Keywords: Diffusion, Dissolution, Laropal®A81, Neutron, Neutron reflectively, Polymer, Solubility, Solvents, Varnish

REMERCIEMENTS

Cette thèse a été réalisée au sein du groupe de recherche Large Scale Structures (LSS) de l'Institut Laue Langevin (ILL) de Grenoble et du Laboratoire Rhéologie et Procédés (LRP) de Grenoble. Ce projet doctoral a été porté par la collaboration étroite et le soutien sans faille de plusieurs acteurs du monde des sciences, de l'art et de mon entourage et je tiens particulièrement à leur exprimer ma gratitude à travers ces quelques écrits.

En premier lieu, j'adresse mes sincères remerciements à mon directeur de thèse, Yahya Rharbi et mes deux encadrants, Philipp Gutfreund et Bernard Cabane. Je vous remercie pour votre soutien, votre implication et la transmission du savoir nécessaire à l'élaboration de ce projet. Tout cela m'a été précieux et j'ai ainsi pu apprendre beaucoup sur les polymères, les gels et la réflectivité de neutron. Merci aussi pour ces nombreuses discussions scientifiques constructives et stimulantes au cours de nos réunions régulières ainsi que de votre patience indéfectible. Grâce à ces échanges, le projet a évolué efficacement en s'axant premièrement dans la construction et le développement des idées ; et dans un second temps, en explorant la compréhension, l'analyse et la discussion des résultats. Travailler avec vous a été un grand plaisir et je vous remercie de m'avoir transmis une part de vos passions scientifiques respectives. Bernard, je vous suis notamment très reconnaissante d'avoir toujours cru en moi et d'être toujours présent dans chaque étape de ma vie professionnelle scientifique, merci beaucoup. Et je me permets de rappeler que sans vous ce projet n'aurait pas vu le jour.

Je remercie sincèrement les rapporteurs et tous les membres de mon jury de l'honneur qu'ils font à ce projet ainsi qu'à moi-même de participer à la lecture de ces travaux et pour leurs présence à ma soutenance. Je remercie vivement Lay-Theng Lee et Carlos Marques d'avoir accepté de rapporter ce travail. Je remercie aussi Giovanna Fragneto et Debora Berti pour leur participation au jury de thèse. Merci à vous de m'avoir apporté vos expertises et d'avoir évalué mon travail.

Merci à Bruno Jean et Marco Maccarini d'avoir suivi le projet en tant que comité de thèse pour l'université, vos conseils ont permis de mieux aborder le travail de thèse et de bien redéfinir le rôle de chacun.

Merci à l'équipe du Large Scale Structures (LSS) et sa directrice Giovanna Fragneto pour leur accueil. J'ai beaucoup appris à votre contact quotidien. Une pensée particulière pour Yuri Gerelli qui en plus de ses conseils et de son soutien, m'a transmis ses connaissances sur l'utilisation et le fonctionnement du QCMD, merci. Je remercie toutes les personnes à l'ILL avec qui j'ai eu la chance de partager tant au travail qu'en dehors.

Mes doux remerciements à mes amis et collègues de l'ILL : Une grande pensée pour Marta qui dès son arrivée dans le bureau a été un petit soleil quotidien et s'est très vite placée comme une alliée dans les bons et les moins bons moments. De cette rencontre est née une belle amitié. Merci pour ton oreille attentive et ton soutien constant. Francesca, il serait difficile de ne pas mentionner ses talents de cuisinière qui étaient un ravissement gustatif au cours de ces 3 années passées à l'ILL. Merci de m'avoir partagé un peu d'Italie ! J'ai aussi une douce pensée pour Elodie, Oonagh et Bruno avec qui j'ai eu la joie de faire de la poterie à l'ILL sur ma première année, sans oublier les autres doctorants avec qui j'ai pu partager quelques soirées, discussions et bout de vie : Loreto, Silvia, Andreas, Murias, Peter, Marion, Charlotte, Palmerina, Quentin, Stanislav, Stella, Kristijan, Tetiana, Irina, Javier et Giuseppe. Sans oublier mes deux copines des cours d'anglais Virginie et Maria, nos repas et discussions vont me manquer! Merci aussi aux personnels de l'ESRF qui m'ont prodigués des conseils avisés et m'ont permis d'utiliser les instruments : microscope optique et l'AFM.

Je remercie l'ensemble des membres du LRP et sa directrice Nadia El Kissi pour m'avoir si bien intégrée dans l'équipe. J'ai beaucoup apprécié le soutien, l'écoute et la bienveillance de l'ensemble du personnel. Je ne pourrais jamais suffisamment exprimer ma gratitude à l'ensemble de l'équipe. Hélène Galliard, pour son implication active les deux premières années, pour m'avoir appris à utiliser les rhéomètres du laboratoire et pour ses précieuses astuces. Mohamed Karrouch, Didier Blèses et Eric Faivre, pour avoir été présents pour moi à chaque fois que j'en ai eu besoin. Frédéric Hugenell, pour nos discussions, son aide précieuse et son expertise dans l'utilisation de la DSC. Vincent Verdoot, pour sa contribution sur cette dernière année. Merci aussi à Denis Roux pour nos quelques échanges au détour du couloir sur l'avancement de mon projet, c'était toujours intellectuellement fructueux.

Mes remerciement affectueux à mes amis et collègues du LRP : Je remercie chaleureusement ma team Girl Power, Alice, Mathilde et Candice, nos soirées filles sont un petit bonheur et d'une grande détente. Alice, merci pour toute la force que tu m'as transmise et l'amitié que tu me portes. Mathilde, merci d'être cette femme entière et vraie qui m'a fait passer des moments forts. Candice, merci d'être un exemple à suivre et de m'avoir rassurée forte de ton expérience. Je pense aussi à tous ceux qui ont rendu cette période de ma vie agréable au travail et en dehors autour d'un verre ou d'un plateau de charcuterie/fromage : Hugues, Moctar et William, qui ont été là depuis le début jusqu'à la fin de ma thèse, et aussi Diego, Mehdi, Louis, Mohamad, Hanna, David, Revaz, Ouattara, Ayoub, Antoine, Adriana, Alexis et Clément. Un grand merci à Martinien, reparti avant la fin de ma thèse au Gabon. Les moments passés ensemble en France et nos discussions ont fortement contribué à mon épanouissement durant cette période active de ma vie. J'espère avoir l'occasion de venir te rendre visite prochainement. Également, j'ai une grosse pensée pour Marguerite Szyc et Olivier Nouaille, deux grands soutiens depuis mes débuts dans le monde de la restauration d'oeuvre d'art. J'en profite aussi pour remercier et témoigner de ma grande affection et reconnaissance à mes proches qui ont été d'une grande aide psychologique : Clémence, ma très chère amie, merci pour ta bienveillance ; Anne-Sophie, mon amie "invisible" et ma grande confidente, toujours là ! ; Léa, l'heureuse retrouvaille Grenobloise ; Fanny, merci chat pour ton soutien sur ces dernières semaines d'écritures, les plus difficiles ! Je ne risque pas d'oublier mes soirées aux Dr. D et mes belles découvertes gustatives ; Jérémie, mon copain de lecture, Batman forever! ; Laetitia, T-Chan, toujours avec moi en pensée ; Stéphanie, tu suis mon parcours depuis presque 10 ans et tu m'a vu passer de la jeune élève à la femme d'aujourd'hui ; Laurie, ma cousine adorée et Houssen ; Stefan, Ghislain, Romain, Audrey et mes copines du lycée que j'ai vu récemment avec grand plaisir (Anaïs, Bianca, Tiphaine et Marie). Merci tout simplement d'être dans ma vie ainsi que pour l'amitié et l'amour que vous me portez. Nos échanges et nos rires contribuent à mon épanouissement. Vos encouragements et votre soutien m'ont grandement aidée dans l'accomplissement de ce projet.

Je remercie aussi mon frère Jonathan, ma soeur Amandine et ma belle-soeur Mélanie, toujours présents dans ma vie pour suivre activement chaque étape et me soutenir dans mes choix. J'ai aussi une douce pensée pour mes neveux et nièces, Grégoire, Alice, Thibaud et les deux derniers nés au cours de ces trois ans de projet doctoral Océane et Baptiste.

Pour finir, je ne peux pas écrire ces remerciements sans penser à mes parents qui m'encouragent et me soutiennent dans tous mes projets. Au-delà du fait que mon existence ne tient qu'à vous deux, je ne serais pas la personne que je suis sans votre aide et les valeurs que vous avez su me transmettre, merci pour tout ! Merci !!! [START_REF] Oswald | Rhéophysique: Ou comment coule la matière[END_REF]) . . . . . . . . . . . . . . . . . . . .

2.16

Poiseuille flow in a cylindrical capillary with its velocity profile and its viscous stress σ υ zr (in module) from reference [START_REF] Oswald | Rhéophysique: Ou comment coule la matière[END_REF] . . . . . . . . . . . . . . . . . . .

3.1 Laropal®A81 formula from references [START_REF] Bonaduce | Mass spectrometric techniques for characterizing low-molecular-weight resins used as paint varnishes[END_REF] and [START_REF] Zhang | Synthesis and structural characterization of urea-isobutyraldehyde-formaldehyde resins[END_REF]

3.26

Assembly for the NR study of polymer film in contact with a solution or a gel .

3.27

In situ Rheo-reflectometry on FIGARO from reference [START_REF] Wolff | Combined neutron reflectometry and rheology[END_REF] Les oeuvres d'art ne durent pas éternellement. Elles sont composés de matériaux évolutifs qui vieillissent dans le temps. Ainsi, les vernis des peintures de chevalet perdent leur aspect visuel initial par dépôt de poussières et des suies en suspension dans l'air, par oxydation et par modification structurelle (effet des radicaux libres). A cause de ces processus, les vernis perdent leur transparence et jaunissent, ce qui empêche une bonne appréciation de l'oeuvre d'art.

Afin de renverser l'évolution de ces processus, les peintures sont périodiquement restaurées avec remplacement des anciens vernis. Ce traitement majeure, qui requiert le gonflement et la dissolution de la couche de vernis polymère par des solvants qui peuvent être pénétrants et polaires. Ces solvants peuvent altérer considérablement la composition et la cohésion des matériaux originaux de l'oeuvre qui sont situés sous les couches de vernis. Il est donc urgent de mieux comprendre les processus employés dans les opérations de restauration, particulièrement lors du remplacement des vernis. Conscient de cette urgence, restaurateurs et scientifiques ont proposé d'utiliser les gels aqueux/solvant pour transférer seulement les quantités de solvants nécessaires à la dissolution du vernis. Les images macroscopiques obtenues avant et après application de ces gels démontrent bien l'efficacité de ce procédé. Toutefois, il apparait des lacunes dans la compréhension des phénomènes qui entre en jeu.

C'est dans ce contexte que s'inscrivent ces travaux de thèse. Ils visent à mieux comprendre la physique des films polymères au contact de mélanges solvant/non solvant et solvant/gel, en suivant les mêmes processus que ceux employés dans la restauration des oeuvres d'art. Dans la thèse, on a utilisé la réflexion de faisceaux de neutrons (réflectivité de neutron et diffusion de neutrons aux petits angles), combinée à des visualisations locales (microscopie optique et AFM). La résine polymère choisie est le Laropal®A81, le solvant est l'alcool benzylique et l'hydrogel est le Pemulen TR-2.

La réflectivité de neutrons permet d'observer in situ le comportement physique de films polymères ultraminces déposés sur des blocs de silicium, pendant la cinétique de gonflement par le bon solvant puis par le mauvais solvant suivi de la dissolution et la disparition du film de vernis. L'eau utilisé est le D 2 O, qui a un densité de longueur de diffusion (SLD) très élevée par rapport à celles du polymère et du solvant. Ceci permet de différencier par leurs contrastes les distributions spatiales du solvent et du non-solvant. On a ainsi déterminé le SLD du Laropal®A81, puis modélisé l'épaisseur du Laropal®A81 et la rugosité des différents éléments. Ensuite, en utilisant ces valeurs d'épaisseur et de SLD, on a calculé les fractions volumique des différentes composants dans le film de vernis. On a discuté les variations de ces fractions de BA φ BA et du D 2 O φ D 2 O qui ont pénétré dans les films en fonction des paramètres investigués c'est-à-dire, l'influence de la concentration de solvant et l'effet de la température pour le cas avec le gel/solvant.

LIST OF FIGURES

En parallèle, un diagramme de phase ternaire utilisant les paramètre d'interaction de Flory-Huggins a été tracé pour le cas du système solvant/non-solvant en utilisant les résultats de NR, les mesures de viscosité intrinsèque et les mesures de turbidité à température ambiante. Les paramètres d'interaction χ LA/BA , χ W /BA et χ LA/W ont été obtenus par calcul du diagramme de phase en utilisant un modèle de Flory-Huggins. La compréhension des phénomènes a été déduite de l'analyse des spectres de NR, complétée par les observations faites en microscopie optique et AFM. L'AFM a surtout permis d'obtenir le profil en profondeur (axe z) des objets apparues dans le films en présence du mélange BA/W. Une expérience de diffusion aux petits angles de neutrons (SANS) sur des films épais (0.5-1.5 µ m) a donné des spectres d'intensités en fonction du temps évolué. Ces spectres ont été modélisés suivant la loi de Porod. L'aire des interfaces a été tracée en fonction des valeurs de χ BA/LA . Ces résultats ont été complétés par des mesures de QCM-D montrent la cinétique du gonflement et de la dissolution sur des heures et jours après la mise en contacte avec le système solvant/non-solvant.

En conclusion, nos études expérimentales ont permis de mieux comprendre le gonflement et la dissolution des films de Laropal®A81 épais et minces déposés sur des blocs de silicium et exposés à un mélange binaire solvant/non-solvant et des gels aqueuses contenants du solvant.

SUMMARY

The swelling and dissolving of varnish of easel paintings: Contribution to the macroscopic and nanoscopic understanding of the physical mechanisms involved during the removal process of altered varnishes.

Artworks do not last forever. They are composed of changing materials which age with the passage of time. Indeed, the varnishes of easel paintings lose their initial visual appearance due to deposits of dust and soot suspended in the air, by oxidation and by structural modification, e.g. the effect of free radicals. Because of these processes, the varnishes lose their transparency and turn yellow, thus preventing a good understanding of the work of art.

In order to reverse the evolution of these processes, paints are periodically restored and the old varnishes replaced. This major treatment requires the swelling and dissolution of the layer of polymeric varnish using solvents that can be penetrating and polar. These solvents can significantly alter the composition and cohesion of the original materials of the painting that are located under the varnish layers. It is therefore imperative to understand the processes used in restoration operations better, in particular when replacing varnishes.

Conscious of this urgency, conservators and scientists have proposed the use of aqueous gels/solvents to transfer only the quantities of solvents necessary for the dissolution of the varnish. The macroscopic images obtained before and after application of these gels demonstrate the efficiency of this method. However, the physical and chemical processes involved are still poorly understood.

The aim of this thesis is to understand the physics of polymer films in contact with solvent/nonsolvent and solvent/gel mixtures better, following the same processes used in the restoration of works of art. To study the physical processes of this method, we have used neutron beam reflection, in our case neutron reflectivity and small angle neutron scattering (SANS) combined with local visualizations, in particular optical microscopy and Atomic Force Microscopy (AFM). The polymer resin chosen is Laropal®A81, the solvent is benzyl alcohol and the hydrogel is Pemulen TR-2.

The neutron reflectivity allows us to observe in situ the physical behaviour of ultrathin polymer films deposited on silicon blocks. This behaviour is observed during the kinetics of swelling by the good solvent then by the bad solvent followed by the dissolution and disappearance of the varnish film. The water used is D2O, which has a very high scattering length density (SLD) compared to those of the polymer and the solvent. It is therefore possible to differentiate by their contrasts the spatial distributions of the solvent and the non-solvent. The SLD of the Laropal®A81 was first determined. Then the thickness of the Laropal®A81 was modelled, as well as the roughness of the various elements. By using these thicknesses and SLD values, the volume fractions of the various components in the varnish film were calculated. The variations of these fractions of BA φ BA and D 2 O φ D 2 O which have penetrated into the films have been discussed as a function of the investigated parameters, i.e. the solvent concentration and the effect of the temperature in the case of the gel/solvent. In parallel, a ternary phase diagram using Flory-Huggins interaction parameters was plotted for the case of the solvent/non-solvent system using NR results, intrinsic viscosity measure-LIST OF FIGURES ments, and turbidity measurements. The interaction parameters, χ LABA , χ W /BA and χ LA/W , were obtained by calculating the phase diagram using a Flory-Huggins model. The understanding of the phenomena was deduced from the analysis of the NR spectra, supplemented by the observations made in optical microscopy and AFM. The AFM allowed us to obtain the depth profile (z axis) of the objects appearing in the film in the presence of the BA/W mixture.

A Small Scattering Neutron Experiment (SANS) on thick films (0.5-1.5 µm) gave spectra of intensities as a function of evolved time. These spectra were modelled according to Porod's law. The interface area was plotted according to the values of χ BA/LA . These results were supplemented by QCM-D measurements showing the kinetics of swelling and dissolution over hours and days after contact with the solvent/no-filler system.

In conclusion, our experimental studies allowed a better and detailed understanding of the swelling and dissolution of thick and thin Laropal®A81 films deposited on silicon blocks and exposed to a solvent/non-solvent binary mixture and to aqueous gels containing good solvent.

INTRODUCTION

Since prehistory, humans have left traces of their existence. Consequently, works of art and artifacts have a major place in our lives. They are a historical marker, a means of expression or propaganda, of political and economic issues. Art is a universal marker of the present and the past and it is an important part of our identity. Preserving it, is therefore essential for future generations. In this context, conservators and restorers are the guarantors of this preservation and transmission. Hence, first they optimize the storage and the exhibition environment. Second, if necessary, they proceed to restoration to preserve their aesthetic and historical roles. According to Cesare Brandi's book 'Teoria del restauro' [1] which is the reference book for conservation and restoration heritage, restoring a work of art is defined as: "il retauro deve mirar al ristabilimento della unità potenziale dell'opera d'arte, purchè ciò sia possibile senza commettere un falso artistico o un falso storico, e senza cancellare ogni traccia del passagio dell'opera d'arte nel tempo." (C. Brandi. 1963 p.36). It means that during restoration treatments, the restorer must act only in order to perpetuate and stabilize the piece of art without compromising its integrity or that of the artist. It is not a question of modifying the piece of art to form a new one.

We have to take into account that the aging of the materials is an integral part of the history of the work of art. If a restoration action is necessary and inevitable, it must use reversible products and materials, and the restorers must limit their actions to the strictest necessary.

However, the restoration treatments are sometimes risky for the works of art and the slightest misstep can be irreparable. The history of restoration includes references to destruction due to over-extensive restoration or due to the action of new species transferred during treatments [2], [3], [4] and [5]. Eugène Delacroix, a famous French artist wrote in particular: " Ce n'est pas un tableau restauré qu'on vous donne, mais un autre tableau, celui du misérable barbouilleur qui s'est substitué à l'auteur du tableau véritable..." [6] which is good example of the controversy between supporters of minimalist conservation-restoration or supporters of advanced restoration. Other opponents of radical restorations have also distinguished themselves, such as Professor Gombrich and Professor Kurz of the Warburg Institute, and Professor Stephen Rees Jones of the Courtauld Institute [2] in their time.

However whatever the outcome of the debate on the degree of restoration needed, the removal of varnish coating is essential because varnishes deteriorate, develop micro-cracks, turn yellow and become more acidic with time [7]. Restorers usually remove this protective layer with solvents which are often penetrative and polar,inducing an irreversible modification of the physico-chemical composition of the painting. In its 'life', the same work of art can therefore undergo several restoration campaigns in only 100 years of life. Unfortunately, each restoration can contribute to the weakening of the constituent materials and the disappearance of the materials of the work of art. The real problem comes mainly from the difficulty of the restorers in controlling the action of solvents during the removal the varnish. Indeed, the presence of the patina and glazes (layer transparent colored on top of the paint layer [8]) complicates the removal of the varnish. A strong argument advanced by the opponents of strong cleaning is the destruction of the patina and glazes by this cleaning treatment. These layers are very thin and sensitive and constitute the last layer of the artist to magnify his work. Destruction was already mentioned by Vasari who gives the artificial patina recipes used in his time [9]. Another LIST OF FIGURES argument mentioned by Stephen Rees Jones is varnish leaching of the binder of the paint layer [2]. Many paintings have organic varnishes and the current synthetic varnishes replacement also have disadvantages that make it necessary to remove them after a while, therefore finding sustainable solutions to limit the destruction during this treatment is a current issue. So, the removal of the old varnish layer is a delicate and a risky treatment which has been controversial since the end of the war. The study of chemical materials on artworks is common. Scientists use several surface spectroscopy techniques such as for example Raman, Photoluminescence, or X-Ray fluorescence (XRF). In the case of bulk materials, chemical and physical information cannot be obtain just by surface spectroscopy. To perform the treatment and investigate the physical phenomena, some studies on the fundamental physics governing the varnish removal process by the use chemical and physical characterization techniques have been carried out in the past, but this remains incomplete and is mainly based only on the R.L. Feller, Graham and Stolow datas [10], i.e. on works of the middle of the twentieth century. The most recent study is that of Michalski [11] in which he collects the scattered data of the latter experiments and some others to propose a partial model of the physical aspects of varnish removal from oil paint. Also he gives a chart of solvent penetration as a function of the time. Since the twentieth century, restoration varnishes have evolved [7]. Many restorers favor the use of these new varnishes as the varnish Laropal®A81 of this study and many paintings have a synthetic varnish. That does not change the problem of the restorers of the removal of varnishes. Removing them from the surface of a painting without risk to the paint layer remains a challenge. And there is a need to have a better comprehension of the fundamental physics governing the process. And the understanding of diffusion of solvent into polymers is also important in others area (for example to identify chain architectures and mechanisms), and the mechanisms that govern the diffusion behaviour are not fully understood. [12] A major part of science research for cultural heritage in the world focuses on the macroscopic/nanoscopic understanding, on the investigation of the degradation and on the evolution of materials; this project is a part of that research. The aim of this study is to understand mainly by the use of neutrons, the nanoscopic behavior of ultrathin, thin and thick films of a synthetic polymer resin (Laropal®A81), which is commonly used by art restorers as a varnish resin and retouching resin on paintings, when they are in contact with solvent/water mixture and gel/solvent mixture; and to observe the impact of several external effects (temperature, shear) on polymer/nonsolvent/solvent and polymer/gel/solvent systems. The basic idea is to answer several questions about physico-chemical mechanisms of swelling and dissolution of layers of polymeric varnish that lead to its disappearance on the paint layer when the restorer treats the varnish with a solvent: How does the film of varnish disappear? Is it layer by layer, dewetting or erosion? Is there nucleation or spinodal decomposition during the process?

This study is composed of 5 chapters:

In the Chapter 1, the context of the thesis will be introduced. First, the history, the place and the role of the varnish in a painting will be discussed briefly. Then, the instability, the reasons that lead restorers to remove these varnishes and the traditional way of the restorers to remove this layer when it becomes undesirable will be explained. Finally, the effects that this treatment of the removal of the varnish coating may have on the paint layer and the current way to offset these effects will be discussed. Second, the theory of polymers physics focusses on the swelling and the dissolution processes by a solvent/non-solvent mixture will be exposed in order to understand the removal of varnish layer treatment. Flory-Huggins theory, interaction parameters and phase diagram theory will be developed. Then, the last step of the disappearance of the polymer film: rupture, dewetting and drop formation of the thin polymer film will be addressed.

LIST OF FIGURES

Chapter 2 is a view of scientific knowledge necessary to understand the physics behind the experiments carried out and gives the scientific context of this project. Three important parts constitute this chapter: Neutron Scattering, Polymer and Comprementary information (QCM-D and Rheology). First, we will explore the basic Physics of polymers and some hypothesis about solvent/nonsolvent/polymer behaviors. Then, Neutron scattering techniques including neutron reflectometry and SANS will be addressed. The basics of QCM will be quickly addressed and we will finish on the basics of rheology.

The materials, the preparation of samples, the instruments and the methods of analysis will be explained in the Chapter 3.

The microscopic and nanoscopic behavior of the polymer model films in contact with a small amount of solvent in water investigated by few techniques (mainly by NR) is exposed in an article published the 13th January 2020 in Soft Matter [13]. This paper is shown unchanged in Chapter 4.

As in the previous chapter, Chapter 5 explores the behavior of the polymer model films by NR but this time in contact with a solvent in a gel of water.

The last chapter, Chapter 6 presented in the form of a paper, investigates the temporal evolution of the polymer model films immersed in a mixture compounds of a small amount of solvent in water in order to understand the origin of instabilities during and after the swelling film.

CHAPTER 1 STATE OF ART

The aim of this chapter is to give the context and the motivation of this PhD project. I begin with a brief, simple view of the historical context of varnish [14], and the organisation and the materials present in an easel painting. This part may appear simplistic to the eyes of a professional or to restorers but will be sufficient and necessary for the comprehension of a wider audience. The role of the varnish and its effects on the paint layer is developed. And we will also address a quick look at the state of the art on methods for removing the varnish layer.

1.1 Restoring a varnish layer, an issue !

A protective and aesthetic layer

A varnish layer is defined as a fluid substance which gives, after hardening, a transparent and amorphous smooth film, and this for a protective and optical purpose [15]. Based on current knowledge, the word "varnish" appeared in the seventeenth century but its use on painted works was widespread well before. Throughout the centuries, preparation techniques have evolved and it were composed of drying oils, gums, resins and/or egg whites. The first varnishes used were natural varnishes. There are two categories: either called 'greasy varnishes' prepared from natural resin and drying oil or so-called 'lean varnishes' prepared from natural resin and alcohol or gasoline. Then, after the discovery and the formulation of synthetic resins, the trend moved to synthetic varnishes (acrylic, ketonic, polyurethane, etc.) prepared from resin dissolved in organic solvents. These varnishes have the advantage of being stronger and have the reputation of being more easily removable because these polymers do not cross-link.

