any half number in-between. For commodity, they are referred to by the whole number of layers of which they are composed, a 3.5 monolayer platelet will then be called "3ML". Fig6.3 shows the atomic structure of the CdSe platelets from different point of views. Because the thickness of the platelet is the only quantum confinement, the number of monolayers also determines the position of the emission peak. Thus, the main emission peak shifts from 394 nm to 463 nm, 512 nm and finally 552 nm, as the platelet thickness is increased by one monolayer (Fig. 6.4). By properly following the synthetic procedure and washing the platelets, it is possible to precisely select their thickness and obtain a single population. Because of the quantum confinement origin of the optical properties, both the emission and the absorption signals of the solution have extraordinarily sharp features. While the emission spectrum has a single peak, the absorption spectrum has two peaks: a principal one, corresponding to the heavy-hole transition, and a less intense peak at shorter wavelengths, originating from the light-hole transition. The "light" and "heavy" denominations derive from the effective mass m * which varies based on the band on which the holes are situated.

Applications of CdSe platelets

The peculiar properties of these systems make CdSe platelets interesting particles for a wide range of opto/electronic applications. The sharpness of the peaks in the absorption spectrum can be used for photodetection, allowing for precise control of the cut-off wavelength, as well as a strong response to illumination [START_REF] Lhuillier | Electrolyte-Gated Colloidal Nanoplatelets-Based Phototransistor and Its Use for Bicolor Detection[END_REF][START_REF] Lhuillier | Investigating the n-and p-Type Electrolytic Charging of Colloidal Nanoplatelets[END_REF]. If the geometry of the platelets is taken into consideration when designing the photodetectors, it is possible to create devices with an improvement by a factor 10 7 compared to standard devices [START_REF] Lhuillier | Nanoplatelets Bridging a Nanotrench: A New Architecture for Photodetectors with Increased Sensitivity[END_REF].

Recent studies have also shown that CdSe platelets, and to a greater degree core/shell CdSe/CdS platelets, could be good candidates for the fabrication of lasers. Due to a combination of suppressed Auger recombination, giant oscillation strength and increased absorption cross section, they exhibit very low lasing thresholds [START_REF] Kelestemur | Platelet-in-Box Colloidal Quantum Wells: CdSe/CdS@CdS Core/Crown@Shell Heteronanoplatelets[END_REF], at times lower than carefully engineered colloids, such as Cd x Zn 1 -x S/ZnS core/shell quantum dots [START_REF] Kelestemur | Platelet-in-Box Colloidal Quantum Wells: CdSe/CdS@CdS Core/Crown@Shell Heteronanoplatelets[END_REF]. The possibility of forming large organised structures with the platelets [START_REF] Jana | CdSe Nanoplatelets: Living Polymers[END_REF] further widens the range of application possibility. By forming long threads of platelets, it would be possible to study the Förster resonance energy transfer (FRET) both for homogeneous structures as well as for threads made up of platelets with different thicknesses. This could lead, for example, to more efficient solar cells.

Synthetic approach and mechanism

The synthesis is done in a high boiling point organic solvent, such as octadecene, between 130 • C and 240 • C, depending on the desired thickness of the platelets. The two starting precursors are a cadmium salt and elemental selenium. The precursors are heated to start the nucleation of CdSe dots, at which point an acetate salt, usually cadmium acetate, is added to the solution. Though the exact process by which the selective growth of only two planes happens is still debated, the presence of the acetate seems fundamental for the formation of platelets.

One of the most interesting aspects of this system is the combination of a zinc-blende structure and a two dimensional growth of the particles. When studying particles whose crystalline system displays anisotropies, the formation of structures such as rods can be usually explained as a preferential binding of the ligands to a particular lattice place [START_REF] Manna | Synthesis of Solube Rod-, Arrow-, Teardrop-, and Tetrapod-Shaped CdSeNanocrystals[END_REF], or a kinetically favoured growth direction [START_REF] Alivisatos | No Title[END_REF]. A different mechanism was proposed for the formation of CdSe platelets with wurtzite structure based on the soft templating of by lamellar mesophases and the formatino of "magic-sized" clusters whihc arrange themselves

ONE-POT SYNTHESIS OF CDSE PLATELETS

123

within the template to form rectangular arrays [START_REF] Liu | Lamellar Assembly of Cadmium Selenide Nanoclusters into Quantum Belts[END_REF][START_REF] Wang | The Magic-Size Nanocluster (CdSe) 34 as a Low-Temperature Nucleant for Cadmium Selenide Nanocrystals; Room-Temperature Growth of Crystalline Quantum Platelets[END_REF]. Such a mechanis was, however, confuted for zinc-blende CdSe nanoplatelets, in a recent paper [START_REF] Riedinger | How semiconductor nanoplatelets form[END_REF]. The authors instead, propose a mechanism by which the acetate induces a phase separation of the precursors from the solution. In such droplets the high concentration of monomers results in island nucleation-governed growth. The anisotropic growth is then explained by showing that the energy barrier for the formation of a new layer is larger compared to that of increasing the lateral size of the platelet.

One-pot synthesis of CdSe platelets

Heat-up vs. hot injection syntheses

In many of the syntheses available for the preparation of nanoparticles, such as the one presented before for the preparation of platelets, as well as for the syntheses of quantum dots and rods, the formation of the colloids is induced by the mixing of two or more solutions, usually at high temperatures. These reactions are called hot injection reactions. While they have been used for the synthesis of quantum dots for more than 20 years and can be tuned to adjust the final shape and size of the colloids, they still present drawbacks. The quality of the final product often relies on a fast mixing of the two precursor solutions. This is necessary for the nucleation to be homogeneous within the solution, which is required for monodisperse particles. Furthermore, many reactions also require fast cooling of the solution after the injection of the precursors. This is in order to limit the synthesis to the nucleation step, without subsequently moving on to a ripening phase, which can reduce the monodispersity. Both of these requirements do not scale up well, making it hard to increase the output of a reaction significantly. The need of injecting one of the two precursors also adds an additional parameter, which can be difficult to reproduce, not only between users, but also between batches. Because of these difficulties, and thanks to the advancements made in both chemistry and the understanding of the formation of nanoparticles, a different approach to the synthesis has also been made available. In these reactions, the reactants are all placed in a flask which is then heated. As the temperature rises, the precursors decompose into monomers and, once the solution reaches the right temperature, the nucleation of the particles begins. In contrast to the first, these new reactions are referred to as heat-up synthesis. The heat-up synthesis approach removes much of the complexity from the execution of the reaction, with no need to inject or mix the precursors rapidly, but transfers that complexity to the planning of the reaction. The precursors have to be chosen in such a way as to insure that the nucleation is sufficiently rapid to produce a large quantity of nuclei in a short amount of time. Furthermore, the nucleation and the growth/ripening steps should be well separated to allow for a monodisperse population. All difficulties notwithstanding, many heat-up synthesis have been published, and this approach is gaining importance in the preparation of colloids of different shapes, size and composition [START_REF] Narayan Pradhan | Synthesis of High-Quality Metal Sulfide Nanoparticles from Alkyl Xanthate Single Precursors in Alkylamine Solvents[END_REF][START_REF] Brennan | The preparation of large semiconductor clusters via the pyrolysis of a molecular precursor[END_REF][START_REF] Zhang | Noninjection Facile Synthesis of Gram-Scale Highly Luminescent CdSe Multipod Nanocrystals[END_REF][START_REF] Van Embden | The Heat-Up Synthesis of Colloidal Nanocrystals[END_REF]. The reaction presented and analysed in this chapter is a heat-up synthesis, for the preparation of 3ML CdSe platelets.

Experimental procedure

The two precursors used are trioctylphosphine selenide (TOP -Se) and a cadmium acetate/oleate mixture (Cd -Ac/Ol). Because of the sensitivity to water and oxygen of the various precursors, the reactions are all conducted in an inert atmosphere. For the selenium precursor, equal molar amounts of Se and TOP are added to a vial and stirred overnight. As the two react to form TOP -Se, the initially black solution turns transparent.

The pure compound is then diluted in octadecene (ODE) by adding 42.7 mg of TOP -Se to 10 mL of ODE, the sealed solution is then stored. The Cd -Ac/Ol is prepared by placing the Cd -Ac (500 mg) and oleic acid (600 µL) in a three-neck flask with 10 mL of ODE. The reagents are then heated to 120 • C for 20 min under vigorous stirring and then brought to 150 • C for another 30 min; the solution is finally sealed and stored for future use. The synthesis of the platelets is done using equal volumes of the two precursors (the Cd -Ac/Ol in ODE and the diluted TOP -Se). The Cd precursor is first placed in a three-neck flask and the atmosphere is purged before injecting the diluted TOP -Se. The solution is then rapidly heated (1 • C s -1 ) to 200 • C. As it approaches a temperature of 160 • C, the solution turns yellow. Once the final temperature is reached, it is maintained for 8 min, during which the yellow color of the solution becomes more intense. After this time, the solution is rapidly cooled down to room temperature. The product is finally washed by adding ethanol and centrifuging. The transparent supernatant is removed and the deposit re-dispersed in hexane. The platelets are not colloidally stable in solution and tend to sediment at the bottom of the vial over a few hours. The absorption spectrum of the CdSe platelets synthesized using the one-pot, heat-ip reaction. The strongest peak at 462 nm indicates that the platelets are 3ML thick, the slightly smaller peak, at shorter wavelength is the light-hole transition. Two small humps can also be seen below 400 nm; those are the signals from some 2ML platelets which have formed during the synthesis.

Characterization techniques for the platelets

Absorption spectrum

The first measurement done on the synthesised platelets is a measure of the absorption spectra which, as described previously, presents sharp peaks whose positions depend on the number of monolayers of the platelets (Fig. 6.5). The spectrum shows two peaks, the main one at 462 nm and the second one around 435 nm, which is consistent with 3ML platelets.

Two smaller peaks are also visible at shorter wavelengths (below 400 nm), indicating the presence of a small population of 2ML platelets in solution.

TEM

The platelets were also imaged using TEM by drop-casting a dilute solution on carbon grids. As can be seen from the images shown in Fig. 6.6, the flat platelets are difficult to distinguish from the background due to the thickness of the samples. The darker areas are places in which multiple layers of the platelets are superposed. This can happen either where the platelets are one on top of another or because of bending in the platelet, which makes it fold over itself. In particular, the three images show three different deformations which are commonly seen with platelets. The particles can be rolled along a cylinder either parallel to the main axis (A), or rotate along a diagonal (B). In this case, the sides of the cylinder are darker as the "thickness" of the platelet with respect to the incoming electron beam is bigger. This rolling of the platelets was studied in an article by Bouet et al. in 2013 [START_REF] Bouet | Two-Dimensional Growth of CdSe Nanocrystals, from Nanoplatelets to Nanosheets[END_REF]. They attribute the bending of the platelets to a combination of the flexibility of the thinner particles (when an extra layer is grown, the particle flattens) and the asymmetric constraints induced by the carboxylic ligand. The platelets can also be twisted, forming a bow-like shape(C), in which case, the center of the particle will appear darker. For the platelets rolled up along the main axis it is possible to measure the diameter of the cylinder.

We found that the radii of the cylinders were between 12 nm and 14 nm. However due to the low contrast of the platelets it is hard to measure their size accurately, as they tend to blend with the background.

In-situ analysis of the platelet growth

Experimental SAXS method

In order to study the formation kinetics of the platelets, time-resolved SAXS and WAXS measurements were performed in-situ during the reaction. Such measurements had to be made at a synchrotron beam line in order to have a high enough intensity of the incoming beam to reduce the exposure time to a minimum. This allows to measure the "instantaneous" scattering pattern of the solution, rather than an average over multiple states. The acquisition frequency used at a synchrotron line can be varied depending on the speed and duration of the experiment. It is, nonetheless, limited by the scattering power of the sample as well as by the speed of the electronics in saving the recorded images to memory. The recording was divided in three phases, during the initial phase the patterns were taken at a fast rate, in order to accurately record the fast changes which occur during the nucleation. The second and third phase are characterized by the slower growth and ripening processes, therefore the rate at which the patterns were recorded was reduced, allowing us to follow the reaction for a prolonged period of time, without filling the cache memory of the detector. The first 70 frames were recorded at a rate of one every 2 s, the following 70 were taken 3 s apart, and the final 60 5 s apart. The result of such measurements is a sequence of SAXS and WAXS patterns following the evolution of the system over time. As the reaction does not require any intervention besides heating up, the measurements were done using a capillary, placed in a Linkhan heating stage, which allows to heat the capillary to the desired temperature. The two precursors are mixed and placed in a glass capillary which is then sealed and inserted in the holder. The temperature of the holder can then be set from the control room, so that the measurements and the heating can be initiated at the same time. A photo of the setup is shown in Fig. 6.8.

Background subtraction

In the first chapter we discussed how the background is normally removed from SAXS measurements by taking the signal of a blank, usually a capillary with the solvent, and subtracting it to the signal of the sample. When necessary, e.g. when quartz capillaries are used, the background has to be corrected to take into account the different thickness of the capillaries. In our experiments the background can be obtained from measurements before the nucleation of the particle, as they are the measurements of the scattering by the capillary and the solvent. However we do have to take into account the effect of the raise in temperature on the scattering curves. As explained, the measurements are initiated along with the heating of the sample, which is initially at 30 • C. As the sample heats up we notice that the raw data immediately shows a variation of the signal. This is due to the the dependence of the scattering power of both the capillary and solvent on the temperature.

Because of this, the background cannot be simply subtracted by taking the any of the signals before the nucleation and removing it from all subsequent curves. Rather, in order to correctly subtract the background it is necessary to find a sequence of curves, before the nucleation, which are constant, indicating a stable condition of the system. To do this we compare the initial curves in order to find a time period over which we have several overlapping curves, we average the signals and store the average as background. It is then subtracted to each subsequent signal in order to obtain the normalized curves. Because of this the plots shown here do not start at t = 0, but at a later time, dictated by when we An example of the signal is shown in Fig. 6.10. By looking at the SAXS data we notice that the signal initially decreases in intensity, it then settles before increasing and starting to exhibit oscillations. The curves between 20 s and 160 s can be taken as backgrounds as they do not vary greatly. If, on the other hand, we look at the WAXS signal we see that it varies greatly in intensity for a greater period of time. Because of this, for the qualitative analysis the background of the WAXS was fitted using a cubic polynomial.

Qualitative analysis

An example of the SAXS and WAXS data obtained during the experiments can be seen in Fig. 6.9. The WAXS patterns show the growth of a peak between 28 nm -1 and 29 nm -1 , indicating the formation of a crystalline structure. The peak is clearly asymmetrical in some instances, closely resembling the superposition of several peaks. This is somewhat is disagreement with the theoretical shape of the peak shown in Fig. 6.11 (the peak was simulated based on Debye's formula, the details will be explained later in the chapter). The signal at small angles is also not in good accordance with that of a solution of platelets.

When plotted in log-log scale, the scattering pattern of flat platelets usually displays a flat signal at very small q, followed by a constant slope of q -2 , up to a wave-vector approximately equal to 2π / t , where t is the thickness of the platelets, at which point the signal decreases Figure 6.11: Theoretical X-ray scattering pattern for a 3ML CdSe platelet. The q values range from 10 -2 nm -1 to 15 nm -1 , covering from ultra-small-angle scattering to part of wide-angle scattering. The initial portion of the curve is flat, followed by a q -2 slope, and finally by a q -4 slope. The oscillation seen between 6 nm -1 and 10 nm -1 is due to the thickness of the particle. The [START_REF] Cretier | The Crystal Structure of the Beta Form of Gold Selenide[END_REF] WAXS peak for the CdSe crystal structures is shown on the right-hand side. Both the SAXS and WAXS signals were simulated using Debye's formula as detailed later in the chapter.

as q -4 . A simulated small-angle scattering curve for a CdSe platelet can be seen in Fig. 6.11 (the curve was simulated using the same software package as for the the WAXS peak).The experimental pattern obtained from the solution on the other hand displays a different behaviour. A) shows very clear oscillations starting from 2 × 10 -1 nm -1 , which increase in intensity as the reaction proceeds. Furthermore, the plateau at small q disappears later in the measurements. The discrepancy in both the SAXS and WAXS patterns can be explained in light of the TEM images shown in Fig. 6.6. The bending of the platelets, on the one hand, induces a stretching/compression of the crystal lattice, which may explain the distortion of the peaks at wide angles, and, on the other, introduces a curved structure in the system, to which the oscillations in the SAXS pattern can be attributed. A more detailed study of the small-angle scattering signal can be done by fitting the pattern to a theoretical model and by studying the Guinier regime and the Porod invariant. Similarly, for the wide-angle part of the data, the theoretical peak of curved structures can be simulated and the peak fitted in order to deduce information from its position, intensity and width.