Natural varnishes

The use of the first protective coatings goes back to ancient Egypt and maybe well before, with the Egyptians sarcophagus. The oldest, on Egyptians sarcophagus dating from 1200-1300 BC, was discovered by A.P. Laurie. The first mentions of the protective layers are those of Vitruve [16] in the 1st century BC and Pline l'Ancien [17] in the 1st century AD with the 'atramentum' d'Appelle (the 4th century BC) but the exact composition of these layers remains unknown. Subsequently, There are many varnish recipes mentioned in various sources [18], [19], [20].

Before the 18th century and more particularly until the appearance of alcohol and gasoline varnishes ('lean varnishes'), according to Theophilus [21], varnishes were formulated with boiling natural resins (sandaraque, rosin, copal, shellac, amber, mastic) from vegetable and animal substances origins ('greasy varnishes'). Over time, the varnish composition has been redesigned (towards the end of the eighteenth century by J. F. Watin [22]. But real changes did not come until the 19th century. At this period, there was reflection about the essential and useless elements which compose varnishes and about the notion of an'ideal varnish': transparency, colorless, elastic, protective, reversible easily and with non-polar solvents or with low polarity. In parallel, the 19th century marks the arrival in Europe (from Asia and subsequently implanted in Southern Europe) of a complex natural resin from the trees of the Dipterocarpaceae family: the Damar resin. This resin was already observed on the old works of art at this age but little used by European restorers. It is the most common natural resin used nowadays by restorers because of its exceptional optical qualities. Many restaurateurs still agree that even the best synthetic varnishes still cannot match it on this point. But unfortunately it tends to yellow quickly, white lead (so-called "fat" preparation), prepares the support for the pictorial layer. In particular, it limits the migration of the oil or binder towards it, thus avoiding oxidation or weakening of the support. It also makes it possible to regularize and erase the irregularities of the support: asperities of the wood and frame of the canvas. It can be colored by a pigment for brown, red or yellow preparations, carbon black for gray preparations. Colored preparations appeared gradually during the 16th century for oil paintings and were described by Giorgio Vasari [30]. The principle is to give more depth to the pictorial layer. Clear preparations were used particularly during the period of neoclassicism and the impressionists. The pictorial layers also called the colored layers, are constituted of pigments finely ground or vegetable (indigo and saffron) and animal (purple or sepia) dyes in a binder (often oil). Most of natural pigments from plant or animal origin are sensitive (discoloration or mutation) to ultraviolet light, temperature changes, pH changes and humidity. Finally, most paintings present a varnish layer because of its protective and aesthetic role (brightness, brilliance and color saturation) [31]. It is the first layer beyond the pictorial layers therefore the one directly in contact with the external environment. It constitutes a barrier against all the harmful external elements (dirt, volatile elements, light rays, etc.) which favor the deterioration of other fragile materials composing the paint and more particularly the pictorial layers and it allows saturation of the colors of the pigments in the binder in order to sublimate them.

In essence, a painting is not a static object but one in slow and constant evolution. And this aging evolution is accelerated by the type of storage or the place of exhibition. Indeed, the materials that compose the work of art are very sensitive to numerous parameters such as pressure, temperature and humidity. Surprisingly, it is also these same parameters which allow art restorers to restore them [3].

Degradation and instability of varnish, removal of the varnishes and effects on other layers

Why the varnish can be removed on paintings?

It is commonly decided to remove the varnish when it impedes the understanding and the appreciation of the work of art. Varnish is not perceived as an original material, unlike the pigment layer, the preparation, the glue and the support because it has not been applied by the artist but by a restorer for the purpose of protecting the colored layer of abrasive exterior elements. So unlike other original materials, it is agreed that it can be removed from the surface.

What is the degradation of the varnish?

Several degradation of varnishes are due to environmental effects or some other more specific reasons and lead a restorer to act on the varnish which obscures the images beneath. For example, the oxidation reactions of the varnish lead to yellowing, cracking and increase of acidity (Fig. 1.2). A thin varnish layer can cause the loss of colored matter and cracking of the material and become a risk factor for the paint layer. Also, anything that affects the deep layers (support, gluing and preparation) has a direct impact on the upper layers (colored layer and varnish)making them thinner and more sensitive. How restorers procede to remove a varnish?

Traditionally, restorers remove the varnish by applying, via a circular motion directly on the surface, a cotton swab soaked in organic solvents. The task is sometimes difficult (oxidized layers) and the varnish cannot be removed with low polar or apolar solvent [18]. Restorers are then forced to use very polar solvents, strong and penetrating solvents [7] [24] [27] [32]. To reduce the amount of strong solvents, restorers mix two solvents with different polarities. For example, they combine a polar solvent and an apolar solvent following the solvents parameters [33], the Teas Diagram [34] [35] [36] [37] such as a predicting tool or restorers lists of solvents. These lists from Cremonesi [38] or Masschelein Kleiner [39] propose numerous solvent mixtures for specific cleaning treatments to remove the unwanted elements on pictorial layers. These lists are known and applied by most of restorers in the world.

...and what about the effect on the paint layer?

In 1971, Stolow wrote about organic varnishes: 'Unfortunately, no varnish has yet been found or devised which adequately fulfills the aesthetic and physical requirements and is also absolutely durable' [10]. In the twentieth century, the advent of the use of synthetic resins as a restoration varnish has changed the game a little with new competitive resins in terms of stability and resistance to external agents. They are used as alternative varnishes to traditional organic resins 1 .

Even if the resins are chosen for their good resistances, stability and transparency, they do not escape the effect of time, yellowing or fouling [8]. Without forgetting that in this very wide choice of existing resins, the restorer can easily get lost and paintings can pay the price with synthetic varnishes difficult or impossible to remove with low-polar solvents. The use of toxic and penetrating solvents repeatedly and over time lead to a risky situation for the user and the paint layer.

Nowadays, the negative effects of the removal of vanish (solubilization, binder depletion, bleaching, embrittlement, swelling and cleavage of the colored layer, etc.) are known by most scientists and restorers. Therefore, they are looking for alternative methods to remove the varnish and deposit a fresh new layer without damaging the paint and deep layers. This approach CHAPTER 1. STATE OF ART of 'how to do better to remove the vanish layer ?' is fairly recent because until the 20th century restorers used solvent cleaning methods without asking any questions about the possible impact of these very penetrating and abrasive treatments. Nevertheless it is a regular treatment of works of art: about half a century in the life of an array of paintings in a museum. The first writings that mention the possible dangers of solvent action on paint film date back to the mid-nineteenth century. In 1851, H. Deon [40] mentioned the negative effects on the use of more and more polar solvents for the cleaning and the removal of the varnish on paintings and in particular the difficulty of dissociating the varnish from the paint, which in some cases form a single heterogeneous layer. In 1930, a committee of the Conference on the Examination and Conservation of Works or Art met in Rome with the object of defining a 'good varnish'.

Afterwards, the solubility, the swelling and the leaching effects of organic solvents on varnish and paint films were studied by Graham for Linoxyn films [START_REF] Graham | The effect of solvents on linoxyn films[END_REF] and Stolow for drying-oil films [42] [43] [44]. Since 1985, the book of Feller, Stolow and Jones serves as a reference on the behavior of resins and solvents used in varnishes of paintings. In addition, Sutherland showed that varnishes may affect the oil paint film. There is extraction of fatty acids from the paint film into the varnish layer depending on the solvent used and the component of the resin [45] [46]. Synthetic varnishes, contrary to what one might think, have not changed the situation. Certainly, they are more stable in time, and for some, more resistant and less rigid therefore less restrictive for the layers below ; but most of them have shown other failures. Namely, that there are problems of adhesion, insolubility and resistance to solvents, increased sensitivity to dust especially on varnishes with low glass transition temperature (T g ) or they could have a too high viscosity. In addition, many restorers find that gasoline varnishes (Dammar and Mastic) can better saturate the colors, give more depth and provide the ideal look of shading or shine and control the light. Others opted for a mixture of one or more layers of natural varnish on which are deposited layers of synthetic varnish. The idea was to combine the advantages of each. So there is not just a simple model of paintings but an infinite combination of material and layer thickness that makes each object unique. The ideal varnish has not been found and old master paintings still have altered.

Restorers are therefore very interested in alternative solutions (gel, microemulsion or laser) to remove varnish and to apply a new coating in the best conditions. And restorers and curators are interested in the investigation of how to remove old varnish coatings in the best condition and the investigation of the 'ideal varnish' to apply a new fresh varnish.

How to counter these effects?

In the 2000s, Wolbers opened the way to use some gels for the cleaning of paintings [47]. The scientific literature of the gels is rich due to the many possible applications in many domains. Therefore, research on gels began long before Wolbers highlighted them for application in the field of art restoration, as well as the work of many scientists who are interested in it. To name a few, Graham was mentioned already [START_REF] Graham | The effect of solvents on linoxyn films[END_REF], [48], and Meunier is the discoverer of the famous gel of 1,3:2,4-di-O-benzylidene-D-sorbitol still used [49]. Subsequently, thanks to Wolbers's book [47], many researches have been undertaken to investigate the properties of gels and develop the way for applying them on art (paintings, fresco, ceramics and papers) and more particularly of microgels and nanogels [50], [51] [52] [53] [54]. Several advantages are advanced by the scientists for the use of these systems in art. First, these gels are composed mainly of water maintained in a network while not limiting the transfer of the solvent contained therein. Secondly, the gel would also provide the material to be applied to transfer very small amounts of solvent. Resolving at the same time the problem of the use of toxic solvents for the restorers and theoretically the risk of the solubilization of the paint layers which would be low because of the low solvent concentration. For the reasons previously stated, gels seem a promising tool CHAPTER 1. STATE OF ART for Cultural Heritage so a lot of restorers, conservators and scientists have investigated and applied them [55] [56] [57] [58] [59] [60]. As shown by the many references already mentioned, Baglioni et al. in Florence, is one of the groups most involved in investigating art restoration issues on works of art, in particular easel paintings, wall paintings and frescoes. They propose numerous innovating methods (soft and hard nanomaterials) for the cleaning and the removing of the non-original materials from the paint layer. The reviews of 2006 [61] and of 2014 [54] and the mini-review of 2017 [62] summarize well the state of the art of cleaning products (micelles, microemulsions and gels) proposed and applied for the conservation-restoration of Cultural Heritage.

These products seems to be effective solutions to transfer solvents in the polymeric vanish layer in order to swell, dissolve and remove it. However, one could nevertheless observe that the work undertaken at the moment on these gels demonstrate their effectiveness visually but that there seems to be a lack of understanding of the physical phenomenon involved in the transfer of a solvent by a gel in the varnish as well as the effects on it (swelling, dissolution or other effects). This will be one of the objectives of this project, but before understanding what is happening in a gel/solvent/polymer system, it will be necessary to have a full understanding of what is happening in a water/solvent/polymer system without molecules of gel.

CHAPTER 2 PHYSICS OF NEUTRON SCATTERING AND BACKGROUND

In this chapter, we provide an overview of neutron scattering and the Atomic Force Microscope used to understand the swelling and dissolution processes of the polymer films which composed the second part of this chapter. Then, complementary theory of rheology is quickly addressed.

Neutron scattering

In 1932, James Chadwick discovered neutrons. In the decades after, thanks to the creation of dedicated high flux sources (ILL, ISIS, LENS, HFIR, ANSTO, LANSCE, FRMII, etc.), it was possible to produce free neutron particles in large quantities allowing the exploration of different areas of research in condensed-matter physics and other areas. Neutron scattering is a powerful tool especially for the study of material science, chemistry, biosciences, and nuclear and elementary particle physics and in engineering sciences as well as magnetism.

Especially for condensed matter investigations neutrons are often applied as a non-invasive probe; they do not change the investigated sample since they do not deposit energy into it. Using them allows e.g. to observe the microscopical structure and dynamics of polymer materials with a high resolution (few Å).

Using neutrons presents undeniable advantages for the investigation of condensed-matter [63]. They interact through short-range nuclear interactions, their wavelengths are comparable to atomic sizes and inter-distance spacing and hydrogen atoms can be replaced by deuterium atoms, which is an advantage to allow better differentiation of the different elements by contrast.

This part is based on the following references [64], [START_REF] Baruchel | Neutron and synchrotron radiation for condensed matter studies[END_REF], [START_REF] Angst | Scattering methods for condensed matter research[END_REF], [63], [START_REF] Lefmann | Neutron scattering: theory, instrumentation, and simulation[END_REF], [START_REF] Squires | Introduction to the theory of thermal neutron scattering[END_REF], [START_REF] Pynn | Neutron scattering: a primer[END_REF], [START_REF] Gutfreund | The microscopic origin of surface slip: a neutron and x-ray scattering study on the near surface structure of flowing liquids[END_REF], [START_REF] Hafner | Full off-specular and specular reflectometry for soft thin film analysis[END_REF] and [72].

Neutrons

These remarkable elementary particles are contained in the atomic nucleus. With protons, they constitute the nuclei of atoms but its mass is a little larger (m n = 1.008664924 u). Neutrons electric charge is supposedly zero. Unlike X-rays which see most of the time only the surface and are highly energetic, neutrons can penetrate deeply into matter and interact with it without being stopped by coulombian barriers (nondestructive particles), hence they are suitable for the study of biological and soft matter samples. Another important particularity of the neutron for neutron scattering is its magnetic moment (µ n = 1.91304275 µ N ) which is given by the neutron's spin angular momentum -γ µ N σ with γ the gyromagnetic ratio (= 1.913), µ N the nuclear magne- ton and σ the quantum mechanical Pauli spin operator. Neutrons wear a 1/2 spin which allows polarisation of the neutron beams and to analyse this polarization before and after magnetic field interactions. Furthermore, according to quantum mechanics neutrons do not have only particle properties but can be considered as a wave with a wavelength (traditionally in Å) given by de Broglie's formula:

λ = 2π h mv , (2.1)
with the Planck constant h = 2π h = 1.034 x 10 -34 Js, m the neutron mass and v the neutron speed. The wavelength is similar to that of X-rays. And its kinetic energy (in eV or meV) is given by: After being thermalized neutrons are further cooled down by liquid deuterium (cold moderator at 20 K) to obtain the energy required, such that their velocity distribution equals a Maxwell-Boltzmann function, which allows to perform NR and SANS experiments used in this study. And the average energy of the Maxwell-Boltzmann distribution is given by:

E = h2 k 2 2m n . ( 2
E = 3 2 k B T, (2.4)
where, k B is the Boltzmann constant and T is the temperature of the moderator (deuterium). At 20 K, the energy is 2.6 meV which corresponds to an average velocity about 700 m.s -1 (eq. 2.5) and an average wavelength λ equal to 5.6 Å(eq. 2.1). [START_REF] Gutfreund | The microscopic origin of surface slip: a neutron and x-ray scattering study on the near surface structure of flowing liquids[END_REF] . Unlike X-rays which interact through electromagnetic interactions with the electron cloud of atoms or electron beams which interact through electrostatic interactions; neutrons interact directly through the strong interaction with the nuclei. There exist two interactions between neutrons and matter, with the nuclei of atoms and with their magnetic moment. The scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave [START_REF] Zettili | Quantum mechanics: concepts and applications[END_REF], defined as:

ν = 2E m n . ( 2
f (θ ) = m 2π h2 d r ′ e -i q r ′ V ( r ′ ), (2.12)
where, f(θ ) is the Fourier transform of the interaction potential V( r ′ ) Its absolute square (eq. 2.13) allows to calculate the scattered intensity.

dσ dΩ = | f ( q)| 2 = m 2π h2 2 V ( r ′ )e i q r ′ d r ′ * V ( r)e -i q r d r, (2.13)
where, V( r) is the scattering potential. Replacing V( r) by V( r ′r), the absolute square scattering amplitude becomes:

dσ dΩ = m 2π h2 2 V ( r ′ -r)V ( r ′ ) * e i q( r ′ -r) d( r ′ -r).
(2.14)

The part V ( r ′ -r) V ( r ′ ) d r ′ is called the pair correlation function.
The Fourier transformation of the scattering potential V( r) is the scattering amplitude.

So, the intensity measured during a scattering experiment is the Fourier transformation of the pair correlation function of the scattering potential in the reciprocal space [START_REF] Gutfreund | The microscopic origin of surface slip: a neutron and x-ray scattering study on the near surface structure of flowing liquids[END_REF].

Another important quantity is the scattering length density (SLD) [76], not to be confused with the scattering length, because it allows to calculate the neutron contrast factors. It is the ratio of scattering length per molecule and molecular volume. In the case of an A m B n molecule with m atoms A and n atoms B, the SLD is given by:

SLD AmBn = b nuclei v AmBn = (mb A + nb B ) v = N av ρ M ∑ nuclei b nuclei , (2.15)
where, (mb A +nb B ) is the scattering length b nuclei per molecule and v is the volume given by v= M N av ρ with N av is the Avogradro's number (N av = 6.10 23 mol -1 ), ρ is the density and M is the molar mass.

Neutron Reflectometry

There are many powerful techniques for the investigation of surface layers such as ellipsometry or optical microscopy ; but only few of them allow us to penetrate the solid/liquid interface, to give informations about interface structure and in particular for ultrathin and thin films. Neutron reflectometry (NR) is one of those and there is no need to prove that it is an indispensable tool and non-destructive probe in the study of polymer films to resolve the internal structure. This term includes two techniques of reflection, specular and off-specular reflectometry (OSS) and grazing incidence small angle scattering (GISANS). Their difference lies in the angles : the outgoing angle θ f in the case of OSS and the azimuthal angle θ y in the case of GISANS).

The refractive index n of materials for neutron reflectometry is very often smaller than 1 : n < 1, leading to total external reflection. Neutron reflectivity was observed for the first time in 1944 by E. Fermi and W. H. Zinn [START_REF] Fermi | Reflection of neutrons on mirrors[END_REF] and the previous affirmation was well confirmed during their experiment on several materials (graphite, aluminium, glass, iron, nickel, zinc, copper and beryllium).

Basically, when a collimated, monochromatic neutron beam, represented by a wave function e ikr [START_REF] Squires | Introduction to the theory of thermal neutron scattering[END_REF] [67] is scattered by a single fixed nucleus into a liquid or solid sample by the strong nuclear forces, the scattering is assumed to be symmetric, because the range of the nuclear forces CHAPTER 2. PHYSICS OF NEUTRON SCATTERING AND BACKGROUND is much smaller than the wavelength of thermal or cold neutrons. A part of neutrons is reflected following a particular geometry called grazing incidence geometry. The reflected beam is collected into the detector so that the signal is subsequently analyzed and can give information on the system studied. The reflectivity is the ratio between the number of reflected neutrons and initial neutrons. Reflectivity of flat interfaces (ideal case) is calculated using Fresnel [START_REF] Parratt | Surface studies of solids by total reflection of x-rays[END_REF] [START_REF] Hamley | Analysis of neutron and x-ray reflectivity data. i. theory[END_REF]. In reality, flat interfaces do not exist, but a finite roughness or inter diffusion is present. The factor of Nevot-Croce [START_REF] Nevot | Caractérisation des surfaces par réflexion rasante de rayons x. application à l'étude du polissage de quelques verres silicates[END_REF] is added to describe real interfaces. Furthermore, neutron reflectivity can be used to study chemically identical species thanks to the sensitivity of neutrons to the nuclei of the material. For example, hydrogen atoms can be exchanged by deuterium. Deuterium atoms contrast better without having any effect on the thermodynamic properties of chemical species. The Flory-Huggins interaction parameter χ (section 2.2.4) is almost the same between protonated and deuterated species [START_REF] Strazielle | Some thermodynamic properties of polymer-solvent systems. comparison between deuterated and undeuterated systems[END_REF].

Specular Reflectivity

Nowadays, specular NR has become a standard technique for the investigation of thin films and interfaces [START_REF] Daillant | X-ray and neutron reflectivity principles and applications[END_REF] similar to optical techniques like ellipsometry. Its spatial resolution is, however, much higher due to the significantly smaller neutron beam wavelength on the order of Å as compared to visible light, giving access not only to total layer thicknesses or material gradients but also to nanoscopic roughness between layers. Moreover, the reflection contrast of layers is not determined by the refractive index as for visible light. In order to characterize the nanoscale structure of interfaces of water/polymer/Si Block systems, a collimated neutron beam (incident beam) is directed at the interface of interest through the Si block, which is practically transparent for neutrons, with an incident angle θ and the reflectivity profile of the reflected beam at an exit angle θ f = θ equal to the incident angle is measured as a function of the momentum transfer perpendicular to the polymer film surface (Fig. 2.6). As can be seen in the figure the difference in momentum transfer normal to the surface before (k i ) and after (k f ) neutron reflection can be defined:

q z = 2π λ * (sin θ i + sin θ f ), (2.16)
where λ is the wavelength.

The resolution of the specular experiment is obtained by the combination of the angles resolution and the wavelength resolution. Nowadays, the mechanical precision is so high and allows us not to take it into account here. The formula becomes:

∆q z q z = ∆θ i + ∆θ f 2θ 2 + ∆λ λ 2 .
(2.17)

a. Application on an interface between two semi-infinite media

The scattering length density SLD AmNn of each material is calculated using the reference [76] using the equation 2.15.

The critical momentum transfer q c (eq. 2.18) and the critical angle of the total external reflection θ c (eq. 2.19 are obtained from the SLD :

q c = 4 √ πSLD.
(2.18)

θ c ≈ λ SLD π . (2.19) CHAPTER 2.

PHYSICS OF NEUTRON SCATTERING AND BACKGROUND

For neutrons, the refractive index n can be obtained using the equation 2.20. As previously mentioned, n is inferior to 1 for most material in reflectivity experiment.

n = 1 - λ 2 π SLD, (2.20)
where, λ = 2π/k. From equations 2.18 and 2.19, it is deductible that n depends of neutron wavelength λ and the SLD. In addition, the Snell's law between the interface of this two media is applicable. Now, let us consider the Fresnel reflection and the transmission coefficients [START_REF] Hafner | Full off-specular and specular reflectometry for soft thin film analysis[END_REF]. The momentum transfer is given by Q

z = p z, f -p z,i = 4π
λ sinθ where p z,i and p z, f are the projection of the incoming -→ k i and the outgoing -→ k f wavevectors on the z-axis. In the context of a single interface between two media, the calculation of the projections p z,0 and p z,1 of the wavevector -→ k on the z-axis above (0) and below (1) of the interface can be obtained as:

p z,1 = p 2 z,0 -p 2 z,c = p 2 z,0 -4π(SLD 1 -SLD 0 ), (2.21)
where, p z,c is the critical wavevector of the total external reflection. SLD 0 and SLD 1 are the SLDs of the material above (0) and below (1) the interface, respectively. Moreover, p z,0

= -→ |k| sin θ i with -→ |k| = 2π λ . If ψ 0 (0) = ψ 1 (0) and their derivatives are ψ ′ 0 (0) = ψ ′ 1 (0), the Fresnel reflection coefficient r F 0,1 (eq. 2.
24) and the Fresnel transmission coefficient t F 0,1 (eq. 2.23) are given by:

r F 0,1 = p 0 -p 1 p 0 + p 1 , (2.22)
t F 0,1 = 2p 0 p 0 + p 1 , (2.23)
where, p 1 = p 2 0p 2 c . Then, the Fresnel reflectivity for a single sharp interface between two semi-infinite media is:

r F j, j+1 = p j -p j+1 p j + p j+1 . (2.24)
where, p j = p 2 0 -4πSLD j an p 0 = 2π λ sinθ i . b. Experimental description Neutron reflectometry can be performed following two methods: the Time of flight (ToF) or the angle dispersive mode. A range of q z values can be obtained either by varying the neutron wavelength λ as done on FIGARO (ToF method) [START_REF] Gutfreund | Towards generalized data reduction on a chopper-based time-of-flight neutron reflectometer[END_REF] or by varying the incident angle θ i at constant wavelength as done on N-Rex + (angle dispersive method).

In ToF mode, the incident angle is constant and the detector is 3-D with two spatial dimensions plus one temporal dimension due to the low velocity ν of each neutron. This methods operates in two points, the white beam is chopped into pulses (∼ 20 µs) with an angle fixed and the beam speed is investigated over a flight path between the chopper to the detector. [64] The wavelength of the neutron is defined from the time of flight from the chopper and the monochromator.

The velocity depends on the wavelengths of the neutrons. In both methods, the wavelengths of cold neutrons is between 2 Å and 27 Å for a velocity around 2000 m.s -1 and 150 m.s -1 . The wavelength resolution is only of few percent 10 -2 < ∆λ λ < 10 -1 [START_REF] Saerbeck | Recent upgrades of the neutron reflectometer d17 at ill[END_REF]. In monochromatic mode the neutrons are monochromatized by a monochromator and the sample is rotated to be CHAPTER 2. PHYSICS OF NEUTRON SCATTERING AND BACKGROUND placed precisely at the center of the beam. The reflected intensity from the sample is captured and measured on the detector. Then the data are transmitted from the detector to the software or they are therefore first reduced with COSMOS in the case of ILL experiment [START_REF] Gutfreund | Towards generalized data reduction on a chopper-based time-of-flight neutron reflectometer[END_REF]. This reduction involves the removal of the background and the normalization by the incident beam intensity. The measured NR data is subsequently compared to simulated NR curves calculated by an optical matrix formalism from a slab model [START_REF] Abelès | Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés-application aux couches minces[END_REF] and the goodness of fit is calculated. This least-squares fitting procedure is repeated until a convergence is found by using MOTOFIT [START_REF] Nelson | Co-refinement of multiple-contrast neutron/x-ray reflectivity data using motofit[END_REF]. The model used here to fit the NR curves consists of an infinitely thick single crystal silicon slab covered by a thin layer of silicon dioxide, which thickness varied between 1 nm and 2 nm among the samples, and several layers of LA on top capped by an infinite layer of liquid. Each of the layers was fitted by allowing its thickness and roughness to change until convergence was found. The SLDs of the LA and water were also fitted, but the SLDs of silicon dioxide and silicon were fixed at the corresponding literature values reported in table 6.1. The roughness of the silicon substrate and silicon dioxide were found to vary between 0.2 nm and 0.5 nm.

Off-Specular reflectivity

This Off-specular reflectivity section is mainly based on the reference [START_REF] Hafner | Full off-specular and specular reflectometry for soft thin film analysis[END_REF]. a. Application on a single rough surface Off-specular scattering can be obtained following several methods, the one used here is the distorted wave Born approximation (DWBA) where the small perturbation from the ideal potential is used as a representation of the rough surface of the material. The ideal potential is calculated with Fresnel theory. The ideal potential V (z) (eq. 2.26) and the small perturbation (eq. 2.27) from the lateral deviations of δV (z) give the scattering potential V( - → r ) at z = 0 (eq. 2.25) [87] [71]. The SLD contrast of two layers is represented by the potential of the small perturbation, the second term of the equation 2.25.