6.5 Different approaches for the analysis of the scattering data

Simulating the scattering pattern

As seen from the comparison between the experimental and simulated scattering patterns, a flat platelet model cannot be used to study the data obtained. We can nonetheless develop a new model based on the observations made on the electron microscopy images. In particular, we noticed the presence of platelets bent in a cylindrical shape. Though this was not the only type of deformation seen, it will be the one we will focus on first.

Introducing particle bending in the SAXS model

The analytical expression for the signal obtained from curved platelets was taken from an article by Constantin [START_REF] Constantin | Solution scattering from colloidal curved plates: barrel tiles, scrolls and spherical patches[END_REF], in which he derives the form factor for a variety of bent platelets. The formalism for his derivation is based on the approach proposed by Stuhrmann and Svergun in 1991 [START_REF] Svergun | New developments in direct shape determination from small-angle scattering. 1. Theory and model calculations[END_REF]. The orientally-averaged form factor is calculated starting from the density distribution of the particle. Provided that no interaction exists between the scatterers, the scattering intensity can then be obtained from the form factor:

I(q) ∝ |F (q)| 2 . ( 6.5)
By using spherical/cylindrical coordinates and spherical harmonics, it is possible to simplify the integration and obtain the solution as a sum of functions. The system presented here will be a platelet of size L × W × t, where L is the length, W is the width and t is the thickness of the platelet, bent around a circle of radius R, as shown in Fig. 6.12.

For simplicity, during the mathematical derivation, the thickness of the particle will be considered negligible compared to the other dimensions, but is added in the simulations by multiplying by a correction factor [START_REF] Constantin | Solution scattering from colloidal curved plates: barrel tiles, scrolls and spherical patches[END_REF]. Because of the shape of the particles, the obvious choice for the coordinate system are cylindrical coordinates, with the height of the platelet aligned along the z-axis. The density distribution of the particle can be separated in two different contributions: one, which we will call G(r, φ), the contribution in plane and the other, H(z), along the main axis. The averaged form factor is then defined as:

|F (q)| 2 = 1 2 π 0 sin(θ) G(q r , η) 2 η H(q z ) 2 dθ. (6.6)
Where G(q r , η) and H(q z ) are the Fourier transforms of G(r, φ) and H(z) respectively, θ is the polar angle, q r = q sin θ and q z = q cos θ. H can easily be found by using a square function as a density distribution.

H(q z ) = ∞ -∞ e -iqzz H(z) H(z) = 1 if -L 2 ≤ z ≤ L 2 H(z) = 0 if z < -L 2 or z > L 2 . (6.7)
The derivation of the contribution from the x-y plane follows the same approach only using polar coordinates and Bessel functions to obtain G as an infinite sum:

G(q r , η) 2 = c 2 J 2 0(qrR) + 2 ∞ k=1 a k J 2 k(qrR) . (6.8)
Here R is the curvature radius, J k is the spherical Bessel function of order k and the coefficients a k = sin (kφ 0 /2) kφ 0 /2 2 , where φ 0 = W/R is the opening angle -the angle of the arc defined by the platelet. By doing the numerical calculation, it is possible to see that the contributions of the terms in the summation rapidly become negligible. No appreciable difference can be found by extending the calculations beyond the 15 th term. By using both of these definitions, the orientationally-averaged form factor simplifies from a triple integral (over η, z, and θ) to a single integral over θ. This last integration can be done numerically on a computer. Though, because of the long time required by the operation (the integral has to be calculated for every value of q for the specific parameters of the particle: L, W , R), the application of this function to a fitting algorithm is impractical. To address the problem, SAXS patterns for different combinations of platelet size and curvature were calculated beforehand and stored in an array. The calculations were done in C language, as it proves to be faster compared to higher level coding languages such as Python, and were run on the cluster of the LPS in order to reduce the computation time further. Using the pre-calculated patterns, we were able to rapidly obtain the theoretical signal produced from a polydisperse sample of platelets. Fig. 6.13 shows how each of the three parameters for the bent platelets influence the final scattering curve. A) shows five different platelets with the same length (60 nm) and curvature radius (15 nm) but with varying widths. As with previous SAXS patterns, each curve is shifted along the y axis for clarity. The smallest platelet (with a width of 20 nm)

shows almost no oscillations, using such parameters the platelet covers only slightly more than a fifth of the circumference, which is not enough to result in clear oscillations, as was noted by Constantin in his paper [START_REF] Slyusarenko | Morphology of gold nanoparticles determined by full-curve fitting of the light absorption spectrum. Comparison with X-ray scattering and electron microscopy data[END_REF]. As the width of the particle increases though, the oscillations become more important and the first minimum slowly shifts to lower q values. Fig. 6.13B) shows the effect of the length of the platelet on the signal. Unlike the previous example, here the position of the oscillations does not vary, and also the amplitude is only slightly affected (the length varies from 20 nm to 60 nm just like the width shown previously). We can notice however, that the way in which the curve reaches a plateau varies with the length. A deeper look at that will be presented in the following pages.

Finally, C) shows the influence of the curvature radius on the scattering. The curvature radius increases from 10 nm, where the oscillations are clearly visible and with a great amplitude, to 30 nm, where they are barely visible. We can also clearly see how, as the curvature radius increases in size, the first minima is shifted to smaller q values.

Particle bending in the WAXS model

Similarly to the SAXS patterns, the scattering peaks for the wide-angle scattering have to take into account the curvature of the platelet. The shape of the peak was simulated using Debye's formula, which was presented in Chapter 2. For this purpose, two different software were used. The positions of the atoms were defined using the commercial software CrystalMaker [189], which allows to define a crystalline structure and repeat it in three dimensions in order to create particles. The software can also be used to distort the structure, such as bending it to a cylinder with a given radius. The crystal structure of the CdSe platelets is zinc-blende with a lattice parameter of 6.08 Å. The position of all atoms can then be exported as a text document and the x-ray scattering pattern can be calculated using the free software Debyer [190]. Debyer creates a histogram of all the pair-distances and uses the aforementioned equation to produce the scattering pattern. Using the two programs, it is possible to create the scattering patterns of curved platelets with various curvature radii and compare them to the experimental ones. We focused on the study of the 220 peak, as it is the most prominent in the measured q range. The position of the scattering planes corresponding to the (220) plane is shown on the crystal in Fig. 6.14A) and B). The position of the WAXS peak is not influenced by the size of the platelets, but only by the distortions of the atomic lattice, therefore the size of the platelet used for the simulations does not interfere with the positioning of the peak. In the case of single crystal particles it does, however, influence the width of the peak, with larger particles having a narrower peak. In our case however, the effect of bending the crystal introduces such an important distortion of the peak that the effect of the crystal size is negligible. Fig. 6.14C)

shows how the 220 peak of the CdSe platelets varies with the radius of curvature. The flat platelet peak (R=∞) shows a sharp peak at 29.2 nm -1 with a slight asymmetry. As the platelet is bent around cylinders with smaller radii, the position of the peak can be seen to shift towards lower q values. At a curvature radius of 50 nm, the peak is located at 29.1 nm -1 , it has also widened and becomes less intense. As the curvature radius is reduced further, the peak widens and keeps shifting. Furthermore, oscillations start to appear due to the new inter-atomic distances which appear upon bending. The amplitude of the oscillations is initially small but it increases as the radius decreases, which eventually hides the main peak.

Guinier regime and Porod invariant

Though it is a practical and straightforward way to study a scattering pattern, fitting the curve to a form factor is not the only way to obtain information from SAXS data.

A different approach is to study the asymptotic behaviour of the scattering pattern, in particular the Guinier regime and Porod invariant. Both of these concepts were already introduced in 2.2.6, in the chapter dedicated to the SAXS technique, but will be briefly re-introduced now. The Guinier regime is the region of the scattering pattern, at small q, where the logarithm of the intensity linearly depends on the square of the wave vector modulus. In particular the two are related by the following equation:

I(q) ≈ ΦV P art e -(qR G ) 2 3 . (6.9)
where R G is the gyration radius, V P art is the particle volume and Φ is the volume fraction.

It is important to note that the Guinier approximation is derived by supposing a dilute . The dotted lines in A) show how the signal was extrapolated to bigger, and smaller, q values, initially as q -2 , resulting in a constant value, and then as q -4 . The shaded area shows the integral of Iq 2 (q). B) has ln(I) vs (q 2 ), with the linear approximation plotted in red. The dotted line shows the continuation of the linear fit beyond the Guiner regime.

suspension of monodisperse particles. It cannot be used for systems which present aggregates or structure factors. Furthermore, the approximation is only valid around the central beam, which is defined as those q values where q < 1 R G . It is thus possible to obtain the gyration radius and the volume fraction of the sample by plotting ln I(q) as a function of q 2 , and doing a linear fit on the initial points. A visualisation of the Guinier approximation is shown in Fig6.15B). The data is plotted as ln I(q 2 ), and the linear fit is superposed. The solid line shows the calculated fit up to the limit of the Guinier regime, and is then extended to larger q values as a dotted line. The gyration radius can be related to the actual size of the platelet by the following equation [START_REF] Hammouda | RADIUS OF GYRATION CALCULATIONS[END_REF]:

R g = 1 3 L 2 2 + H 2 2 + t 2 2 (6.10)
We can simplify this relationship by ignoring the contribution of the thickness, which is negligible compared to the other two dimensions, and we can further reduce the number of variables by imposing that the platelets are square. While not necessarily true, this will

give us an idea of the evolution in size of the particles. The equation then simplifies to: .11) An analogous reasoning can be done using the gyration radius of a cylinder instead of a platelet, producing a similar relationship if the platelet is rolled to a complete circle, in this The Porod invariant, on the other hand, is a value which is obtained by integrating the signal times the wavevector squared. It is directly related to the volume fraction of the colloids in solution (2.26). The equation holds only for bi-phasic systems, furthermore, as with Guinier's approximation, the system has to be dilute and no aggregates have to be present in solution. Finally, since Porod's invariant requires to calculate the integral of I(q)q 2 over the interval [0, ∞), there are two more considerations to make. Firstly, in order for the integral to converge, the intensity at large q eventually has to decrease as q -3 or faster. Secondly, as the signal measured is limited to a finite range of q values, the curve has to be extended. To do this, we impose that the curve follows I(q) ∝ q -2 up to q = 2π t (where t is the thickness of the platelet), after which it is extended as I(q) ∝ q -4 . At shorter q values the scattered intensity is supposed constant. This agrees with the theoretical behaviour of scattering by platelets -as shown in Fig. 6.11 -and satisfies the need for the signal to decrease rapidly at large q. A graphic representation of Porod's invariant is shown in Fig. 6.15A). The solid black line is the data plotted as Iq 2 (q), while the dashed lines show how the signal was extrapolated to longer and shorter q values. The shaded area shows the integral of the function, which is the Porod invariant, and from which the volume fraction can be calculated. From the results of the Guinier regime analysis and the Porod invariant, an approximation of the number of particles in solution can then be derived. By dividing the volume fraction (φ = n×t×L 2

R 2 g = L 2 6 . ( 6

V

) by the volume of a single platelet we obtain the number of particles per unit of volume.

Position and size of the WAXS peak

As with the shape of the curve at small angles, the shape of the peaks at wide angles can reveal a lot with regards to the colloidal particles in solution. Using Scherrer's formula, the full-width at half-maximum can be linked to the size of the crystallites within the particles [START_REF] Scherrer | No Title[END_REF][START_REF] Patterson | The Scherrer Formula for X-Ray Particle Size Determination[END_REF] using the following equation

L = 2πK ∆q . (6.12)
In this formula, L is the linear size of the crystal, K is a numerical constant which is commonly set to 0.9, and ∆q is the breadth of the peak -the FWHM. The linear size value provides the lower bound for the size of the crystals in the particles, and is valid for grains smaller than 100 nm. Finally, the area of the peak is tied to the amount of crystalline material that is scattering. Then, the evolution of the amount of CdSe in solution can be followed by measuring the area of the peak throughout the experiment.

Due to the distortions which affect the particles, Scherrer's formula may become inaccurate as the rolling of the platelets broadens the peak. On the other hand, the area of the peaks will still provide information regarding the volume of crystalline CdSe in solution and its shift compared to the theoretical position provides insight about the stress within the particle.

To determine the three parameters (position, width and intensity), the experimental peaks had to be fitted to a distribution. This was done by fitting the data using a cubic polynomial plus a pseudo-Voigt distribution. The polynomyal was used to fit the background and was subtracted from the experimental data. The pseudo-Voigt function is the result of the linear combination of a Gaussian and a Lorentzian distribution. In particular, the center of both distributions, as well as the full width half maximum and the amplitude of both, is shared between the two functions, leaving the relative weight as the only differentiating parameter [START_REF] Newville | LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python[END_REF]. This profile was chosen in place of a simple Lorentzian or Gaussian becasue it has been shown to more accurately describe the shape of Bragg peaks [START_REF] Young | Profile shape functions in Rietveld refinements[END_REF] 6

.6 SAXS results

We initially studied a synthesis conducted at 200 • C, as a reference. The measurements were repeated several times using precursors prepared in slightly different fashions. The presence of clear features, such as the oscillations in the SAXS pattern, help the fitting of the curve.

SAXS fitting

As described in the previous section, the fitting of the small-angle signal was done by using a set of pre-calculated curves and by finding the distribution which resulted in the best possible fit of the data. While the scattering intensities were calculated in C, the fitting procedure was done in python using the LMFIT package [START_REF] Newville | LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python[END_REF], also used to fit the spherical colloids (Chapter 2). Seven different parameters were used, the average length and height of the platelet, the average radius of curvature, along with the standard deviation for the three, and a multiplicative factor to fit the intensity. The results of the fit at four different times are shown in Fig. 6. [START_REF] Nie | Janus and Ternary Particles Generated by Microfluidic Synthesis: Design, Synthesis, and Self-Assembly[END_REF]. By comparing the theoretical curve with the experimental one in all four graphs, we can see that the oscillations are well fitted at all times. This indicates that both the curvature radius and the length of the platelet can be determined accurately. The particles have an average length of about 40 nm and they are bent along a circumference with a radius of 13.5 nm. The first curve, recorded 233 s after the beginning of the reaction, is from particles with a slightly smaller length, which can be appreciated by the smaller amplitude of the oscillations. It is interesting to note that the radius of curvature -and therefore the positions of the oscillations -does not change throughout the reaction, not even in the initial moments when a difference in length is measured. While the oscillations can be made to match, the experimental and theoretical curves do not align well at small q.

Even in the first curve shown, which is the best fitted one, the experimental data, in the range 7 × 10 -2 nm -1 -2 × 10 -1 nm -1 , increases in intensity at a different rate compared to the simulated curve. Furthermore, as the reaction proceeds, the low-angle levelling of the curve slowly disappears and the intensity increases at a steady rate over the whole q range. The final scattering curve can be approximated as a straight line with oscillations at large q values. While one could be tempted to explain this by simply assuming that the particles increase in size, this can be shown to not be the case. A growth in the width of the platelet (W ) can be swiftly excluded, as it would vary the amplitude, and to a smaller degree the position, of the oscillation as seen in Fig. 6.13. An increase in the length, on the other hand, does shift the plateau to shorter wavevectors, but it does not alter the shape of the curve at higher q values. The effect of the length of the particle on the scattering curve was already studied earlier but is represented here in Fig. 6.17. In this plot the simulated curve is aligned to the experimental data using the oscillations at high q, this was to do make the effect of the length on the behaviour at small q clearer. As can be seen, the difference between the experimental value and the theoretical one cannot be explained as just a difference in size of the particles. We can then suppose that the growth of the signal at small q is to be attributed to the particles forming larger aggregates, rather than to a continuous growth of the particles along one direction.

Guinier regime and Porod invariant

The results of the analysis are shown in the three graphs in Fig. 6.18. The first plot shows the growth of the side of the platelet as a function of time, calculated as described in the previous section. The growth rate can be followed up to 400 s, at which point the gyration radius cannot be calculated any more as the inequality R G q < 1 does not hold true, and so the pre-requisites for the Guinier regime are not fulfilled. This problem had already been foreshadowed when trying to fit the signal to the simulated curves, which had proven impossible at small q due to the fact that the signal increased too rapidly.

After comparing the signal to that of platelets with increasing lengths we had shown that such a behaviour was not compatible with an increase in size, but better attributed to the formation of aggregates. This would also explain why the fitting of the Guinier regime ends up outside the validity range at 400 s.