V ( - → r ) = V (z) + δV (x, z), (2.25)
where, the ideal potential is:

V (z) = 2π h2 m SLD ; z > 0 0 ; z < 0 (2.26)
are indispensable in industry and in applied fields like in art restoration where the constituent elements of paintings and products of restorations are mainly polymers. This section is based on the following references : [START_REF] Miller-Chou | A review of polymer dissolution[END_REF] [92] [START_REF] Flory | Principles of polymer chemistry[END_REF] [94] [START_REF] Bonaduce | Mass spectrometric techniques for characterizing low-molecular-weight resins used as paint varnishes[END_REF] [96] and [START_REF] Baughman | Neural networks in bioprocessing and chemical engineering[END_REF].

Mechanisms of dissolution and swelling

Swelling

The swelling process is the diffusion of the solvent into the polymer which undergoes a transition from glassy to rubbery state. It depends on several factors as the affinity of the polymer with the solvent or the molecular weight of the polymer to name a few. The solvent/polymer mixing process in a good solvent is explained by fundamental thermodynamics. During solution, there is a change in the Gibbs energy (eq. 2.39). This means, the solvent breaks its own interactions and its liquid cohesion in order to create the necessary space (entropy of mixing) for the incorporation of the polymer. In parallel, when the polymer/solvent interactions are stronger than the chain attraction forces, the polymer absorbs the liquid solvent in the empty spaces (enthalpy of mixing) which increases the total volume of the polymer matrix and changes the coils size. The swollen polymer film increases until a quasi-stationary state is reached. It is the 'swollen limit' of the polymer by the solvent (Ueberreiter, 1968 [98] [91]).

Dissolution of a rubbery polymer

The dissolution of the rubbery polymer by a 'good' solvent proceeds as follows:

• the solvent diffuses into the rubbery polymer (swelling of the polymer)

• the onset of dissolution in the diffusion boundary layer by chain disentanglement

• and, the free displacement of the disentangled chains into the solvent via Brownian motion in the solvent, leading to the complete dissolution of the rubbery polymer.

When the solvent concentration goes beyond a critical concentration in the polymer, it dissolves thanks to the disentanglement until the total disappearance of the glassy state. According the review of Koenig et al. [START_REF] Miller-Chou | A review of polymer dissolution[END_REF], there are two kinds of dissolution: the 'normal dissolution' or the fast disappearance of the polymer due to the absence of gel layer creation. The dissolution depends on several parameters which can affect the dissolution process: 1) the temperature, 2) the molecular weight of the polymer, 3) the T g of the polymer, 4) the polymer structure, composition and conformation; and 5) the type of solvent used

1) The dissolution in solvent has to happen above glass transition temperature. The gel layer thickness becomes weaker with decreasing temperature. Below a certain gel formation temperature, the polymer cracks leading to polymer fragmentation (Asmussen and Raptis, 1965 [START_REF] Miller-Chou | A review of polymer dissolution[END_REF]).

2) The transition layer increases with the molecular weight of the polymer. A polymer at high molecular weight will be more difficult to dissolve than at low molecular weight by the same solvent.

3) when the T g of the polymer is low, it is easier to dissolve the layer with a 'good solvent'. 4) As a function of the polymer chemistry, the polymer dissolves by swelling or by cracking (Ouano and Carothers, 1980 [99], [START_REF] Miller-Chou | A review of polymer dissolution[END_REF].

5) The solubility rate depends on the chosen solvent. For example, a small amount of nonsolvent mixed with a solvent, allows to slow down the dissolution rate of the polymer (Cooper et al. 1986 [100] [91]).

CHAPTER 2. PHYSICS OF NEUTRON SCATTERING AND BACKGROUND

Brownian movement, displacement of solvent molecules in solvent/nonsolvent mixture The Stokes-Einstein law describes the relationship between the speed of movement of molecules and their size. Thus, the larger the molecules, the lower the speed of their movement. The diffusion coefficient D of a solvent molecule in water is given by the following equation:

D = k B * T 6π µR , (2.31)
where, k B is a Boltzmann constant (1.38 * 10 -23 m 2 .kg.s -2 .K -1 ), T is the temperature in Kelvin, µ is the viscosity of the sample in Pa.s and R is the radius of a molecule of solvent.

And the diffusion time from a Benzyl alcohol molecule as function of the thickness of the nonsolvent has for equation:

t = e 2 2D , (2.32)
where, e is the thickness and D is the diffusion.

In a solvent/non-solvent system applied on the polymer varnish film, one can ask what is the necessary time for a BA molecule to go to the surface of this film. A question which allows the restorers to predict how long the film should be in contact with the solvent/nonsolvent mixture to have the best result. Using the equations 2. The diffusion time of the solvent is a function of the deposited thickness. This is the average time that molecules will need to travel a certain distance. The previous results are valid for solvent/water mixture. And the thicker the water layer, the longer the diffusion time.

Thus, two cases occur: a) case of the thin layer of water and b) case of thick layer of water. a) In the case of a thin water thickness, for example 200 microns, on average, the solvent molecules will take less than 30 seconds to cover this distance, which is a very short. As a result, the molecules of the top of the solvent arrive almost at the same time as those which were already at the bottom of the gel. This time finally has so little effect that it is negligible compared to the penetration time in the varnish. b) In the case of thick water thickness, for example 1200 microns, on average, the solvent molecules will take 1007 seconds or 17 minutes to cover this distance. Therefore, either if the water is removed from the polymer film surface early (well before 17 minutes), the top of the solvent is useless because its molecules do not reach the varnish. If one abrades later, all molecules have time to arrive. In this case, the concentration of solvent molecules that will be in the varnish film depends on the waiting time. But the risk is that, while the last molecules arrive at the surface of the varnish, the first molecules will continue their progression in the varnish and could reach the pictorial layer. This will depend on the concentration of solvent at the start but also the thickness of the varnish and its capability to swell and dissolve.

Of course, these results only take into account the displacement of the solvent in the water, with the gel, the kinetics of displacement is a little different. The gel molecules delays the diffusion of the solvent in the solvent/gel layer. If the solvent passes through the varnish and reaches the paint layer, it may solubilize the components of the latter and change the structure. To avoid any damage, it is better to apply a thin gel layer. The solvent is thus diffused quickly and the varnish film can be lightened layer-by-layer. The paint layer is safe and the restorer can control its action.

Solutions of polymers in Good Solvent

To assess the size of a polymer molecule, we need to talk about the dimensions of Random-Walk chains and their End-to-End Distance and the Radius of Gyration in a linear chain consisting of N bonds of length b [START_REF] Miller-Chou | A review of polymer dissolution[END_REF]. The end-to-end distance of the chain (root-mean-square end-to-end distance) is the root main square of the end-to-end vector R f .

Considering the average end-to-end distance defined as R f =N 1/2 b and the whole chain contains in a sphere of diameter R f , the square of the root-mean-square radius of gyration R g 2 is defined as the mean square distance between the monomers R n and the center of the mass R G . The radius of gyration R g of a polymer chain [101] is the root-mean-square distance of the segments of the molecule from its center of gravity of the ideal chain is given in eq. 2.33:

2R g 2 = 1 N N ∑ n=1 < (R n -R g ) 2 >, (2.33)
Which give the information about the size of the random coil shape. For large N ideal chains (N ≫ 1):

R g 2 = Nb 2 6 , (2.34)
where, the ratio of R f and R g is 6 1/2 . Indeed, the Fourier Transform of the average density of segments of the chain, g(q) is given by the following equation:

g(q) = drg(r)exp(iq • r) = 1 N N ∑ n=1 N ∑ m=1 < exp[iq • (R m -R n )] > . (2.35)
When N tends to infinity in the ideal random walk, g(q) gaussian for a Gaussian ideal polymer coil was solved in 1946 by P. Debye and is the Debye equation:

g(q) gaussian = 2N Q 2 [Q -1 + exp(-Q)], (2.36)
where, q = (qR g ) 2 .

For polymer coil in solution in long range interactions, the ideal and Gaussian chain exists only at the theta point. Outside this special condition, the random walk disappears in favor of a self-avoiding walk model. The solvent power can be changed by changing the temperature. It affects the coil size. When the temperature reaches the good solvent regime, the size of the coil increases. At the theta temperature θ (a very narrow temperature), the coil is Gaussian. Each polymer/solvent couple has its own θ -temperature value. It is the Flory temperature. In the case of temperature below the θ -temperature, the homogeneous mixture becomes unstable, the coils of the polymer collapse (phase separation) and form a precipitate.

Flory-Huggins Theory applied to bulk mixtures

Considering polymer chains as random walks on a lattice, Flory and Huggins assumed that the solvent and the polymer monomers are able to rearrange arbitrary themselves in this lattice model [START_REF] De Gennes | Scaling concepts in polymer physics[END_REF]. Each monomer occupies a specific site and the solvent molecules are in the free space which are not already occupied by the polymer. It is assumed that the free volume of each molecule or monomer is the same for all. Φ is the fraction of sites occupied by monomers and depends on the monomers concentration per cm 3 : Φ = ca 3 , where a 3 is the volume of the cubic site in the lattice [START_REF] Baughman | Neural networks in bioprocessing and chemical engineering[END_REF]. P.J. Flory [START_REF] Flory | Principles of polymer chemistry[END_REF] described the entropy of mixing ∆S for three-component mixture (nonsolvent (1), solvent (2) and polymer (3)) as:

∆S = -R(n 1 lnφ 1 + n 2 lnφ 2 + n 3 lnφ 3 ), (2.37)
where, n i is the number of moles and φ i is the volume fraction and R is the gas constant. And the equation of the enthalpy of mixing∆H is:

∆H = -RT (χ 13 φ 1 φ 3 + χ 12 φ 1 φ 2 + χ 23 φ 2 φ 3 )(m 1 n 1 + m 2 n 2 + m 3 n 3 ), (2.38)
where, χ i j is the Flory interaction parameter and m i is the ratio of the molar volume.

According to De Gennes [START_REF] De Gennes | Scaling concepts in polymer physics[END_REF], χ is dimensionless and it depends on several external parameters such as temperature and pressure. By its value, χ differentiates good solvents (low χ) from bad solvents (high χ) . When the free energy originates only from the entropy of mixing, the solvent interaction is close to the polymer and χ = 0. When the solvent is very good, temperature has no impact on the solvent/polymer interaction. The solvent is then called athermal. However, most of the time the interactions between polymer/solvent, polymer/nonsolvent and solvent/nonsolvent is mainly Van der Waals attraction and the Flory interaction parameter is positive and χ is not independent of the temperature.

A solvent with χ ≪1/2 including negative χ, is considering as a 'good' solvent. And conversely, a solvent with χ > 1/2 is a 'bad' or 'poor' solvent. The higher the χ solvent , less the solvent is able to dissolve the polymer. A solvent is called nonsolvent when it is unable to dissolve the polymer.

The free Gibbs energy depends on two factors, the strength of the intermolecular interactions which corresponds to the enthalpy of mixing ∆H (eq. 2.38) and the driving force at a given temperature which corresponds to the entropy of mixing ∆S (eq. 2.37):

∆G = ∆H -T ∆S.
(2.39) And the chemical potential µ i is: To estimate regions where the interactions parameters are favorable or unfavorable, we have to find the Flory-Huggins parameters assuming the mixing of polymer/solvent such as the effect of both enthalpy of mixing and entropy of mixing described by the free Gibbs energy of mixing, given then by:

∆ µ i RT = ( dG dn i ) T,P,n . (2
∆G M RT = n 1 lnφ 1 + n 2 lnφ 2 + n 3 lnφ 3 + g 12 (u 2 )n 1 φ 2 + χ 13 n 1 φ 3 + χ 23 n 2 φ 3 , (2.41)
where, g i j is the concentration-dependent interaction parameters and u 2 =φ 2 /(φ 1 +φ 2 ). [START_REF] Sharma | Instability of thin polymer films on coated substrates: rupture, dewetting, and drop formation[END_REF], the film becomes unstable due to a negative disjoining pressure given by attractive intermolecular interactions.

Spinodal decomposition or nucleation of the film irremediably change the initial smooth surface of the film by hole formation. Holes grown up and slowly expend with a constant velocity until the coalescence. The system tends always to minimize its total free energy. This expansion is due to the conjoining pressure near the interface polymer/substrate and the tension force of the surface which comes from to the circumferential curvature. Eventually, a thick polymer rim forms around the hole, because the flow imposes a viscous resistance on the polymer which varies as µH -3 with H is the local thickness of the deformed film. However, the surface tension force limits the growth of the rim. And, its expansion velocity depends of the initial thickness of the film. The hole/rim formation is faster for a thick film. Eventually, the rims of the holes can touch each other leading to coalescence. In this case, they form fluid pockets by capillarity instability comparable to the instability of Rayleigh. The last step is the formation of a pattern of droplets on the substrate by static ribbons forming the polygons of the rim movement at the edges of the holes (Rayleigh instabilities). The average distance between the holes is proportional to the square of the film thickness. Furthermore, the size of the holes does not depend on the interfacial energy of the interface of the substrate-film.

The dewetting of ultra-thin films of polystyrene (Ps) deposited onto silicon wafers was studied by Sharma and Reiter in 1996 [START_REF] Sharma | Instability of thin polymer films on coated substrates: rupture, dewetting, and drop formation[END_REF], by Xie et al. [START_REF] Xie | Spinodal dewetting of thin polymer films[END_REF] and by Reiter in 2001 [START_REF] Reiter | Spin-cast, thin, glassy polymer films: highly metastable forms of matter[END_REF]. Holes on the film surface were observed with an asymmetric rim and the inside wall of the hole is very steep unlike the outer part. The rim appears progressively. The number density of holes is given by Reiter [START_REF] Reiter | Unstable thin polymer-films-rupture and dewetting processes[END_REF] as r ∼ h -4 where h is the film thickness. To improve the understanding of the dewetting, a theoretical model to explain the difference between the rim outside and inside the hole was proposed by de Gennes et al. in 2002 [START_REF] Saulnier | Dewetting of thin polymer films near the glass transition[END_REF]. They demonstrated that the size of the holes and the rims depend on the initial film thickness and also the experimental time.

Then,inspired by the work of Reiter and Sharma [START_REF] Reiter | Spin-cast, thin, glassy polymer films: highly metastable forms of matter[END_REF], Seemann and al. [START_REF] Seemann | Dynamics and structure formation in thin polymer melt films[END_REF] proposed a new theoretical view of the study of dewetting of thin polymer films on a hydrophobic substrate by the use of a 2-D form of the lubrication model. They investigated the evolution of perturbations in the dewetting process at different boundary conditions (mainly no-slip and Navier slip conditions) at the liquid/solid interface. They showed that no-slip and slip-dominated cases lead to different rim profiles.

More recently, Pahlavan et al. [START_REF] Pahlavan | Thin films in partial wetting: stability, dewetting and coarsening[END_REF] have proposed a new model to explore the partialdewetting regime for thin liquid films on solid substrates by a thermodynamic framework.

Rheology and viscosity measurement

Theory

Rheology is the study of deformations and flows of material (gas or fluid), as a function of the forces applied on it. It applies to complex fluids, viscoelastic material, liquids and solids. Thus, it covers a wide range of products and materials as well as many fields (cosmetics, agri-food, material resistance, etc.).

The deformation depends on the material. Solid bodies can be deformed elastically (perfect solids). The energy required for the deformation is equal to the energy recovered after the applied stresses. For liquids and gases, the deformation is irreversible (ideal fluids) so the deformation energy is converted into heat in the fluid and cannot be recovered as such [START_REF] Schramm | A practical approach to rheology and rheometry[END_REF].

The relationship between applied stress and the resulting shear rate is called viscosity. Its influence was demonstrated as early as 1687 by Isaac Newton thanks to a simple shear experiment (Figure 2.12) between 2 plates, one fixed and the other with a translational movement under the action of an force -→ F , a pasty, molten liquid material. Leading to Newton's law which defines shear stress as the dynamic viscosity multiplied by the shear rate. Newton's experience has been redesigned and improved with the use of other geometries for viscosity measurements to adapt to any type of material but it is a model that is still valid nowadays and its law too [START_REF] Oswald | Rhéophysique: Ou comment coule la matière[END_REF]. The dynamic viscosity µ (Table 2.2), in Pascal seconds or g.cm -1 .s -1 , can be defined as the resistance to laminar flow of incompressible matter. It corresponds to the coefficient of the shear stress τ (Pa) necessary to obtain a gradient of flow velocity also called shear rate γ (s -1 ). The shear stress, in Pascal Pa, is the force F applied on the surface S of the sample, τ = F S with F in Newton and S in m 2 . The shear rate is the temporal derivative of the deformation, γ = dγ dt . In Newtonian fluids (constant viscosity whatever the stress or the shear rate), the kinematic viscosity can be define as the ratio of dynamic (absolute) viscosity to density. It can be obtained by dividing the absolute viscosity of a fluid:

υ = µ ρ , (2.42)
with the fluid mass density ρ in g/m 3 and dynamic viscosity µ in g.cm -1 .s -1 (or Pa.s). 1.0x10 -3 1.0x10 -6 oil 10 -2 to 1 10 -5 to 10 -3 molter polymer 10 2 to 10 4 10 -1 to 10

In order to analyse the rheological properties of the fluids, it is possible to measure the viscosity during shear deformation stress; this is rheometry. In addition to the shear rate effect on viscosity, some other factors influence the fluid behavior such as the pressure and mainly the temperature. In the case of a liquid, an increase in temperature leads to a separation of molecules and reduces their mutual attractions, which reduces viscosity. An increased pressure does the opposite.

Fluids can be Newtonian or non-Newtonian. The non-Newtonian fluids [START_REF] Oswald | Rhéophysique: Ou comment coule la matière[END_REF] [START_REF] Macosko | Rheology: principles, measurements, and applications[END_REF] are much more numerous and they correspond to all the fluids whose viscous stress is not proportional with the applied shear gradient.

Unlike Newtonian fluids (water and some mineral oils), the viscosity of non-Newtonian fluids does not remain constant but depends on the shear rate or applied stress. The viscosity of shear-thinning liquids change according to the shear rate following the Oswald model is given by :

µ( γ) = K| γ| m-1 , (2.43)
with K, a constant representing the consistency of the liquid and m, the fluid index of pseudo plasticity (m ≤ 1). If m = 1, the behavior is Newtonian, if m = 0, then the behavior is plastic. The law of power (eq. 2.44) and the Herschel-Buckeley's law (eq. 2.45), an generalization of Bingham's law (eq. 2.3.1) makes it possible to describe the behavior of non-Newtonian fluids even if it is not the only model. τ = K γn .

(2.44)

τ = τ 0 + K γn , (2.45)
where, n is the flow index.

CHAPTER 2. PHYSICS OF NEUTRON SCATTERING AND BACKGROUND is invariant, the Navier-Stokes formula in cylindrical coordinates (r, theta, z) becomes:

- δ P δ z + η 1 r d dr (r dυ z dr ) = 0.
(2.47)

Figure 2.16 -Poiseuille flow in a cylindrical capillary with its velocity profile and its viscous stress σ υ zr (in module) from reference [START_REF] Oswald | Rhéophysique: Ou comment coule la matière[END_REF] The velocity profile is parabolic and the viscous stress σ υ zr is maximum on the surface of the tube and decreases linearly towards the center of the tube so the shear is not constant.

The average flow of the fluid is proportional to the pressure gradient and inversely proportional to the fluid viscosity. It is given by the Poiseuille law which gives the flow Q and the average speed η z of the fluid in the tube:

Q = πR 2 η z = π(∆P)R 4 8ηL .
(2.48) Figure 3.5 -Polyacrylic acid during the process of swelling (from an image by Claire Dupuy [START_REF] Dupuy | Les solvants organiques neutres épaissis pour le nettoyage d'une couche picturale. comparaison des acides polyacryliques et des éthers de cellulose comme épais-BIBLIOGRAPHY sissant des solvants organiques[END_REF] It can stabilize until a high oil concentration (50wt % of oil) that is to say, much more than the majority of surfactants. Pemulen TR-2 (PTR2) was used for cleaning painted surfaces at these high concentrations to form an emulsion [47]

Rheology of the gel

Informations about the rheometer used in this study and the method of analysis are presented later in the section 3.3.8.

The more PTR2 in the Pemulen/water mixture, the more viscous the gel is (Fig. 3.8 and Fig. 3.9). By increasing the pH (stable between pH 3 and pH 9) with for example some triethanolamine or sodium hydroxide NaCl, the gel becomes more viscous (Fig. 3.10). The presence of a small amount of BA (between 0 % and 1 % BA) slightly decreases the viscosity of the Pemulen TR-2 gel at fixed pH (Fig. 3.12). The flow behavior index n from the law of power equation 2.44 corresponding of the slope of the rheology curves (Shear stress as function of shear rate) in the Fig. 3.9 and Fig. 3.12 are ∼ 0.5, so less than 1 which is characteristic of pseudoplastic behavior (viscosity decreases as shear rate increases) of this gel. It is consistent because most non-Newtonian fluids are pseudoplastic. Moreover, the flow behavior index is higher with the increasing concentration of PTR2. The gel has a very slight slip behavior which means the adhesion to the interface of the cone-plane/gel and gel/support is good (Fig. 3.13). So, the rheology of Pemulen TR-2 samples show a non-newtonian shear thinning behavior with a slight thixotropy (apparent viscosity decreases over time under constant stress). The gel with and without BA appeared physically stable, even after several weeks at room temperature. The apparent viscosity depends on the concentration of Pemulen TR-2 and the amount of BA contained. It is also sensitive to the temperature. Its behavior and its formulation are close to those of the Carbopol® resins. Pemulen TR-2 gel is a crosslinked copolymer of acrylic acid and a hydrophobic C10-C30 alkyl acrylate co-monomer (Fig. 3.6) [START_REF] Goddard | Principles of polymer science and technology in cosmetics and personal care[END_REF].

Preparation of samples and measurement of thickness

Film preparation can be made using several methods such as spin coating, dip coating, spraycoating, casting or flow coating methods but the first one is most widely used for depositing thin polymer layers on flat solid substrates [START_REF] Sahu | Fundamental understanding and modeling of spin coating process: a review[END_REF]. Spin coating method is mainly used because of its simplicity of use and the repeatability of the samples [START_REF] Hall | Spin coating of thin and ultrathin polymer films[END_REF]. It quickly became an indispensable tool for industrial application and scientific research. However, this is not a suitable technique to make thick layers, in which case, the method by dip coating is preferred and allows us to obtain homogeneous thick films.

Thin and Thick Films formation by spin coating for NR and SANS

Ultrathin film (∼ 100 nm) and thin film (between 200 nm and 500 nm) are obtained by spin coating which is a common reproducible techniques for applying uniform thin and ultrathin films of few nanometres to a few microns thicknesses on plane surfaces of substrates by spreading a polymer liquid solution on a horizontal rotating substrate. The polymer solution is previously achieved by polymer solubilization in a solvent. Then, the polymer fluid is deposited on the wafer which spreads by high speed rotation evenly across the surface of the substrate. At the end, the aim is to obtain a uniform film layer with the thickness previously chosen.

Cleaning of wafers and blocks

Before spin-coating the polymer solution, substrates and single crystal silicon blocks were rigorously cleaned subsequently 15 min sonication in water/Decon 90 (1 drop) mixture, ethanol, acetone, chloroform and ending with clean water and dried with filtered nitrogen at room temperature. Then, the thickness of the SiO 2 layer was determined by ellipsometry (3.2.3).

CHAPTER 3. EXPERIMENTAL

Ultrathin and thin films by Spin-coating

Predicting thicknesses and homogenize the layer on the flat substrates is a challenging task which depends on several factors (the polymer concentration and viscosity in liquid state in solvent, the evaporation rate of solvent, the angular velocity, the rotation time and the substrate roughness) not governed by fixed rules but based on empirical models. These factors impact the surface state and are at the origin of common spin coating defects (air bubbles, comets, streaks of flares, swirl pattern, center circle, uncoated areas and pinholes) which are described and analysed in reference [130]. A simple model of spin coating as a function of the polymer concentration, the polymer viscosity and the spin speed was proposed by Bornside, Macosko and Scriven in 1989 [START_REF] Bornside | Spin coating: one-dimensional model[END_REF]. This study was completed by Hall, Underhill and Torkelson in 1998 [START_REF] Hall | Spin coating of thin and ultrathin polymer films[END_REF] by carrying out a study on the thickness of the PS and PMMA films obtained by spin coating as a function of the spin speed (Fig. 3.16) and by showing the impact of a highly volatile or low volatile solvent on the thickness of the film.

Taking into account these factors and the studies of the review [START_REF] Sahu | Fundamental understanding and modeling of spin coating process: a review[END_REF], thin films of Laropal®A81 at ∼100 nm (Fig. 3.19), ∼200 nm, ∼300 nm and ∼500 nm were achieved by spin coating for neutron reflectometry and SANS studies on the SÜSS MicroTec Lithograhy GmbH (Ak-200609) shown in Fig. 3.15. The spin coating method was always the same: pure toluene was deposited and spread by high speed rotation. Then, LA polymer resin diluted in toluene of a certain concentration was deposited on the center of the substrate. The solution was spread on the substrate by high speed rotation. Then, the excess solution was ejected from the substrate. After solvent evaporation, a thin film was formed on the substrate. Films thicknesses were measured by ellipsometry (3.2.3).

To find the best parameters to obtain homogeneous ultrathin films, first a test with different spin speed (500 RPM to 3000 RPM) at 20 g/L LA and 40 g/L LA on silicon wafers was done. The density (1.11 g/cm 3 ) and the chemistry of LA are similar to PS (1.04 g/cm 3 ) and PMMA (1.18 g/cm 3 ). As only a few data are present in the scientific literature for LA, PS and PMMA polymers was chosen such as references because of their chemical similarities with LA. In order to approach 100 nm thick films, LA concentrations were chosen following the PS and PMMA spin-coating investigation (fig. [START_REF] Hall | Spin coating of thin and ultrathin polymer films[END_REF]) from Hall et al. in the reference [START_REF] Hall | Spin coating of thin and ultrathin polymer films[END_REF]. Between 1200 RPM and 3000 RPM, ultrathin films of 43 nm (2 %) and 90 nm (4 %) homogeneous films were obtained. For spin speed, numerous defects on LA films were observed, such as streaks, center circle or swirl pattern and the thickness varied too much on the film and it was difficult to obtain a real value by ellipsometry. Instead of the fitted SLD values of the polymer layer the total excess volume fractions of BA φ BA and that of D 2 O φ D 2 O inside the varnish layer are reported by applying the following boundary conditions, which assumes constant density and mass conservation of the varnish, obviously only applicable before dissolution of the film:

1 + φ D 2 O + φ BA = d d dry d d dry * SLD = φ D 2 O * SLD D 2 O + φ BA * SLD BA +( d d dry -φ D 2 O -φ BA ) * SLD LA , (3.2)
where, d and d dry are the swollen and dry layer thicknesses, respectively, and SLD D 2 O , SLD BA and SLD LA are the swollen SLD and the bulk SLDs of D 2 O, BA and LA, respectively. The total swelling ratios r of the whole film is defined by the layer thickness:

r = d/d dry . (3.3)
As shown in table 6.1 the SLD contrast between heavy water and all other components is significantly higher than between BA and the polymer. This will dictate the sensitivity of the

AFM measurements

Atomic force microscopy (AFM) [START_REF] Binnig | Atomic force microscope[END_REF] is used to investigate the dewetting on LA films after its swelling by BA/W mixture. This powerful imaging technique is able to scan the surface of a film by using a sharp tip (< 10 nm) at the end of a cantilever (around 100-500 µm in length). It allows to obtain topographical images of the surface and of the objects or alterations that are on it. The resolution is highly accurate with a scale of the order of a nanometer (Fig. 3.32). Informations from the surface film is obtained thanks to the electronic attraction and repulsion forces (Van der Waals and steric interactions), generated between the sample and the tip. The tip scans and maps the sample during its displacement in the x, y, z direction. Thanks to piezoelectric actuators, the movement of the sample is very precise. Similarly, the cantilever is fixed at a piezoelectric driver to oscillate at its resonance and its resonant frequency. The cantilever behaves as a damped spring. For soft material structure, the tapping mode is chosen. This mode does an intermittent contact and a high amplitude oscillation which prevents the tip from making a frictional force on the material surface and damaging the sample. The operation of the AFM for the investigation of a polymer film on a Si wafer is shown in the Fig. 3.31.

QCM-D measurements

The piezoelectric effect was discovered by the Curie brothers in 1880. A few years after, in 1959, Sauerbrey [START_REF] Sauerbrey | The use of quarts oscillators for weighing thin layers and for microweighing[END_REF] brought to light the relation between the mass per unit area loaded on a quartz crystal surface and the resonance frequency shift (eq. 3.4) and laid the foundations of QCM for the study of a rigid film in a liquid. The theory and application of quartz crystal microbalance (QCM) is described in the review by Xiaoxi Qiao et al. in 2016 [START_REF] Qiao | Progresses on the theory and application of quartz crystal microbalance[END_REF].

Quartz Crystal Microbalance, a nondestructive technique, is a sensitive mass balance which allows us to measure the mass per unit area of a material (nanogram to microgram) by oscillation frequency measurement on quartz crystal chips with two electrode sensors and an AT-cut quartz crystal (Fig. 3.33). QCM is based on the piezoelectric effect [START_REF] Ward | In situ interfacial mass detection with piezoelectric transducers[END_REF] [146] of 'acentric' materials class crystals of which Quartz is part. By application of a driving voltage between the two electrodes sensors, the quartz crystal is deformed in thickness-shear-mode.

∆m f = -C ′ * 1 n * ∆ f , (3.4)
where, ∆m f is the mass change, ∆ f is the frequency change, C' is a constant depending of the crystal used (for a 5 MHz-AT cut quartz crystal at room temperature, C' ∼ 17.7 ng /(cm 2 .Hz)) and is the overtone number. Some pellets of LA81 resin was previously placed in contact of a small concentration of BA (0 %, 0.4 %, 0.6 %, 0.8 % and 1 %) in D 2 O. 4 mg of LA81 samples resin, with and without immersion in BA solutions (0.3 %, 0.5 % and 0.7 %), were loaded into aluminium capsules previously weighed which are then sealed. One by one, a sample and an empty closed aluminium reference capsule were placed in a DSC instrument at room temperature. The samples were heated between 0˚C to 130˚C at a rate of 10˚C/min in four separate runs. The glass transition temperature (T g ) was obtained from the average of the second, third and fourth runs using TA Instruments Thermal Advantage (Fig. 3.35).

Rotary rheometer

The characterization of the gel was made on the rheometer AR-G2 by TA Instruments from the Laboratoire de Rhéologie et Procédés, Grenoble. It was chosen to use the geometry cone-plane (Fig. 2

.15).

Rotary rheometry is most used for measuring the viscosity of the material studied (gel, polymer, etc.). It allows to make a relation between the stress and the deformation. It presents mainly two geometries, cylinder-cylinder and cone-plane. The use of one or the other depends of the type of sample and the viscosity expected by eyes. The cone-plane geometry (Figure 2.15) is the most appropriate to use for this study because it allows a constant shear rate to be maintained in the space between the cone and the plane, whatever the angle θ and the radius R of the plane.The viscosity measurement is done by measuring the combined amount of the couple γ and the rotation speed ω. For this, one of the two is imposed. It depends of the rheometer. The theory of rheology was previously exposed in 2.3. For this project, the rheometer chosen imposed the stress via the geometry cone-plane (Fig. 2.15) and thanks to a rotary motor. The material is then deformed and its displacement or the resulting torque is recorded and processed by the software.

Capillary rheometer

Theory of capillary rheometry is given in the part 2.3. In order to propose a ternary phase diagram model, the three Flory-Huggins interaction parameters in LA(3)/BA(2)/W(1) systems is determined by combining both viscosity measurement with a capillary rheometer and Flory-Huggins energy calculation. Viscosity of a homogeneous solution of LA/BA at very low polymer concentration (0.1 %, 0.2 %, 0.4 %, 0.6 %, 0.8 % and 1 % LA) is obtained by capillarity measurements at 25.2°C ± 0.1°C allowing the calculation of the intrinsic viscosity of LA as function of the concentration of LA in BA showing in Fig. 3.37. A Ubbelohde capillary rheometer n°538-20 of the LRP was used. Its range was from 4 to 6 mm 2 /s which corresponds to a capillary tube of 0.70 mm.

The Ubbelohde capillary rheometer consists mainly of three tubular parts. The main one is the capillary tube (on the right in the Fig. 3.36) because it is the part where the measurements of the fluid travel time are made between the marks A and B. A liquid is placed into the sphere of the pre-flows above the mark A. Once the pressure is removed, the fluid begins its descent towards the capillary tube (down), subjected to gravity. The measurement begins at the moment where the fluid passes the mark A. The time taken for the liquid to travel from mark A to mark B is recorded with a ViscoClock, an electronic timer for determining absolute and relative viscosity which automatically measures the flow time through the viscometer of the liquid at a fixed temperature with a high resolution of 0.01 second. The kinematic viscosity is deduced from the measured passage time following this formula υ = K(tδ ) with K = 0.1, the constant relating to the capillary used and δ = 0.12, the kinematic energy correction which is function of the passage time.

CHAPTER 4 SWELLING, DEWETTING AND BREAKUP IN THIN POLYMER FILMS FOR CULTURAL HERITAGE

This chapter is focused on the first paper of this project which was submitted the 2 October 2019, accepted the 25th November 2019 and published the 13th January 2020 in Soft Matter in the issue 16 on pages 1485 -1497 [13]. In addition, this paper gave rise to a web story on the ILL page, an article in the Sunday Telegraph by Dalya Alberge on March 15, 2020 and on the website, an article in the Picture Perfect of the Laboratory News on may, 2020 (pages 20-21), an article entitled "Gentle approach to the restoration of valuable paintings" in the Farbe und Lack and an article online entitled "Protecting works of art with neutrons" in the pro-physik.de website.

The aim is to understand the macroscopic and nanoscopic behaviors of a film of a polymer (Laropal®A81) currently used in the Cultural Heritage and more particularly as a varnish coating on paint layers. Ultrathin films were observed in different conditions: annealed a few minutes, immersed in water and the most important result, immersed in BA/water mixture. It represents a long research work and leads in particular to the analysis of the reflectivity data. It also shows the use of a large number of techniques and materials (NR, DSC, low viscosity polymer viscosity measurement, Optical Microscope and AFM) leading to exploitable results and consistent discussion about the kinetics of swelling of the film and the distribution profiles of solvent (BA) and nonsolvent (heavy water) inside the polymer.

This work reveals at a certain BA concentration the apparition of holes with a significant bump on the polymer films models and that after immersion few hours in BA/water. These holes was observed by Optical microscope and AFM. Holes with bump is characteristic of a dewetting process of thin polymer film.

Swelling, Dewetting and Breakup in thin polymer films for cultural heritage

Amélie Castel 1,3 , Philipp Gutfreund 1 * , Bernard Cabane 2 and Yahya Rharbi 3 *

The removal of ultrathin amorphous polymer films in contact with nonsolvent/solvent binary mixtures is addressed by means of neutron reflectometry and atomic force microscopy. The high resolution of neutron scattering makes it possible to resolve the distribution profiles of heavy water and benzyl alcohol inside Laropal®A81, often employed as a protective varnish layer for Culture Heritage in restoration of easel paintings. The swelling kinetics and distribution profiles were recorded as a function of time and increasing benzyl alcohol concentration in water. The varnish film swells by penetration of the good solvent. At higher concentrations water-filled cavities appear inside the varnish and grow with time. Contrary to homogeneous dissolution dewetting is observed at late stages of exposure to the liquid which leads to the Breakup of the film. The high resolution measurements are compared to bulk behaviour characterized by the ternary phase diagram and the Flory-Huggins interaction parameters are calculated and used to predict the swelling and solvent partition in the films. Distinct differences of the thin film to bulk behaviour are found. The expectations made previously for the behaviour of solvent/non-solvent mixtures on the removal of thin layers in the restoration of easel paintings should be revised in view of surface interactions. Keywords: Art restoration; Diffusion; Laropal®A81; Neutron reflectivity; Polymer; Solvents; Swelling; Ternary Phase Diagram; Thin film

Introduction

Thin films of glassy polymers or varnishes are frequently used to protect a substrate from physical or chemical agents. They can be deposited through a variety of techniques, usually involving a liquid to solid transition of a solution of the polymer in a volatile solvent. 1 It appears that the removal of such thin films has not been studied as extensively as their deposition, although there exists a detailed review of polymer dissolution. 2 Yet there are many fields where a better control of polymer dissolution and removal is highly desirable: industrial applications 3 such as the fabrication of microchips, the recycling of plastics and the manufacturing of polymer membranes, and also biomedical applications such as the tissue regeneration and drug delivery. 4 A particularly demanding field is the restoration of works of art 5 6 7 8 , particularly old paintings that have been altered by exposure to ambient conditions (urban air, humidity) over very long 1 Institut Laue Langevin, Grenoble, France. * gutfreund@ill.fr, rharbi@ujf-grenoble.fr periods of time. Indeed, the varnish layers that ancient painters have applied originally to protect the paintings may deteriorate in many ways: capture of airborne particles 9 , formation of microcracks or change in color and acidification 5 just to name a few. The classic restoration treatment consists in removing most of the old varnish layers and replacing them with a fresh varnish, which will restore the protective and aesthetic functions. The removal of the old varnish is achieved through the addition of solvents, which enter the solid varnish and transform it into a liquid polymer solution. A condition for safe removal of the old varnish is that it should have no effect on the pictorial layer. This raises a question regarding the depth of penetration of the solvent that has been applied to the film. The quantity of solvent applied by the restorer is adjusted to liquefy a certain number of varnish layers, but not all of them; however, controlling the quantity of solvent does not imply that the penetration depth is controlled. 7 8 10 A safe varnish removal would have full respect for the integrity of the innermost varnish layer, which means that the solvent would never reach it. At present, they are few studies that give indications of whether or not this condition is met. 5 11 12 13 In recent years, restorers have employed two approaches to this problem: On the one hand, they have tried to decrease the chem-

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ical potential of the solvent, and thus make it less aggressive to the inner layers of the painting. Accordingly, the restorer may dilute the solvent with a bad-solvent for the varnish 14 and, by trial and error, determine which compositions and volumes of solvent mixtures appear to be harmless to the pictorial layer at the time of observation. 15 16 On the other hand, some restorers are using delivery systems for the solvent, such as hydrogels, sponges or nonwoven fabrics that contain the solvent. Several studies propose to use a solvent/water system to reduce the toxicity of the process to the operators. 17 However, the effects of a solvent/nonsolvent mixture may not be extrapolated from those of a solvent alone, especially when the nonsolvent is water. In order to understand and model these phenomena, it is necessary to use a technique that makes it possible to measure the depth of solvent and nonsolvent penetration in the films with a high special resolution. Ultimately, it should be possible to construct a model that takes into account the relative locations of all molecules in the films and their interactions, and makes it possible to predict the spatial and temporal features of the dissolution process. For very thick films, the imaging of the film during dissolution through Fourier Transform Infra-Red spectroscopy (FTIR) has produced spectacular maps showing the locations of macromolecules and of the solvent and nonsolvent molecules in the films. These maps have revealed different patterns of dissolution depending on the solvent/nonsolvent composition 18 ; they also show that dissolution/condensation processes have a large effect on the dissolution rates. 18 19 However, the experiments by FTIR imaging have a limited spatial resolution and, in addition, the films (∼ 150 nm) were sandwiched between two salt plates, which is far from the coating procedure employed in varnishes. Usually varnish films are deposited through classical coatings techniques.

Neutron reflectometry (NR) is a technique that yields both structural and chemical information thanks to targeted hydrogen/deuterium (H/D) labeling. It is an ideal tool to observe the solvent penetration in real time and has already proven this in similar experiments. 6 20 21 It is a non-destructive and noninvasive technique for the investigation of thin polymer films. It is a powerful technique for the study of liquid/solid and liquid/liquid interfaces with a resolution of a few Ångstrà ¶ms. For aqueous systems the replacement of water with heavy water can yield an excellent contrast. In addition, NR makes it possible to record the kinetics of the transformations that take place between the initial and the final state of the films. To complement the NR results optical and atomic force microscopy (AFM) is also used in this study together with thermodynamic calculations based on the bulk ternary phase diagram. Note that while NR gives a statistically averaged concentration depth profile over a large area AFM gives a local snap-shoot of the surface morphology. Therefor NR is essential for a complete view of the system. What we would like to obtain from the NR is the concentration profiles of solvent and nonsolvent, and a detailed picture of the solid-liquid transition in the varnish layer as a function of solvent uptake. This transition may be quite different from the solid-liquid transitions of non-polymeric materials. Unlike nonpolymeric materials, polymers do not dissolve instantaneously and the classic dissolution process of a polymer involves trans-port processes, namely solvent diffusion and disentanglement of the polymer chains. 1 The first stage is penetration of a few solvent molecules that plasticize the polymer. As a result, the macromolecules can cross the polymer/solvent interface. If the molecular weight of the polymer is high enough, they will form a gel layer at the surface of the film. The next stage is the disentanglement of the macromolecules and their escape from the gel layer into the solvent. But there are also cases where the polymer cracks before any gel layer is formed. At present, we do not know which is the dissolution process (i.e. with or without a gel layer) of thin and ultrathin varnish films.

Motivated by new emerging technologies the physics of swelling and dissolution of thin polymer films has been the subject of several literature reports. 2 18 19 It involves the synergy between several interconnected phenomena: solvent/polymer interaction, polymer dynamics, molecular and macromolecular diffusion in glassy material and the physics of the glass transition in the presence of solvent moieties. This problem becomes even more intriguing in ultrathin films because of the dimensional reduction, the confinement and the surface/polymer interactions. Because there are several indications that confinement in ultrathin films induces deviation of several polymer properties (glass transition, polymer dynamics, thermal expansion) one might question how confinement affects swelling and dissolution. The behavior of the varnish in dissolution largely depends on the polymer mobility inside the films. Initially the varnish polymers are in an amorphous glassy state where the glassy dynamic inhibit chain mobility and the amorphous structure leads to a good transparency. The glassy state is characterized by a glass transition temperature (T ). The intrusion of small solvent molecules with a low T will eventually reduce the T of the system below ambient temperature. When this happens the varnish polymer will cross to a gel or liquid state with substantial chain mobility. In the vicinity of non-adsorbing interfaces, the glass transition temperature is lower than in the bulk and therefore ultrathin polymer films may cross the solidliquid transition earlier than thick films. 22 23 24 25 There remains some controversy on the variation of T as a function of distance to the interface in ultrathin polymer films. 26 27 28 There may also be an effect of the Van der Waals attractions between the film and its substrate. 29 30 31 If a binary solvent is used the situation becomes even more diverse because of three-body interactions in such confined systems.

Here we present a quantitative characterization of the swelling and dissolution mechanisms of supported ultrathin films of the amorphous glassy polymer by solvent/nonsolvent mixtures. This work is carried out on a glassy amorphous varnish Laropal®A81 (LA) to address the scientific aspect of varnish removal from easel paintings which is one of the most destructive treatments in the field of art restoration. We use time-resolved neutron reflectometry to probe the swelling kinetics of supported thin LA films (70 -200 nm) on silicon substrates by mixtures of benzyl alcohol (BA) and deuterated water (W). The quantitative analysis of the NR spectra reveals two very distinct swelling regimes at low and intermediate solvent concentrations: At low solvent concentrations the varnish is penetrated by the good solvent (BA) and exhibits only swelling perpendicular to the interface followed by a verti-

2 | 1-13
cal swelling at higher BA concentrations. At these stages no water penetration is visible. The delay in vertical swelling is explained by swelling asymmetry induced by polymer adsorption to the substrate by van der Waals (VdW) forces. At higher BA concentrations instead of a continued swelling and dissolution a dewetting type process starts leading to the appearance of holes in the polymer film filled with water. These holes grow with time and/or BA concentration and eventually the bulk of the film departs into the liquid phase leaving only some islands or droplets on the subtrate.

Experimental

Materials

The Laropal®A81 polymer (LA) from (BASF) 32 is a synthetic thermoplastic polymer synthesized from urea, isobutyraldehyde, and formaldehyde. Size-exclusion chromatography (SEC) analysis of this polymer yield Mw = 3640, and Mn = 1266 Da. 33 Its molecular structure was detailed in reference. 34 The T measurement was carried out on a Mettler-Toledo DSC823 apparatus in Nitrogen gas environment in the heating mode. This yields a T value of 47 °C. The LA density is 1,1 g/cm 3 at 20°C. Its reflective index is 1.503. 35 36 As solvents, Benzyl alcohol (Sigma-Aldrich, 99.8 %), deuterated water (Eurisotop ref D214L, 99,9 % D) and doubly deionized water were used in these experiments.

Thin film preparation and characterization

Laropal®A81 thin films were prepared by spin-coating using Delta 6 RC TT (SÜSS MicroTec Lithography GmbH). 37 The substrates (Sil'Tronix France) 8x5x1 cm 3 and 5x5x1 cm 3 single crystal silicon blocks (Si) were rigorously cleaned before spin-coating subsequently sonicate in water plus one drop on Decon 90 mixture, clean water, ethanol, acetone, chloroform and ending with clean water during 15 min for each products and dried at room temperature. The LA/toluene solutions at 30g/L and 80g/L were spin-coated at 2250 rpm for 44 seconds at room temperature (21°C). 38 Film thicknesses were measured using a Beaglehole Picometer Light Ellipsometer with a monochromatic laser beam. Note that the final film thickness prepared from the same solution on a 2 inch wafer of 0.7 mm thickness was not the same as the one prepared on a 10 mm thick silicon block. Therefore the size of the substrate clearly has an influence on the spin-coated polymer film. In the following only results obtained on 10 mm thick Si blocks are shown. The film thickness was found to be uniform (<10 % thickness variation over the whole film), this yields two set of films with thicknesses ∼ 70 nm and ∼ 230 nm. Given the commercial origin of the polymer the sample preparation is delicate. A large number of samples was prepared in advance of neutrons experiments and only samples that showed a homogeneous dry layer in water were used in this study.

Neutron Reflectometry

In NR a collimated neutron beam (incident beam) is directed at the Si/LA/W interfaces through the Si block, which is practically transparent for neutrons, with an incident angle and the reflectivity profile of the reflected beam at an exit angle = equal to the incident angle is measured as a function of the momentum change perpendicular to the polymer film surface (see Fig. 1). As can be seen in the figure the difference in momentum normal to the surface before ( ) and after ( ) neutron reflection can be defined:

= 4 * sin( ). (1)
A range of values can be obtained either by varying the neutron wavelength (time-of-flight (ToF) method) or by varying the incident angle at constant wavelength (monochromatic method). NR experiments were performed on FIGARO at the Institut Laue-Langevin (ILL), Grenoble, France, and on N-Rex + at the Forschungs-Neutronenquelle Heinz Maier-Leibnitz (FR rching, Germany. On the ToF reflectometer FIGARO 39 with horizontal sample geometry, a wavelength band between 2 Å and 20 Å was used with a relative wavelength resolution of 2.1 % (FWHM). The two dimensional multitube detector allows the measurement of specular and off-specular reflectivity simultaneously. The detector has a size of 25 x 48 cm 2 and a resolution of 2.2 x 4.8 mm 2 (FWHM) at a distance of 2.8 m from the sample. Two reflection angles were used to cover the full q-range: 0.622 and 2.622 degrees. The collimation slits were set to ensure a constant relative angular resolution of Δ ∕ = 2 % and the footprint on the sample was 40x40 mm 2 . The raw data was converted to absolute reflectivities as a function of momentum transfer by using the data reduction software COSMOS. 40 N-REX+ 41 at FRM2 is an angle dispersive fixed wavelength (4.4 Å, resolution 3 %) reflectometer with horizontal sample geometry. A 20 x 20 cm 2 position sensitive detector was used allowing for specular and off-specular reflectivity measurements although only the specular data was analyzed here. LA Films on silicon blocks were first measured in air and then in D 2 O. Subsequently, the LA films were measured in solutions of D 2 O containing an increasing BA concentration -(0 %, 0.05 %, 0.1 %, 0.15 %, 0.2 %, 0.25 %, 0.3 %, 0.35 %, 0.4 % and 0.5 %). All NR samples were measured at room temperature (21 °C). Time resolved NR spectra were integrated over 5 min and the measurement repeated several times between 1 h and 12 h in total.

Fig. 1 Sketch of the specular reflection geometry at the water/polymer/Si substrate system. Note that the reflection angles are exaggerated for illustration, in a real experiment the neutron beam enters and leaves the silicon substrate from the sides rather than the bottom.

Analysis of specular reflectivity

The measured NR data is subsequently compared to simulated NR curves calculated by an optical matrix formalism from a slab 1-13 | 3 model 42 and the goodness of the fit is calculated. This leastsquares fitting procedure is repeated until a convergence is found by using MOTOFIT. 43 The model used here to fit the NR curves consists of an infinitely thick single crystal silicon slab covered by a thin layer of silicon dioxide, which thickness varied between 1 nm and 2 nm among the samples, and a layer of swollen LA on top capped by an infinite layer of D 2 0/BA. The fitting model uses several fitting parameters, the BA and D 2 O concentration profiles in LA, the thickness and the roughness of each layer. Several models can be chosen to describe the solvent profiles within the film: constant concentration , a linear, adsorbed or brush model. 44,45 In the first stage the constant profile model was used to quantify the average film thickness and concentrations and the interface roughness. Each of the layers was fitted by allowing its thickness and roughness to change until convergence was found. The SLDs of silicon dioxide and silicon were fixed at the corresponding literature values reported in table 1 and the SLDs of the swollen LA and D 2 0/BA phases were fitted. The thicknesses and the roughness of all layers were fitted as well. The silicon substrate and silicon dioxide were found to be atomically smooth (between 0.2 nm and 0.5 nm) and therefore are not discussed further. In an other set of analysis, a concentration profile of the solvent within the film was added to the three steps profile described above (Si/LA/W), including the roughness of the Si/LA and LA/W interfaces, and the resulting reflectively data was compared to the experimental one. From the combination of the fitted film thicknesses and SLD values, the volume fractions of BA ( ∕ ) and D 2 0 ( ∕ ) are calculated assuming mass conservation of the polymer (equation 4). This assumption is obviously applicable only before film dissolution or breaking. Starting from 0.3% of BA in water a single polymer layer model was not giving satisfactory fits to the NR data anymore. For higher concentrations the LA layer was split into three sub-layers with individual SLDs, roughness and thickness. In these cases the mass conservation of LA was not assumed anymore, but instead it was assumed that the polymer thickness swelling is solely due to BA uptake (no thickness swelling due to water).

The total vertical swelling ratios is calculated using the swollen and the non swollen film thicknesses:

= ℎ∕ℎ 0 (2)
, ℎ being the swollen film thickness and ℎ 0 the initial dry thickness.

Off-Specular neutron reflectivity

As the neutron reflectivity spectra were recorded using 2D detectors the off specular neutron reflectivity (OSS) is also accessible. 46 The OSS intensity corresponds to the intensity scattered at a condition were ≠ . In this case the total momentum transfer also comprises an in-plane component:

= 2 (cos -cos ). (3)
This allows one to determine SLD variations parallel to the interface but due to the geometry the momentum transfers are typically two orders of magnitude smaller than in specular reflectometry and therefore the spatial resolution is much lower probing micrometer sized structures. The width of the reflected beam was also extracted from the COSMOS data reduction software in order to monitor any broadening coming from buckling of the layer on a length scale of mm or cm. 47

Ternary phase Diagram

The LA/BA/W ternary phase diagram was measured using turbidity measurements at room temperature. LA/BA mixtures with different concentrations were prepared by dissolving LA pellets in BA solution between 10 % and 80 % LA under rigorous agitation for more than 48h. Hydrogenated water was added drop-wise to LA/BA solutions in a 15 mL clear Vial (2 cm in diameter and 7 cm in height) and the mixture was agitated and then left to rest for several hours. The turbidity of the solution is monitored for each step until turbidity appears. Because of the high viscosity above 55 % LA only samples below 50 % were considered in this study. The quantification of the second single phase in the water rich corner of the ternary phase diagram was carried out by dissolving aliquots of LA powder in BA/water solutions at 0.5 % and 0.1 % at room temperature. The limit of the binodal curve was taken as the solubility limit of LA in the BA/water.