The second plot shows the volume fraction of CdSe in solution. Unlike the Guinier regime, the only two requisites in this case are that the system be bi-phasic and dilute. The volume fraction can then be calculated for the whole reaction. From the graph, we see a constant increase in the volume fraction, which triplicates from 200 s to 600 s. This is an indication that new CdSe is forming, either in the form of new nuclei or as a lateral growth of the particles.

As the concentration of particles is calculated from both the gyration radius and the volume fraction it can only be followed up to where the Guiner regime holds true. What we notice during this time is that the number of particles increases during the first 300 s but, as the growth rate increases while the volume fraction grows at a constant rate, the number concentration starts to rapidly decline. Because of the impossibility to distinguish between aggregation and growth, we cannot conclude that there is a decrease in concentration, which could be explained by Ostwald ripening. We do know though that the volume fraction of CdSe is increasing, which is not consistent with only Ostwald ripening. What we can say then is that the reaction evolves until the end of the measurements, with new material forming. New particles nucleate up to 300 s, and keep growing in size. After this point, particle aggregation starts to appear, making it impossible to distinguish between crystalline growth and formation of aggregates, making the measurement of particle concentration invalid.

WAXS results

WAXS fitting

The information obtained from the small-angle scattering can be used to study the shape of the (220) wide-angle peak. A first analysis of the effect that bending a platelet around a cylinder has on the scattering peaks was shown in Fig. 6.14C). Fig. 6.19A) shows three different scattering patterns. The large dots are the experimental data, from which the background has been removed. The dotted line shows the theoretical peak of flat platelets, while the dashed line shows the peak produced by an ensemble of platelets, with curvature radii between 12.5 nm and 13.5 nm. As can be seen, averaging the curvature radius over a small range, smooths the high frequency oscillations, but does not change the overall shape of the curve. Though not perfectly aligned with the experimental data, this second curve has a similar shape. The reason for the shift can be attributed to the lattice parameter chosen for the structure of the platelets. Our simulations were done based on the values found in [START_REF] West | Basic Solid state Chemistry[END_REF], which mention a lattice parameter of 6.08 Å. Howeveer, other sources such as [START_REF] Riedinger | How semiconductor nanoplatelets form[END_REF] use 6.20 Å for their calculations. A larger lattice would in fact cause the scattering pattern to be shifted to lower q values, yielding a better match between the simulated values and the experimental ones. In this case, a variation of 2% in the lattice parameter would shift the peak by about 0.5 nm -1 . The results of expanding the lattice can be seen in 6.19B). The expansion to 6.2 Å clearly shifts the position of the peak. It appears as though the lattice was expanded too much, as the simulated peak is now at lower q values than the experimental one. One could then come to the conclusion that the lattice constant is somewhere in between, but the position of the peak is influenced by several other factors. So, while we can say that the deformation of the peak can be explained by the bending of the platelets, we cannot obtain the lattice constant for the structure based on it's position. A more in depth study at how the platelet can be bent in different ways and the effects it has on the scattering peaks is done in the Appendix.

Size, position and shape of the 220 peak

The scattering peak is then fitted to a pseudo-Voigt distribution, as described above.

The result of the fits for some of the scattering patterns is shown in Fig. 6.20A). Here, the asymmetric shape of the 220 peak, which exhibits what looks like a double peak, is evident when compared to the fit. The position, amplitude and FWHM of the fitted distributions are plotted as a function of time in Fig. 6.20B). The first plot shows the area of the curve, which is related to the amount of crystalline material scattering the incoming beam. As such, it is related to the Porod invariant and, in much the same way can be seen to increase throughout the reaction at a constant slope ≈1, with only the last few points reaching a stable value. The curve also presents the same kink at around three quarters of the reaction.

The second plot shows the position of the peaks with respect to the theoretical position as a percentage. The peak is shifted by 3% towards smaller values of q, indicating an expansion of the lattice compared to the simulated one. The evolution over time shows a very small variation between 3% and 3.15%. It does however show a trend, with a sharp decrease in the expansion at 500 s.

The third plot of 6.20B) shows the average crystallite size as calculated from Scherrer's formula. The average size of the crystals increases from 3.5 nm to 6.5 nm over 300 s. At that point, the average crystallite size remains constant.

The study of the WAXS peak confirms what had already been deduced from the Porod invariant: new CdSe crystal is grown throughout the reaction until the end of the measurements. We also confirm that the experimental lattice constant is larger than the theoretical 6.08 Å, with a shift of about 3%, which remains constant during the growth of the platelets. Finally, the width of the peak indicates a growth of the crystallite size which continues up to 500 s. While the information regarding the volume of CdSe and the lattice parameter are consistent with the other analysis made, it is important to reiterate that the shape of the peak differs from that of a flat platelet, therefore the fit using a simple pseudo-Voigt distribution is not exact, and the results have to be compared with other measurements. This is possible with the first two (the volume fraction and the expansion), but not for the size of the crystals. As the peak is deformed by the oscillations originating from the bending, the width of the fitted distribution is larger than what it would be for a flat platelet with the same structure. The value obtained using Scherrer's formula is consequently smaller than the true one.

Study of the effect of temperature

After studying the scattering pattern at both small and wide angles for the basic reaction, we proceeded to analyse the reaction at different temperatures. The set-up of the reaction was the same, but the final temperature of the solution was varied between 180 • C and 240 • C at 20 • C intervals. In all the experiments, the temperature was raised at a constant rate of 1 • C s -1 , up until the set value at which point it was kept constant until the end of the measurement. Such a study can aid in understanding the mechanism behind the nucleation and growth of the platelets, as well as help find the ideal temperature and duration for the synthesis. For this experiment, the scattering pattern was recorded every second for the first 240 frames, after which 100 frames were recorded 5 s apart, and the last 100 frames were recorded 10 s apart. As with the previous patterns, the results are a set of scattering curves at both small and wide angles. An example of scattering curves for the reaction done at 220 • C is shown in Fig. 6.9B). We notice that in the SAXS the oscillations are not visible in contrast with the previous synthesis but the intensity at small q flattens rather than grows. Also the WAXS peak is wider and less accentuated. Because of both these factors, the analysis was done primarily by studying the Guinier regime and Porod invariant -for the SAXS -and by fitting the WAXS peak with a pseudo Voigt distribution. x -axes in all graphs is log-scaled. The top row shows the length of the side of the square whose radius of gyration is equivalent to that of the platelets in solution. As explained earlier, this is a rather blunt simplification but it allows us to identify a reasonable size without imposing any values to either the width or the height of the platelet. The second row of graphs is the volume fraction obtained from the Porod invariant. Finally, the graphs in the bottom row shows the particle concentration calculated as the ratio of the two previous values. During the initial seconds, the data cannot be used because of the need to find the background (as previously explained).

It is important to note that the length of the particle calculated using the gyration radius obtained from the Guinier regime fitting is not as reliable as the volume fraction. As mentioned when presenting the Guinier regime, there are several hypothesis which are imposed in order for the log(I(q)) vs. q 2 relationship to be verified. In particular the particles have to be monodisperse, a condition which we cannot assure in our sample.

Furthermore, in order to obtain the size of the particle from the gyration radius we had to make some further simplifications, namely the particles were approximated as infinitely thin square particles. The size of the platelets presented in the graph has to be taken within this context, allowing for some interpretation of the data. Since the particle concentration is calculated starting from the particle size, similar considerations have to be made with regards to this value. Conversely the volume fraction is calculated from the Porod invariant, which imposes less stringent conditions on the system. Consequently the behaviour of the volume fraction is a more reliable value to analyse. We will however try an interpret the data obtained from the Guinier regime, keeping its restrictions in mind.

A In this case however, the drop is less intense and the curve quickly returns to its original value. In order to exclude the formation of bubbles in the capillary, which could explain the sudden dip in intensity, we studied the transmitted intensity. The transmitted intensity is measured by a diode place on the beam-stopper and the formation of bubbles in the sample is detectable by a sharp change in the intensity of the transmitted beam. We do not, however, notice any such variations. We can therefore exclude this hypothesis.

We can finish the study of the Porod invariant and the Guinier regime by comparing how the two evolve during the measurement. It is again important to keep in mind that the size of the particles has to be subject to interpretation, therefore the same concerns have to be expressed with regards to the number of particles in solution. That being said, if we look at the curves at 180 • C, we notice that both the size and volume fraction keep growing up until the last measurement, while the concentration of particles (plotted in the last row) rapidly reaches a plateau. We can deduce that the nucleation of the particles stops early, and the system subsequently evolves by growing the seeds. Similarly for the other samples, the growth of the particles can be seen to progress for somewhat longer compared to the concentration of particles in solution. The only exception is the sample at 200 • C, in which the size of the particles seem to gradually decrease after reaching a maximum. This could indicate a partial dissolution of the particles, in favour of new nucleation.

The drop in volume fraction at both 220 • C and 240 • C is reflected in the concentration of particles. As the drop in number of particles in solution is only seen at higher temperatures, and appears earlier and more prominently as the temperature increases, we can suppose that it is a third stage of the reaction which follows the nucleation and growth, and which involves the dissolution of some of the particles. As both of the reactions finish with the size of the platelets slowly increasing again, we can also suppose that part of the monomers in the solution provide further growing material for the existing particles.

Wide angle scattering peaks

The analysis was continued on the WAXS signal, in particular on the 220 peak. An example of the fitting for the sample prepared at 220 • C at different moments during the reaction is shown in Fig. 6.22. The peak for these samples is more symmetric, which results in a better fit with a pseudo-Voigt, as can be seen from the superimposed fit black curves.

The data is shifted along the y-axis for clarity. The vertical dashed line shows the theoretical position of the peak of the bulk crystalline structure was not stressed. The fit was done on all measurements for all four experiences, and the results of the analysis are shown in • C, the reaction is faster, reaching a stable point at around 700 s after the beginning of the experiment. Finally, the two reactions made at the highest temperatures reach a stable value early on and they both show the same behaviour as noticed studying the SAXS signal. At 220 • C, the area of the peak drops slightly starting at 700 s but recovers before the measurement ends. For the reaction conducted at the highest temperature, a plateau in the peak area is reached after 200 s but, 5 min later, the intensity falls by almost half and, even after recovering, stays below the previous value. This further supports the idea that as the temperature is raised the reaction is faster, eventually leading to a phase of partial reduction of the crystalline material.

The middle row plots the expansion of the lattice throughout the reaction. The value appears to remain constant for almost all the reactions. Only the system at 240 • C shows a slight decrease of the distortion towards the end. On average however, the lattice for all experiments is expanded by about 2.6% as compared to the theoretical one. This distortion appears as soon as the peak is first visible, indicating that the particles have a tendency to bend in much the same way independently of the size. This confirms what had already been noted in the SAXS pattern where the oscillations only varied in amplitude and not in position. Finally, the linear size of the crystallites is plotted in the bottom row. Although we stressed that this quantity can be misleading due to the bending of the platelets, its evolution is nonetheless interesting. As already mentioned, we can assume that the platelets are all curved in a similar fashion independently of the reaction temperature or the time.

Therefore, any variation within a measurement and between sets can be attributed to a difference in the size of the crystallites. All the curves have a similar shape, characterized by a rapid growth in the size of the crystallites during the first moments followed by a slower growth for the rest of the reaction. The final size of the initial growth, which ends somewhere between the 100 s and 200 s, increases with increasing temperature. At 180 • C, the average crystallite is slightly less than 4 nm, while at 240 • C it is more than 5 nm. The second phase also seems to vary with temperature. The size of the crystallites remains constant for the second part of the reaction at the lowest temperature, but increases by almost a nanometer when the platelets are synthesised at 240 • C.

Conclusion

The study mode on the SAXS and WAXS patterns, using both simulations and other types of analysis, shows a coherent picture for this heat-up synthesis. The oscillations in the SAXS pattern, as well as the particular shape of the WAXS peak, confirm that the platelets are bent in solution during the synthesis and that the distortion is not simply an effect of drying the sample for the TEM. Furthermore, a study of the oscillations in the SAXS indicates that the radius of curvature does not vary during the reaction, while the inspection of the position of the WAXS peak shows that it does not depend on the reaction temperature either. Thus, there is a preferred curvature for 3ML CdSe platelets.

The behaviour at small q also indicates that the platelets have a tendency to form larger aggregates during the reaction. By studying the Guinier regime and Porod invariant at small angles, as well as the (200) peak at wide angles, we are also able to draw conclusions on the dependence of the reaction on the temperature. At 180 • C, the platelets nucleate and grow at a slow rate, the reaction is still not complete after more than 25 min. As the temperature is increased, the reaction is predictably faster, it reaches a stable point within 10 min. However, if the temperature is increased both the SAXS and WAXS data shows that the the amount of CdSe crystal in solution decreases, possibly indicating an instability of the platelets. Consequently, the reaction is a valid heat-up synthesis for the preparation of 3ML particles, we also saw that, provided the system is not kept at high temperatures for prolonged periods of time, the reaction can take place up to 240 • C.

Chapter 7

CdSe-nanoplatelets/Au-beads heterodimers Within the framework of the study of heterodimers, we decided to explore the possibility of producing heterodimers starting from semi-conducting CdSe platelets. In particular, we were interested in growing a metal on the semiconducting colloids, as great interest has been shown in the last decade towards these Au/CdSe bifunctional nanoparticles. The first example of CdSe-Au particles was published in 2004 by Banin et al., who presented a CdSe-rod/Au-dot heterosystem [START_REF] Mokari | Selective Growth of Metal Tips onto Semiconductor Quantum Rods and Tetrapods[END_REF]. The most promising aspect of these heterodimers is the interaction between the two materials at the interface. In bulk materials, the properties which arise from the junction between semiconductors and metals have led to the development of light emitting diodes [START_REF] Özguür | A comprehensive review of ZnO materials and devices[END_REF], field effect transistors [START_REF] Storm | Field-effect transistor (FET) bibliography 1967[END_REF], and solid state lasers [START_REF] Nolte | Semi-insulating semiconductor heterostructures: Optoelectronic properties and applications[END_REF] among others [START_REF] Khon | Suppression of the Plasmon Resonance in Au/CdS Colloidal Nanocomposites[END_REF]. With the development of smaller hybrid structures, new properties of the metal-semiconductor junction became apparent. These hybrid particles have been shown to be useful for the degradation of pollutants [START_REF] Yu | Cu 2 ZnSnS 4 -Pt and Cu 2 ZnSnS 4 -Au Heterostructured Nanoparticles for Photocatalytic Water Splitting and Pollutant Degradation[END_REF], enhanced photocatalysis, and efficient water splitting for the production of H 2 gas [START_REF] Costi | Visible Light-Induced Charge Retention and Photocatalysis with Hybrid CdSe-Au Nanodumbbells[END_REF][START_REF] Bao | Self-Templated Synthesis of Nanoporous CdS Nanostructures for Highly Efficient Photocatalytic Hydrogen Production under Visible Light[END_REF][START_REF] Elmalem | Growth of Photocatalytic CdSe-Pt Nanorods and Nanonets[END_REF][START_REF] Berr | Colloidal CdS nanorods decorated with subnanometer sized Pt clusters for photocatalytic hydrogen generation[END_REF]. The enhanced photocatalytic effect has been attributed to the combination of ultra-fast electron transfer between the semiconductor and the metal and to the charge separation which results for the storage of electrons in the metal [START_REF] Prashant | Manipulation of Charge Transfer Across Semiconductor Interface. A Criterion That Cannot Be Ignored in Photocatalyst Design[END_REF]. Photo-generated electrons in the semiconducting particles can be transferred to the metallic moiety, thus reducing the probability of electron-hole recombination -which causes the quenching of the fluorescence of the platelets. The speed and efficiency of this process depends on both the relationship between the conduction band of the semiconductor and the Fermi level of the metal [START_REF] Sakthivel | Enhancement of photocatalytic activity by metal deposition: characterisation and photonic efficiency of Pt, Au and Pd deposited on TiO2 catalyst[END_REF], and on the method by which the metal is grown on the semiconductor [START_REF] Gratian | Photoassisted hydrogen production from a water-ethanol solution: a comparison of activities of Au-TiO2 and Pt-TiO2[END_REF]. The metallic part also functions as a storage space for the electrons, as can be seen by the red-shift in the absorption spectra in the case of semiconductor-Au hybrids [START_REF] Mongin | Ultrafast Photoinduced Charge Separation in Metal-Semiconductor Nanohybrids[END_REF]. The stored electrons can then be transferred to an accepting molecule (such as H + ions), thus completing the reaction [START_REF] Prashant | Photophysical, Photochemical and Photocatalytic Aspects of Metal Nanoparticles[END_REF].