Viscosity measurement

The simulation of the ternary phase diagram requires knowing the LA/BA Flory-Huggins (FH) interaction parameter which is calculated using the concentration dependence of the intrinsic viscosity and the method proposed in reference. 48 Viscosity of diluted LA in BA solution (0.1 %, 0.2 %, 0.4 %, 0.6 %, 0.8 % and 1 % LA) were measured in an Ubbelohde capillarity viscosimeter ( n°538-20) at room temperature. The flow time is measured automatically with a resolution of 10 ms. The kinematic viscosity is deduced from the measured passage time following this formula = ( -) with K = 0.1 and = 0.12.

Optical microscopy observations

After immersion in 0.3 % and 0.5 % BA, ultrathin films was observed by optical microscopy with the Microscope Olympus BX61 at several magnifications (10x, 20x, 50x and 100x) and its associated software.

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Atomic Force Microscopy (AFM)

Similar to NR experiment, LA films of 100 nm were spin coated on 5x5 cm Si block and subsequently immersed in 0.3% BA in D 2 O during 19 hours and finally dried by a nitrogen stream just before the measurement. Then, the surface of this thin film was investigated in air by a Veeco Dimension 3100 operated in tapping mode.

Results

Effect of thermal annealing

Ultrathin polymer films were deposited by spin-coating onto silicon single crystals. These films were then annealed at 114°C for 30 min. Optical microscopy observation shows that the films do not de-wet from the silicon substrates during annealing, despite the fact that they were in the fluid state, and regardless of their thickness, in the range between 50 -1500 nm and therefore one can consider the thin LA films to be in thermodynamic equilibrium in air. Fig. 2 shows the NR data of a spin-coated thin film before and after annealing at 116°C for 30 min. No apparent dewetting 49 was noticed corroborating the optical microscopy observation. On the other hand the quantitative analysis of NR spectra for films between 70 and 232 nm reveals 14-16 % reduction of the film thickness of upon annealing. This could either be due to evaporation of entrapped solvent or due to a collapse of the out-of equilibrium structure induced by spin-coating. 50 However, mass density differences due to different chain conformations are unlikely to produce a 15 % difference. In fact, NR has shown that toluene retention in spin-coated amorphous polymers depends on both molecular structure and film thickness. For example, toluene retention in freshly spin-coated films was found to be few percent (<3 %) in polymethyl methacrylate (PMMA) and almost nothing in polystyrene (PS). The high toluene retention in LA films (14-16 %) compared to PMMA and PS, suggests a low toluene diffusion in LA. Indeed, making thick LA films by evaporation from toluene solution at room temperature was found to take more than a year, comforting the high toluene retention observed in the NR experiment. In the following all reflectivity experiments are carried out on pre-annealed films.

Swelling in pure water

To understand the role of water in the swelling and dissolution of LA films, the reflectivity was first measured on films immersed in pure D 2 O for a period ranging from 10 min to 12 h (Fig. 3). The analysis of the NR spectra shows that, upon immersion in D 2 O, the fitted film thickness does not increase, within the detection limit of NR experiment, which in this case is about 0.5 % or 4 Å for a total film thickness of 70 nm. Moreover, the width of the reflected beam remained unchanged pointing to the absence of buckling, which again corroborates the observed absence of water swelling. The absence of any significant swelling after 12 h of immersion raises the question of whether this is an equilibrium or a kinetic property, resulting from slow diffusion of D 2 O in the vitreous polymer. By taking a typical value of the diffusion coefficient of small molecules in a glassy polymer (10 -12 m 2 /s) and calculating the time necessary to reach equilibrium, a characteristic equilibrium time of 10 ms is obtained. This time is many orders of magnitude shorter than experimental times scales (5 min). Accordingly, the low water absorption by ultrathin films of LA must be due to unfavorable interactions between LA and water.

Swelling in binary W/BA mixture

In contrast to pure water, the features of the NR spectra of films immersed in W/BA solutions point to a significant swelling, which is clearly enhanced with increasing ∕ . A quantitative analysis of these spectra yields two distinct structural features of the swollen films: a) Vertical distribution profiles of all three species in the direction perpendicular to the interface, which is examined by the specular component of the NR spectra. And b) in-plane structure, parallel to the substrate, which is extracted from the full scattering pattern. The kinetic changes of these structural features are deduced from the time evolution of the NR spectra. From Fig. 4, the relative thickness change ℎ∕ℎ 0 shows four swelling regimes depending on ∕ : onset of swelling at low BA concentration (below 0.1 % BA), intermediate regime (0.1-0.25 % BA), high concentration (0.25-0.5 % BA) and critical conditions (above 0.5 % BA).

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Shift of glass transition temperature?

One should not forget, however, that dewetting necessitates a structural reorganization of the polymer. Looking at Fig. 8 and Fig. 7 and explained in section 3.3.3, one clearly observes slow kinetics incompatible with Fickian diffusion meaning that these kinetics are controlled by the polymer dynamics in the bulk of the film or close to the surface. In the former case the dynamic acceleration would be due to the T reduction upon increasing BA. Using the T mixing model of a binary system

1 = 1- ( ) + ( )
and the T ( ) =168 K 62 , with T ( ) =50°C and =0.05, one recovers an average T ( ∕ ) value of around 35°C. This value is not far from room temperature especially taking into account the large polymer polydispersity leading probably to mobile parts at room temperature. Furthermore, there are several indications that amorphous confined polymers exhibit different behavior from bulk. For example, few aspect of the polymer dynamics in the glassy regime where found to be activated in confined geometry 63 which might accelerate the dynamics and enhance polymer reorganisation at room temperature. DSC measurements of the LA after prolongated contact with BA/Water mixtures showed, however, only very slight decrease in far away from R.T. Also increasing temperature of the sample above did not significantly accelerate the dewetting process. Another reason for the dynamic acceleration could be breaking of surface/polymer links upon swelling. Indeed, one should not forget that the polymer/surface adsorption sites could act like grafting points or cross-links which could reduce the swelling and slow down the intrinsic polymer dynamics. Indeed, at low BA concentration no vertical swelling was observed while horizontal expansion was seen as buckling. This leads to a delayed onset of vertical swelling contrary to the predicted linear swelling as seen in Fig. 13. Breaking the links would allow certain inhibited chain movements, reduce the T and might accelerate the polymer dynamics.

Simple dewetting?

There are, however, at least two observations that point out that the here observed process is not a simple dewetting scenario. Firstly, in the AFM images it can be seen that only small holes actually perforate entirely the polymer film. As soon as the holes grow larger than about 1 micrometer in diameter an apparent wetting layer of about 24 nm thick LA is covering the substrate again. This thickness is obviously much larger than expected for a simple wetting layer due to dipolar forces, which should extend a few nm at most. Secondly, in contrast to simple dewetting, experiments at concentrations above 0.6% BA in water clearly show the disappearance of the bulk of the layer into the liquid phase, obviously violating the mass conservation of LA on top of the substrate. Even at 0.5% BA concentration NR shows a total LA mass decrease as function of time. We speculate about two possibilities, which would lead to the disappearance of the varnish above the critical concentration, namely emulsification or (heterogeneous) break up. Molecular dissolution of LA in water/BA can be excluded because control experiments have shown that the solubility limit of LA in water/BA mixtures of 0.5% BA is less than 5*10 -6 while the NR cell had a total liquid volume leading to a total polymer concentration of 10 -4 in the experiment. Continued breaking of polymer/surface links induce more in plane heterogeneities resulting in more holes and, finally, not enough links are left (critical BA concentration above 0.5%) leading to film break up by lifting and floating away. There is, however, a contradictory observations to this scenario: In no case during the film swelling/breakup a water enrichment was observed close to the Si substrate. This would have been apparent in NR due to the high contrast of heavy water (see broken green line in Fig. 5). On the contrary, a 24 nm water-free LA film was observed for sufficiently big holes as seen in Figs. 9 and 10 showing that the solid substrate is covered by LA just before the breakup. An alternative pathway of the mechanism to remove the polymer from the substrate could be analogue to emulsification of swollen LA in water/BA because of the presence of polar species in the LA which could stabilize an emulsion in forms of small droplets by a reduction of surface tension similar to a surfactant.

Conclusion

The swelling and breakup of thin films of Laropal®A81, a synthetic varnish commonly used in art restoration, supported by silicon substrates exposed to a binary solvent/non-solvent mixture is studied here using a combination of neutron reflectoemtry, atomic force and optical microscopy as well as thermodynamic calculations based on turbidity measurements. The sample set-up follows a recent approach in art restoration to use a bad solvent as a matrix containing small amounts of (good) organic solvent in order to reduce the total amount of good solvent in the system limiting the risk of irreversible dissolution of all varnish and paint layers on easel paintings 14,17 . As solvent benzyl alcohol is chosen, which is dissolved in a matrix of water, a common system for art restoration. The swelling and dissolution process of the thin films while increasing the good solvent concentration and/or increasing exposure time is found to happen sequentially following several regimes, which are distinct from the swelling and dissolution in bulk. At very low solvent concentrations an asymmetric swelling of the varnish by the good solvent is found: The swelling ratio parallel to the interface, observed as buckling, is instantly following the increased concentration of good solvent, while the out-of-plane thickness swelling is retarded and only happens at a sufficiently large solvent concentration (≥ 0.1% BA in water). This phenomenon is explained by strong van der Waals forces acting like anchoring sites for the polymer close to the Si substrate. For higher solvent concentrations the vertical swelling catches up the behaviour predicted by bulk measurements. For concentrations below 0.3% BA no water absorption is observed into the hydrophobic varnish. For larger solvent concentrations the behaviour changes drastically. Probably due to the solvent-weakened polymer structure heterogeneous nucleation of water-filled holes appears and those holes grow with time on an hour time scale ending in the loss of the film (>0.5 %). By hypothesis, we can surmise that the solvent weakens the film by homogeneous swelling which dynami-

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cally activates the dewetting type process probably nucleated due to structural inhomogemneities of the film (either thickness variations or acidic group agglomerations). In summary, this study shows unambiguously that the dilution of good solvent by a bad solvent can activate surface induced dewetting processes of thin polymer films due to the presence of the bad solvent that are not at all predicted in bulk systems. Therefore care has to be taken on this approach and surface energies (long and short-ranged) have to be taken into account.

CHAPTER 5 STABILITY OF FLUID ULTRATHIN POLYMER FILMS IN CONTACT WITH SOLVENT-LOADED GELS FOR CULTURAL HERITAGE

This chapter is focused on the second paper of this project which is ready for submission and will be submitted in June or July 2020.

In the same line as the paper "Swelling, Dewetting and Breakup in thin polymer films for cultural heritage" (chapter 4) [13] , this second paper is part of the study of swelling and dissolution of ultra-thin films for Cultural Heritage using neutron reflectivity. Contrary to the first paper [13], this time, the solvent (BA) is not only mixed with water but is transferred to the film of polymer (Laropal®A81) by the use of a solvent-loaded gel (Pemulen TR-2).

For this experiment, ultrathin films of Laropal®A81 were made by spin-coating and then annealed for a few minutes following the same process as the first paper [13]. Then, films were studied in several conditions: in air, in contact with a solvent-loaded gel at room temperature, and with a successive increase in temperature and solvent concentration, using neutron reflectivity on the FIGARO instrument at ILL.

Results obtained by the solvent-gel mixture on the macroscopic and nanoscopic behaviour of ultrathin films were compared with those obtained by the solvent water mixture of the first paper [13]. Similar to the solvent/non-solvent mixtures, a dewetting-type process was observed in the system in the form of water-filled cavities. The dewetting kinetics are accelerated by an increasing concentration of BA contained in the gel. NR has also revealed differences between the dewetting observed on the film immersed in binary mixture and in the gel matrix such as the absence of rims in this second case. Then, the influence of the temperature on the solvent/gel/polymer system was shown. Above T g , the kinetics of dewetting are not significantly accelerated but the combination of temperature with solvent influences the stability of the film.

Introduction

Removing protecting thin glassy polymer films from a substrate is a critical step for numerous applications such as photonic band-gap materials, 1 microelectronics, 2 nanolithography 3 and lab-on-chip devices. 4 It is also a particularly crucial step in the restoration of easel paintings and the one bearing the highest risk. Indeed, all surfaces of old paintings and many surfaces of the contemporary paintings are covered by polymer films (varnish) which act as a protecting barrier for the pictorial layer against environmental exposure. However, due to natural ageing, external and environmental factors (dirt, light, humidity) these layers undergo irreversible changes over time. Consequently, the aesthetic and artistic aspects of the pieces of art change irreversibly due to (micro-)cracks, colour changes, oxidation, etc.

Hence regular restoration of the altered varnish layer is needed. A Common restoration procedure consists of manually transferring a good solvent to soften the altered varnish layer and mechanically removing it by abrasion. During this process, the risk of irreversible damage of the pictorial layer underneath is very high because of two factors: 1) the solvent diffusion in thin layers is difficult to control, 2) collapsing the fragile granular structure of the pictorial layer under excessive stress during manual abrasion could also lead to non visual but irreversible structural damages affecting its stability. 5-10 Therefore there is an urgent need to conduct precise investigations of the physical mechanisms involved during the various restoration steps. 8,11,12 In order to limit the amount of aggressive solvent in the cleaning process it was proposed to work in so-called 'mild conditions' by diluting the solvent by water. 13 However, the results preceding this work on such binary mixtures obtained by neutron reflectometry 14 showed that above a solvent fraction of 0.3% the water invades the whole film through a dewettingtype process destroying the entire varnish and exposing the underlying layer to the bare liquid. On the other hand, at the beginning of the 1990s, to reduce the capillary penetration and the concentration of liquid solvents on surfaces, Wolbers suggested to increase the viscosity of the products by using polymer solutions as a matrix for the cleaning agent, so-called Wolbers gels. 15 The high viscosity of the gel and the low concentration of solvent allow to reduce significantly the action of the solvent such as its penetration power. Thanks to the increase in the retention time of the products/solvents maintained in the gel matrix, the product is slowly transferred and the restorer can adapt the gel/surface contact time.

Quite quickly these gels were commonly employed in cultural heritage conservation. 16 Gels have been widely studied since because of their applications in numerous industries such as cosmetics, food, health and even in products for safety (bulletproof vests). New innovating gels appeared, which could be suitable in art restoration like tough-gels, 17 micro-emulsion gels, 18 emulsion-gels, 19 and nano-gels. 20 In two recent reviews Baglioni et al. emphasize chemically cross-linked gels as a promising tool for the conservation of cultural heritage. 21,22 In contrast to the here studied Wolbers gels, chemical gels do not need a subsequent cleaning after application to remove the gelling polymer residues from the surface. However, the application of gels in general and its effectiveness to remove non-original materials on a macroscopic scale are impressively demonstrated by visual images, the potential microscopic penetration of liquids into the original layers, and therefore potential irreversible changes are not investigated. In addition, after transferring a small amount of solvent by a gel into varnish, a mechanical action must follow to remove the swollen varnish. This step obviously bears risks on its own. From a scientific viewpoint film removal seems straightforward in thick films where diffusion times and distances are macroscopic. Although the solid-to-liquid transition of polymers may be quite different from non-polymeric materials: Unlike non-polymeric materials, polymers do not dissolve instantaneously and the classic dissolution process of a polymer involves transport processes, namely solvent diffusion and disentanglement of the polymer chains. 23 The first stage is penetration of a few solvent molecules that plasticize the polymer. As a result, the macromolecules can cross the polymer/solvent interface. If the molecular weight of the polymer is high enough, they will form a gel layer at the surface of the film. The next stage is the disentanglement of the macromolecules and their escape from the gel layer into the solvent. But there are also cases where the polymer cracks before any gel layer is formed. 24 In the case of ultrathin films the situation is more complex as surface effects and reduced dimensionality may effect the physical properties of the polymer such as chain conformation, glass transition temperature and polymer dynamics. 25 Van der Waals interactions of the substrate may also play a role for these thin films. 26 And, last but not least, many films may become unstable below a certain threshold thickness leading to dewetting when heated close or above their glass transition temperature (T g ). 27 The phenomenon of dewetting is relatively well studied for unpolar polymer films 28 but systems with a significant amount of polar groups, as the case in the present study, may significantly alter the film stability. 29-31 The use of a single solvent is the easiest case of polymer film dissolution. In this study, however, a binary solvent-non solvent mixture suspended in an emulsifier solution is used.

The case of a binary solvent without the emulsifying co-polymer was already studied before 14 and revealed a dewetting-type polymer film removal due to the different surface affinities of the solvents. Using viscosity-enhancing emulsifiers to promote thin film removal, as studied here, generates new challenges in polymer physics and raises particularly one important question about the emulsification mechanisms in confined media. Due to the presence of the co-polymer, the matrix is now able to absorb the hydrophobic polymer layer in form of an emulsion. 32,33 This increases the diversity of chemical interactions in the system and may shift the solvent partitioning.

Similar to our previous study 14 we will determine the solvent penetration inside the polymer and follow the film break-up by using specular and off-specular neutron reflectometry (NR).

NR was found an effective technique that yields both structural and chemical information thanks to targeted hydrogen/deuterium (H/D) labeling. It is an ideal tool to observe the solvent penetration in real time and has already proven this in similar experiments 14,34-36 . It is a non-destructive and non-invasive technique for the investigation of thin polymer films, liquid/solid and liquid/liquid interfaces with a resolution of a few Ångströms. In addition NR can be linked to complex sample environment like cone/plate rheology 37 as was done here as well. In contrast to our previous study 14 we cannot easily complement NR by microscopy as the gel cannot be removed from the film after application without destroying the system.

As in our previous study 14 we will use ultrathin (∼100 nm) polymer films of Laropal R A81 (LA), a resin commonly used as varnish on paintings, in contact with a small quantity of benzyl alcohol (BA) dissolved in a bulk aqueous solution. In the preceding study we observed a swelling of the varnish layer by BA penetration at small BA quantities in the water matrix and a dewetting of the varnish by appearance of holes as depicted in Fig. 1 at BA concentration above 0.3% BA at room temperature (R.T.). The dewetting process, however, showed two remarkable differences when compared to the dewetting of polymer films from solids in air: a) The wetting layer underneath the holes was unusually thick (see Fig. 1) and b) clear loss of polymer at late stages of dewetting was observed. We identified the affinity of the water matrix to the hydrophilic substrate underneath the hydrophobic polymer to be the driving force for the film instability when in contact with the BA/water binary solution.

The fact that the dewetting process started only above a threshold BA concentration in water lead us to speculate about the plasticizing effect of BA inside the polymer film reducing its glass transition temperature close to room temperature initiating polymer flow. In the present study we will vary the temperature significantly above T g to test this hypothesis.

The second difference in the current study is the addition of a gelling agent to the aqueous phase: Pemulen TR-2 as proposed for varnish removal in art restoration. Unlike the earlier studied case of water/solvent mixtures the case of physical gels containing solvent is indeed used in Cultural Heritage, so the latter system is closer to the real application.

Finally, in order to go towards the abrasion of the swollen varnish, we will test the influence of gentle mechanical stress on the system by shearing the sample in a rheometer and watching it with NR in situ. Fitted SLD of a similar LA film in a BA/water mixture versus distance from the substrate. Note that the annealing time is longer for the AFM measurement leading to significantly larger holes and rims. This data is taken from Ref. 14 .

Experimental Materials

Laropal R A81 (LA) from BASF 38 is a synthetic polymer resin synthesized from an urea, isobutyraldehyde, and formaldehyde and is a reference varnish in cultural heritage because of its stability, its resistance and transparency. 39 The LA structure, was reported to consist of 4-hydroxy-6-isopropyl-5,5-dimethyl-tetrahydropyrimidin-2(1H )-one and aldehydic compounds. 40 LA is a small molecular weight polymer with a typical weight-average molecular weight (Mw) of 3640 Da and number-average molecular weight (Mn) of 1266 Da as deduced from gel chromatography (GC). 41 The T g measured by differential scanning calorimetry (DSC) is 48 ˚C. 14 Benzyl alcohol (Sigma-Aldrich, 99.8 %), Deuterated water (D 2 O, Eurisotop ref D214L, 99,9 % D), Pemulen TR2 (Lubrizol) and Triethanolamine (98%, CTS France 42 ) were used as received. Pemulen TR-2 (PTR-2) 32,33,43,44 is an anionic polymeric emulsifier 33 made of a slightly crosslinked acrylic acid backbone (-

[CH 2 -CH-(COOH)-] n -)
and few hydrophobic pendent alkyl molecules, 10 to 30 carbons long. It is used as a primary emulsifier and a viscosity enhancing agent 45 . Triethanolamine (TEA) from CTS, a ternary amine used in cosmetic and art restoration applications is used as buffering agent for Pemulen gel preparation.

Thin film preparation and characterization

In order to make ultrathin polymer films, LA/toluene mixtures of 20 g/L were deposited by spin coating using a Delta 6 RC TT (S ÜSS MicroTec Lithography GmbH) 46 at 2500 RPM for 44 seconds onto silicon crystal blocks (5x5x1 cm 3 (111) from Sil'Tronix France or 7x7x1 cm 3 (100) from Crystec, Germany) rigorously cleaned following a precise protocol (20 min in deionized water, in acetone, in ethanol, in formalmyde and in water). These films were subsequently annealed at 114˚C for 30 minutes in a vacuum oven. During this heating process, all of the toluene is evaporated and an apparent homogeneous film of LA is observed. The film thickness measured by ellipsometry are 74 nm ± 1 nm. These films did not show any apparent dewetting by optical microscopy. The films were subsequently placed in contact with different concentrations of BA (0%, 0.3%, 0.5%, 0.6% and 0.7%) in D 2 O with Pemulen TR-2 gel at pH 7 (adding TEA) and observed by NR as a function of shear, time and temperature.

Preparation of the gelly matrix

The LA film was studied in contact with a polymer solution of Pemulen TR-2 from CTS France (Lubrizol). This dispersion is prepared by following the suggestions from Stravroudis 44 at 0.1% of PTR-2 in D 2 O at pH 7. First, 0.1w% dry powder of PTR-2 is mixed with water and dispersed by stirring it overnight to obtain an uniform mixture. Then, the final pH of the preparation is adjusted by adding some drops (about 0.1% in total volume) of TEA previously dissolved in D 2 O to the PTR-2/D 2 O mixture until reaching a homogeneous solution of pH 7 ± 0.2. 32,44 Then, a chosen amount of BA is added to the polymer solution, mixed 1 hour and left 48 hours at room temperature. At 0.1% PTR-2, the solution has a low viscosity and it can flow through the tubing connected to the relfectometry cells.

NR experiments

Neutron reflectomery (NR) was performed to extract the vertical swelling of the polymer film by directing a collimated neutron beam at the Si/LA/W interfaces through the Si block, and measure the reflected intensity as a function of momentum transfer normal to the interface.

For a short introduction of NR on the here studied system the reader is referred to our previous publication. 14 NR experiments were performed on the time-of-flight (ToF) reflectometer FIGARO 47 at the Institut Laue-Langevin (ILL), Grenoble, France. The samples were either placed in air with the neutrons reflecting up to investigate the dry polymer layer or were contained in a heated solid/liquid cell with reflection down geometry to enable potential air bubbles to drift away from the interface (see Fig. 2 for a sketch of the experiment). Some measurements were performed inside a rheometer (Anton Paar MCR501) installed in situ on the beam line 37 to impose a shear stress on the LA film during the passage of the neutron beam. This was done in reflection down geometry, as well. In all cases a wavelength band between 2 Å and 20

Å was chosen with a relative wavelength resolution of 3.0 % (FWHM). The detector, which allows at the same time the specular and the off specular reflectivity to be measured, has a resolution of 2.2x4.8 mm 2 (FWHM) and a size of 25x48 cm 2 at a distance of 2.8 m from the sample. The full q-range was obtained with two reflection angles of 0.622 and 2.622

degrees. The beam footprint on the sample was set to 39x39 mm 2 for both reflection angles.

The raw data was normalized to the incident beam spectrum by the data reduction software COSMOS. 48 Ultrathin polymer films on silicon single crystals were first placed in contact with pure D 2 O in order to have a reference state before swelling with BA. These films were then placed in contact with Pemulen/D 2 O mixture containing various fractions of BA in a closed cell.

Subsequently, the temperature was increased each 15 min until 70˚C and the structural scattering lengths and isotope weights. 52 The SLDs and the corresponding chemical sum formulas used in this study can be found in Tab. S2 in the supporting information (SI). The thickness and the roughness of all layers were fitted as well. The silicon substrate and silicon dioxide were found to be atomically smooth (between 0.2 nm and 0.5 nm) and therefore are not discussed further.

Several morphological models were envisaged for the LA layer to fit the data including 1) A dewetting profile consisting of three sub-layers as shown in Fig. 1: Dry wetting layer, layer perforated by water-filled holes and a projected layer due to rims as used in our previous study about the same films in contact with BA/water, 14 2) LA layers with holes that cross the films down to the substrate without a wetting nor a rim layer, 3) Similar to 2) but with limited depth holes (see Fig. 3 Bottom) and 4) a single homogeneously mixed layer consisting of LA/BA/water. Note, that models 2) and 4) cannot be distinguished by specular reflectometry alone, as for each of these models the SLD profile is estimated by in-plane averaging the LA and D 2 0 fractions. The NR spectra were calculated using Motofit or Refl1D with a modified model corresponding to the morphological case, and compared to the experimental spectra using a step by step least-squares fitting procedure. In order to justify the in-plane averaging of the SLDs, the size of the defects are supposed to be smaller than the in-plane neutron coherence length.

Note that the scaling of the fitted reflectivity curves was fixed to one in one set of analysis. The lower scaling of the measured curves at an advanced stage of layer destruction is due to enhanced off-specular scattering as explained in the Supplementary Information. In these cases the low q part of the NR curves was excluded from the fitting procedure. In another set of analysis the scaling factor was adjusted when the OSS becomes important and the low q part of the NR was also fitted. This analysis strategy lead to good fits as well, the resulting SLD values were not physically reasonable, though.

In order to extract quantitatively the partial volume fractions from the NR spectra two approaches were used: First the system was simplified into only two components: The polymer with a SLD LA value of 0.9 * 10 -6 Å-2 and solvent with the fitted SLD s values from the critical edge positions of the NR curves. From the fitted mean SLD values SLD and thicknesses h of the layer the resulting 'dry' volumes of the polymer v pol (normalized to the dry LA volume) and solvent v s fractions were extracted using the following formula:

v pol = h(SLD-SLDs) h 0 (SLD LA -SLDs) v s = h h 0 -v pol (1)
Here h 0 is the dry thickness of the polymer. This approach does not assume mass conservation but can only extract two unknowns from the two measured values. Assuming conservation of the polymer mass (v LA = 1) as done in our previous work for low BA concentrations 14 one can extract the BA (excess) volume fraction φ BA/LA as well as the water fraction φ W/LA inside the polymer layer from the following boundary conditions:

1 + φ W/LA + φ BA/LA = h h 0 h h 0 * SLD = φ W/LA * SLD w + φ BA/LA * SLD BA +( h h 0 -φ W/LA -φ BA/LA ) * SLD LA , (2)
where SLD BA is the bulk SLD of BA.

Off-Specular neutron reflectivity

As the neutron reflectivity spectra were recorded using 2D detectors the off specular neutron reflectivity (OSS) is also accessible. 53 The OSS intensity corresponds to the intensity scattered at a condition away from the mirror reflection (NR). In this case the total momentum transfer also comprises an in-plane component. This allows one to determine SLD variations parallel to the interface but due to the geometry the momentum transfers are typically two orders of magnitude smaller than in specular reflectometry and therefore the spatial resolution is much lower probing micrometer sized structures. The 2D OSS patterns were simulated in wavelength vs. scattering angle space using the Distorted Wave Born Approximation (DWBA) assuming exponentially decaying in-plane correlation functions. 54 This gave access to one additional parameter, namely the mean size of in-plane inhomogeneities.

Results

Film morphology in contact with BA/TR2/water gel from specular

NR analysis

A first-glance analysis of the NR spectra suggests a substantial LA film swelling in contact with BA/water/pemulen (Fig. 3). In accordance with the previous study which has shown that the LA thin film dewets the Si substrate when exposed to BA/water mixtures, 14 one could extrapolate this process to explain the NR data in contact with BA/water/pemulen as well. Dewetting leads to holes and rims and yields typically an averaged SLD profile as depicted in Fig. 1. When, however, the NR spectra of films exposed to BA/water/pemulen are fitted in terms of this dewetting induced SLD profile with various rim morphologies (height, width and fractions), the χ 2 values were found minimum for a rim fraction equal to 0 (Fig. 4). This strongly rejects rims as a potential morphology in the present case.

The second significant difference compared to LA films immersed in only solvent/non-solvent mixtures studied previously 14 is the absence of a well-defined wetting layer. Only models of constant SLD profile or SLD gradients over the entire layer (no sharp SLD step, see Fig. 3) lead to reasonable χ 2 values. In all cases the growth of the average SLD of LA exposed to BA/water/pemulen is apparent resulting either from holes that cross the film, non crossing holes or heterogeneous zones of LA/BA/water/Pemulen inside the films. These models can all reasonably fit the specular NR spectra with small variation depending on the fraction of BA and temperature. The best goodness of fit for the 0.3% BA concentration with χ 2 values around 4 was achieved assuming a gradient in SLD across the whole layer starting with the SLD value of the polymer layer when in contact with pure D 2 O close to the Si substrate and an increasing SLD towards the aqueous phase. This profile corresponds to a distribution of hole depths with only few reaching the Si substrate (penetrating the whole film). Typical reflectivity fits and SLD profiles using this model can be seen in Fig. 3. For higher BA concentrations, in addition to the gradient, the SLD of the LA in contact with Si had to be fitted as well to reach similar χ 2 values. This resulted in flat SLD profiles inside LA corresponding to water-filled holes crossing the whole film. A typical NR fit in this case can be seen in Fig. 4.

If the scaling factors of the NR data were adjusted in the fit, qualitatively similar results

were obtained particularly for the total film thickness, however, the absolute SLD values gave nonphysical results. Figure 3: Top) Typical reflectively curves (multiplied by q 4 z ) vs. momentum transfer q z on a logarithmic scale for LA films in pure D 2 O (black circles) and in aqueous solutions of 0.3% BA and 0.1% Pemulen at two different temperatures as depicted in the legend. The solid lines in the same color code are fits to the data. Bottom) The corresponding SLD profiles in the same color code. z ) vs. momentum transfer q z on a logarithmic scale for an LA film in aqueous solutions of 0.5% BA and 0.1% Pemulen at 27 • C (data points). The solid line in the same color code is the best fit to the data assuming no rims. The broken line is the best fit to the data assuming a rim fraction as in Fig. 1 left. Inset: Normalized least square value χ 2 vs. fraction of rims φ rim for various heights of rims as indicated in the legend deduced from fitting the specular NR spectra to a model of LA containing a fraction of holes and rims.

Effect of temperature and BA concentration on film swelling in BA/pemulen/D 2 O gel Fig. 5 shows significant swelling of LA films when exposed to BA/Pemulen/D 2 O gels for all the cases investigated here. For the case of 0.3%, the swelling ratio (SWR) is calculated as the ratio of the film thickness in the presence of BA/Pemulen/water to that in pure D 2 O. This is justified by the fact that LA films do not swell in the presence of pure D 2 O even after 24 h at least within the resolution of the NR experiment. 14 At room temperature (21 ˚C), Fig. 5 shows that the LA film swells by 4.5% at a BA concentration of 0.3% which is the exact same swelling ratio found without the gel. 14 D 2 O is unlikely to swell LA films to the extent to be measurable by NR because the Flory-Huggins interaction parameter χ LA/D 2 O exceeds 4 at room temperature and therefore can safely be excluded as the swelling molecule. 14 LA NR curves with a two-polymer-layer model as described in the Experimental section. The resulting total volumes of solvent and polymer within the layer without imposing polymer mass conservation are plotted in Fig. 6. As can be seen in the graph the polymer mass seems to be conserved until 38 • C with an increasing solvent faction with temperature. Above this temperature there is clearly (irreversible) loss of polymer observed on the expense of more and more solvent penetrating the film. Therefore below this temperature the mass conservation can be assumed and a more detailed partial swelling can be extracted differentiating between water and BA (eq. 2).

This result is presented in Fig. 7. Assuming no loss of materials: cWater cBA As suggested above from the Flory-Huggins interaction parameters indeed the swelling at R.T. is mainly attributed to BA with no significant penetration of water. However, with increased temperature (and time) it seems that the volume fractions of both water and BA are increasing. It has to be noted, however, that the increase in BA fraction with temperature is reversible but the water fraction increase is not. Therefore it seems that there are two parameters influencing the partitions: Increased chemical compatibility of BA and LA with temperature and onset of dewetting by water filled cavities with time.

The fact that the presence of hydrophobic domains from the Pemulen TR2 side group (C10 to C30) does not shift the partitioning balance of BA or water is an important result as Pemulen effectively acts as an emulsifier. This could only infer that the number of hydrophobic moieties at this PTR2 concentration of 0.1% is not enough to perturb the swelling equilibrium. Recovering the same SWR with or without Pemulen at room temperature for 0.3% is a first important result for restoration processes as this means that there is no need to increase the BA concentration when using Pemulen to control solvent transfer to the varnish layer at least when working at room temperature. assuming LA mass conservation using the least square method yields similar tendencies for the dependence of the surface fraction of holes (φ hole ) on temperature for fully penetrating holes and for holes with finite depth (see Fig. 8). φ hole was found to increase slightly for 0.3% with increasing the temperature up to 70 • C. On the other hand φ hole for 0.5% strongly increase up to the breaking temperature and for 0.6% increases rapidly between 37 • C up to the breaking temperature of 49 • C. The absolute values of φ hole are higher if the LA mass is allowed to decrease, but the qualitative trend stays the same. We will therefore present the SLD of the fitted LA layer rather than φ hole in the following in order to be less model dependent.

Film heterogeneities from OSS

In all NR measurements a clear Yoneda-type scattering was observed around the critical momentum transfers (see Fig. 9). This points towards in-plane SLD correlations present in the system. Quantitative fits of the 2D scattering patterns 54 clearly showed that the origin of this scattering comes from inhomogeneities inside the bulk of the film filled with water.

The interface roughness as the only origin of the scattering can be clearly excluded as this would lead to much less scattered intensity. Moreover, it became evident that the SLD contrast contributing to this scattering must come from D2O rich phases inside the polymer, which is the largest SLD contrast when looking at Table S2 in the supporting information.

This bares striking similarities to our previous study of LA films in binary water/BA mixtures, 14 where water-filled holes were the origin of the OSS scattering as evidenced by AFM.

In the present case AFM measurements were not possible as the gelly solution was sticking to the polymer films and impossible to be removed without detachment of the LA film as well. Figure 9: Left: OSS of a LA film in contact with 0.3% BA and 0.1% PTR-2 in D 2 O at 72 • C. Right: Simulation using the same instrument parameters as in the measurement and using the fitting results from the specular fits and in-plane inhomogeneities filled with water assumed to follow an exponentially decaying SLD on average with a characteristic length of 0.7 µm.

From the quantitative fits of the OSS intensity to an exponentially decaying in-plane SLD inhomogeneity one can extract a characteristic in-plane correlation length, which would correspond to an average hole radius in case of holes. This is plotted in Fig. 10 for a 0.5% BA solution in 0.1% Pemulen as a function of temperature. In addition the SLD from the specular fits is shown on the same graph. In order to put these results into perspective with the pure water case the results from a similar LA film in contact with a 0.5% BA solution in pure water are added to the graph. These are from the preceding study done at room temperature only. 14 Here another apparent difference between the varnish in contact with a gel and with pure water, both containing BA, can be appreciated: While the SLD is on the same order for both cases at low temperatures it clearly increases significantly for the gelly case at elevated temperatures. The SLD increase is linearly related to the volume fraction of water-filled holes inside the layer, which means that the volume fraction of holes is significantly higher in the Pemulen solution at elevated temperatures compared to the pure water case at R.T. On the other hand the size of the holes is smaller in the case of the polymer dispersion, even at the highest temperature investigated here. This unambiguously testifies a significantly higher hole density in the case of the Pemulen solution. Assuming the hole size extracted from the quantitative OSS fits to be the hole radius, the hole density at R.T for 0.5% BA in pure water is about 0.1 µm -2 and for the same BA concentration inside the Pemulen solution at 49 Interface between varnish films and PTR2/BA aqueous solutions

The microscopic roughness of the polymer/liquid interface deduced from NR analysis is found to be around 0.6 nm at room temperature and low BA concentrations, while increasing to up to 1.2 nm at higher temperatures or BA concentrations. These values are manifestly higher than the reported one in the case of binary BA/D 2 O mixture 14 which never exceeded 0.3 nm.

This suggests that adding Pemulen into the aqueous phase favors surface roughness.

An immiscible polymer/polymer interface should develop an interface width σ corresponding to the squared sum of the intrinsic roughness σ i coming from chemical interactions and scaling with the monomer size a, 55 and the capillary wave roughness σ CW due to interfacial tension γ if the sample is in equilibrium 56 :

σ 2 = k B T 2πγ ln( l c a ) + σ 2 i , (3)
where the capillary wave spectrum is cut by the neutron coherence length l c . k B denotes the Boltzmann constant. The intrinsic width for a high Flory-Huggins interaction parameter χ can be estimated by 55 :

σ i = a √ N 3 χ/2 * N -1 , (4)
with the polymerization N . The surface energy of Laropal R A81 was determined by measuring the contact angle of different liquids on top of a macroscopic LA film 57 and turned out to be around 30 mN/m.

Using water as the "monomer" with a typical size of a water molecule of 1.8 Å58 one gets indeed around 3 Å roughness of the interface using the χ values between 2.5 and 4 and N = 30

as determined in our previous study 14 . Using around 1 nm as the size of the monomer results in roughness between 4.5 Å and 5.5 Å for the binary mixture. In the case of the lower surface tension of the gelled solvent of around 56 mN/m 32 we get indeed higher values between 3.6 Å and 5.9 Å using 1.8 Å or 1 nm as the monomer size, respectively, assuming the same χ values as for the binary mixtures. This slight roughness increase can explain the interface width of the polymer/D2O/Pemulen system measured at R.T. which is around 6 Å for 0.3% or 0.5% BA, especially taking account that the Pemulen acts as an emulsifier, although its volume fraction is very low (0.1%). The increase of the roughness with temperature up to 70 • between 1 Å and 2 Å for the 0.3% or 0.5% BA mixtures, respectively, is, however, more than what would be expected by a mere reduction in interfacial tension with increasing temperature. Moreover, the roughness values above 1 nm in the case of 0.6% BA cannot be explained by a decreased interfacial tension alone, but have to involve a reduction of the Flory-Huggins interaction parameter as a function of temperature. This result is in accord with the increased BA swelling of LA at elevated temperature as observed in Fig. 7.

Interestingly the temperature induced roughness increase of the aqueous/polymer interface seems to plateau at a certain temperature as can be seen in Fig. 11. The origin of this effect remains somewhat unclear. This temperature is close to the glass transition temperature if calculated using the binary mixing model as will be explained later. One could therefore imagine that 'unfreezing' of stresses could be the origin of this stagnation. Note, however, that the change in roughness is reversible as the value at room temperature was measured twice at different moments during the heating protocol (see the two points at R.T.

in Fig. 11). Therefore this behaviour is unlikely to be related to non-equilibrium properties.

On the other hand, starting from 40 • C a loss of polymer mass is observed (see Fig. 6) by formation of water-filled cavities. It is therefore possible that the roughness contribution due to these cavities is significantly larger than the intrinsic interface roughness and therefore screens the latter as specular NR measures only the sum of the two contributions. Again, the reversibility of the roughness increase even after the appearance of cavities contradicts this hypothesis. Another possibility is that the interaction between BA and LA becomes athermal above 40 • C meaning no further improvement of the polymer/solvent compatibility at higher temperatures. A counter indication to this explanation is that in a test a LA/BA mixture (5% BA) was cooled down to -20 • and showed no indication of phase separation, meaning the BA at room temperature is already far away from theta condition, also consistent with the very low Flory-Huggins parameter around zero.

Finally, the roughening of the polymer/liquid interface could also be attributed to the presence of TEA. The presence of weak surface-active molecules might help the formation of interfaces, increasing the actual roughness or lead to a larger SLD gradient upon adsorption, visible as an increased interface roughness (rather than a distinct layer) due to the small size of TEA. Temperature and solvent influence on the stability of the film

An important outcome of this experiment regarding art restoration field is the onset of film breaking and destruction. Indeed while increasing the temperature most of films investigated here, except for 0.3 %, breaks within the NR experiment yielding a non quantifiable NR spectra. The critical temperature (T crit ) for film breaking is found to to be BA fraction dependent and decreases with increasing BA from room temperature to above 72 ˚C (Fig. 12). At 0.3 %, the film never breaks until the temperature limit of this study (16.5 to 73 ˚C). At 0.5 %, the temperature of the film breaking was 72 ˚C, at 0.6 % BA at 44 ˚C and at 0.7 % BA only at 21 ˚C.

The basic idea behind the strategy of adding moieties of good solvent to a bad solvent gel in art restoration is softening the varnish film to promote its mechanical removal by abrasion.

This would lead to reducing its T g below room temperature via solvent plasticising. The results presented here show that the mechanism is more complex and the chemical interaction plays an important role in this process.

The T g of the binary LA/BA mixture can be estimated using the partitioning constant of BA between LA and water from NR experiments on thin films 14 and the mixing model:

1 T g = 1 -φ BA T g(LA) + φ BA T g(BA) , (5)
Using T g(BA) = -105.15 • C 59 for BA and T g(LA) = 47 • C for LA and the φ BA/LA concentrations from our previous study. 14 The resulting glass transition temperature as a function of Φ BA/W A is plotted in Fig. 12 as a black line and decreases from around 35 • C at 0.3% BA to 18 • C at 0.7% BA, the highest solvent concentration examined in this study. The temperature at which a sudden increase in mass loss is observed (film removal) is at 44 ˚C for 0.6% BA, 72 • C for 0.5% BA and above 72 • C for 0.3% BA, which is 20-37 • C above the respective glass transition temperature. This suggests that the sudden 'unfreezing' of the film's surface tension stress is not the main motor for film breaking because at 0.3% and 0.5% BA concentrations the film remains largely intact. This does not mean, however, that residual stresses cannot be the origin of hole nucleation as observed for other polymer thin films. 60 Another important outcome of the fact that the film remains largely intact for extended periods of time more than 20 • C above T g is that the kinetics driving the film destruction are not controlled by the polymer viscosity. As LA is a low molecular weight polymer its viscosity should decrease by orders of magnitude when crossing T g . If 'normal' dewetting, which kinetics are governed by viscosity, were to be the origin of film destruction in the here studied case the kinetics should accelerate by orders of magnitude above T g as observed with thin polystyrene films dewetting from functionalized silicon substrates: An acceleration of a factor 10 was observed when heating the sample by 10 • C above T g . 61 In the here studied case the polymer film in contact with a co-polymer solution containing 0.3% BA was withstanding more than 10 h at temperatures significantly above T g showing a clear layered structure observed by Kiessig fringes in the NR curves despite a high fraction of holes present. If, on the other hand, the BA concentration in the solution is increased to 0.7% the film is almost completely lost within only 3.5 h at 19 • C, which is around T g . In essence, clearly the BA concentration inside the polymer is driving the kinetics of film destruction and not the polymers' viscosity.

The fact that the polymer softening is not the main driver for film break-up can also be appreciated by the concentration and temperature dependence of the different stages of film destruction. In Fig. 12 the information from T g estimations, specular and off-specular NR on the state of the varnish film is summarized in a film stability diagram. The boundaries in this diagram are chosen to separate three regimes of film stability depending on φ BA/W

and temperature: a) The area below the black line corresponds to the solid zone below T g as calculated from eq. 5, b) At higher temperature the polymer is liquid but does not show pronounced hole formation as evidenced by low OSS intensity. It is chosen to separate this phase from the inhomogenous zone at higher temperatures by a threshold of Yoneda peak intensity of 10 4 counts per minute (see Fig. S4 in the supporting information), marked by a blue line. This choice is arbitrary but its exact value will only shift the temperature of the boundary keeping the qualitative behaviour with BA concentration the same. Finally, the red line marks the temperature at which a sudden loss of most of the film's material is observed.

Looking at this film stability diagram it is obvious that the boundaries of film destabilisation are uncorrelated with the T g evolution: While T g is decreasing almost linearly with the BA concentration in the investigated range with a rather small slope, the other boundaries 29 show a much steeper BA dependence and are not necessarily linear. . The lower black line corresponds to the T g as calculated from eq. 5 by using the BA in LA volume fractions from the bottom axis. The blue line in the middle corresponds to the threshold temperature where the OSS intensity is 10 4 counts per minute in Fig. S4 from the SI and the red line in the upper right corner marks the temperature at which a sudden loss of most of the film's material is observed. The latter two lines relate to the upper x-axis (BA fraction in water) and are deduced from the experimental data.

Discussion

Given the clear indications that the appearance of water-filled holes growing with time is responsible for the here studied film destruction, dewetting might seem to be the most likely scenario. Moreover, a very similar behaviour of the scattering curves at late stages of film destruction, compared to the case of pure water where dewetting was observed, can be shown as evidenced in the Supporting information. Clearly the driving force is the hydrophilicity of the used substrate attracting the polar emulsifier and/or water as observed in our previous study. 14 The role of polar forces in dewetting of thin hydrophobic polymer films was also shown for polystyrene supported by silicon wafers immersed in poor solvents 30 or non solvent/poor solvent mixtures. 31 However, several contradictions to the process of dewetting are observed. The most significant one is probably the fact that the kinetics are not governed by the polymer viscosity, but linked to the amount of solvent swelling. Clearly the retardation of dewetting is gradually switched off by increased solvent concentration inside the polymer. Suppression of dewetting was already observed for thin polystyrene films when their chain ends were functionalized by polar groups, explained by their bonding to the polar substrate and between the chains stabilizing the film. 29 Laropal is known to incorporate a significant amount of polar groups as well 40 and in our previous study of LA films in contact with water/BA mixtures we observed a wetting layer which was not perforated by the dewetting holes testifying the strong bonding of annealed LA to the polar substrate. 14 However, at higher BA concentrations or longer exposure the vast majority of the film vanished, eventually. In the aforementioned study we also observed a retarded swelling of the LA film when exposed to aqueous solutions containing increasing amounts of BA: While for small solvent concentrations almost no swelling was observed, a linear swelling behaviour was recovered as predicted for bulk LA at BA concentrations above 0.2%. We argued that bonding or cross-linking of some sites of the polymer to the substrate were responsible for this swelling retardation, which would be gradually suppressed by the addition of BA.

It is possible that a similar mechanism is at play in the here studied case of the same LA film in contact with a BA containing viscous polymer dispersion. Indeed, for 0.3% BA we again observe a quasi water-free zone close to the substrate (see Fig. 3 Botttom) although this 'wetting layer' is much less pronounced compared to our previously investigated case without the Pemulen. In addition, contrary to our previous study, at higher BA concentrations this 'dry' layer is not visible anymore. This could be, however, due to the much more polar -OH groups contained in the co-polymer in comparison to water. Therefore the scenario of dewetting retardation due to polar group interactions inside the polymer film and with the polar substrate, which are gradually screened or broken by the polar BA seems to be the most likely scenario. The highly stable film state could be also appreciated by a test where in situ shear was applied to the BA swollen film not altering its structure as shown in the supplementary information.

Another contradiction with typical dewetting (and the previous study on binary water/solvent systems) is the here observed absence of rims. However, this could be explained by a) the fact that the polymer/substrate interaction is effectively weaker due to the presence of highly charged groups of the Pemulen, similar to the absence of rims observed for films experiencing plug flow, 62 b) the smaller size of holes, similar to early stages of dewetting of polymer films on non-adsorbing substrates, 28 or most importantly c) the fact that the films are effectively fluid, being above the T g while the dewetting speed is retarded and thus not limited by viscosity giving the films the time to reach their equilibrium thickness at any stage of dewetting.

Due to the presence of an emulsifier in the system (Pemulen TR-2) we cannot exclude a gradual emulsification of the LA film by its incorporation into the aqueous phase due to the hydrophobic side groups of Pemulen, leaving behind voids leading to holes in the film. Due to the high viscosity of the solution it is technically challenging to establish an equilibrium phase diagram of the here studied system in contrast to the water-based system studied before. 14 However, Pemulen TR-2 is known to form a microgel with typical droplet sizes in the (sub-)micron range when stabilizing an emulsion. 33 Therefore an emulsification process starting from the polymer/gel interface should engender a significant roughening of the poly-mer surface. As seen in Fig. 11 the measured polymer film roughness for a BA concentration of 0.3% never exceeds 1 nm testifying a molecularly smooth layer just before film rupture.

We note that the amount of benzyl alcohol inside the Pemulen solution was up to 0.7% in the current study that is significantly lower than the solubility limit in water (4%). We therefore expect the solvent to be homogeneously distributed as is the case in pure water.

Finally, the presence of TEA being a weak surface-active molecule might help the formation of interfaces and intermediate steps in the first stages of dewetting, kinetically favoring the process leading to the observed higher coverage of smaller holes.

On an application level, the results of this paper, such as the presence of holes or the temperature effect, provide new information for painting conservators and restorers. In case the holes pierce the entire varnish layer, the penetration of the solvent contained in the Wolbers gel can reach and get into the paint layer. Thus, inducing an irreversible risk of deformation, swelling and dissolution of this fragile layer. The appearance of (sub-)micron sized holes would also reduce the transparency of the coating. It has to be noted, however, that the here used silicon substrate is slightly hydrophilic and thus not generally representative for the pictorial layer supporting the varnish, being typically hydrophobic.

Nonetheless, deeper layers in an easel painting can be hydrophilic as the glue typically used to support the preparation. This could be exposed to the varnish in cases of cracks. Another difference in real paintings is of course the absence of sharp boundaries between the layers.

These gradual boundaries have a stabilizing effect on film cohesion.

On the other hand, the results of the combined action of temperature and solvent show that it is possible to remove varnish without mechanical stress, as is currently the case. Now, restorers have a better understanding of the process of removing varnish from paintings using solvent-loaded gels and can re-evaluate this approach in order to guarantee the safety of the paint layer.

Conclusion

The above results on the destruction of Laropal R A81 films in contact with solvent containing viscous polymer dispersions clearly show striking similarities with binary solvent/non-solvent mixtures studied earlier, 14 which points towards a dewetting-type process in the here studied system as well. As in the former case the appearance of water-filled cavities in the film is initiated by the addition of good solvent and significantly accelerated if the amount of solvent is increased. An increase in temperature above T g , in turn, is not accelerating the dewetting kinetics as much, clearly showing that the dewetting speed is not viscosity limited as it is the case for pure non-polar polymers pointing towards a retardation of film destruction as seen for polymers having polar groups incorporated. 29 It is argued that the addition of polar solvent is screening or breaking the polar interactions inside the film and/or with the polar substrate leading to accelerated film destruction. Another similarity to the pure water case is the loss of polymer mass at late stages of dewetting.

There are, however, significant differences in the here studied case of a gelly matrix in comparison to the dewetting of Laropal R A81 in binary mixtures: No rims are observed, no clear wetting layer is seen and the size of the holes is significantly smaller, although their volume fraction is similar inside the layer. The smaller size of the holes and thus larger hole density can be explained by an increased spreading coefficient of the gel on the Si substrate due to the presence of highly charged -OH groups from the gel. It was shown that the hole density in dewetting polystyrene films on treated Si substrates is larger when in contact with higher energy surfaces. 63 The smaller size of the holes in turn partially explains why no rim is visible as the rim is not present for holes at early stages of visco-elastic film dewetting from non-adsorbing substrates 28,64 . In this case the altered interaction at the polymer/solid interface could be also the reason why no wetting layer is observed. Another explanation for the absence of rims could be the fluid nature of the film as the dewetting speed is obviously not viscosity limited.