Among the different possible combinations of semiconductor-metal, CdSe -Au heterostructures have already been shown to exhibit particularly interesting photocatalytic properties [START_REF] Sakthivel | Enhancement of photocatalytic activity by metal deposition: characterisation and photonic efficiency of Pt, Au and Pd deposited on TiO2 catalyst[END_REF]. Furthermore, synthesis procedures exist for the preparation of different types of heterodimers. Starting from quantum dots, it is possible to obtain two-sided spheres, or acorn-like structures by growing gold on the existing particles [START_REF] Mokari | Formation of asymmetric one-sided metal-tipped semiconductor nanocrystal dots and rods[END_REF]. Similarly, if semiconducting rods are used as a starting point, it is possible to grow gold only on their tip, forming dumbells and tetrapods [START_REF] Mokari | Selective Growth of Metal Tips onto Semiconductor Quantum Rods and Tetrapods[END_REF][START_REF] Chakrabortty | Asymmetric Dumbbells from Selective Deposition of Metals on Seeded Semiconductor Nanorods[END_REF]. Conversely one can grow pentapods or flower like structures from gold nanospheres [START_REF] Kanta | Hybrid Colloidal Au-CdSe Pentapod Heterostructures Synthesis and Their Photocatalytic Properties[END_REF][START_REF] Kanta Haldar | Formation of Heteroepitaxy in Different Shapes of Au-CdSe Metal-Semiconductor Hybrid Nanostructures[END_REF]. These systems have been shown to reduce methylene blue -a model molecule for pollutants -when illuminated by visible light, they can also store the energy and reduce the molecule at a later time in the dark [START_REF] Costi | Visible Light-Induced Charge Retention and Photocatalysis with Hybrid CdSe-Au Nanodumbbells[END_REF]. Because of their novelty, platelets had never been used as starting point for the preparation of hybrid particles. Since our initial interest and development of the system, a comprehensive article has been published by Bigall et al., studying the growth of different noble metals on CdSe nanoplatelets and their photocatalytic properties [START_REF] Naskar | Site-Selective Noble Metal Growth on CdSe Nanoplatelets[END_REF]. In this chapter, we will present the synthesis of the CdSe-Au platelets which we developed. We also present some high-resolution STEM (HRSTEM) images that show the lattice planes of both the metal and the semiconductor, which are missing in [START_REF] Naskar | Site-Selective Noble Metal Growth on CdSe Nanoplatelets[END_REF]. These images can be used to further understand the noble metal-semiconductor interface.

Synthesis

The CdSe-Au heterostructures are prepared by growing gold beads on top of 5ML platelets or "boards". The platelet synthesis is done using Se and Cd -oleate as precursors.

The Cd -oleate is prepared from stoichiometric quantities of Cd -nitrate and Na -oleate, by dispersing them in ethanol and heating them up to 60 • C for several hours. The Cd -Oleate is then easily purified by centrifuging and washing with ethanol. 405 mg of the freshly prepared Cd -Oleate are then dispersed in 25 mL of octadecene along with 27 mg of Se.

The atmosphere is purged with Ar several times before setting the temperature of the flask at 245°. As the system approaches 200 The heating source is then removed and 1 mL of oleic acid is injected. The acid acts as a ligand and stabilizes the colloids. After cooling down, the solution is washed with ethanol in order to remove dots and platelets of other thicknesses that might have formed during the reaction. The final product is re-dispersed in hexane. The monodispersity of the thickness of the synthesised colloids is controlled by absorption spectroscopy. The subsequent growth of Au beads on the platelets is done in toluene, as opposed to hexane; thus, the platelets have to be dried under vacuum and redispersed in the correct solvent. It is important to rapidly dry the colloids, as a slow drying process leads to the formation of long threads, as shown in [START_REF] Jana | CdSe Nanoplatelets: Living Polymers[END_REF]. Such structures reduce the colloidal stability and could impede the growth of gold. The orange powder is then re-dispersed in toluene. In order to control the concentration of platelets, the amount of toluene added is determined by measuring the light absorption of the solution. Enough solvent is added to bring the absorption of the main peak (552 nm) to 1.76. This is then used as a stock solution. The synthesis of the hetero-structures is done by preparing a growth solution for the gold. 2 mmol of HAuCl 4 are solubilized in 10 mL of toluene using 5 mmol of tetraoctylammonium bromide (TOAB), giving an orange-coloured 200 mm solution of HAuCl 4 . A small amount (between 100 µL and 400 µL) of the salt solution is then added to enough toluene to obtain 1 mL of solution.

To this is added 1 mL of 0.27 m dodecylamine (DDA) solution in toluene, which acts as the reducing agent for the gold salt. The growth solution is then stirred vigorously at room temperature and 2 mL of the stock platelet solution are added. The solution rapidly changes color, becoming brown. The exact hue depends on the amount of gold salt placed in the growth solution, with more salt resulting in a darker final product. After 20 min, ethanol is added to the solution and the colloids are precipitated by centrifuging. The washing is done several times in order to ensure the full removal of all DDA. The product is then finally dispersed in toluene and stored. As described in the previous chapter, the position of the main absorption peak (552 nm)

Absorption spectrum

identifies the platelets as 5ML platelets. Fig. 7.1B) shows the different spectra of the solutions obtained using 100 µL, 200 µL and 400 µL of the HAuCl 4 solution. As more gold is introduced in the reaction, there is a definite change in the shape of the curve. In the pure platelet solution, as well as in the 100 µL reaction, the baseline has a very small slope at high wavelengths and there are three very visible and clearly separated peaks.

As more gold precursor is added to the reaction, the slope of the baseline increases. The absorption peaks also appear less intense, due to the valleys between them decreasing in depth. This is the effect of the gold particle adding their absorbance spectrum to the one of the CdSe platelets, and becomes more evident as the amount of gold precursor used increases. An even more dramatic effect is the quenching of the fluorescence of the platelets. As explained at the beginning of the chapter, the metal acts as a attractor for the electrons in the electron/hole pairs. The electrons are transported to the gold particle through ultra-fast electron transfer, inhibiting the recombination of the the electron/hole, and therefore quenching the fluorescent emission. This effect is immediately visible even when small amounts of gold precursor are used and can be seen by the naked eye. Solutions Rather than growing on the corners, they also grow at the center of the shorter size, forming two ovals at the ends of the platelet. Some smaller spheres can also be seen along the longer sides. In some cases, the gold particles from two different platelets appear to have fused together, forming a long bridge between two CdSe particles. The distribution in radius of the Au beads for the four different systems is shown in Fig. 7.4. The histograms confirm that, as more HAuCl 4 solution is added, the average size of the gold spheres increases. It is also apparent that the size distribution not only shifts towards larger values, but broadens as well. This can be explained by the presence of smaller beads along the long sides of the platelets as well as by the larger Au particles which bridge multiple platelets.

As the particles get larger the platelets also appear to lose some of their regularity in shape. Almost all of the platelets seen in Fig. 7.2A) have four sides and right angles. As we progress from Fig. 7.3A) to Fig. 7.3D), the rectangles show less defined shapes. This can be attributed to two factors, both of which tend to etch CdSe platelets. In [START_REF] Mokari | Selective Growth of Metal Tips onto Semiconductor Quantum Rods and Tetrapods[END_REF], the authors show that dodecydimethylammonium bromide (DDAB), which they use in place of the TOAB to solubilize the gold salt in organic solvents, has the tendency to reduce the size of the rods. At the same time, the reduction potential of Au (Au 3+ /Au 0 ) is higher than than of the selenide (Se 4+ /Se 2 -) [START_REF] Bouroushian | Electrochemistry of the Chalcogens[END_REF], which results in the selenide reducing the gold ions to gold atoms on the surface of the platelets [START_REF] Teng | Cadmium Selenide-Gold (CdSe-Au) Hybrid Nanowires: Synthesis and Study of Charge Transfer[END_REF]:

2 AuCl 3 + CdSe 2 Au + Cd 2+ + Se 4+ + 6Cl -. This can further be seen if the growth is done without the addition of DDA. Even without the reducing agent, gold beads appear on the platelets, indicating that the reducing action can also be provided by something other than the DDA.

Both the presence of the DDAB and the reduction of Au ions by the selenide result in part of the platelet being dissolved during the growth process.

High resolution STEM

The images taken using traditional TEM methods allow us to study the size of the gold beads as well as the variation in shape of the platelets but they cannot provide information with regards to the crystallographic orientation of the two domains. In order to probe the system at such a scale, it is necessary to use other techniques such as high-resolution scanning transmission electron microscopy (HR-STEM).

Working principle of HR-STEM

A STEM is a variation of the TEM which allows for recording high-resolution images and using different modes of imaging compared to conventional transmission electron microscopy. In TEM, the electron beam is focused on the whole region of the sample which has to be imaged; the electrons which are not scattered by the sample are then focused on a fluorescent screen. The resulting image is called a bright-field image due to the fact that the background area, where very little electron scattering occurs, appears brightly lit on the fluorescent screen. In STEM however, the electron beam is focused in a narrow spot which is scanned over the desired area. In much the same way as with traditional TEM, STEM can measure the number of electrons which pass through the sample without being scattered and produce a bright-field image, however, in virtue of the scanning technique, other imaging techniques, such as electron energy loss spectroscopy (EELS), energy dispersive X-ray (EDX), and annular dark field (ADF) imaging can be used. All these techniques rely on the fact that, at any instant during the measurement, the information arriving to the detectors is originating from a very small region rather than the average over the whole image. In particular, we will focus on ADF imaging, which allows us to image individual atoms. In this imaging mode, the camera records the atoms scattered by the sample by using a detector which collects the electrons on a circular ring around the transmitted beam. Therefore, the image will be bright in areas where the sample strongly scatters the electrons and will be dark where the electrons are not scattered (such as the background), hence the name dark-field in contrast to bright-field images. The detector can be positioned to measure either the electrons scattered by Bragg scattering (in which case, we talk of medium-angle annular dark-field or MAADF), or those originating from incoherent scattering (in which case, the technique is called high-angle annular dark-field or HAADF). In the first case, the scattering (and therefore the intensity in the image) is correlated to the crystallographic structure, while in the latter the scattering is related to the atomic number (Z) of the atom being probed. Fig. 7.5 shows a schematic representation of how the three imaging modes work along with the same image taken using the three detectors. The difference between bright-field (Fig. 7.5A) ) and dark-field (Fig. 7.5B) C) )

imaging is immediately visible due to the inverted contrast. In these images, it is harder to see a difference between the two dark-field imaging modes as gold always has a stronger scattering power compared to CdSe.

HR-STEM analysis on the CdSe -Au system

The HR-STEM images were taken on the NION STEM at LPS by Mathiew Kociak.

The analysis is done on Gatan's DigitalMicrograph [219] using the fast Fourier transform (FFT) to remove the noise and enhance the crystalline structure. We start by determining the orientation of the gold particle. To do so, we select an area which contains only gold and apply a FFT. We then select the bright spots in the FFT, mask the rest of the image, and apply an inverse Fourier transform (IFFT). The resulting image has only the periodic structures visible. By measuring the distance between the parallel rows (2.136 Å) and comparing them with the spacing between planes in a gold lattice, we found that the closest match was with the (200) planes, which have a reticular spacing of 2.04 Å. We can attribute the difference between the two values to a slight rotation of the crystalline structure compared to the direction of the beam an safely consider that the planes seen in the image are those corresponding to the (200) planes in gold. We then proceeded to do the same thing on one of the platelets. In this case, we can two sets of bright spots after the FFT and the IFFT; the dots with the highest intensity are the Cd atoms, while the dimmer ones are the Se atoms. By measuring the distance between the cadmium atoms, we can find the (020) direction for which we measure an inter-plane distance of 2.77 Å compared to the theoretical distance of 3.0 Å. Again, this discrepancy can be attributed to the particle not laying flat on the grid. Fig. 7.6 shows the various steps used for measuring both the Au (top) and the CdSe (bottom) crystal planes.

The same measurement can be made on different images to obtain the crystalline planes from different orientations. Fig. 7.7 shows three different high-resolution images of the CdSe -Au system with the planes identified on both the gold and the semiconducting platelet. A) refers to the image analysed before, it shows the two planes ((200) for the Au and (020) for the CdSe) drawn in red. We also notice that the two planes are not aligned.

B) shows a platelet on its side, the Cd planes (020) are clearly visible, with a separation of 2.9 Å, the (020) plane of the gold can also be seen as the platelet is rotated by 90°. Here, again, we do not see any alignment between the crystalline planes of the gold and the Previous works on the growth of Au on CdSe structures, in particular nanorods, tend to attribute the growth of the gold to the formation of an interfacial AuSe layer [START_REF] Mokari | Selective Growth of Metal Tips onto Semiconductor Quantum Rods and Tetrapods[END_REF] as described in [START_REF] Cretier | The Crystal Structure of the Beta Form of Gold Selenide[END_REF] rather than an epitaxial growth. While the structure of the rods is different from that of the platelets (wurtzite in the first case, zinc-blende in the second), it seems to be the case in this system as well. This also explains the formation of the beads on the corners of the platelets where the selenium can be accessed with greater ease. The corners, moreover, are often defect sites, further increasing the facility with which the gold can nucleate [START_REF] Mokari | Selective Growth of Metal Tips onto Semiconductor Quantum Rods and Tetrapods[END_REF]. This can be seen in the image analysed in Fig. 7.6, in which two gold beads can be seen in the lower right corner of the platelet where the imperfect shape of the particle produces two corners. We do, however, see from the high resolution images that the gold tends to grow inwards, covering the Cd layer, rather than outward. We can see it clearly from Fig. 7.7B), in which the system is imaged from the side of the platelet. Here the interface between gold and CdSe is not perpendicular to the (010) planes, as would be expected if the gold grew on the surface of the platelet. It is important, to keep in mind that due to the difference in contrast between the Au and the CdSe, the two crystalline structures are hard to image at the same time. We were, however, able to obtain better results using MAADF compared to HAADF, which was used in the article published on these structures, because the intensity is not as strongly dependent on the atomic number of the scatterers [START_REF] Kimoto | Spatially resolved diffractometry with atomic-column resolution[END_REF], but it remains hard to have a clear picture. Furthermore, due to a possible misalignment of the lattice to the beam and the positioning of the structures with respect to each other, it is hard to precisely determine the interface between the two materials.

Conclusion

The system presented in this chapter is a semiconducting/noble-metal heterodimer, synthesised starting from CdSe platelets. The combination of the two materials has already been shown to produce new or enhanced properties using nanorods as starting point, the use of platelets could however provide added benefits. As described in the previous chapter, the original structure of the platelets results in enhanced opto-electrical properties. In the case of catalysis, for example, the platelet structure can prove to be more efficient thanks to the high molar absorption coefficient [START_REF] Yeltik | Experimental Determination of the Absorption Cross-Section and Molar Extinction Coefficient of Colloidal CdSe Nanoplatelets[END_REF] coupled with the fast fluorescent lifetime [START_REF] Ithurria | Colloidal nanoplatelets with two-dimensional electronic structure[END_REF].

We developed, at almost the same time as another group at the Leibniz Universität at Hannover, a simple procedure for the synthesis of CdSe platelets decorated with gold beads at the corners. The reaction is done at room temperature in toluene over 15 min. We showed how the size of the beads can be tuned between 1.2 nm and 2.5 nm by adjusting the amount of gold precursor used. The average size of the gold beads was measured using electron microscopy. The growth of gold changes the absorption spectrum of the solution; this can be seen by the change in color of the solution which passes from bright orange to pink. By placing the solution under UV light, one can also see that the fluorescence of the colloids is quenched as a result of the ultra-fast electron transfer from the semiconductor to the metal.

We completed the study of the platelets by recording high-resolution STEM images. Using the MAADF imaging mode, we were able to see both lattices, albeit not at the best resolution, and consequently try and interpret how the two structures interface. We saw that the two structures do not appear to align, with the (200) plane of the Au rotated with respect to the [START_REF] Nolte | Semi-insulating semiconductor heterostructures: Optoelectronic properties and applications[END_REF] and (020) planes of the platelet. The beads furthermore appear to cover the platelet as they grow, rather than nucleating on the side and growing out. We do know however, both from the experiments and from literature [START_REF] Bouroushian | Electrochemistry of the Chalcogens[END_REF], that the reduction of the gold can be done by the selenium, and that the platelets are partially dissolved during the growth. The gold could therefore nucleate on the corners and grow at the expense of the platelet.

Chapter 8

Conclusion

The bottom-up approach to nanostructuring is a promising field which has greatly benefited by the advancement in colloidal science in the last two decades. Because of their mostly isotropic interactions, colloidal particles have been used to create simple lattices such as hexagonal, or face-centered cubic. More sophisticated approaches, such as using DNA as linker between particles, can be used to engineer complex structures but they require extensive work for the preparation and they are hard to implement for anisotropic interactions. The development of chemical techniques for the preparation of hetero-structures has opened the door to a new range of accessible interactions and structures. Most of the work published on the self-assembly of janus nano-particles has, however, been theoretical. As seen in the introduction, the results from the in-silico analysis have shown that there is a rich phase diagram to explore by tuning the parameters which govern janus self-assembly (the size/shape of the particles, the size of the patches, the interaction range, etc.). In this thesis, we started to explore this phase diagram by creating simple dumbbell-like particles where the two halves have opposite hydrophilic characteristics.

The first two chapters introduced the reader to the subject by detailing the characteristics and physical background of small-angle X-ray scattering (SAXS) and the state-of-the-art synthesis procedures for the preparation of gold nanoparticles. We explained both how small-angle scattering works and how the data obtained from the measurements can be analysed to obtain information on the particles in solution. We also highlighted the benefits of this technique when studying colloids. In particular, we saw the sensitivity of the scattering curve to small changes in the mean size of the particles, as well as the huge number of particles which are averaged to obtain the signal. The second chapter focused on the synthesis of gold nanoparticles, which is one of the oldest synthesis for the preparation of nanospheres and has therefore been extensively studied. As we have shown, there is nevertheless new research being published which deepens our understanding and mastery of the procedure. Two modifications to the traditional Frens synthesis, based on a more accurate understanding of the nucleation and growth mechanism, allowed us to prepare more spherical and monodisperse particles. Namely, inverting the order in which the precursors are added, which results in a faster and more homogeneous nucleation and using a multi-step synthesis rather than a one-pot or a two-step synthesis, which separates the growth and Ostwald ripening phases.

In chapter three, we introduced the heterodimers used for the self-assembly. The original synthessi was taken from an article published in 2010 from Chen et al. [START_REF] Chen | Scalable Routes to Janus Au-SiO 2 and Ternary Ag-Au-SiO 2 Nanoparticles[END_REF], we proceeded however to optimize the parameters for our case using new particles and conditions. We found that the synthesis resulted in a large amount of individual gold and silica particles in solution along with the janus colloids. We therefore studied the effect of varying the amount of gold and TEOS used, in order to reduce the number of unwanted particles. What we found in our results was that a small amount of silica and gold particles were always present in solution. Decreasing the amount of silica precursor resulted in a larger number of bare gold particles in solution. By varying the amount of gold particles, we were able, on the other hand, to increase the proportion of janus particles. We found that the concentration of the initial gold solution could be increased up to two-fold before the amount of janus particles decreased in favour of bare gold nanospheres. We also used a different synthesis for the gold colloids. This resulted in a better final product as the particles are more spherical in shape compared to the elongated particles used in the original article. The resulting heterodimers are therefore more homogeneous, a sought-after characteristic for self-assembly.

The fourth chapter delineates the procedure used to induce the self-assembly of the colloids and the techniques used to study the clusters. To introduce an attractive interaction on the particles, we exploited the strong interaction between thiols and gold surfaces to exchange the ligand on the gold moiety with an alkanethiol. The thiol rendered the gold half hydrophobic, which drove the formation of clusters in the aqueous environment. The presence of a silica shell on one of the two hemispheres played the double role of defining the attractive patch size and providing steric interaction. The combined effect is to prevent the clusters from growing too much and forming large aggregates. The formation of the clusters was evidenced by a change in color of the solution. This was studied by timeresolved absorption spectroscopy which showed the appearance and growth of a coupling plasmon, confirming that the gold particles had come in close proximity to each other (a few nanometres). Using singular value decomposition, we divided the formation of the colloids in three phases, the initial and final ones characterized by only two species in solution. This interpretation is corroborated by the presence of two isosbestic points, one visible during the first ten hours and the second one which appears after the fortieth hour. We expanded the analysis by preparing samples with thiols with different tail lengths. The position of the coupling plasmon and its intensity showed that shorter chains take longer to induce the assembly and cause the particles to pack closer together. The absorption spectra analysis was supplemented by the study of the structure factor derived from SAXS.

The result obtained by fitting the signal using a Monte-Carlo approach gave us the average cluster size as well as the average inter-particle distance. We showed that the cluster size had an upper limit of 5 janus particles, confirming that the silica provides the protection needed to stop the growth of the clusters. We also found a linear relationship between the length of the thiol chain and the average inter-particle distance, the slope of which indicates inter-digitation between the ligands.

The sixth chapter was dedicated to a different system: CdSe nanoplatelets. In particular, we analysed the nucleation and growth of thin 3ML platelets, with a focus on the rolling of the platelets into cylinders. The deformation is documented at the end of the synthesis by electron microscopy images. We used SAXS and WAXS measurements to follow the evolution of the platelets during their formation. A first study at 200 • C showed that the 3ML platelets have a tendency to fold into cylinders with an average radius of ≈13 nm from the beginning of the synthesis. This is seen both from the presence of oscillations in the SAXS and the position and shape of the peaks in the WAXS regime. A study of the effects of the reaction temperature on the final product showed that the speed of the reaction is directly related to the temperature at which the reaction is conducted. We also noticed that at high temperatures (220 • C and 240 • C) the volume fraction undergoes a rapid but significant dip in intensity when the solution is kept at the reaction temperature long after the particles have formed. The decrease is only temporary and can be seen both by SAXS and WAXS. The origin of this behaviour is still being investigated.

The CdSe platelets were also studied as the starting point for the synthesis of heterodimers.

In this case, 5ML platelets were used and gold beads were grown on each corner. We showed how the size of the beads can be tuned by varying the amount of gold precursor, as well as its effects on the absorption spectrum. Through HR-STEM imaging, we also showed the orientation of the crystals, although as already experienced by other groups, it is difficult to probe the interface of such systems using electron microscopy.

This thesis provides the basis for future developments on both the Au -SiO 2 system and the semiconducting platelets. For the first system, we have shown that the self assembly of nanometric particles in solution is possible but we have just scratched the surface of what is theoretically predicted. Our particles were all produced following the same procedure and therefore we were only able to test one of the parameters in the multi-dimensional phase diagram for janus self-assembly: the attractive interaction. By carefully varying the ratio between the two ligands, we could envision to vary the size of the attractive patch on the colloid, exposing more or less of the gold surface to the thiols. The size of the gold particles was also kept constant in all our experiments. By preparing janus particles starting from gold colloids with different diameters, we would change the shape of the heterodimers and influence how they interact. This could be easily achieved considering that the synthesis for the gold particles is step-wise. We saw in the chapter on the synthesis of the janus particles that the size of the silica moiety cannot be reduced by changing the amount of precursor, we could nevertheless add stoichiometric amounts of HF to reduce the size of the silica, thus changing the steric interaction between particles in the cluster. All of these adjustments to the particles would allow us to explore the various regions described in simulation by the various articles mentioned in the introduction [START_REF] Sciortino | Phase Diagram of Janus Particles[END_REF][START_REF] Munaó | Cluster formation and phase separation in heteronuclear Janus dumbbells[END_REF][START_REF] Preisler | Equilibrium phases of one-patch colloids with short-range attractions[END_REF][START_REF] Munaó | Phase separation and self-assembly of colloidal dimers with tunable attractive strength: from symmetrical square-wells to Janus dumbbells[END_REF].

Up until now, we have only studied the assembly of the particles in solution but experiments could be prepared to place the particles at the interface between two liquids or at a liquid/air interface. This has also been the subject of theoretical calculations which have shown interesting structures arising from interacting janus particles [START_REF] Shin | Theory of two-dimensional self-assembly of Janus colloids: crystallization and orientational ordering[END_REF]. The challenges here would be to induce the particles to come at the interface without causing aggregation, as well as finding a suitable technique to follow the interaction between particles. Brewster angle microscopy could be used to study the movement of the particles to the interface, especially when working at liquid/air interfaces, but would become more complex for liquid/liquid interfaces. Grazing-incidence small-angle X-ray scattering could also be used to probe the structure at the surface. Furthermore, if the particles were to form large films, they could also be studied through electron microscopy without interfering with the structure.

With regards to the investigations of the kinetics of the CdSe platelets, there are some additional studies which could be made to better understand the mechanism. We could, for one, repeat some of the experiments using flow cells in place of standard glass capillaries. This would not only provide us with a more accurate measurement of the thickness of the capillary, and thus of the concentration of particles in solution, but it would also allow us to do the reaction while agitating the solution. As we saw, we could not accurately fit the experimental curve using the simulated data due to the behaviour of the signal at small q.

We attributed the increase in the signal to an aggregation of the particles in solution, as it could not be explained by an increase in the size of the particles. By flowing the solution, as well as stirring the liquid in the flask, we could minimize both the aggregation of the particles and the possible deposition on the glass surface. This would allow us to better fit the particles at all times and follow the growth more accurately.

The last system, CdSe -Au, is still in the early stages of analysis. We have shown that we can control the size of the gold beads but at the same time we cannot increase the diameter beyond ≈3 nm without degrading the nanoplatelets and the orderly nucleation of the beads at their corners. The particles might be protected by creating core-shell CdSe -CdS platelets, allowing us to grow larger gold beads without reacting with the selenium in the particles, and thus maintinging the rectangular shape. We could also try and apply a step-wise synthesis to the gold. This could result in more homogeneous spheres even when larger amounts of gold are added. We are also interested in studying the nucleation of gold on the platelets. This could be done by inspecting the WAXS peak during the first instances of the nucleation. The position of the peak, along with its shape, could provide information regarding the deformation of the crystal lattice, thus giving us clues with regards to how the gold nucleates. The reaction is relatively fast, so such studies would have to be done at a high flux facility, such as a synchrotron, in order to have short exposure times. Finally, in line with the work done by Jana et al. [START_REF] Jana | CdSe Nanoplatelets: Living Polymers[END_REF] on the formation of threads of platelets, we could study the effect of the beads on the assembly of the platelets. Provided the gold beads can be grown enough to fill the gap between platelets in the threads, the gold could either disrupt the formation of threads or force the platelets to place themselves at a larger distance from each other. points can be imported in a n matrix, where n is the number of atoms in the platelet (for a 60 nm by 40 nm 3ML platelet n is equal to approximately 100 000 atoms). The position of the atoms can then be changed to introduce the desired distortion by finding the appropriate transformation for each coordinate. In order to do so we can imagine the platelet in a Cartesian coordinate system as shown in Fig. A.1, with the length aligned along the z -axis, and its width along the x coordinate. We place the lower width of the platelet on the x -y plane, with the z -axis passing through its center. We then bend it around an imaginary cylinder with its main axis along the z direction. Because of how we set up the system, the z coordinate of the atoms is not affected by the transformation and vice-versa, the transformation does not depend on the z position of the atom. We can therefore imagine to take only one slice of the platelet, obtaining a rectangle made up of layers of Cd and Se, with the center on the origin (O) (Fig. A.2A) B) ). Once we determine how to bend this layer, we will simply have to repeat the same operation independently of the z coordinate.

The transformation we want to apply will have to map the original x and y coordinates of the atoms in the rectangle to new x' and y' coordinates along a circular corona. Before approaching this problem we can, however, further simplify it by reducing the dimensionality again. Instead of starting from a rectangle, we can "compress" the atoms on a line, map them on a circumference, and later move the atoms along the radial direction to restore the thickness of the platelet (A.2C)-D)-E)-F) ). We are therefore, now reduced to a line of points along the x -axis and a circumference along which to bend them. The circumference is placed in such a way as to be tangential to the row of atoms in the origin. A point P along and negative angles clockwise). Now that we have defined the system, we want to find the transformation for x which will map to x' without altering the bond length between neighbours. We know that x is the distance from the origin, which on the circle must be equivalent to the length of the arc. 1 We can therefore, given a value for x, find a corresponding angle θ by using the definition of a radiant, which defines the relationship between the length of an arc (s), the radius of the circle (r) and the angle it subtends (θ):

θ = s r . (A.1)
1 N.b. This will not maintain the distance from the origin (an atom at a distance πR from the origin would end up diametrically opposite, therefore only 2R from the origin) but it will maintain almost unvaried the distance between two adjacent atoms -there will be a slight compression, but as we will see later it can be ignored. constant in eq(A.1). The fact that the bonds are being expanded rather than compressed is due to the arbitrary decision to place the cylinder around which the platelet is bent on the "inner" surface of the platelet. By shifting the position of the circle towards the other face of the platelet, we can find three different regimes for the bending of a platelet. The first, which is the one we used to derive our transformation, has r ef f ≥ r, all the bonds between atoms in the same layer are then equal to or greater than those of a flat platelet. A second type of bending occurs when the circle is placed within the platelet. In this case, r ef f can be both greater or smaller than r, consequently the inter-atomic distance is smaller inside the circle, and greater outside. Finally, if the circle is placed in contact with the outermost layer, r ef f will always be smaller than r and all the bonds will be compressed. A schematic explanation of the effect can be seen in Fig. A.4 In all three cases, the atoms on the circle will maintain the same intra-atomic distances Because of the differences between these three bending regimes, we can intuitively suppose that the scattering spectra at wide angles will vary depending on how we apply the transformation. By bending the whole platelet on the outside of the cylinder the majority of the bonds will be stretched, it stands to reason then that the peak will be shifted to lower q values (the scattering process brings us into the reciprocal space). Conversely, if the platelet is bent on the inside of the cylinder, it will have almost all the bonds compressed, which will shift the peak to larger wave-vectors. This can be clearly seen in our algorithm, with the pattern from the Crystal Maker structure, we can draw conclusions on how the software distorts the platelet. The WAXS pattern obtained from the Crystal Maker structure follows the curve of what we called the "external" bending, where the whole structure is stretched. This was predictable, as the algorithm is designed to bend a single sheet of graphite in a nanotube, thus it simply tries to wrap the structure around the cylinder trying to keep it aligned. This is something to keep in mind when analysing the data presented in Chapter 6. In this chapter, we presented how the possible reason for the shift in the peak position could be due to the lattice parameter, which in some references is given as 6.20 Å instead of 6.08 Å. However, as we have shown here, the fashion in which the platelet is bent also plays an important role on the scattering at wide angles and cannot be ignored.

A.3 Conclusion

The simulations of the distortion of the platelets show that the fashion in which the particles are bent has a strong influence on the shape and position of the WAXS peaks.

By varying the amount of compression and stretching in the platelet when bending the particles, the WAXS signal can be made to move to lower or higher q, or remain stationary.

Furthermore, other distortions, such as twisting the platelets, also alter the shape of the peaks, making it hard to determine the exact origin of the experimental peak profiles. Title : Self-assembly of Janus Nanoparticles Keywords : Heterodimers, Self-Assembly, SAXS,CdSe nanoplatelets, CdSe-Au heterostructure.

Abstract : "Janus nanoparticles" is the term used to refer to colloidal nanoparticles made of two halves with different physical and chemical properties. Over the last years, several theoretical studies have been published on the self-assembly possibilities offered by these particles (in particular by Sciortino, F. et al.), but little experimental work has been done on them. The theoretical studies suggest that many interesting behaviors appear when the size of the particles approaches the interaction range of the forces at play (tens of nanometers in the case of van der Waals and hydrophobic forces). In this manuscript, we show the formation of clusters of Au -SiO 2 heterodimers with sizes of less than 100 nm. The self-assembly was induced by exchanging the hydrophilic ligand on the Au surface with a hydrophobic one, which provided the attractive interaction. The assembly was followed by time-resolved absorption spectroscopy and small-angle X-ray scattering. We found that shorter thiols have a longer induction period, and cause the particles to come closer together, compared to thiols with longer tails. We also study a second system: CdSe na-noplatelets. These are semiconducting quasi-2D structures with unique optical properties. These properties result from their reduced size in one of the dimensions. Because of their novelty and particularity, the nucleation and growth mechanism of these particles is still being studied. We followed the synthesis using in-situ SAXS and WAXS, to obtain information with regards to this mechanism and to study the deformation which occurs in some of these systems which leads to rolled up sheets of CdSe. The CdSe nanoplatelets were also used to create hybrid CdSe -Au structures. The combination of these two materials has already proven to produce unique effects such as enhanced catalysis and, combined with the reduced dimensionality and control of the platelets, could result in even more interesting characteristics. We propose a synthesis method which results in the formation of small gold spheres on the corners of the platelets. We show that the size of the spheres depends on the amount of precursor used, and show high resolution electron microscopy images which highlight the crystalline structure of both materials.