In summary, the destruction of LA varnish films as used in art restoration when in contact with Pemulen TR-2 aqueous solutions containing small amounts of solvent is not principally driven by reduction of the polymer's T g but clearly governed by the good solvent swelling.

The destruction is clearly occurring by the appearance of water-filled holes, similar to the previously reported dewetting-type process of the same films in binary solvent/non-solvent mixtures. Obviously, this behaviour would be catastrophic for art-restoration, it has to be noted, though, that the here used support (silicon) is hydrophilic, while the surfaces supporting the protective varnish layers in easel paintings are typically hydrophobic. However, the presence of polar groups inside Laropal R A81 seems to play a determining role for film stability, which is gradually screened by addition of polar solvent. This brings to evidence the importance of polar interactions in LA film removal, which should be taken into account in restoration recipes.

The presence of the gellifying polymer, however, apparently changes the interface width between the varnish and the polymer solution without shifting the solvent partition in the bulk of the materials. This opens a way for art restoration to tune the chemical and surface interactions, not only by varying the concentrations of the involved materials but notably by changing temperature. This is potentially a way to make varnish removal safe for art restoration by the use of gels in a temperature-controlled way. The smaller size of the holes can be also less evident concerning optical distortions.

CHAPTER 6 TEMPORAL EVOLUTION OF VARNISH FILMS IN THE PRESENCE OF SOLVENT/NONSOLVENT MIXTURES FOR CULTURAL HERITAGE

This chapter is presented in the form of a paper for an upcoming publication. It is a continuation of the article "Swelling, Dewetting and Breakup in thin polymer films for cultural heritage" [13] which focuses this time on a thick film and shows whether the thickness of the film has an influence on the behaviour of Laropal®A81 Film in contact with a small amount of benzyl alcohol in water or whether the results are similar to thin films. It brings together the data obtained by the QCM-D and SANS experiments for thick Laropal®A81 films immersed or not in a benzyl alcohol/water mixture. The analysis of these data mainly gives information about the kinetics of benzyl alcohol and water invasion during the swelling of Laropal®A81 thick films. The data reveal that the behaviour of these films immersed for a few hours in a benzyl alcohol/water mixture is similar to that of thin films. Indeed, like thin films, the swelling of thick films is accompanied by instability. These instabilities take the form of holes, characteristic of the dewetting phenomenon. The growth of the holes depends on the increasing concentrations of BA in contact with the film. When the amount of BA is sufficient, the holes can pass through the entire polymer film and come into contact with the substrate. Above a critical concentration (0.6 % BA), the films break irreversibly. This rupture is accompanied by water penetration and departure of Laropal®A81.

Temporal evolution of varnish films in the presence of solvent/nonsolvent mixtures for cultural heritage † Amélie Castel * a , Philipp Gutfreund b ‡ , Bernard Cabane * c and Yahya Rharbi * d

Abstract: The removal of thick amorphous polymer films in contact with nonsolvent/solvent binary mixtures is investigated by means of small-angle neutron scattering. A distribution profiles of benzyl alcohol and heavy water in Laropal®A81 (LA) was given in order to address the scientific aspect of one of the most destructive treatments in art restoration, the removal of varnish from easel paintings. During immersion, the structural change of thick films was observed. The film swells followed by instabilities. Then, structural defects until the polymer is completely dissolved. The purpose of this article is to understand whether the origin of these instabilities is intrinsically due to this swelling. The behaviour of thick polymer films in contact with solvent/nonsolvent mixtures is compared to the behaviour of thin polymer film under the same conditions. A similar behaviour was determined by comparing the predictive swelling and distribution of solvents in the thin (Amélie Castel et al. [13]) and thick films. For this, the structure of thick polymer films prepared by dipping was observed during kinetic penetration of the solvent by small angle scattering (SANS).

Introduction

Remove a polymer film on a surface by the action of a solvent is a challenging task which impacts many industrial applications such as microlithography, membrane science, recycling CHAPTER 6. TEMPORAL EVOLUTION OF VARNISH FILMS IN THE PRESENCE OF SOLVENT/NONSOLVENT MIXTURES FOR CULTURAL HERITAGE plastics, drug delivery, tissue regeneration [START_REF] Miller-Chou | A review of polymer dissolution[END_REF] and art restoration. In the field of Cultural Heritage, polymers films are present on painting to protect the paint layer from external abrasive agents and most of paintings have a varnish film. The film is usually deposited during restoration campaigns on the paint layer. For this operation, the restorers remove the old vanish and apply a fresh one. In function of the surface state and the desired film thickness, restorers choose to depose the polymer by brush or spray techniques directly on the paint surface thus forming the protective polymeric film. The techniques used and the number of the layers deposited, define the thickness of the final varnish film: thin [13] (<100 nm) or thick (>100 nm).

The physics of swelling and dissolution of glassy polymer films is essential in Cultural Heritage in order to remove altered varnish films on paintings by the use of solvents. The most difficult part is never reach, swell and dissolve the colored layer located just below. The risk is that solvents penetrate into the deeper layers, weaken the structure of the paint layer (cracks, loss of materials, etc.) and change irreversible the physico-composition of the painting. To avoid the destruction of the original material of the painting, it is essential to understand each physical mechanisms governing the swelling and instabilities formation, the dissolution [START_REF] Ueberreiter | The solution process[END_REF] and the rupture of the polymer [START_REF] Miller-Chou | A review of polymer dissolution[END_REF] film regardless its thickness and the concentration of solvent in contact with it.

The kinetic of the swelling and the dissolution of ultrathin polymer (Laropal®A81) films (∼ 100 nm) by a solvent/nonsolvent binary mixtures was well studied by neutron reflectometry (mainly FIGARO, ILL, Grenoble) and atomic force microscopic (ESRF, Grenoble) in 2020 in a previous paper "Swelling, Dewetting and Breakup in thin polymer films for cultural heritage" by Amélie Castel et al. published in Soft Matter [13]. The aim was to investigate if the swelling of the Laropal®A81 polymer by a solvent (benzyl alcohol) or a solvent/nonsolvent mixture is done by a homogeneous or a heterogeneous process. It was shown that the swelling of the polymer or the surface state is most probably heterogeneous. Indeed, the presence of heterogeneities (holes) of large sizes was confirmed in addition to the neutron reflectivity by images with an atomic force microscopic. The presence of these instabilities inside the film are characteristic of dewetting and film rupture. The spatial scale and the volume fraction of these heterogeneities was determined. Finally, the role of the bad solvent in the apparition of the dewetting was poured.

The behaviour of ultrathin polymer films which includes swelling with instabilities, holes coalescence and film dissolution, until film breakage has been accurately investigated and understood. Now the question is whether changing the film thickness to a thicker film will give the same or different results. The capillary pressure of a thicker polymer film is lower, but the Van Der Waals forces are lower than for thinner films. It can be expected that the physics of swelling and dissolution of thick polymer films is different (fast and without dewetting process) compared to thin films. The physics of swelling and dissolution of thick polymer films can be expected to be different (fast and without dewetting process) compared to thin films. Thicker films should dissolve faster than thinner films due to imperfections (pores and cracks) created during the manufacturing and annealing time of the film. These imperfections increase the free volume and surface area [START_REF] Pekcan | Real-time monitoring of swelling and dissolution of poly (methyl methacrylate) discs using fluorescence probes[END_REF]. Molecules preferentially lodge in these free volumes and promote rapid dissolution of the thick film.

In this paper, a quantitative view of the swelling and dissolution of thick amorphous glassy polymer films with a small amount of solvent in a non-solvent by SANS was presented. Given the initial motivation to remove the varnish layer from easel paintings without altering the paint layer below, Laropal®A81 (LA), a polymer resin currently used as a varnish by art restorers, CHAPTER 6. TEMPORAL EVOLUTION OF VARNISH FILMS IN THE PRESENCE OF SOLVENT/NONSOLVENT MIXTURES FOR CULTURAL HERITAGE was chosen for this study. Small angle neutron scattering is a very powerful technique for studying polymer materials. It allows to establish the critical concentrations at the off set of the film dissolution and to perform experiments to understand the effect of benzyl alcohol and D 2 O penetration on LA films. The solvent/non-solvent on thick Laropal®A81 films will be compared to the previous paper on thin polymer films [13].

Experimental

Materials

Laropal®A81 is a condensation product of urea and aliphatic aldehydes. This low molecular weight resin is in the form of small semi-transparent pellets. Its glass transition temperature (T g ) is 48 °C. It is soluble in alcohols, esters, ketones and aromatic hydrocarbons and is very heat stable. Size-exclusion chromatography (SEC) estimated its weight-average molecular weight (Mw) to be 3640 Da and its number-average molecular weight (Mn) to be 1266 Da [28]. Its molecular structure was characterize by Bonaduce et al. using flow injection analysis coupled to electrospray ionisation and quadrupole time-of-flight mass spectrometry (FIA-ESI-Q-ToF) and gel chromatography (GC). They concluded that Laropal®A81 is a product of the reactions between 4-hydroxy-6-isopropyl-5,5-dimethyl-tetrahydropyrimidin-2(1H)-one and aldehydic compounds. In addition, they have shown that that hydroxyl groups have a strong effect on the physical properties of the polymer [START_REF] Bonaduce | Mass spectrometric techniques for characterizing low-molecular-weight resins used as paint varnishes[END_REF]. This resin is often used by art restorers to make the varnish layers and as a correction material for paint retouching [32]. The Laropal®A81 used in this study was produced by BASF [121]. The softening point indicated by the manufacturer is 80-95 ˚C. Its density is 1,1 g/cm 3 at 20 ˚C. It can be dissolved in aprotic and dipolar solvents and is insoluble in water.

Thick film preparation and characterization

For QCM-D experiment, LA films were deposited on the quartz sensor by spin-coating and annealed for 30 min at 114 ˚C taking care not to make a thermal shock on the fragile sensor. The quartz sensor was rigorously cleaned before spin-coating. The LA/toluene solutions at 170 g/L were spin-coated at 2250 rpm for 44 seconds at room temperature (21°C). Film thicknesses were measured using the mass measured as function of the coated surface. The film thickness was ∼ 500 nm.

For SANS experiment, LA films were produced by dip-coating on single quartz cells. Substrates was immersed in a solution of 400 g/L Laropal®A81 in toluene at a constant and controlled speed. The single quartz cells was rigorously cleaned before dip-coating subsequently sonicate in water plus one drop on Decon 90 mixture, clean water, ethanol, acetone, chloroform and ending with clean water during 15 min for each products and dried at room temperature. All samples were annealed at 114 ˚C during 30 min in an oven vacuum. Film thicknesses were measured using a contact profilometer across a scratch. The thickness measured was approximately 1.2 µm.

QCM-D

Quartz Crystal Microbalance with Dissipation Monitoring (QCM-D) is a nanogram sensitive technique which allows to measure in real-time the mass of the polymer films on the quartz sensor by measuring the resonance frequencies of a vibrating piezoelectric quartz crystal [START_REF] Dixon | Quartz crystal microbalance with dissipation monitoring: enabling realtime characterization of biological materials and their interactions[END_REF]. CHAPTER 6. TEMPORAL EVOLUTION OF VARNISH FILMS IN THE PRESENCE OF SOLVENT/NONSOLVENT MIXTURES FOR CULTURAL HERITAGE Three LA films of 500 nm on quartz sensor were measured in solutions of D 2 0 containing an increasing BA concentration φ BA/W (pure D 2 O, 0.2 % BA until 0.7 %). Frequency changes were monitored during few hours on the QCM-D. It has been verified that each film gave the same results for the repeatability of the experiment, but only the results of one sample are presented afterwards.

SANS

SANS experiments were performed on D11 [START_REF] Lindner | The d11 small-angle scattering instrument: a new benchmark for sans[END_REF] at the Institut Laue-Langevin (ILL), Grenoble, France. Three sample-to-detector distances were used to cover the full q-range, namely 1.4 m, 8 m and 39 m at a constant neutron wavelength of 0.55 nm. In front of the sample a 14 mm circular diaphragm was placed. Measurement times were set to 10 min for the short detector distance, 30 min for the intermediate one and between 30 min and 4 h for the longest sample-to-detector distance.

LA films of approximately 1.2 µm on single quartz cells were put in vats of 4.6 x 2.5 x 0.5 cm 3 containing the solutions of different concentrations of benzyl alcohol in D 2 O (0 %; 0.2 %; 0.4 %; 0.6 % and 0.7 %) or D 2 O+H 2 O (0.6 %) at the beginning of the experiment and the temporal evolution of the SANS spectra was recorded. The background emerging from a cell filled with the same solution, but without a polymer film, was subtracted from the spectra. SANS measures the scattering of neutrons at small angles arising from variations of the neutron scattering length density (SLD) of the bulk material. The SLDs involved in this experiment are depicted in Table 6.1. Table 6.1 -Scattering length densities of the materials used in this study. For LA the range of measured values during different experiments is given [13]. In case of the other materials literature values are given assuming the chemical composition of BA to be C 7 H 8 O at 1.02 g/cm 3 density.

Material

bulk SLD [10

f (x) = A * x pow + y 0 (6.1)
with Y 0 is held at zero as it is common to use the law of power. This equation following the correlation length model:

I(q) = 1
q s * C 1 + (qχ) m + B, (6.2)
where, χ is the characteristic length. m is the high-q Porod exponent. And, S is a "stretching" factor in the low-q mass fractal structure. Basically, from equation 6.1, the A represents the signal intensity and x pow is the scattering invariant q. CHAPTER 6. TEMPORAL EVOLUTION OF VARNISH FILMS IN THE PRESENCE OF SOLVENT/NONSOLVENT MIXTURES FOR CULTURAL HERITAGE

Results and Discussion

The figure 6.1 shows typical SANS spectra for a 1.2 µm LA polymer film immersed in D 2 O containing 0.7 % of BA as a function of time. For completeness, the SANS curve of the dry film is also shown as well (red crosses) although the SANS signal for this sample is close to the background, making it difficult to extract the actual foreground. A similar curve was obtained for a LA film immersed in pure D 2 O (not shown). Although the error bars largely include zero diffusion cross section for these curves (error bars omitted for clarity in this figure), it appears that the diffusion cross section is not zero at small q-values but of the order of 1000 cm -1 , which is clearly not compatible with a homogeneous homo-polymer melt. This result is consistent with SAXS measurements performed on 1 mm self-supporting films of the same polymer. It is clear that some inhomogeneities are present even in dry films. As soon as the film is placed into contact with a solution containing BA, the SANS signal increases significantly, showing clear Porod diffusion. And, the q-dependence is given by dσ dΩ ∼ q -4 typical for surface appearance. The large scattering cross section of 10 5 cm -1 to 10 6 cm -1 at low q values shows that a strong SLD contrast has to exist across the interface. Looking on table 6.1 the contrast has to come from D 2 O. Indeed a control experiment where the water was contrast matched to LA by dilution with H 2 O showed zero scattering corroborating the D 2 O/BA interface to be the origin of the observed SANS signal.

In order to extract quantitative information the SANS curves were fitted with the Porod law for low q-values where background did not affect the curve: dσ dΩ (q) = 2πS(∆SLD) 2 q -4 , (

where S represents the total area and ∆SLD the difference in SLD between the two phases across the interface. The resultant plot of the pre-factor A = 2πS(∆SLD) 2 is plotted in Fig. 6.2 as a function of time for two BA concentrations. It can be seen that in contact with the 0.6 % BA solution the signal increases rapidly as compared to the dry film and reaches a maximum after about 3 h. Afterwards a decrease is observed although still significantly above the level of the dry film followed again by a slight increase after about 10 h of immersion. Similar, but apparently accelerated behaviour is observed for the highr BA concentration. In the latter case the initial increase in intensity happens faster than the observed time window and also the minimum is reached already after 7 h to be followed by an increase again. In order to understand this cyclic behaviour of the scattered intensity we refer to our previous CHAPTER 6. TEMPORAL EVOLUTION OF VARNISH FILMS IN THE PRESENCE OF SOLVENT/NONSOLVENT MIXTURES FOR CULTURAL HERITAGE work on the same system, but using about ten times thinner films [13]. In this work we highlighted the presence of dewetting type holes for 100 nm thin films immersed in BA/W mixtures beyond 0.3 % BA by using neutron reflectometry (NR) and atomic force microscopy (AFM). A visual inspection of the 1.2 µm thick films used in this study showed clearly an opaque appearance after contact with the BA/W mixture, very similar to the films in our previous work. This corroborates the assumption that also in this case a de-wetting type phenomenon takes place. In this case the initial rapid increase in surface area could be the appearance and growth of holes filled with D 2 O. Indeed for 100 nm thick films this process was leveling off after about 1 h at 0.5 % BA [13]. The same timescale is observed for ten times thicker films at 0.6 % (2-3 h). At 0.7 % BA the 100 nm films were already in a too advanced strage of de-wetting to be analyzed by NR after 20 min. For the micron thick films the initial maximum is also reached before the first SANS spectrum was recorded at 5 h immersion time. For the following decrease in SANS intensity two possible explanations are discussed. 1) Part of the film could disappear into the bulk due to dissolution or an emulsification process as discussed in our previous work. 2) An alternative explanation would be the coalescence of holes leading to fewer holes and thus smaller surface area. In order to shed further light onto the dissolution process QCM-D measurements were performed on 500 nm thick films. In case of no change of viscoelastic properties of the film fequency change in QCM-D is directly proportional to the bound mass to the quartz crystal. Fig. 6.3 shows the frequency change as a function of time of the film immersed in D 2 0 and at increasing concentrations of BA as indicated in the graph (0 %, 0.2 %, 0.3 %, 0.4 %, 0.5 %, 0.6 % and 0.7 % BA). After a short equilibration in pure D 2 O the frequency slightly lowers for BA concentrations below 0.3 % probably mainly due to BA swelling as also observed in our NR study [13]. Starting from 0.3 % a significant mass uptake is seen in accordance with the appearance of water filled holes. At 0.7 % BA the same cyclic behaviour of mass uptake and loss is observed on similar time scales as for the SANS experiment.

Conclusions

In this work the late stages of Laropal®A81 film destruction were investigated by means of SANS and QCM-D. BA in water concentrations of 0.6 and 0.7 % were used which were found to be critical concentrations of immediate film rupture in the case of ultra-thin films investigated previously [13]. Similar to our previous work the process of film destruction is an intrinsically heterogeneous dewetting type process by hole formation. The micrometer thick films, which are closer to real applications in art restoration, behave similar to thin films, so this seems to be an intrinsic feature of Laropal®A81. This is not trivial as van der Waals forces are much weaker on a micron length scale. On the other hand the Laplace pressure of a film droplet with a radius equal to the film thickness is much weaker for a thicker film. The thickness of the polymer film and the concentration of solvent have an influence on the kinetics of swelling, dissolution and the rupture of the polymer film. It was observed cyclic changes of bound mass and SANS scattering signal, which could be explained by two opposing effects, on the one hand dewetting of the film leading to incorporation of water and on the other hand the (emulsified or patchy) dissolution of the polymer. An alternative explanation for this cyclic behaviour could be the growth and coalescence of holes.

GENERAL CONCLUSION

Varnish inevitably changes over time. This change, a normal degradation of the material, can lead to alteration of the paint layer or impeding the appreciation of the painting. Its removal is a difficult treatment involving the deposition of solvent conducing to its swelling and eventually to its breaking. During this process, restorers must be able to guarantee the safe removal of the varnish. With current knowledge, it is no longer necessary to prove that using pure solvents and solvent mixtures is a risky treatment for the painted layer because of the difficulty of controlling the process. Soft materials have an important wide range of applications. In the case of moisturizer in cosmetics, the aim is to penetrate the skin barrier by water molecules in a gel mixture. If one compares the skin barrier to the polymer film barrier and the water to the solvent, gels can also be applied to the proceed of the removal of varnish treatment. In this case, gels are composed mainly by water (∼ 90% or more) and a little amount of solvent in the water/gel mixture. With the use of this solvent/gel system, theoretically it seems possible to have a better control of the action of the solvent, to predict the kinetics of the solvent molecules into the varnish film, to reduce the amount of solvent transferred, to facilitate the application and to allow a short or long action time. The visual macroscopic results of using these kinds of materials of high molecular weight shown by scientists or restorers prove the effectiveness of the action of these solvent/gel systems on the polymer film. But there is a lack of knowledge in the understanding of the physics of the interactions between the polymer/solvent, polymer/water, polymer/solvent/gel and polymer/gel. And that was exactly the purpose of this study.

In summary, the microscopic and nanoscopic behavior of thin and ultrathin synthetic, hydrophobic polymer film of Laropal®A81 in contact with two systems was investigated: water/solvent solutions and gel/solvent mixture. The impact of shear and temperature was also explored. This work has been possible by the use of many instruments (AFM, Optical Miscroscopy, DSC, QCM, ellispometry, X-rays and rheology) and more particularly by the use of neutrons (NR and SANS) mainly at ILL in Grenoble.

First of all it was necessary to fix the materials of the study. It was chosen to use a resin of Laropal®A81 (LA), a synthetic resin commonly used for Cultural Heritage composed from urea, isobutyraldehyde, and formaldehyde, as a model varnish polymer film of this study. The solvent was benzyl alcohol (BA), a solvent also used by restorers to remove the varnish from the paint layer. For water (W), D 2 0 at 99,9% D for neutron scattering experiments, AFM and SAXS was chosen ; and MilliQ water with a resistance superior to 18MΩcm for others experiments. The Pemulen TR-2 in form of powder was the gel of this study. Pemulen TR-2 makes it possible to associate a hydrophobic solvent with water thanks to its ability to form a stable emulsion at low or high concentrations of the oil phase and also at very low viscosity. The approach of this study was to cover all the fields which allow the global comprehension of each element which composes the project according to 6 axes: I. Historical and material context of the varnish as well as the initial motivations of this project from Cultural Heritage, II. Scientific knowledge of Neutron scattering and polymers, III. Description of the materials chosen, Experimental protocol and Instrumentations, IV. The first paper submitted entitled "Swelling, Dewetting and Breakup in Thin Polymer Films for Cultural Heritage" [13] on the behavior of ultrathin film in contact with a solvent/nonsolvent mixture mainly by NR and AFM, V. The second paper submitted soon entitled "Stability of fluid Ultrathin Polymer Films in contact with solvent-loaded Gels for Cultural Heritage". on the behavior of ultrathin film in contact with a solvent/gel mixture by NR, and finally, VI. the results of the behavior of thick film immersed in a solvent/water mixture by SANS and QCM-D presented also in the form of a short publication. Then describing the problem encountered and the state of the art about the problem. This allows us to have a good overview of the subject and adjust to the best target the difficulties of the removal of the varnish layer, this risky treatment for the painted layer. II. Then, the basic physics of polymers and of neutron scattering, which are the main parts of this project, give the essential scientific aspects to understand the key points of this subject. III. A specific protocol was established in order to produce identical samples, reproducible and adapted to the constraints of each instrument. Thick films more than 1 µm were produced by dip coating and casting process for SANS and SAXS experiments, thin films of 500 nm were made by spin coating process for QCM-D and NR and ultrathin films were made by spin coating for NR, SANS, AFM, and Optical Microscopy. And that accompanied by several mixtures of water/BA, water/gel, water/gel/solvent were prepared. Materials of LA, BA and Pemulen TR 2 gel were characterized by an extensive literature review and the state of art and some complementary experiments. The LA was characterized by DSC measurement. The DSC allows us to measure the glassy transition (T g ) of LA immersed or not in BA/W. The T g decreases when BA is transferred into the polymer film. This allowed highlighting the role of the T g in the process of destruction of the varnish film. The swelling and dissolution process was first studied by measuring of the change of mass per unit area of LA thanks to oscillation frequency measurement with a QCM-D. The Pemulen TR-2 gel was characterized by rotary rheology experiments with a cone-plate geometry. The influence of the quantity of Pemulen TR-2 and solvent on the viscosity change of the gel at fixed pH were observed. The viscosity increased with increasing amount of Pemulen TR-2 and decreased with solvent addition. The Pemulen TR-2 gel behaves as a non-Newtonian shear thinning with a slight thixotropy. And it has a good adhesion when it is in contact with a rough or flat surface. These observations corroborate well the known elements of the literature on this gel.

IV. Neutrons scattering is a fantastic tool to explore thin polymer films during the process and to obtain various information such as the thickness, the roughness and the SLD of the polymer films. Thanks to these neutron data, the partial volume fractions of φ BA/LA and φ W /LA or φ PT R2gel/LA in LA films were calculated. In parallel, the study of the Yoneda peak, the OSS scattering intensity close to the total reflection, allowed us to follow the kinetics of the swelling in situ. In contact with a solvent/nonsolvent mixture, ultrathin film followed a dewetting process inducing holes and rims. The size of holes depends of the amount of solvent. Beyond a critical concentration, films breaks.

V. Thanks to neutron scattering, significant results were obtained in the comprehension of the swelling, dewetting and breakup of thin polymer films in contact with solvent-loaded gels for Cultural Heritage. Pemulen TR-2 gel matrix plays a role during the swelling and dissolution processes. As well as the solvent/nonsolvent case, the swelling of ultrathin film in contact with a solvent-loaded gel is accompanied by a dewetting process. It appears in the form of holes. However, there are some differences compared to the typical dewetting, in particular the absence of rims. The combination of temperature with solvent also has a high impact on the stability of the film. Beyond a critical temperature which depends on the solvent fraction, the film breaks.

VI. Small angle neutron scattering (SANS) allows the investigation of thick polymer films dry or immersed in a solution mixture. Experiments carried out with SANS and QCM-D have shown that the behaviour of thick films in contact with a solvent/non-solvent mixture is the same as for thin films. The destruction of film is accompanied by a heterogeneous dewetting process observable in the form of holes on all the film surface.

3. 20

 20 Thickness as a function of the withdrawal speed U 0 for the dip coating process. The minimum is achieved at the crossover between these two coating regimes. (Faustini et al. 2010) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.21 Schematic representation of the 4 regions during the withdrawal of the film by dipping. These regions are the wetting zone (a), the constant thickness area (b), the dynamic meniscus (c) and the static meniscus (d) . . . . . . . . . . . . . . 3.22 Dip coating, immersion stage (left) and drying stage (right) . . . . . . . . . . . 3.23 Beaglehole Picometer Light Ellipsometer of ILL . . . . . . . . . . . . . . . . . 3.24 Overall organization chart of project experiences . . . . . . . . . . . . . . . . . 3.25 Schematic layout of the FIGARO reflectometer from [72] . . . . . . . . . . . .