Université Paris-Saclay Espace Technologique / Immeuble Discovery Route de l'Orme aux Merisiers RD 128 / 91190 Saint-Aubin, France

A. 1

 1 Bending the platelets along a cylinder . . . . . . . . . . . . . . . . . . . . . A.2 Exploring different deformations . . . . . . . . . . . . . . . . . . . . . . . . A.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

Figure 2 . 1 :

 21 Figure 2.1: Working principle of small angle x-ray scattering. The focused incident beam interacts with the sample and forms a pattern on the detector. A beam stopper (not shown in the image) is used to protect the detector from the direct beam.

Figure 2 . 2 :

 22 Figure 2.2: Process for passing from a 2-dimensional pattern (A)to a 1-dimensional pattern (B) through radial averaging. The image is a simulated scattering pattern for spherical nanoparticles with an average radius of 7 nm and a σ of 0.3 nm.

Figure 2 . 3 :

 23 Figure 2.3: A) Scattering pattern of nanospheres with a radius ranging from 2 nm to 5 nm and with a constant σ of 0.1 nm along with the corresponding Gaussian distributions (C). B) Scattering pattern of nanospheres with a constant radius of 5 nm and a σ which varies from 0.1 nm to 0.6 nm along with the corresponding Gaussian distributions (D)

Figure 2 . 4 :

 24 Figure 2.4: Simulated scattering patterns produced by two samples, one of the samples has no correlation between the nanoparticles in solution, while in the other the particles are placed in an organized structures of 5 nanoparticles. The particles are placed on two rows, one of three and the other of two spheres, in an hexagonal like lattice (the second row is x shifted by with respect to the first by cos(2π/3), and y shifted by sin(2π/3) ). The inset shows the structure factor of the assemblies as calculated by Debye's formula as whell as a scheme of the structure.

Figure 2 . 5 :

 25 Figure 2.5: Schematic drawing of the SOLEIL structure, displaying the linear accelerator (LINAC), the booster ring and the storage ring, along with the different beamlines. Image by: EPSIM 3D/JF Santarelli, Synchrotron Soleil taken from the Wikimedia collection

Figure 2 . 6 :

 26 Figure 2.6: These two graphs show the two steps necessary for converting the raw data to absolute intensities. A) The glassy carbon pattern obtained from the experimental measurements is compared

Figure 2 . 7 :

 27 Figure 2.7: SAXS patterns of PbS nanoparticles, with their fitted curves. The data points are shifted by ×10 each in order to make the graph easier to read. The graphs on the right show the distribution function for each of the fitted curves respectively.

Figure 2 . 8 :

 28 Figure 2.8: PbSe spherical nanoparticles. A guess on the polydispersity of the particles can be made based on the oscillations visible in the pattern. The samples can be assumed to be fairly monodispere since there are at least 3 very distinct oscillations in each pattern.

Figure 2 . 9 :

 29 Figure 2.9: Au nanoparticles in aqueous solution stabilized by citrate. The reaction is a step growth from less than 6 nm in diameter to just under 30 nm.

Figure 2 . 10 :

 210 Figure 2.10: Larger Au nanoparticles synthesized using fewer steps. The seeds are roughly 20 nm in diameter and the nanoparticles grow to more than twice their original size in only four growth steps.

Figure 2 . 11 2. 7 )Fig. 2 . 11 .

 2117211 Figure 2.11

Figure 3 . 1 :

 31 Figure 3.1: When an electromagnetic wave interacts with a metallic nanoparticle, the conduction electrons are free to oscillate in the electric field. When the incoming wave has the same frequency as the resonant frequency of the electron cloud, we observe a maximum in the absorption spectrum, called surface plasmon (Fig.3.2)

Figure 3 . 2 :

 32 Figure 3.2:The absorption spectrum of a sphere is independent of the incident angle between the incoming radiation and the particle due to the isotropic shape of the particle. When light interacts

Fig. 3 .

 3 Fig.3.3 shows the results obtained by the three techniques, with an estimate of the width of the distribution, where possible. TEM always gives slightly bigger particles compared to the SAXS fits, but the two are in good agreement. UV-Visible spectroscopy shows a shift in tendency, underestimating the size in the initial growth steps, and overestimating the size for the last steps of the synthesis. Overall, the three techniques give comparable results, with UV-Visible spectroscopy showing the most discrepancy compared to the other two.

Figure 3 . 3 :

 33 Figure 3.3: Comparison between the average radius of the nanoparticles in solution found using SAXS (blue), UV-Visible spectroscopy (red ) and TEM (green). All three techniques are in good agreement, with UV-Visible spectroscopy being the one which varies the most with respect to the other two.

100 mL of a 0 .

 0 254 µm aqueous solution of HAuCl 4 in a round bottom flask are placed to heat at reflux with vortex stirring. After 10 min, a hot (70 • C) solution of trisodium citrate in water (34 mm) is rapidly injected in the flask. The solution is kept at reflux for 30 min. During this time, the solution changes from its original pale yellow to a pale blue, indicating the nucleation of gold clusters, and finally to a bright red. The solution is then cooled down to room temperature and stored in a dark and cool environment. The 17 nm particles are then used as seeds for the preparation of the 44 nm colloids. 100 mL of 0.254 µm aqueous solution of HAuCl 4 are placed in a round bottom flask and brought to boiling while stirring vigorously. 4 mL of the gold seed solution are filtered using a 0.45 µm filter and are subsequently injected in the boiling solution, followed by 1 mL of 34 mmol dm -3 trisodium citrate aqueous solution. The solution is kept at boiling for 30 min and then cooled down to room temperature. The dark red colloidal solution is stored in a sealed glass container in the fridge.

3. 6

 6 Multi-step synthesis of 44 nm Au nanoparticles3.6.1 Experimental methodFollowing the improvements found on the Turkevich procedure, Bastus et al published in 2011 a reaction protocol which integrates the two improvements presented in section 3.3.2. This new procedure produces gold nanoparticles with a low polydispersity and highly spherical in shape, along with a higher concentration of the colloids. The synthesis starts with the preparation of gold seeds, by injecting 1 mL of 25 mm HAuCl 4 aqueous solution in 150 mL of boiling water with sodium citrate (2.2 mm). The solution rapidly turns blue and then pink, because of the acetonedicarboxylic acid molecules already present in solution when the gold salt is injected; the induction time is very short. Once the gold salt has finished reacting (∼10 min), the flask contains a solution of ∼18 nm sized gold spheres.The temperature of the heating mantel is then lowered to 90 • C in order to start growing the seeds. Once the flask reaches the set temperature, 1 mL of 25 mm gold salt precursor solution is injected into the solution and allowed to react for 30 min. The procedure is repeated until the particles have reached the desired size. After every third injection though, 55 mL of the nanoparticle solution are removed and replaced with the same amount of 2.2 mm sodium citrate in distilled water. The nanoparticle growth is followed by UV-Visible spectroscopy and the reaction is stopped when the nanoparticles reach the desired size of ∼44 nm.

Figure 3 . 4 :

 34 Figure 3.4: UV-Visible absorption spectra for both syntheses. The spectra of the particles prepared using the multi-step synthesis is shown both for the synthesis as is and after dilution to obtain the same concentration as the two-step synthesis. The peak of the multi step synthesis is slightly shifted compared to the two step, indicating slightly smaller particles. The peak of the tow step synthesis is also wider. This qualitatively indicates a more polydisperse population

Figure 3 . 5 :

 35 Figure 3.5: TEM images of nanoparticles prepared using both synthesis procedures. (A) Au nanoparticles produced using the two-step procedure proposed by Chen et al. as the starting point for the syntheses of heterodimers. Most of the nanoparticles are elongated, with a few bigger particles. (B) Au nanoparticles prepared following the procedure proposed by Bastús in his paper on the controlled growth of Au colloids. While some irregular particles are present they are all for the most part round and of similar size.

  .5B)). It is possible to see that the first procedure, proposed by Chen et al., results in more oval particles, many almost rectangular or triangular, with several larger particles. The second procedure, proposed by Bastús et al., on the other hand, results in more regular particles.

Figure 3 . 6 :

 36 Figure 3.6: Histogram comparing the eccentricity of the particles produced using the two syntheses.The graph shows that the multi-step synthesis does produce more circular particles, with a narrower distribution.

Figure 4 . 1 :

 41 Figure 4.1:A) The shadow effect from physical deposition techniques can be used to produce heterodimers. A similar approach is to embed the particles in a wax substrate or at the interface of emulsions (B and C). More chemical oriented techniques include using both a lattice mismatch (D), or epitaxial growth (E). Different ligands can also be used, and is chosen correctly will segregate on the surface (F).

Fig. 4 .

 4 1A)). This was shown by evaporating

  like Au -Fe 3 O 4 , Au -Ge and Ag -Se[START_REF] Read | Au-Ge and Ag-Ge Heterodimers with Tunable Domain Sizes: A Supersaturation-Precipitation Route to Colloidal Hybrid Nanoparticles[END_REF][START_REF] Yu | Dumbbell-like Bifunctional Au-Fe 3 O 4 Nanoparticles[END_REF][START_REF] Gao | Controlled Growth of Se Nanoparticles on Ag Nanoparticles in Different Ratios[END_REF] (Fig.Fig. 4.1E)). Incompatibility between ligands can also be used as a means of obtains a division in the surface properties. It has been shown that when molecules with little affinity for each other, are placed on a nanoparticle, they tend to segregate, forming patchy particles or heterodimers[START_REF] Vilain | Study of metal nanoparticles stabilised by mixed ligand shell: a striking blue shift of the surface-plasmon band evidencing the formation of Janus nanoparticles[END_REF][START_REF] Robert | Self-assembly of amphiphilic gold nanoparticles decorated with a mixed shell of oligo(p-phenylene vinylene)s and ethyleneoxide ligands[END_REF] (Fig.4.1F)). This last approach is the one used by Chen et al. as a starting point for the synthesis of the Au -SiO 2 particles used in this manuscript[START_REF] Chen | Scalable Routes to Janus Au-SiO 2 and Ternary Ag-Au-SiO 2 Nanoparticles[END_REF].

4

 4

. 3 .

 3 According to their interpretation of the phenomena the segregation is due to the different hydrophilicity of the two ligands, which brings to a near-equilibrium condition of separation of the molecules on

Figure 4 . 2 :

 42 Figure 4.2: Two different ligands are bound on the surface of the gold nanoparticle. The different nature of the two molecule eventually leads to segregation and the formation of two hemispheres.

  are the driving forces of this process. As mentioned in the 2008 paper by Chen et al.[START_REF] Chen | Controlled Assembly of Eccentrically Encapsulated Gold Nanoparticles[END_REF], this kind of behaviour has been suggested before, and experiments have shown that when ligands exhibiting different characteristics are placed on the same surface, they tend to form domains[START_REF] Vilain | Study of metal nanoparticles stabilised by mixed ligand shell: a striking blue shift of the surface-plasmon band evidencing the formation of Janus nanoparticles[END_REF][START_REF] Gentilini | Formation of Patches on 3D SAMs Driven by Thiols with Immiscible Chains Observed by ESR Spectroscopy[END_REF][START_REF] Stranick | Phase Separation of Mixed-Composition Self-Assembled Monolayers into Nanometer Scale Molecular Domains[END_REF][START_REF] Harkness | Nanoscale Phase Segregation of Mixed Thiolates on Gold Nanoparticles[END_REF]. For the most part though, the size of the domains found in experiments are limited in size to a few nanometres[START_REF] Chen | Scalable Routes to Janus Au-SiO 2 and Ternary Ag-Au-SiO 2 Nanoparticles[END_REF][START_REF] Stranick | Phase Separation of Mixed-Composition Self-Assembled Monolayers into Nanometer Scale Molecular Domains[END_REF][START_REF] Stewart | Controlling Assembly of Mixed Thiol Monolayers on Silver Nanoparticles to Tune Their Surface Properties[END_REF][START_REF] Stranick | Nanometer-scale phase separation in mixed composition self-assembled monolayers[END_REF][START_REF] Tamada | Surface Phase Behavior of n -Alkanethiol Self-Assembled Monolayers Adsorbed on Au(111): An Atomic Force Microscope Study[END_REF], while the gold nanoparticles used in the experiments have a size of several tens of nanometers. It is difficult then to explain how, in this case, the segregation seems to produce domains which are about

Figure 4 . 3 :

 43 Figure 4.3: TEM images showing the effect of varying the ratio between the two competing ligands. A)B)C) are taken from the original paper published by Chen in which the separation of the ligands on the surface of the gold nanoparticles is presented [103]. A) shows the TEM image of nanoparticles prepared using only the hydrophilic ligand and the diblock co-polymer. B) and C)show the variation in the system as different amounts of the hydrophilic ligand are added. The TEM images D),E) and F) are a parallel of the previous three but taken from the subsequent article which shows the growth of silica on the Au colloids. In both systems, it is clear that the addition of the second ligand induces the formation of a more eccentric structure.

2. 5 OH

 5 mL of iso-propanol under vigorous stirring, making sure to add the particles slowly, so that they maintain their colloidal stability. Two stock solutions containing the ligands are previously prepared by dissolving 4-mercaptophenylacetic acid(4-MPAA) in ethanol (5 mm) and poly(acrylic acid) in millipore water (0.645 mm). The solutions are then stored by sealing with parafilm and placing in the fridge. Once the nanoparticles are well dispersed in iso-propanol, 20 µL of each of the ligand solutions are added to the nanoparticles. The nanoparticles and ligands are then left under stirring for ∼30 min to allow the ligands to assemble on the gold surface (second step of the scheme in Fig.4.2). After the assembly, 600 µL of 8.9 µm tetraethyl orthosilicate (TEOS) in water are added, followed by the injection of 90 µL of ammonium hydroxide solution (23%) in the solution. The reaction vial is then capped and left to react overnight at room temperature under vigorous stirring. The TEOS in basic environment reacts with water and undergoes a series of hydrolysis reactions which lead to the formation of intermediates of the form Si(OC 2 H 5 ) 4 -X (OH) X . These intermediates then further react with each other through a condensation reaction which creates the -O-bridges between the Si atoms and either ethanol or water as by-product.The particular environment and ligand distribution on the surface of the gold nanoparticles direct the nucleation of the TEOS on the surface of the gold colloids protected by the MPAA. The resulting particles are dumbbell particles of gold and silica (Fig.4.2 last image).

Figure 4 . 4 :

 44 Figure 4.4: Absorption spectra of the various steps for the preparation of Au -SiO 2 heterodimers. The inset shows the exact position of the plasmon peaks at every step.

Figure 4 . 5 :

 45 Figure 4.5: SAXS patterns for both the pure Au nanoparticles and for the Au -SiO 2 heterodimers.The growth of the silica on half of the gold surface did not influence the shape of the curve, apart from a slight increase in scattering at very small q values. This change can be attributed to an increased attractive interaction following the change of solvent (iso-propanol / water mixture) and the new ligand (PAA).

Figure 4 . 6 :

 46 Figure 4.6: Synthesis of Au-Silica heterodimers following the procedure proposed by Chen's paper [17]. The bar on both images is 100 nm

4. 5 . 2

 52 Effects of the amount of TEOS on the systemBecause of the large excess of silica in the final product, in some of the reactions we explored the effects of varying the total amount of silica precursor -namely TEOS -on the end result. Five different reactions were prepared using the original amount of TEOS, as well as 7 / 8 , 3 / 4 , 1 / 2 , 1 / 4 of the original amount. The result of the reactions was studied by counting the number of janus, gold, and silica nanoparticles seen in TEM images. Multiple images were analysed and the results are summarized in Fig.4.7F). Fig.4.7A)-E) are sample images of each of the syntheses with the different markers overlaid on the image. The three populations counted were: the janus nanoparticles, the silica nanoparticles and the gold nanoparticles, marked in red, blue and green respectively. As can be seen from the bar graph (Fig.4.7F)), which presents a summary of all the analysed images, as the amount of TEOS used in the reaction decreases, the number of bare gold nanoparticles increases noticeably. At the same time both the number of Au-SiO 2 heterodimers and of the silica nanoparticles tends to fall as the amount of silica precursor is decreased. The procedure for the synthesis of the heterodimers is based on the Stöber synthesis, used for the production

Figure 4 . 7 :

 47 Figure 4.7: Analysis done on the different syntheses using varying amounts of silica precursor (TEOS):(A) using the original amount of TEOS, (B) 7 / 8 of the original amount of TEOS,(C) 3 / 4 of the original amount of TEOS, (D) 1 / 2 of the original amount of TEOS, (E) 1 / 4 of the original amount of TEOS. All the scale bars in the images are 200 nm. (F) Shows the relative concentration of gold, silica and heterodimer.

  with the previous analysis, Fig.4.8A)-D) are sample TEM images of the different reactions, while Fig.4.8E) is a bar graph which summarizes the analyses done on all of the collected images. The graph shows that there is in fact a correlation between the amount of free gold in solution and the resulting ratio of janus-gold-silica particles at the end of the reaction. As the relative concentration of gold nanoparticles increases from 1 to 1.5 and finally 2, the ratio of janus nanoparticles increases from around 0.4 to over 0.6. At the same time, the amount of silica nanoparticles which nucleated homogeneously decreases from more than 50% to less than 30%. It is also interesting to note that the number of gold nanoparticles remains fairly constant throughout, indicating that the reason for the homogeneous nucleation of the silica can be attributed to the low availability of free gold surface on which to grow. If the amount of gold nanoparticles is further increased (2.5 times the original concentration), the number of bare gold nanoparticles increases again, at the cost of the janus nanoparticles. Fig.4.9 presents two more TEM images of a synthesis prepared using twice the amount of gold nanoparticles as the original synthesis proposed by Chen et al.. Fig.4.9A) also shows as inset a detail of one of the janus nanoparticles.

Figure 4 . 8 :

 48 Figure 4.8: Analysis done on the different synthesis using varying concentration of gold nanoparticles:(A) using the gold nanoparticle concentration indicated in Chen's 2010 paper. (B) 50% more nanoparticles were used compared to the original.(C) double the concentration was used in this case. (D) 150% of the original amount of nanoparticle. All the scale bars in the images are 200 nm. (E) shows the histogram with the relative concentration of each of the three populations: gold, silica and heterodimers.

Figure 4 . 9 :

 49 Figure 4.9: TEM images showing the result of a reaction prepared using twice the concentration of gold nanoparticles compared to the original synthesis. Th inset in figure A) shows a detail of one of the janus particles .

Figure 4 . 10 :

 410 Figure 4.10: Summary of the six reactions prepared in parallel to study the reproducibility of the system. With the exception of the first reaction, which shows signs of failure, the other five indicate a balance between the number of heterodimers and silica nanoparticles which are formed in the synthesis

Figure 5 . 1 :

 51 Figure 5.1: Two examples of nanoparticles which formed organized structures during the drying on TEM grids. (A) shows the nanoparticles forming a 2D hexagonal lattice along with the FFT of the image. (B) is a TEM image of two 2D lattices stacked on top of each other, along with the corresponding FFT. The scale bar in both TEM images is 50 nm.

Figure 5 . 2 :

 52 Figure 5.2: Schematic reppresentation of the theoretical self-assembly process. An alkanethiol is added to the solution of heterodimers. Because of its higher affinity to gold, the alkanethiol substitutes the PAA which previously stabilized the gold moiety. After the ligand exchange, the hydrophobic effect brings several heterodimers together, forming a micelle like structure.

Figure 5 . 3 :

 53 Figure 5.3: Schematic reppresentation of the formation of the bonding and antibonding modes which appear as two plasmonic particles come closer together.

Figure 5 . 4 :

 54 Figure 5.4: Spectroscopic evolution of a Au-SiO 2 solution after the addition of 50 µL Toluene solution of dodecanethiol (32.25 mm). The evolution was followed over a period of 80 h. While the intensity of the coupling plasmon peak increases, the total absorption at 450 nmdecreases, indicating that some particles have in fact sedimented.

Figure 5 . 5 :

 55 Figure 5.5: A) Spectroscopic evolution of a Au-SiO 2 solution after the addition of a toluene solution of dodecanethiol. All the curves have been normalized at 450 nm in order to account for the sedimentation effect on the shape of the spectra. The inset shows a zoomed area of the graph where most of the curves intersect, called an isosbestic point. B) The shift in the coupling plasmon from its appearance (at time t=20 h). The coupling plasmon starts close to the original peak

  Value Decomposition (SVD) is a mathematical operation used to decompose a set of m points in n dimensions, into their basic components. The result of applying the SVD to a given matrix M (m × n), are three matrices U (m × m), Σ (m × n) and V (n × n) such that: M = UΣV T .(5.1)

Fig. 5 .

 5 Fig.5.6A) is originally 1 980 × 3 140 pixels, for a total of 6 217 200 pixels. Once the SVD is applied to the image, the three matrices UΣV are produced, with sizes 1 980 × 1 980, 1 980 × 3 140 and 3 140 × 3 140 respectively, though Σ only contains information on the diagonal elements. The total amount of information after the decomposition has increased to 13 781 980 elements (counting only the diagonal elements of Σ, and not the whole matrix).If we analyse the values of the diagonal elements of Σ, we can see that the importance of the components rapidly decreases, indicating that the first few components contain most of the information on the image and that the rest only add minor adjustments. It is then possible to try and reconstruct the image using increasing numbers of components; the operation is shown in Fig.5.6. For each image, given that p components are used, the resulting total size of the image is given by S = 1 980p + 3 140p + p. So, for example, the image reconstructed using only one component, will be obtained from 5121 values, while for 10 components, 51 210 data points will be needed, and so on. While taking p = 1 is obviously not sufficient to reconstruct the image (Fig.5.6B)), for p = 10 the basic shape of the image is fairly clear (Fig.5.6C)), and by the time 50 components are used, almost all the important details are reproduced in the reconstructed image (Fig.5.6C)). This means that this image, initially composed of 6 217 200 points can be adequately reproduced using only 256 050 values, which is roughly equal to 4% of the information.

Figure 5 . 6 :

 56 Figure 5.6: A) Original image with a resolution of 1 980 × 3 140 pixels. B) The image reconstructed from the SVD matrices using only the first component, the resolution is the same, but the number of data points stored is only 5121. The reduction in quality can clearly be seen by the loss of shapes in the image. C)The reconstructed image using 10 components. The number of values stored has increased by a factor 10 and now the subject of the image can be clearly discerned. The details are still not clear and the image is blurred along horizontal and vertical lines. D) The image reconstructed using 50 components is very clear, with no immediate difference from the original. In order to reconstruct the image, 256 050 data points had to be stored, which is only about 4% of the original image. E) If more components are used, in this case 60, no real increase in the quality of the reconstruction can be found without closely looking at the picture.

Figure 5 . 7 :

 57 Figure 5.7: A)A set of blue data points placed along the line y = x, disturbed by Gaussian noise applied to both the x and y coordinates. The red dots on the axes are the projections of the points and show how dispersed the points are along both directions. B) The red and green dotted lines added to the Cartesian plot are the new axes found by applying the SVD to the data points. The red line is the direction of highest dispersion while the green orthogonal line is the direction of least dispersion. The red dots show the projection of the data on the new Cartesian system. C) If the data is reconstructed using only one component (effectively only using the information from the red axis), the general trend of the data is kept.

Figure 5 . 8 :

 58 Figure 5.8:The top row shows the three components obtained after transforming the SVD while the bottom row shows the corresponding coefficients, as a function of time. The components are placed in the order in which they appear in the spectra. The red one is the predominant signal for the first 10 h, after which the blue spectrum becomes the most important one. Finally, towards the end of the reaction, the green spectrum is the highest of the three.

  stages: an initial stage during which the only species present are the monomers and the dimers (for the first 10 h), a final stage during which all the monomers have disappeared and the only species in solution are the dimers and the multimers (after more than 40 h), and an intermediate stage, in which all three species are present at the same time. The earliest and latest stages of the reaction are then particular because only two species exist. Then, two isosbestic points should be visible, one at the beginning of the observations and one towards the end. Isosbestic points are points in a time resolved spectroscopy measurements where the absorption intensity does not vary. They appear when a reaction consists of a specie A converting into B, both of which have a unique optical response. During the reaction the absorption at the wavelength at which the two spectra meet does not change in intensity as the optical response of the solution at that wavelength does not vary. This can be seen in Fig.5.9A) and Fig.5.9B) where the two isosbestic points are identified. The

Figure 5 . 9 :

 59 Figure 5.9: A) Top: Detail of the spectrum evolution after the addition of the thiol over the first 28 hours. Bottom: The absorption of the sample at 566 nm over the whole measurement shows that during the first few hours, the absorption stayed constant, before slowly decreasing. B)Top: Detail of the absorption spectrum evolution starting 40 h after the addition of the thiol. Bottom:

Figure 5 . 11 :

 511 Figure 5.11: Structure factor of the heterodimer assemblies obtained as the ratio between the two scattering patterns showed in Fig.5.10.

Figure 5 .

 5 Figure 5.12: A) An example of 2D isospectral distributions of points. For a given the set of distances between the particles, it is possible to construct both distributions. B) Same as A) but the particles are now placed in a three dimensional space.

Figure 5 . 13 :

 513 Figure 5.13: Example of the sequential fitting of the experimental structure factor to possible configurations. The structure factor of a single sphere is omitted because it is S(q) = 1.

  absorbance kinetics. It can, nonetheless, be used to confirm the results obtained through the fitting of the structure factor by comparing the calculated absorption spectrum of the simulated configuration to the experimental spectrum. The toolbox used for simulating the spectrum of an arbitrary assembly of Au nanoparticles is the Metallic Nano-Particle Boundary Element Method (MNPBEM)[START_REF] Hohenester | MNPBEM -A Matlab toolbox for the simulation of plasmonic nanoparticles[END_REF], which is implemented in Matlab. As the name states, it uses a boundary element method to solve Maxwell's equations for metallic nanoparticles in dielectric media. It manages both the construction of the system as well as the resolution of the problem. Within the simulation, the dielectric constant of the environment (water/iso-propanol mixture) is considered constant at all wavelengths and set to 1.375 2 . This value is obtained from a paper by Thompson et al. on the densities and refractive indices of various water/alcohol mixtures[START_REF] Chu | Densities and Refractive Indices of Alcohol-Water Solutions of n-Propyl, Isopropyl, and Methyl Alcohols[END_REF]. The dielectric constant for the gold nanoparticles is, on the other hand, a function of the excitation frequency. The exact value is calculated by spline interpolation of a series of data points. The table containing

Figure 5 . 14 :

 514 Figure 5.14: Comparison between the experimental absorption spectrum of Au nanoparticles and the simulated spectrum of a set of Au nanoparticles obtained by fitting the structure factor.

Figure 5 . 15 :

 515 Figure 5.15: The three graphs show the evolution of the peak position and intensity of the coupling plasmon as a function of time. Three different thiols are represented: A) hexadecanethiol (16C), B) dodecanethiol (12C) and C) decanethiol (10C). The upper curve in all three graphs is the position of the peak as a function of time while the lower curve is the ratio between the intensity of the coupling plasmon and the surface plasmon of a single nanoparticle (at t = 0).

Figure 5 . 16 :

 516 Figure 5.16: The average surface-to-surface distance between first neighbours as a function of the number of atoms in the carbon chain. The slope of the fitted linear function is 0.11 nm/atm

.3) 117 Figure 6 . 1 :

 11761 Figure 6.1: Qualitative representation of the density of states for systems with 3,2,1 and 0 dimensions. E g is the energy gap of the semi-conductor.

Figure 6 . 2 :

 62 Figure 6.2: A) Photo of sample of CdSe quantum dots with sizes ranging from 2 nm to 5 nm. The solutions are illuminated by UV light to show the fluorescence of the particles. B) Typical emission spectra of quantum dots in the same range of sizes.

Figure 6 . 3 :

 63 Figure 6.3: A) Side view of the four possible thicknesses which can be obtained by using the synthesis [23]. B) and C) show two different views of a 3ML platelet.

Figure 6 . 4 :

 64 Figure 6.4: Light absorption spectra for platelets of 2, 3, 4, and 5 ML. As the thickness of the platelet grows the peaks shift towards longer wavelengths.

Figure 6 . 5 :

 65 Figure 6.5: The absorption spectrum of the CdSe platelets synthesized using the one-pot, heat-ip reaction. The strongest peak at 462 nm indicates that the platelets are 3ML thick, the slightly

Figure 6 . 6 :

 66 Figure 6.6: Three TEM images of the platelets, which show how the platelets are twisted. Each image shows a different deformation of the platelet, with a small scheme of the deformation in the corner for clarity.

Figure 6 . 7 :

 67 Figure 6.7: Two TEM images of the rolled platelets with some of the measured distances indicated.

Figure 6 . 8 :

 68 Figure 6.8: Photograph of the setup used for the in-situ experiments done at ESRF.

Figure 6 . 9 :

 69 Figure 6.9: Evolution of the sample SAXS and WAXS during the preparation of CdSe platelets. For both graphs, only some of the patterns are shown, and they are shifted along the y axis for clarity.

Figure 6 . 10 :

 610 Figure 6.10: SAXS and WAXS signal before the subtraction of the background

Figure 6 . 12 :

 612 Figure 6.12: 3D rendering of a platelet to show the parameters used when referring to a curved platelet.

Figure 6 . 13 :

 613 Figure 6.13: The effects of changing the three available parameters (width, length and curvature radius) on the scattering pattern of the platelets are shown in A), B) and C) respectively. The standard values used for the parameters which were not varied were: a length of 60 nm, a width of 60 nm and a curvature radius of 15 nm.

Figure 6 .

 6 Figure 6.14: A),B) the (220) plane of the CdSe platelets shown from two different points of view. C) The deformation of th peak originating from the (220) peak as the platelet is bent around cylinders with smaller radii.

Figure 6 . 15 :

 615 Figure 6.15: Visual represantation of the Porod invariant (A) and the Guinier approximation (B). The dotted lines in A) show how the signal was extrapolated to bigger, and smaller, q values,

6. 5 .

 5 DIFFERENT APPROACHES FOR THE ANALYSIS OF THE SCATTERING DATA139case the relationship is: R = g

Figure 6 . 16 :

 616 Figure 6.16: Comparison between the experimental and fitted curves at various instances during the reaction. The positions of the oscillations fits well with platelets bent to form a cylinder with a radius of 12.9 nm. The theoretical curve, though, does not follow the experimental one for lower values of q.

Figure 6 . 17 :

 617 Figure 6.17: Evolution of the small-angle scattering as the height of the platelet is increased. As the platelet grows, the plateau shifts to smaller q values but the curve at larger values remains the same. Because of this, the discrepancy between the experimental an theoretical data cannot be attributed solely to an increase in size of the platelets.

Figure 6 . 18 :

 618 Figure 6.18: Temporal evolution of the threeproperties obtained from studyin gthe Guinier and Porod's invariant. Left: The length of the platelet, obtained from the gyration radius. The plot stops before the end of the measurements due ot the fact that the conditions for calculating the Guinier stop being true. Center : The volume fraction obtained from Porod's invariant. Here the data is availabel untill the end of the measurements. Right: The particle concentration of the platelets, as this value is obtained from the two previous ones it can only be calculated where both exist, and therefore is limited by the gyration radius measurement.

Figure 6 .

 6 Figure 6.19: A) Comparisone between the experimental (220) peak, the simulated peak of a flat CdSe platelet, and the peak resulting from a population of platelets bend around cylinders with varying radii between 12.5 nm and 13.5 nm. B) Effect of expanding the lattice of the platelets on the position of the (220) peak. As the lattice gets larger, the peak is shifted to smaller q values.

Figure 6 .

 6 Figure 6.20: A) 220 WAXS peak at different moments during the reaction, along with the fitted curve superimposed in black. B) Three graphs showing the different values which can be obtained from fitting the WAXS peak. Top: The area of the peak, which is directly related to the amount of crystalline material in solution. Middle: The expansion of the lattice, calculated as a percentage from the shift of the peak compared to tabulated values. Bottom:Tthe average size of the crystallites obtained from Scherrer's formula usign the FWHM of the fitted sitribution.

Figure 6 . 21 :

 621 Figure 6.21: Side by side comparison of the Porod and Guinier analysis for the four samples heated to different temperatures. The top row shows the average length of the platelets calculated from the gyration radius, as described in the previous text. The middle row contains the graphs showing the volume fraction as a function of time, and the curves in the bottom indicate the concentration of platelets in solution.

6. 8 . 1 Figure 6 .