CHAPTER 1 .Figure 1 . 2 -

 112 Figure 1.2 -Detail of L'Enfant, la Vierge et Sainte Anne, oil on canvas, painting before (left) and after (right) the removal of the varnish layer. At the left of the picture the varnish is yellow and inhomogeneous

Figure 2 . 1 -

 21 Figure 2.1 -Schematic of Nuclear Fission from reference [73]

2. 1 . 3

 13 Neutron scattering techniques There are four main kinds of neutron scattering techniques: a) Transmission Measurement, b) Elastic Neutron Scattering, c) Quasi-Elastic and Inelastic Neutron Scattering and d) Neutron Spin-Echo (Fig. 2.2). One difference which allows us to distinguish them is the energy exchange as is shown in the example of the neutron scattering spectrum in Fig. 2.3. We will only develop b) in the following text.

Figure 2 . 2 -

 22 Figure 2.2 -Schematic representation of the four types of neutron scattering methods from reference[63]

Figure 2 . 6 -

 26 Figure 2.6 -Sketch of the specular reflection geometry at the water/polymer/Si substrate system. Note that the reflection angles are exaggerated for illustration, in a real experiments the neutron beam enters and leaves the silicon substrate from the sides rather than the bottom

  31 and 2.32, the diffusion of a molecule in a nonsolvent can be calculated. The results are shown in the Fig. 2.10.

Figure 2 . 10 -

 210 Figure 2.10 -Transfer of one molecule of solvent in a non-solvent

CHAPTER 2 .

 2 PHYSICS OF NEUTRON SCATTERING AND BACKGROUND 2.2.3 Effect of the Temperature on the Solvent Goodness

2. 2 . 6

 26 Rupture, Dewetting and Drop Formation of thin polymer filmsDewetting is the processes of the transformation of a homogeneous film into droplets (rupture). The film becomes unstable and leads to dewetting of the film. Reiter et al.[START_REF] Sharma | Instability of thin polymer films on coated substrates: rupture, dewetting, and drop formation[END_REF] proposed four stages of dewetting: rupture of the film, size change and coalescence of holes, disappearance of polymer ridges (Rayleigh instability); and instability of hole rims on low wettability coatings.

Figure 2 . 11 -

 211 Figure 2.11 -Schematic of the hole and rim in a thin polymer film on a substrate

Figure 2 .

 2 Figure 2.12 -2-D representation of Newton experiment at a speed U and a force F

  [START_REF] Shahin | Optimized formulation for topical administration of clotrimazole using pemulen polymeric emulsifier[END_REF] [START_REF] Stulik | Solvent gels for the cleaning of works of art: the residue question[END_REF]. It can form stable o/w emulsions even with low emulsifier concentrations (0.15 %) 3.11 and also at high concentrations. According to N. Ravenel, the conservation lab at Shelburne Museum use Pemulen TR-2 in a 1 % concentration in the gel since R. Wolbers introduced them to this gel in 2007[START_REF] Ravenel | Pemulen® tr-2: an emulsifying agent with promise[END_REF]. Wolbers proposed to use the triethanolamine (TEA) to neutralize the Pemulen TR-2 and the water/Pemulen TR-2/TEA mixture has quickly become the standard mixture among restaurateurs. Physical informations of TEA are in table3.3.

Figure 3 . 6 -

 36 Figure 3.6 -Formula of Acrylate / C10-30 Acryl Acrylate Crosspolymer (Goddard et al. 1999)

Figure 3 . 7 -Figure 3 . 9 -

 3739 Figure 3.7 -The repulsive force due to the aqueous gel layers that surround each droplet of oil, keep the o/w emulsion in a state of great stability (Lubrizol-Technical data sheet. 2007)

Figure 3 .

 3 Figure 3.10 -Effect of pH on the viscosity of Pemulen TR-2 with 5 % Mineral Oil (Lubrizol-Technical data sheet. 2007)

Figure 3 . 15 -

 315 Figure 3.15 -Spin coater (left) used for the deposition of polymer film on Si substrate. Rotating support with a sample of LA film after spin coating (right).

Figure 3 . 18 -

 318 Figure 3.18 -Thickness of LA thin film on Si Crystal Blocks (black) and on Si Wafers (grey) substrates obtained by spin coating method at 1250 RPM for 44 seconds as function of the concentration of LA in toluene

Figure 3 . 19 -Figure 3 . 28 -

 319328 Figure 3.19 -Sample of 100 nm LA thin film on Si crystal block

3. 3 . 4 Figure 3 . 30 -

 34330 Figure 3.30 -Microscope Olympus BX61 of ESRF at Grenoble

Figure 3 . 33 -

 333 Figure 3.33 -Schematic illustration of (a) the work principle of QCM and (b) the quartz crystal ship from reference[START_REF] Qiao | Progresses on the theory and application of quartz crystal microbalance[END_REF]

Figure 3 .

 3 Figure 3.34 -QCM Samples

Figure 3 . 35 -

 335 Figure 3.35 -Tg of LA81 before and after immersion in a small quantity of BA (0 %, 0.4 %, 0.6 %, 0.8 % and 1 %) in D20

  2 ESPCI ParisTech, Paris, France. 3 Laboratoire de Rhéologie et Procédés, Grenoble, France. (a) Univ.Grenoble Alpes -LRP, F-38041 Grenoble, FRANCE (b) CNRS, LRP , F-38041 Grenoble, FRANCE

Fig. 2

 2 Fig. 2 Neutron Reflectivity from a polymer film of LA in air before and after annealing (114°C /30 min). The modelling of the data (solid line) shows a reduction of film thickness from initially 232 nm to 200 nm.

Fig. 3

 3 Fig. 3 Neutron reflectivity from a 200 nm polymer film of LA immersed in D 2 O.

37

 37

Figure 1 :

 1 Figure1: Left) Surface height versus in-plane position across a dewetting hole as seen by AFM in air of a LA film after prolonged exposure to a water/BA binary mixture. Right) Fitted SLD of a similar LA film in a BA/water mixture versus distance from the substrate. Note that the annealing time is longer for the AFM measurement leading to significantly larger holes and rims. This data is taken from Ref.14 .

13

 13

Figure 4 :

 4 Figure 4: Reflectively curve (multiplied by q 4z ) vs. momentum transfer q z on a logarithmic scale for an LA film in aqueous solutions of 0.5% BA and 0.1% Pemulen at 27 • C (data points). The solid line in the same color code is the best fit to the data assuming no rims. The broken line is the best fit to the data assuming a rim fraction as in Fig.1left. Inset: Normalized least square value χ 2 vs. fraction of rims φ rim for various heights of rims as indicated in the legend deduced from fitting the specular NR spectra to a model of LA containing a fraction of holes and rims.

Figure 6 :

 6 Figure 6: Normalized (excess) volumes of the polymer (red x-crosses, left axis) and liquid (blue crosses, right axis) inside the LA layer from NR of 0.3% BA and 0.1% PTR-2 in D 2 O according to the boundary condition eq. 1 as a function of temperature. Note: The two points at R.T. for each fraction were measured at two different times, once at the very beginning and a second time after heating to 40 • C indicating that the polymer loss is irreversible, but the solvent penetration is reversible within error.

Figure 7 :

 7 Figure 7: Normalized volume fractions of BA (red x-crosses) and water (blue crosses) from NR of 0.3% BA and 0.1% PTR-2 in D 2 O according to the boundary condition eq. 2 as a function of temperature.

Figure 10 :

 10 Figure 10: Left axis: SLD as a function of temperature from a LA polymer film in contact with 0.5% BA and 0.1% PTR-2 in D 2 O (open squares). Right axis: Extracted hole radius from the OSS simulations of the same sample (filled squares). The triangles correspond to the SLD (open triangle) and the hole radius (filled triangle) of a LA film in contact with a 0.5% BA solution in pure D 2 O after 2 h immersion.

Figure 11 :

 11 Figure 11: Roughness of the aqueous/polymer interface deduced from NR for a solution of 0.3%BA and 0.1% PTR-2 in D 2 O as a function of temperature.

Figure 12 :

 12 Figure12: Film stability diagram using the T g and NR results. The lower black line corresponds to the T g as calculated from eq. 5 by using the BA in LA volume fractions from the bottom axis. The blue line in the middle corresponds to the threshold temperature where the OSS intensity is 10 4 counts per minute in Fig.S4from the SI and the red line in the upper right corner marks the temperature at which a sudden loss of most of the film's material is observed. The latter two lines relate to the upper x-axis (BA fraction in water) and are deduced from the experimental data.

Figure 6 . 1 -

 61 Figure 6.1 -SANS spectra, scattering cross-section of 1.2 µm LA films in contact with 0.7 % BA in D 2 O as function of time.

Figure 6 .

 6 Figure 6.2 -A (intensity) obtained from fitted SANS data by Porod's law of 1.2 µm LA films in contact with 0.6 % BA and 0.7 % BA in D 2 O.

CHAPTER 6 .Figure 6 . 3 -

 663 Figure 6.3 -Frequency change of a 500 nm Laropal®A81 film prepared by spin coating and immersed in an increasing concentration of BA in D 2 O as a function of time as reveled by QCM-D.

CHAPTER 6 .

 6 TEMPORAL EVOLUTION OF VARNISH FILMS IN THE PRESENCE OF SOLVENT/NONSOLVENT MIXTURES FOR CULTURAL HERITAGE I. The motivation was exposed by guiding the reader in the global understanding of what restoration, varnishes are used and how restorers use them.

TABLE OF CONTENTS

 OF FIGARO at ILL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

TABLE OF CONTENTS

 OF Appendix A: Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic properties of the neutron . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Some dynamic and kinematic viscosity values for some materials at atmospheric pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic of the stratigraphy of a painting (not to scale) . . . . . . . . . . . . . 1.2 Detail of L'Enfant, la Vierge et Sainte Anne, oil on canvas, painting before (left) and after (right) the removal of the varnish layer. At the left of the picture the varnish is yellow and inhomogeneous . . . . . . . . . . . . . . . . . . . . . . Sketch of the specular reflection geometry vs Off-specular scattering . . . . . . 2.8 Schematics representation of SANS technique from reference [63], not to scale (vertical sizes in cm and horizontal distances in m) . . . . . . . . . . . . . . . 2.9 Various fractal Porod exponents from reference [63] . . . . . . . . . . . . . . 2.10 Transfer of one molecule of solvent in a non-solvent . . . . . . . . . . . . . . . The different fluids ranked according to their rheological behavior with, on the left, the flow curve and on the right, the viscosity curve . . . . . . . . . . . . . 2.14 Comparison of Bingham and Casson laws for an iron oxide suspension. Example of Threshold Fluid from reference [118] . . . . . . . . . . . . . . . . . . .

	LIST OF TABLES 2.1 LIST OF FIGURES 1.1 LIST OF FIGURES 2.13

3.1 Physical properties of Toluene . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Physical properties of Benzyl alcohol . . . . . . . . . . . . . . . . . . . . . . . 3.3 Physical properties of triethanolamine . . . . . . . . . . . . . . . . . . . . . . 3.4 thickness of films according to the concentrations of LA in toluene at 3000 rpm/44s spin coating program . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Scattering length densities of the materials used in this study. For LA and D 2 O the range of measured values during different experiments is given. In case of BA, silicon and silicon dioxide the literature values are given assuming the chemical composition to be C 7 H 8 O, Si and SiO 2 with densities of 1.02 g/cm 3 , 2.33 g/cm 3 and 2.2 g/cm 3 , respectively. . . . . . . . . . . . . . . . . . . . . . . 6.1 Scattering length densities of the materials used in this study. For LA the range of measured values during different experiments is given [13]. In case of the other materials literature values are given assuming the chemical composition of BA to be C 7 H 8 O at 1.02 g/cm 3 density. . . . . . . . . . . . . . . . . . . . . 2.1 Schematic of Nuclear Fission from reference [73] . . . . . . . . . . . . . . . . 2.2 Schematic representation of the four types of neutron scattering methods from reference [63] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Schematic example of a neutron scattering spectrum as a function of exchanged energy at a given Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Scattering geometry experiment where r is the point of the scattered neutrons, θ , Φ are the angles, dΩ is the small solid angle and dS is the area of the beam from the reference [68] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Neutron scattering cross sections for few elements. Circles are drawn to scale from reference [74] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Sketch of the specular reflection geometry at the water/polymer/Si substrate system. Note that the reflection angles are exaggerated for illustration, in a real experiments the neutron beam enters and leaves the silicon substrate from the sides rather than the bottom . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 2.11 Schematic of the hole and rim in a thin polymer film on a substrate . . . . . . . 2.12 2-D representation of Newton experiment at a speed U and a force F . . . . . . 2.15 Geometry cone-plane (according to

  . . . . . . . . . . . . . 3.2 Toluene structure from Sigma-Aldrich . . . . . . . . . . . . . . . . . . . . . . ] at room temperature and obtained by rheology measurements at the LRP. The higher the concentration, the more the gel is viscous and difficult to shear. . . . . . . . . . . . . . . . . 3.10 Effect of pH on the viscosity of Pemulen TR-2 with 5 % Mineral Oil (Lubrizol-Technical data sheet. 2007) . . . . . . . . . . . . . . . . . . . . . . . . . . . . Observation of the slip of the gel by a marking during a very slow shear at room temperature. The gel exhibits no slippage. . . . . . . . . . . . . . . . . . . . . 3.14 Mixing and homogenization of the PTR2 gel sample by slow rotations with a rotary rheometer with blades. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.15 Spin coater (left) used for the deposition of polymer film on Si substrate. Rotating support with a sample of LA film after spin coating (right). . . . . . . . . . 3.16 Film thicknesses h f as a function of spin speed and initial polymer solution concentration for PS and PMMA in Toluene (Hall et al. 1998) . . . . . . . . . 3.17 Surface of LA thin films on Si Crystal Blocks obtained by spin coating using three concentrations of LA in toluene, 20 %, 25 % and 40 % LA, spread on substrates at 1250 RPM for 44 seconds, highlighting the apparent colors as function of the thickness of the film . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.18 Thickness of LA thin film on Si Crystal Blocks (black) and on Si Wafers (grey) substrates obtained by spin coating method at 1250 RPM for 44 seconds as function of the concentration of LA in toluene . . . . . . . . . . . . . . . . . .

	LIST OF FIGURES
	3.13
	3.11 Effect of Mineral Oil concentration on the viscosity of Pemulen TR-2 at pH
	5.5± 0.2 neutralized with 18 % NaOH (Lubrizol-Technical data sheet. 2007) . .
	3.12 Shear stress [Pa] of a Gel of Pemulen TR-2 at 0.03 % at fixed ph ∼ 7 and with an

3.3 Benzyl alcohol structure from Sigma-Aldrich . . . . . . . . . . . . . . . . . . 3.4 Geometry a) (100) wafer, b) (111) block . . . . . . . . . . . . . . . . . . . . . 3.5 Polyacrylic acid during the process of swelling (from an image by Claire Dupuy [124] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Formula of Acrylate / C10-30 Acryl Acrylate Crosspolymer (Goddard et al. 1999) 3.7 The repulsive force due to the aqueous gel layers that surround each droplet of oil, keep the o/w emulsion in a state of great stability (Lubrizol-Technical data sheet. 2007) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Effect of NaCl concentration on the viscosity of Pemulen TR-2 with 5 % and 30 % Mineral Oil and at pH 7± 0.2 neutralized with 18 % NaOH (Lubrizol-Technical data sheet. 2007) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 Shear stress [Pa] of a Gel at different concentration of Pemulen TR-2 (0.03 % to 2.5 %) at fixed ph ∼ 7 as function of shear rate [s -1 increasing concentration of BA as function of shear rate [s -1 ] at room temperature and obtained by rheology measurements at the LRP. BA slightly decreases the viscosity of the gel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.19 Sample of 100 nm LA thin film on Si crystal block . . . . . . . . . . . . . . .

  . . . . . . . . . . 3.28 Schematic layout of the N-REX+ reflectometer from [136] . . . . . . . . . . . Examples of AFM images of LA polymer surface immersed 19 hours in 0.3 % BA in D 2 O obtained by tapping mode . . . . . . . . . . . . . . . . . . . . . . 3.33 Schematic illustration of (a) the work principle of QCM and (b) the quartz crystal ship from reference [144] . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.34 QCM Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.35 Tg of LA81 before and after immersion in a small quantity of BA (0 %, 0.4 %, 0.6 %, 0.8 % and 1 %) in D20 . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.36 Schema of Ubbelohde Viscosimeter with A and B the upper and lower measurement marks and C the limit of the reservoir . . . . . . . . . . . . . . . . . . . . 3.37 Intrinsic viscosity of LA as a function of LA concentration in BA mixture. . . .

	LIST OF FIGURES
	3.32 RÉSUMÉ
	Le gonflement et la dissolution des vernis des peintures de chevalet : Contribution à la
	compréhension macroscopique et nanoscopique des mécanismes physiques en jeux pen-
	dant le traitement d'enlèvement des vernis altérés.

3.29 Schematic layout of the SANS reflectometer from [72] . . . . . . . . . . . . . 3.30 Microscope Olympus BX61 of ESRF at Grenoble . . . . . . . . . . . . . . . . 3.31 Schematic of AFM, not to scale (according to a figure from [142]) . . . . . . . 6.1 SANS spectra, scattering cross-section of 1.2 µm LA films in contact with 0.7 % BA in D 2 O as function of time. . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 A (intensity) obtained from fitted SANS data by Porod's law of 1.2 µm LA films in contact with 0.6 % BA and 0.7 % BA in D 2 O. . . . . . . . . . . . . . . . . . 6.3 Frequency change of a 500 nm Laropal®A81 film prepared by spin coating and immersed in an increasing concentration of BA in D 2 O as a function of time as reveled by QCM-D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  Nuclear reactions allow us to obtain neutrons by two possibles ways : by accelerated charged particles like electrons and protons, and by fission or fusion. At ILL and MLZ, neutrons are produced by fission of the fuel element Uranium 235 thermalized by deuterium oxide (moderator), hence we will only focus on this reaction 2.3 for the following part. Fission was discovered in 1938 by three German scientists Otto Hahn, Lise Meitner and Fritz Strassmann. During this reaction, the 235 U nucleus (heavy nuclei) absorbs a thermal neutron. Then, it becomes excited until it splits into several fragments (fig.2.1). This releases neutrons but also the energy. The fission reaction is:

	CHAPTER 2. PHYSICS OF NEUTRON SCATTERING AND BACKGROUND
	A free neutron does not live forever and its lifetime is 886 ± 3 s. General properties of the neutron are summarized in table 2.1.
	Table 2.1 -Basic properties of the neutron
	mass spin charge	1.674927471 x 10 -27 kg 1 2 0
	magnetic moment	-1.91304273 µ N
	n + 235 92 U → fission product 1 + fission product 2 + 3n.	(2.3)
			.2)

  Interaction parameter in the Phase Diagram for a solvent/nonsolvent/polymer mixture A Phase Diagram is a representation of the physical states of a single or of mixed substances including polymer. It demonstrates the equilibrium and non-equilibrium phases of this system.

	CHAPTER 2. PHYSICS OF NEUTRON SCATTERING AND BACKGROUND
	2.2.5
	.40)

Table 2 .

 2

	2 -Some dynamic and kinematic viscosity values for some materials at atmospheric
	pressure.
	material	µ (Pa.s)	υ (St)
	Air (0°C) water (20°C)	1.7x10 -5	1.7x10 -8

Table 3 .

 3

	3 -Physical properties of triethanolamine
	Formula Molecular weight 149.19 g/mol C 6 H 1 5NO 3
	Density	1.124
	Flash point	21.6˚C
	Boiling point	335.4˚C

Table 3 .

 3 5 -Scattering length densities of the materials used in this study. For LA and D 2 O the range of measured values during different experiments is given. In case of BA, silicon and silicon dioxide the literature values are given assuming the chemical composition to be C 7 H 8 O, Si and SiO 2 with densities of 1.02 g/cm 3 , 2.33 g/cm 3 and 2.2 g/cm3 , respectively.

	Material	bulk SLD [10 -6 Å -2 ]
	D 2 O	6.1 -6.25
	BA	1.298 (literature value)
	Silicon	2.07 (literature value)
	Silicon dioxide	3.47 (literature value)
	Laropal®A81	0.9 ± 0.1

Table 1

 1 Scattering length densities of the materials used in this study. For LA and D 2 O the range of measured values during different experiments is given. In case of BA, silicon and silicon dioxide the literature values are given assuming the chemical composition to be C 7 8 O, Si and SiO 2 with densities of 1.02 g/cm 3 , 2.33 g/cm 3 and 2.2 g/cm 3 , respectively.

	Material	bulk SLD [10 -6 Å -2 ]
	D 2 O BA Silicon Silicon dioxide Laropal®A81	6.1 -6.25 1.298 (literature value) 2.07 (literature value) 3.47 (literature value) 0.9±0.1

  Whatever the exact model used for fitting the specular NR of LA in BA/PTR2/D 2 O, a SLD growth with temperature (and time) of the LA film is observed, which can only suggest D 2 O invasion into the LA film as it is the largest SLD constituent as quantitatively shown above. The film invasion with water can result either from creation of penetrating or nonpenetrating holes filled with D 2 O or formation of LA/BA/D 2 O mixed zones. Assuming holes as the reason for increased water fractions it is possible to calculate SLD density profiles by assuming a Gaussian distribution of cylindrical water filled holes around a mean depth inside a LA film of fitted total thickness. The detailed analysis of the NR spectra with this model

  • C is about 3 µm -2 if the holes are not overlapping.

	SLD [10 -6 Å -2 ]	2.8 2.6 2.4 2.2 2.0 1.8	SLD 0.5% BA no gel SLD 0.5% BA + 0.1% TR2 Hole size 0.5% BA Hole size 0.5% BA + 0.1% TR2	0.5 0.4 0.3 0.2	Hole size [µm]
		1.6 1.4					0.1
		20	30	40	50	60	70
					T [ºC]

  Analysis of SANS dataThe measured SANS data is analyse using Igor Pro software. Data are reduced and plotted by a model of Porod. The Igor's Power Law fit function is:

		-6 Å -2 ]
	D 2 O	6.36 (literature value)
	H 2 O	-0.57 (literature value)
	BA	1.298 (literature value)
	Laropal®A81	0.9±0.1
	6.2.5

for the most part Damar or Mastic

Acknowledgements

We thank the ILL for neutron beam time on FIGARO (doi:10.5291/ILL-DATA.1-03-34) and MLZ for neutron beam time on the N-Rex + instrument operated by MPG at the Heinz Maier-Leibnitz Zentrum (MLZ), Garching, Germany. We thank the Partnership for Soft Condensed Matter at ILL and ESRF for the use of complimentary techniques. We thank Alain Panzerella from the ESRF for performing the AFM measurements. The authors gratefully acknowledge the financial support provided by JCNS to perform the neutron scattering measurements at the Heinz Maier-Leibnitz Zentrum (MLZ), Garching, Germany. We acknowledge the help of Olaf Soltwedel during the NR measurements at MLZ. The Laboratoire Rhéologie et Procédés is part of the LabEx Tec 21 (Investissements d'Avenir -grant agreement n°ANR-11-LABX-0030) and of the PolyNat Carnot Institut (Investissements d'Avenir -grant agreement n°ANR-11-CARN-030-01). We acknowledge Dr. Hélène Galliard, Vincent Verdoot, Fréderic Hugenell for their technical support. We thank Michel Manu for fruitful discussions on the choice of the system to be used for this project. We acknowledge BASF for providing the varnish for this study.

Acknowledgement

We thank the ILL for neutron beam time on FIGARO (doi.ill.fr/10.5291/ILL-DATA.1-03-36). We thank the Partnership for Soft Condensed Matter at ILL for the use of complimentary techniques. The Laboratoire de Rhéologie et Procédés is part of the LabEx Tec 21 (Investissements d'Avenir -grant agreement n • ANR-11-LABX-0030) and of the PolyNat Carnot Institut (Investissements d'Avenir -grant agreement n • ANR-11-CARN-030-01).

Acknowledgements

We thank the ILL for neutron beam time on D11 (doi:10.5291/ILL-DATA.1-03-36). We thank the Partnership for Soft Condensed Matter at ILL for the use of complimentary techniques. We thank Yuri Gerelli for the help during the QCM-D measurements.

Appendix

Flory-Huggins model equations for thermodynamic ternary phase diagram

The FH model can be extended empirically 54 so that the Gibbs free energy of mixing is given by:

(5) where R is the universal gas constant, T is the temperature, is the concentration-dependent interaction parameters and 2 = 2 /( 1 + 2 ). Subscripts refer to nonsolvent (1), solvent (2) and polymer (3) parameters.

This expressions can be obtained following the definition of the chemical potential:

The intrinsic viscosity is calculated using: 7) where M is the molecular weight in Da. And the polymer/solvent interaction parameter 23 can be obtain by:

where A 2 is the polymer-concentration-independent, 3 is the polymer density and V 2 is the molar volume of the solvent. E-mail: gutfreund@ill.fr; yahya.rharbi@univ-grenoble-alpes.fr

Abstract

The removal of ultrathin amorphous polymer films in contact with an aqueous gelled solution containing small amounts of good solvent is addressed by means of specular and off-specular neutron reflectometry. The distribution of heavy water and benzyl alcohol is revealed inside Laropal R A81, often employed as a protective varnish layer for Culture Heritage in restoration of easel paintings. The swelling kinetics, interface roughness and film morphologies were recorded as a function of temperature and increasing benzyl alcohol concentration in the dispersion of Pemulen TR-2, a hydrophobically modified acrylic acid copolymer. The addition of small amounts of good solvent results in the appearance of water-filled cavities inside the varnish, which grow with time. It is shown that while increasing the solvent concentration greatly enhances the hole growth kinetics an increase in temperature above the glass transition temperature has not such a big effect on the kinetics.

Supporting Information Available

Additional NR fitting results, pre-characterization of LA layers, comparison of NR and OSS between LA films in contact with gel and pure water containing high BA concentrations and additional optical micrographs of LA films after long exposure to pure water and BA. In situ Rheo-NR of BA swollen LA films in contact with gel+BA.

Appendices APPENDIX A PUBLICATIONS

A. Castel, Y. Rharbi, P. Gutfreund