 816 Figure 6.21 presents the three quantities obtainable from the Guinier regime and Porod invariant as a function of time for all four experiments. It is important to note that the

  comparison of the evolution of the size of the platelets at different reaction temperatures shows the difference in speed of the reaction. At 180 • C the platelets keep growing until the very end of the measurement, indicating that the reaction is still proceeding. As the reaction temperature is raised, the growth of the platelets is faster. However, the final particles appear to have a similar final size. A study of the volume fraction of CdSe in solution confirms that the reaction at the lowest temperature proceeds at a slower rate, barely finishing to evolve before the end of the measurement. As the temperature is raised however, the curve appears to be shifted to the left, with the initial growth becoming faster, and a stable volume fraction being reached earlier. At 200 • C the rapid increase in crystalline volume is curbed between 200 s and 600 s, but the volume fraction keeps increasing until the end of the measurements. At 220 • C and 240 • C however, the volume fraction behaves differently. There are two phases clearly distinguishable: a first one governed by a rapid increase in volume fraction, followed by a second in which the amount of CdSe in solution does not increase. This second stable phase is reached after 500 s when the solution is kept at 200 • C, but appears after only 300 s when the temperature is raised to 240 • C. Overall the study of the volume fraction shows a dependence of the growth of the crystals on the temperature of the reaction An interesting feature visible in the curve at 240 • C, is the sudden dip in the volume fraction at around 500 s. The drop is very rapid, and is then quickly recovered, though the volume fraction remains slightly below the original maximum. Under closer inspection, the volume fraction of the sample at 220 • C appears to have a similar behaviour towards the very end.

Figure 6 . 22 :

 622 Figure 6.22: Example of the fitting of the (220) WAXS peak using a pseudo-Voigt distribution. The curves whown here are from the sample prepared at 220 • C

Fig. 6 . 23 .

 623 Fig.6.23. As for the Porod and Guinier analyses, the four reaction temperatures are shown in the four columns, and the x -axis in all graphs is log-scaled. The top-most row shows

Figure 6 . 23 :

 623 Figure 6.23: WAXS analysis done on all four samples. Each column shows the three graphs (the peak area, the distortion and the size of the crystallites) for the reaction done at a different temperatures.

Fig. 7 .

 7 Fig.7.1 shows how the absorption spectrum of the platelets changes after the growth of the the Au beads. Fig.7.1A) is the original spectra of the platelets before the reaction.

Figure 7 . 1 :

 71 Figure 7.1: A) UV-Visible absorption spectrum of 5ML platelets with the main absorption peak at 552 nm. B) UV-Visible spectra of four different samples of CdSe -Au heterostructures, prepared using growing amounts of Au growth solution. The photos show the solution for the respective systems.

7. 3 TEMFig. 7 .

 37 Fig.7.2B). The CdSe -Au heterodimers are even easier to image due to the presence of the gold beads. The dark spheres facilitate the setup of the instrument and the identification of the particles. Fig.7.3 shows 4 images obtained using different amounts of gold precursor. Fig.7.3A) was taken from a grid prepared with the sample with the least gold precursor (100 µL). The beads are very small and they are situated primarily on the corners of the boards. Furthermore, not all the corners have beads. This is visible in a few of the platelets in the image where only three of the corners have a gold sphere attached. By doubling the amount of gold precursor solution (Fig.7.3B), the gold spheres increase in size but the overall growth of the gold is similar. The beads tend to grow on the corners of the platelets, and most of the boards have all four corners covered. As the amount of gold salt solution is further increased (C) 300 µL and (D)400 µL), the spheres become increasingly larger.

Figure 7 . 2 :

 72 Figure 7.2: TEM images of 5ML platelets as synthesised. When dropcasted and dried rapidly, the platelets tend to lay flat on the TEM grid as seen in A). Conversley, if the sample is older or the solution is dried slowly, small stacks will tend to form. These are visible in electron microscopy as a series of dark, parallel lines, as shown in B). The scale bar in both images are 50 nm.

Figure 7 . 3 :

 73 Figure 7.3: Electron microscopy images of four different CdSe-Au samples prepared using varying amounts of gold precursor solution. A) 100 µL of gold solution. The gold beads are very small. B) with 200 µL, as a result the beads are larger.C) and D) were prepared with 300 µL and 400 µL respectively, and present larger spheres. The spheres also appear more oval, and in some cases join two platelets together. The scale bars in all images are 50 nm.

Figure 7 . 4 :

 74 Figure 7.4: Size distribution for the radius of the Au beads in the four systems presented in Fig.7.3.

Figure 7 . 5 :

 75 Figure 7.5: Schematic representation of the three imaging modes discussed in the text along with the resulting image. A)Bright field microscopy. The image is similar to that obtained by traditional HR-TEM techniques. B) Medium-angle annular dark-field. The bright spots are from electrons which were scattered at medium angles through Bragg scattering. C) High-angle annular dark-field.The signal arises from incoherently scattered electrons.

Figure 7 . 6 :

 76 Figure 7.6: Procedure used for finding the orientation of the Au (top) and CdSe (bottom) crystals. The columns show in order from left to right: the original image, the FFT before and after applying the mask, the reconstructed image starting from the masked FFT, and the profile along the red line.

Figure 7 . 7 :

 77 Figure 7.7: Three different HR-STEM images showing both theAu and the CdSe crystalline structures. In all three examples one of the planes for each material is indicated by two red lines, along with the indices and the measured reticular spacing.

Figure A. 1 :

 1 Figure A.1: A) A flat platelet placed in a cartesian coordinate system, resting on the x -y plane with its length along the z axis. B) Representation of the platelet being bent around an imaginary cylinder, here shown in red.

Figure A. 2 :

 2 Figure A.2:A) The platelet is placed in the Cartesian space. As the bending will take place along the z axis we can simplify hte system by taking a single slice of the platelet. B) The single slice of the platelet as seen on the x-y plane. C) The system is further simplified by collapsing all the atoms on a single line. The circumference along which the platelet is bent is placed tangential to the atoms. D) The atoms are placed along the circumference based on their distance from the origin (0,0). E) In order to correctly reconstruct the slice of the platelet, the atoms have to be shifted radially based on their original layer. F) The fully reconstructed slice, bent around a circle.

Figure A. 3 :

 3 Figure A.3: A schematic representation of how a single row of atoms can be bent along a circle.

  Fig.A.5, which shows the scattering curves at wide-angles for the three different regimes, alongside the peak for a flat platelet. By comparing the results obtained by bending the platelet using

Figure A. 4 :

 4 Figure A.4: Three possible bending regimes can be considered. The red area shows where the bonds are compressed while the blue area indicates where the bonds are stretched. The dashed arc shows where the circle is placed with respect to the platelet.

Figure A. 5 :

 5 Figure A.5: Comparison of the WAXS patterns for the three different bending procedures. In black the peak obtained by scattering by a flat platelet. As predicted, the bending in a stretching regime produces a left-shifted peak, while the one in compression give a right-shifted one. Finally, when both compressing and stretching the platelet, the position of the peak does not change and is only affected by the new distances, decreasing in intensity and broadening.

Figure A. 6 :

 6 Figure A.6: Thee possible ways in which the twist angle can be made to depend on the z coordinate: linear, localized, and exponential.

  Mots clefs : Hétérodimères, Auto-assemblage, SAXS,Nanoplaquettes de CdSe,Hétérostructures de CdSe-Au Résumé : L'expression "nanoparticules Janus" est utilisée pour se référer aux nanoparticules colloïdales faites de deux moitiés qui présent deux propriétés physiques et/ou chimiques différentes. Au cours des dernières années, plusieurs études théoriques ont été publiées sur les possibilités d'auto-assemblage offertes par ces particules (en particulier par Sciortino, F. et al.), mais peu de travail expérimental a été fait sur ce sujet. Les études théoriques suggèrent que beaucoup de comportements intéressants apparaissent quand la taille des particules s'approche de la portèe d'interaction des forces en jeu (des dizaines de nanomètres dans le cas des force de Van der Waals et des forces hydrophobes). Dans ce manuscrit, nous montrons la formation d'aggrègats des hétérodimères de Au -SiO 2 d'une taille inférieure à 100 nm. L'auto-assemblage a été déclenché par un échange du ligand hydrophile sur la surface de l'or par un ligand hydrophobe induisant une interaction attractive. L'assemblage a été suivi par spectroscopie d'absorption résolue dans le temps et diffusion des rayons X aux petits angles. Nous avons constaté que les thiols les plus courts ont une période d'induction plus longue et forcent les particules à se rapprocher davantage, comparé à des thiols avec des chaînes plus longues. Nous étudions également un second système: des nanoplaquettes de CdSe. Celles-ci sont des objets quasi-2D en matériau semiconducteur avec des propriétés optiques uniques. Ces propriétés résultant de leur taille réduite dans une dimension. Du fait de leur nouveauté et de leur particularité, leur nucléation et le remarquable mécanisme de croissance de ces particules sont toujours étudiés. Ainsi nous avons suivi leur synthèse par SAXS et WAXS in situ, afin d'obtenir des informations en ce qui concerne ces deux tapes, et notamment d'étudier la déformation de certains de ces systèmes sous forme de feuillets enroulés de CdSe. Les nanoplaquettes de CdSe ont été aussi utilisés pour créer des structures hybrides CdSe -Au. La combinaison de ces deux matériaux a déjà montré des effets uniques, comme une meilleure efficacité catalytique et, combiné avec la dimension réduite et le contrôle des plaquettes, pourrait aboutir à des caractéristiques encore plus intéressantes. Nous proposons une méthode de synthèse qui aboutit à la formation de petites sphères d'or sur les coins des plaquettes. Nous montrons que la taille des sphères dépend de la quantité de précurseur utilisée, et des images de microscopie électronique à haute résolution mettent en évidence la structure cristalline des deux matériaux.

Table 2 . 3 :

 23 Summary of the fitting shown in Fig.2.9. The increase in radius rate is steady thoughout the whole reaction as the nanoparticle solution was continuously diluted in order to reduce the number of nanoparticles in solution. It is also important to note that even though the width of the distribution more than triples, the actual polydispersity of the nanoparticles decreases from 13.8%

	Sample	R(Å)	σ (Å)	Poly. (%)
	E1	20.67	3.67	17.77	Gaussian
	E2	27.60	2.18	7.89	Gaussian
	E3	31.13	2.04	6.55	Gaussian
	E4	35.27	1.95	5.52	Gaussian
	E5	38.87	2.66	6.84	Gaussian
	Table 2.2: Summary of the fitting of the PbSe nanoparticles shown in Fig.2.8. All the fitting was
	done using a normal distribution for all samples. The increase in size between successive samples,
	which is very clear in the experimental data, remains rather small (at most 7 Å); a difference which
	would be difficult to detect using other methods.

Table 2 . 4 :

 24 Summery of the fitting shown in Fig.2.10. The increase of radius in this case is les consistent due to the dilutions done every three steps. As with the synthesis of smaller nanoparticles the width of the distribution increases with every step, the actual polydispersity though decreases because of the increase in size.

	Sample	R(Å)	σ (Å)	Poly. (%)	Fit
	Au1	103.40	15.14	14.64	Schultz
	Au2	127.29	18.31	14.39	Schultz
	Au3	146.32	18.99	12.98	Schultz
	Au4	187.27	21.36	11.41	Schultz
	Au5	215.96	25.86	11.97	Schultz

Table 3 . 1 :

 31 Taken from Frens' paper in which he studies the effect of varying the ratio of the two precursors on the size of the resulting gold sols. The amount of gold salt is kept the same in all reactions but the volume of the reducing solution is varied from 1 mL to 160 µL.

	Sample Volume of Na 3 -Citrate	Particle Diameter (nm) Sol Color
		(mL)
	A	1.00	16.0	Orange
	B	0.75	24.5	Red
	C	0.50	41.0	Red
	D	0.30	71.5	Dark Red
	E	0.21	97.5	Violet
	F	0.16	147.0	Violet

Table 3 .

 3

		1.9	2.96±0.41 3.44±0.31
	Au2	2.7	3.70±0.50 4.45±0.49
	Au3	3.6	4.49±0.61 5.36±0.55
	Au4	4.5	5.37±0.70 6.34±0.61
	Au5	5.4	6.34±0.78 7.19±0.82
	Au6	6.6	7.42±0.89 8.93±0.84
	Au7	7.9	8.57±0.98 9.47±1.34
	Au8	9.4	9.87±1.09 11.2±1.43
	Au9	11.8	11.3±1.19	12.6±1.3
	Au10	12.6	12.9±1.36 14.7±1.42
	Au11	16.7	14.7±1.46 16.3±1.53

2: Summary of the comparison between the size results obtained from UV-Visible spectroscopy, SAXS and TEM. For these last two techniques, a standard deviation is also available. The different techniques give comparable results and as such will be used throughout the manuscript without the need to take multiple measurements for each synthesis.

  • C, it turns yellow, and at 208 • C, 150 mg of Cd -acetate are added to the solution. As stated in the previous chapter, this step is crucial as the acetate is what ensures the lateral growth of the platelets. The solution is then kept at 245 • C for 15 min, during which time the solution becomes a very deep orange.

Acknowledgements

The work presented this manuscript was done at the Laboratoire de Physique des Solides (LPS), and as such I would like to start off by thanking the lab for all the resources they put at my disposal which allowed me to work for theses three years. Many thanks also go to the administrative group, in particular Veronique Thieulart, Ciham Zaaboul, and Sabine Hoarau, who helped me navigate the treacherous seas of the administration.

A thank you to all the members of the jury who are here today to assist at my defence.

Thank you to Giuseppe Foffi for accepting the role of president of jury, and to Elodie Bourgeat-Lami for her time and presence here today as member of the jury. A particular

Appendix A

WAXS simulation

In the chapter dedicated to the study of the kinetics of the heat-up reaction for the synthesis of 3ML Cd -Se platelets, we introduced the possibility of creating a lattice and introducing distortions in it before simulating its scattering. The lattice was constructed using Crystal Maker [189], a software dedicated to the 3D rendering of crystalline structures.

One of the options it offers is the possibility to distort a structure by bending it around a cylinder of given radius. As described in the manual, this command is specifically designed for the creation of carbon nanotubes. This is highlighted by the fact that the default radius of curvature suggested by the software is such that the two ends of the sheet meet to close the cylinder (the actual radius can then be modified by the user, which is what we did to create the bent platelets). Consequently, we became interested as to how the software carried out the bending of the structures. In order to do so, we decided to implement an algorithm which would allow us to bend a flat platelet and save the deformed structure.

By importing such a structure in Debyer [190], it is then possible to compare the WAXS spectra of "our" structure with that of the commercial software.

A.1 Bending the platelets along a cylinder

The algorithm was written in Python, using Numpy as the main library for handling the import/export of the data, as well as the handling of the matrix containing the coordinates of the atoms. The coordinates of all the atoms in the constructed platelet were exported in a ".xyz" file, which is a comma-separated-value format with four columns: the first one contains the name of the atom while the other three the x, y and z coordinates. All of the By using x as the length of the arc, we can easily calculate the position along the circle of the atom. The x and y coordinates are then given by: and by how much, the bond length has been affected. We know that the initial distance between two neighbouring atoms (d) is 6.08 Å. Given how we built the system, we also know that the distance along the circle between the same two atoms has not been altered;

the linear distance on the other hand will have changed. The new bond distance is equal to the length of the chord (c) which subtends the angle θ, and is given by:

).

(A.4) by using both eq.(A.1) and eq.(A.4) we can find the ratio between the new and the starting bond length, c and d respectively:

The ratio is the cardinal sine of θ/2 which is 1 for θ/2 ≈ 0, so, given eq.(A.1), as long as the curvature radius is much larger than the distance between the atoms we can say that the bond length between neighbouring atoms is constant.

We have now bent all the atoms along the circumference but, in order to do so, we had to "compress" the structure so that we could deal with a one dimensional system. We now have to find a way to "expand" the system back to its original size. We therefore have to shift the atoms radially outwards as shown in Fig.A.2E). For this we introduce an effective radius r ef f = r + δ, where δ is the distance of each layer from the first Cd row.

The equations for the x and y coordinates then become:

The resulting platelet will have flat edges and the distance between neighbouring atoms on the first layer will be the same as that of a flat platelet; furthermore, the distance between layers will remain unchanged. However, the distance between atoms in the successive layers will inevitably be larger if we want to maintain a flat edge, as r is increased but θ is kept

A.2 Exploring different deformations

Once the basic algorithm for importing the matrix with the atomic positions in the platelets was setup, we decided to introduce new distortions into the platelet which had been inaccessible from Crystal Maker. In particular, we had seen in the TEM images platelets twisted around their midpoints. In order to introduce a twist, we need to use a new set of equations for the transformation: