Léo Lavaur
email: leo.lavaur@imt-atlantique.fr

Marc-Oliver Pahl
email: marc-oliver.pahl@imt-atlantique.fr

Yann Busnel
email: yann.busnel@imt-atlantique.fr

Federated security approaches for IT and OT

Fabien Autrel

IMT Atlantique, Cyber CNI fabien.autrel@imt-atlantique.fr Abstract-The Internet of Things has begun to spread over a variety of domains, including industry and finance. It represents an increasing threat for both IT and OT. The lack of collaboration results in the same attacks targeting different organizations one after the other. Often employed as an answer to this problem, cyber threat-intelligence sharing induces its own set of challenges: trust, privacy, and traceability.

This thesis takes advantages of a distributed sharing-oriented architecture and to enhance the security of industrial infrastructures. We study Federated Learning algorithms to build a distributed, autonomic system for detecting and characterizing attacks, as well as providing counter-measures.

Experiments on real-world testbeds at the chair Cyber CNI allow us to validate the theoretical assumptions against realistic infrastructures and scenarios, fitting industrial use-cases.

Index Terms-IT, OT, threat intelligence, cooperative sharing, federated learning, distributed ledgers

I. MOTIVATION

This thesis takes place in IMT's chair Cyber CNI, which focuses its work toward the protection of Critical Networked Infrastructures. The chair is supported by industrial partners, allowing to study real-world use-cases and benefit from their inputs -see section IV. The purpose of this thesis is to study the automated sharing of threat intelligence, particularly in critical infrastructures.

Over the years, multiple attacks have been reported to aim the Information Technologies (IT) and Operational Technologies (OT), including the Industrial Control Systems (ICSs) [START_REF] Neshenko | Demystifying IoT Security: An Exhaustive Survey on IoT Vulnerabilities and a First Empirical Look on Internet-Scale IoT Exploitations[END_REF]. These threats include information leakage, device takeover, or even physical damages in critical infrastructures. To protect organizations, security systems often rely on network-based attack detection like Intrusion Prevention System (IPS) to identify attacks, and block the traffic. This approach is however inefficient against novel attacks and Advanced Persistent Threat (APT), like Stuxnet in 2016. Behavior-based anomaly detection based on Machine Learning (ML) is often considered the future of attack detection.

More importantly, the same attack can damage different organizations using the same mechanics before its operation is characterized, and actionable threat intelligence can be shared. Botnets are a good example since they infect a considerable amount of devices using the same vulnerabilities. In 2016, the Mirai botnet has been used for multiple world-scale Distributed Denial of Service (DDoS) attacks. One of them targeted the DNS provider Dyn, and is responsible for shutting down parts of the Internet [START_REF] Kolias | DDoS in the IoT: Mirai and Other Botnets[END_REF]. The malware is still active and new devices get compromised every day, showing the lack of cooperation among the security community. Consequently, detection systems need to move from a siloed architecture to a federated approach; thus unifying the localized ML models.

The discussed situation leads to the following observations: (a) there is a lack of unified knowledge in cybersecurity, and more particularly in the Internet of Things (IoT) [START_REF] Wagner | Cyber threat intelligence sharing: Survey and research directions[END_REF]; (b) trust and privacy are major hurdle for stakeholders to share data [START_REF] Wagner | Cyber threat intelligence sharing: Survey and research directions[END_REF]; (c) centralized systems represent a Single Point of Failure (SPoF) and can induce a communication overhead [START_REF] Rathore | BlockSecIoTNet: Blockchain-based decentralized security architecture for IoT network[END_REF]; (d) the siloed architecture of detection systems is an obstacle to their effectiveness [START_REF] Aledhari | Federated Learning: A Survey on Enabling Technologies, Protocols, and Applications[END_REF].

II. CURRENT STATE

Observations (a) to (c) represent research questions that have been independently addressed by the research community. Our current work is focused on the literature overview of the collaborative aspects of security in the IT and OT. Following some of the precepts of the Systemic Literature Review methodology, we survey the state-of-the-art multiples overlapping domains: Federated Learning (FL) and its limitation, privacy-preserving information sharing, collaborative threat intelligence, distributed ledgers, and attack detection for the IoT and Industrial Internet of Things (IIoT) -see ??.The questions that our survey tries to answer are as follows:

• What are the most important attacks over the past 10 years, where federated approaches could work? • What are the topics covered by the academic literature over that rime? • In which venues or journals was the literatures published?

• Which groups are active in this area?

• What are the still open questions according to existing surveys?

Threat intelligence sharing is often proposed as a solution to observation (a) [START_REF] Cha | Blockchain-Based Cyber Threat Intelligence System Architecture for Sustainable Computing[END_REF]. Game-theory is studied to provide incentives to stakeholders to make the participants actively involved in sharing communities. Platforms such as MISP [START_REF] Wagner | MISP -The design and implementation of a collaborative threat intelligence sharing platform[END_REF] have emerged to overcome these issues, and the blockchain is frequently considered in order to provide trust, traceability, and non-repudiation [START_REF] Wu | Towards Improved Trust in Threat Intelligence Sharing using Blockchain and Trusted Computing[END_REF].

To solve observations (b) and (d), FL is proposed in association with detection algorithms. FL allows training a global ML for a distributed system containing multiple nodes without sharing the analyzed data itself. Instead, nodes train their models locally, and share their parameters with each other. Architectures based on FL are expected to provide accurate and faster results in addition to adding privacy and security [START_REF] Li | DeepFed: Federated Deep Learning for Intrusion Detection in Industrial Cyber-Physical Systems[END_REF].

To address observation (c), distributed ledgers such as blockchain or Directed Acyclic Graph (DAG) could support decentralized systems while guaranteeing the integrity of the exchanges. Distributed architectures also diminish the communication overhead in federated systems, allowing to reduce both the bandwidth consumption and the latency [START_REF] Rathore | BlockSecIoTNet: Blockchain-based decentralized security architecture for IoT network[END_REF].

The first findings of our research identified the following research question. What federated strategies could be applied to local ML-based detection systems to improve the security of IT and OT realms? Several sub-questions arise from the latter, such as:

• What are most appropriate FL approaches? Which strategies for model aggregation? • What are the security limitations of such approaches?

• What kind of architecture would best support these systems?

III. RELATED WORKS Several surveys have covered parts of the subject, especially the state-of-the-art of FL approaches [START_REF] Aledhari | Federated Learning: A Survey on Enabling Technologies, Protocols, and Applications[END_REF] or the collaborative threat intelligence [START_REF] Skopik | A problem shared is a problem halved: A survey on the dimensions of collective cyber defense through security information sharing[END_REF], but none covers both aspects. On the technical side, several security architectures have been introduced to tackle the current issues of the IoT. The authors of [START_REF] Haddadpajouh | AI4SAFE-IoT: an AI-powered secure architecture for edge layer of Internet of things[END_REF] propose an AI-enabled architecture to secure the physical layer of the IoT, using modules dedicated to one use-case, while the authors of [START_REF] Rathore | BlockSecIoTNet: Blockchain-based decentralized security architecture for IoT network[END_REF] proposed detection system based on Software-defined networking (SDN) using blockchain-based FL on a three-layer architecture.

FL and blockchain have both been well addressed in the literature, the former for its ability to reduce the communication overhead while improving privacy, the latter to support information-sharing while guaranteeing trust, non-repudiation and tampering resistance. The authors of [START_REF] Li | DeepFed: Federated Deep Learning for Intrusion Detection in Industrial Cyber-Physical Systems[END_REF] present DeepFed, a deep FL detection system tailored to deal with Cyber-Phisical Systems (CPSs) while maintaining a centralized architecture. On the other hand, FLchain [START_REF] Majeed | FLchain: Federated Learning via MEC-enabled Blockchain Network[END_REF] uses the distributed aspects of the blockchain to remove the single point-of-failure.

The blockchain is also studied to provide incentives to stakeholders and improve participation. Cha et al. [START_REF] Cha | Blockchain-Based Cyber Threat Intelligence System Architecture for Sustainable Computing[END_REF] propose a blockchain-based Cyber Threat Intelligence (CTI) architecture that provides reliability, privacy, scalability, and sustainability. The proposed system reduces network load, and measures organizations' contributions to motivate participation.

IV. NEXT STEPS

As mentioned in section II, current work focuses on the literature analysis. Then, we will implement FL algorithms fitting the use-cases of our chair partners. Two use-cases have been currently identified. (I) The first one is the security of the OT, where FL could be implemented to detect attacks targeting CPS at scale. The chair already work on a cyberphysical testbed [START_REF] Pahl | A Mixed-Interaction Critical Infrastructure Honeypot[END_REF] that will eventually allow us to run attack scenarios on multiple scale-models at once, letting us to use FL to detect the anomalies. (II) The second identified use-case is the smart building that are currently appearing all around the world. FL would be used to detect behavior anomalies, allowing the detection of physical intrusions. A real-world testbed will be made by deploying sensors and devices in our office to emulate smart-building equipments.

Another approach that deserves to be considered is the impact of geographical and geopolitical context on the attacks. In fact, a lot of today's event in the cyberspace are the transposition of real-world conflicts or tensions. This implies a completely different set of challenges due to the linking of abstract concepts taken from social sciences with the technical representation of such event. If addressed, this part of the thesis will probably require collaboration with other teams.


Khalid Ferji

Cécile Nouvel

Jérôme Babin

Min-Hui Li

Cédric Gaillard

Erwan Nicol

Christophe Chassenieux

Jean-Luc Six

Polymersomes from Amphiphilic Glycopolymers Containing Polymeric Liquid Crystal Grafts

Keywords: vesicles, cholesterol-based polymer, polysaccharide, dextran, drug delivery systems

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Since many decades, researchers have been attempting to design model artificial membranes that can mimic the more complex biological ones by using phospholipids whose self-assembly in aqueous medium leads to vesicles commonly named liposomes. [1] More recently, polymeric counterparts of liposomes, so-called polymersomes, have been developed through the use of copolymers. [2] Usually, polymersomes are hollow spherical nano-objects composed of a hydrophobic compact bilayer membrane with hydrophilic inner and external surfaces. It was shown that this hydrophobic bilayer, thanks to its polymeric nature, enhances the mechanical stiffness and decreases the permeability to both solvent and solute than the ones of the liposomes. [3][START_REF] Kumar | Proc. Natl Acad. Sci[END_REF][START_REF] Dao | [END_REF] Such polymersomes were often produced by the selfassembly of amphiphilic block copolymers and found applications as drug delivery systems or nanoreactors. [6][7][8][9] Many reviews can be found dealing with the polymersome formulations from coil-coil diblock or triblock copolymers or with the experimental methods to investigate their vesicular morphology. [10][11] In order to improve the mechanical properties of the polymeric membrane, rod-coil diblock copolymers with block containing stiff moieties such as cholesterol or polypeptide were used. For instance, some mesogenic polymeric blocks have been considered in combination with various hydrophilic ones [12][13][14][15][16][17][18][19][20][21][22] and have been shown to result in stimuli responsive polymersomes, which can be disrupted upon applying one external stimulus. [6,[23][24] The design of smart polymersomes either responding to pH, temperature, redox, magnetic field or light stimuli [6,11,[25][26][27] has also been achieved thanks to the processing of new polymerization techniques and of chemical couplings. Biological polymers [7][8][9][28][29][30][31] like polypeptides, polynucleotides or polysaccharides as well as biodegradable polymers such as polylactic acid (PLA) or poly(-caprolactone) (PCL) were also considered to produce polymersomes of interest for biological applications, especially when combined with biocompatible polyethylene glycol (PEG) block that leads to stealthy polymersomes. [32] However, the formation of polymersomes using other polymeric architectures than block copolymers such as graft copolymers has been reported in a far less extent. To the best of our knowledge, only four graft copolymers forming polymersomes have been investigated in the literature so far: poly(2hydroxyethyl aspartamide)-g-oligo(lactic acid) [33] , poly(bamino ester)-g-(PEG/PLA) [34] , chitooligosaccharide-g-PCL [35] and poly(3-hydroxyoctanoate-co-3hydroxyundecanoate)-g-PEG [36] .

The aim of the present study was to investigate the selfassembling propensity in solution and at liquid/liquid interface of graft glycopolymers (called Dex-g N -PDEGCholA F ) containing liquid-crystal (rod) grafts that were previously reported by us. [37] In these glycopolymers, Dextran is used as the hydrophilic polysaccharidic backbone and poly(diethylene glycol cholesteryl ether acrylate) (PDEGCholA) as hydrophobic polymeric grafts. Various Dex-g N -PDEGCholA F were synthesized using a "grafting from" four-step strategy described in scheme S1. [37] N and F, which are respectively the number of PDEGCholA grafts per 100 glucopyranosic units of dextran backbone and the weight fraction of PDEGCholA in glycopolymer, have been varied in some extent (Table 1). [37] In bulk, PDEGCholA grafts appeared to exhibit both single glass transition and liquid crystal to isotropic transition temperatures. Between these two transition regimes, the bulk displayed at the microscopic scale typical smooth fan-shape birefringent textures, which indicated a smectic A phase further confirmed by X-ray scattering measurements. [37] By comparing the lamellar period to the DEGCholA monomer length, we established that an interdigitated smecticA phase (SmA d ) was formed. This peculiar mesomorphism of the grafts was preserved once they were grafted onto a dextran backbone. [37] Table 1. Characteristics of Dex-g N -PDEGCholA F. and of their corresponding nanostructures formed in aqueous media.

Entry Copolymers characteristics

Solvent

(before dialysis) Nanostructure characteristics Dex-g N -PADEGChol F a) of grafts [g/mol] b) Ɖ c) R H d) [nm] R G e) [nm] Polydispersity f) t g) [nm] C1
Dex-g 24 -PADEGChol and Đ of dextran were estimated equal to 34800 g mol -1 and 1.14, respectively [37].

b)

of each PDEGCholA graft estimated from , where and are the initial molar concentrations of monomer and ATRP initiator groups carried by the macroinitiator (after steps i and ii, Scheme S1, [37]), respectively. M 0 is the molecular weight of monomer unit of PDEGCholA (528 g mol -1 ).

c) Dispersity of the corresponding acetylated copolymers (before step iv, Scheme S1, [37]) measured by SEC in THF. In the present paper, we will focus more on the properties displayed by these graft glycopolymers when dispersed in solution. First, we will establish that these graft copolymers exhibit interfacial activities. Then, we will focus on the influence of the chemical structure of these copolymers onto the characteristics of their self-assemblies in water. Finally, we will show that these self-assemblies are actually of polymersome type.

Results and Discussion

1. Interfacial properties of Dex-g N -PDEGCholA F glycopolymers

In order to estimate the propensity of such glycopolymers to stabilize interfaces, we have dissolved two of them (entries C3 and C4, Table 1) in toluene (concentration lower than 0.2 g L -1 ). After waiting 12 hours at room temperature, in order to reach thermodynamic equilibrium, the interfacial properties of each Dex-g N -PDEGCholA F were evaluated by steady state interfacial tension () measurements at the toluene/water interface as function of copolymer concentration. As shown in Figure S1, the interfacial tension of a pure toluene/water interface was equal to 28.8 mN m -1 . By adding the graft glycopolymer,  steadily decreased until A 1 = 1.5 mg L -1 (case of Dex-g 5 -PDEGCholA 79 , entry C3, Table 1) or A 2 = 6.2 mg L -1 (case of Dex-g 1.5 -PDEGCholA 50 , entry C4, Table 1) where the decrease of was much more pronounced. As shown in Table 1, each studied glycopolymr exhibits Đ1 meaning they are heterogeneous in composition (number and length of graft). Nevertheless, as the length of the PDEGCholA grafts is roughly the same for both copolymers, the number of grafts onto the dextran backbone could account for such a difference: decreasing this number increased the concentration at which  decreased. Above A 1 or A 2, decreased more steeply with increasing polymer concentration. Unfortunately, when the Dex-g N -PDEGCholA F concentration was too high, we observed a white polymeric layer located at the interface that prevented reliable measurements of  Consequently, the concentration range where the investigations were possible is rather limited. Nevertheless, the decrease of upon increasing polymer concentration can be related to their ability to stabilize toluene/water interface as molecular surfactant does. Furthermore the grafted nature of these amphiphilic copolymers and mesomorphic transitions of grafts could account for the broadening of the transition, which is far from being critical by opposition to what is encountered with molecular surfactants or even amphiphilic diblock copolymers.

Self-assembly of Dex-g N -PDEGCholA F glycopolymers

The ability for self-assembly of these graft glycopolymers was further investigated in water (figure S2). First, Dexg N -PDEGCholA F were dispersed either in THF at 25°C or in DMSO at 100 °C, and then dialyzed against water (a selective solvent for dextran) during two days. Finally, the morphology of their self-assemblies was investigated by dynamic and static light scattering (DLS and SLS, respectively) and by cryogenic transmission electron microscopy (cryo-TEM). The characteristics of these nano-objects are summarized in table 1. Nanostructures obtained with the copolymer Dex-g 1.5 -PADEGChol 50 (entry C4, table 1) dissolved in DMSO or in THF are denominated or , respectively.

Depending on the number and the length of the grafts, two situations have been encountered. For copolymers containing a high number of short hydrophobic grafts ( of graft < 7.000 g mol -1 , entries C1 and C2, Table 1), a precipitate was formed during dialysis, whatever the organic solvent we used (THF or DMSO). By opposition, when copolymers containing a moderated number of long grafts ( of graft # 11.500 g mol -1 , entries C3 and C4, Table 1) were considered, nano-objects were produced.

In these last cases, the dispersions are characterized by a single distribution of relaxation times in DLS over the whole scattering range investigated (from q=4.6 x 10 -3 nm -1 to 2.55 x 10 -2 nm -1 ) as shown in figure 1 that displays typical examples of autocorrelation functions measured at the same scattering angle for each dispersion. The relaxation time derived from the auto-correlation functions displayed a q² dependence (figure S3), which meant that diffusive motions of the scatterers were probed and which allowed us to estimate their hydrodynamic radius (R H ) using the Stokes-Einstein equation (Equation S2). As shown in table 1, R H ranged between 47 nm and 68 nm with a polydispersity close to 1 (see supporting information). In addition, the radius of gyration (R G ) for each dispersion was estimated by static light scattering measurements using the Guinier approximation. As shown in table 1, R G ranged between 47 nm and 63 nm. For all the nano-objets ( , , and ), the ratio R G /R H was estimated to be close to 1, which accounted for a vesicular morphology of the self-assemblies [38,39] and Figure 1. Autocorrelation functions C(q,t) as a function of time and corresponding relative distribution of relaxation times recorded at a scattering wave vector q=4.6 x 10 -3 nm -1

(θ=20°) for different nanostructures dispersed in water. (a) ,

,E-05 1,E-04 1,E-03 1,E-02 1,E-01 1,E+00 C(q,t) t/s (c) 0,0 (b) , (c) , (d) . 0,0 0,2 0,4 0,6 0,8 1,0 1
,E-05 1,E-04 1,E-03 1,E-02 1,E-01 1,E+00 C(q,t) t/s 0,2 0,4 0,6 0,8 1,0 1
,E-05 1,E-04 1,E-03 1,E-02 1,E-01 1,E+00 C(q,t) t/s (d) 0,0 0,2 0,4 0,6 0,8 1,0 1
,E-05 1,E-04 1,E-03 1,E-02 1,E-01 1,E+00 C(q,t) t/s (a) 0,0 0,2 0,4 0,6 0,8 1,0 1
indicated that hollow spherical structures were obtained whatever the initial non selective solvent used (THF or DMSO).

To further investigate the morphology of the nanostructures, we have studied the dispersions of C3 and C4 by cryogenic Transmission Electronic Microscopy (cryo-TEM). As shown in Figure 2a (case of ), vesicles with radius equal to 35 nm (z-average) were actually observed. A schematic representation of such a vesicle is drawn in figure 2b. The higher radius of vesicles found by DLS analysis compared to that estimated by cryo-TEM could be explained by hydration effects of the dextran corona that is extended in water. Moreover, dextran is less visible by cryo-TEM considering its swelling in water, leading to a low electronic contrast compared to water. [40] Supplementary images of the same nano-objects yet observed by TEM are presented in supporting information (figure S4). A more quantitative description of the self-assemblies has been achieved thanks to Static Light Scattering measurements. Figure 3 displays the scattered intensity as function of the scattering vector for each suspension ( , , and ). The results could be fitted with a model developed for vesicles (Equation S4). [41,42] We can then derive the thickness of the membrane (t) knowing the hydrodynamic radius of vesicle, the refractive index of aqueous medium (1.33) and that of the membrane made of PADEGChol (1.38) as reported in table 1. A higher membrane thickness is obtained in case of copolymer Dex-g 5 -PADEGChol 79 , which contains a higher number of grafts compared to that obtained for Dex-g 1.5 -PADEGChol 50 . That could be explained by the stiff nature of the PADEGChol grafts. [37] Actually, in case of and suspensions, the polymeric membrane may consist in partially interdigitated grafts due to a higher grafting density onto the dextran backbone leading to steric hindrance. By opposition, in case of and , the polymeric membrane may consist in fully interdigitated grafts as shown in the schematic representation of figure 3. The difference in the membrane thickness for and samples could be related to the better solubility of PDEGChol grafts in THF. Improved studies will be done in the future to confirm these observations.

Conclusions

After the synthesis of this first class of grafted glycopolymer containing liquid-crystal PDEGCholA grafts and dextran backbone and the study of their mesomorphic properties, the ability of Dex-g N -PDEGCholA F to stabilize liquid-liquid interfaces were firstly proved. Then, self-assembly of such glycopolymer was studied after dissolution in THF or DMSO and dialysis against water. Dynamic and static light scattering allowed the observation of spherical nanostructures (R H between 47 and 68 nm, R G /R H close to 1), which are formed depending on the Dex-g N -PDEGCholA F structure. Finally, cryo-TEM observations clearly showed an hollow vesicular structure known as polymersome. Based on these results, a proper design of Dex-g N -PDEGCholA F led to polymersome formulations. It seems that moderate number of long PDEGCholA grafts allows an adapted copolymer folding and a bilayer membrane formation, which is stabilized due to the liquid-crystal properties of PDEGCholA grafts. Deeper analyses of such Dex-g N -PDEGCholA F self-assemblies will be performed to gain a better understanding of the organic solvent influence and to investigate in-depth these vesicular morphologies. Nevertheless, such graft copolymers could have an interest for drug delivery systems: firstly, the materials involved in these copolymers (dextran and PDEGCholA) are biocompatible. Secondly, neutral dextran backbone may confer a stealthly character to nanostructures like PEGylation coverage. [43] Thirdly, hydroxyl groups present on dextran could be used for functionalizing the surface of the nano-objects with sufficient and consequent amount of "bioactive" molecules like specific peptides for instance. [43] Figure 3. Scattered intensity (I) of vesicles as function of scattering vector (q) of: (▲) , (∆) , (♦) and (◊)

. Dashed lines are fits to equation S4. Schematic representations of vesicles and of their membranes are given.

  and F are the number of PDEGCholA grafts per 100 glucosidic units of dextran backbone and the weight fraction of PDEGCholA in amphiphilic glycopolymer, respectively.

  d) Hydrodynamic radius determined by dynamic light scattering. e) Radius of gyration determined using Guinier plot. f) See supporting information. g) Membrane thickness of vesicles determined by fitting the Rayleigh ratio of the suspensions using equation S4. *: Membrane thickness was estimated equal to 25 nm from Figure 2a.

Figure 2 .

 2 Figure 2. (a) Cryo-TEM image of polymersome obtained in water after dialysis of Dex-g 5 -PADEGChol 79 dispersed in THF(case of ). (b) schematic representation of such vesicle.

ACKNOWLEDGMENT

K. Ferji was supported by a grant of the French Ministry in charge of Research.

Funding Sources

French Ministry in charge of Research.

ASSOCIATED CONTENT

Supporting Information: Copolymers synthesis strategy, Interfacial Tension Measurements, Copolymers self-assembly procedure, Dynamic and static light scattering (SLS and DLS), Transmission Electronic Microscopy. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author

* jean-luc.six@univ-lorraine.fr

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

For Table of Contents Use Only

Polymersomes from amphiphilic glycopolymers containing polymeric liquid crystal grafts.

Khalid Ferji 1,2,3 , Cécile Nouvel 1,2 , Jérôme Babin 1,2 , Min-Hui Li [START_REF] Kumar | Proc. Natl Acad. Sci[END_REF] , Cédric Gaillard 5 , Erwan Nicol 3 , Christophe Chassenieux 3 , Jean-Luc Six 1,2* Dextran-g N -PDEGCholA F Self-assembly


Khalid Ferji

Pierre Venturini

Franck Cleymand

Christophe Chassenieux

Jean - Luc

Frequently, the classical self-assembly techniques applied to amphiphilic glycopolymers lead to primitive morphologies, i.e. spherical micelles/nanoparticles. Herein, we report a facile and rapid one-pot synthesis and self-assembly of grafted amphiphilic glycopolymers using photo-initiated Polymerization-Induced Self-Assembly (Photo-PISA) under UV-irradiation at room temperature. Such glycopolymers were based on dextran as hydrophilic steric stabilizers backbone and poly(hydroxypropyl methacrylate) PHPMA as hydrophobic grafts. Transmission electron microscopy and light scattering analysis reveal formation of a broad set of advanced glyco-nanostructures ranging from spherical micelles to worm-like micelles and vesicles depending on both PHPMA grafts length and the solids content.

Over the last decades, polymeric nanostructures, 1 including spherical/worm-like micelles and vesicles, have been extensively investigated and exploited in various application fields. In vivo drug/gene vectorization is particularly one of their most attractive applications. 2 Nanostructures covered with poly(ethylene oxide) (PEO) 3 have emerged as gold standard nanomaterials approved by the Food and Drug Administration (FDA), given the stealth properties of PEO. However, after almost a half-century of clinical uses, some studies have claimed that the intravenous injection of PEGylated carriers can induce formation of anti-PEO antibody, hypersensitivity reaction and complement activation. 3a,4 Given their inherent biodegradability, immunogenicity and bioactivity, some neutral polysaccharides have been recently reported as suitable alternatives to PEO. 5 Dextran is probably the most important neutral polysaccharide for medical and pharmaceutical industries. [START_REF] Heinze | polysaccharides II[END_REF] Owing to its hydrophilicity, nontoxicity and tunable biocompatibility, dextran has been approved by FDA as a plasma expander. [START_REF] Mehvar | [END_REF] During the last two decades, great achievements 8 have been made regarding the synthesis of well-defined amphiphilic copolymers (called glycopolymers) combining hydrophilic natural polysaccharides and hydrophobic polymeric moieties, using mainly grafting from 9 and grafting onto 10 strategies. However, more work is needed to optimize their self-assembly. Indeed, unlike synthetic polymeric amphiphiles which can easily selfassemble into a broad set of morphologies, 2 only spherical micelles and core-shell nanoparticles have been systematically reported for glycopolymers.

8

Reports on advanced glycopolymer-based nanostructures (glyco-nanostructures) morphologies such as nanocapsules 11 and vesicles 12 are actually scarce. This may be attributed to the unsuitable classical self-assembly processes currently used e.g. solvent exchange or nanoprecipitation. The use of an organic solvent which should be a good one from the thermodynamical point of view is a requirement that fails to be achieved for most of amphiphilic glycopolymers. Polymerization induced selfassembly (PISA) is an emerging one-pot technique enables to produce nanostructures based on self-assembled amphiphilic copolymers in aqueous media. In PISA, the aqueous radical polymerization of a suitable monomer, which forms a waterinsoluble polymer, is carried out using either a soluble macroinitiator or a macromolecular Chain Transfer Agent (macro-CTA). Amphiphilic copolymers are progressively obtained, leading to an in situ phase separation that finally generates stable colloidal polymeric nanostructures.

Depending on the nature of the monomer used, PISA process could be performed either in emulsion polymerization, 13 when using a water-insoluble monomer or in dispersion polymerization, 14 with a water-soluble one. During the last five years, PISA has been extensively carried out using synthetic steric stabilizers, i.e. PEO 15 or poly(glycerol monomethacrylate) PGMA, 16 with hydroxypropyl methacrylate (HPMA) as a watersoluble monomer leading to a water-insoluble biodegradable poly(hydroxypropyl methacrylate) (PHPMA) 14 . Some efforts have recently been devoted to use polysaccharides as efficient water-soluble steric stabilizers in PISA to produce glyconanostructures, but only spherical nanoparticles have been obtained and no higher order morphologies being achieved.

Charleux and coworkers 13b reported preparation of submicronic latex particles using aqueous RAFT polymerization of vinyl acetate from a dextran derivative as a macro-CTA.

Neufeld and coworkers

13c demonstrated the formulation of spherical micelles when methyl methacrylate was polymerized from alginate macroinitiator in water/methanol mixture. Thermal initiation is currently the most commonly used way for aqueous PISA. 14,17 However, some recent studies 17,18 have reported an evolution of the nanostructures morphology reached at high temperature (60°C-70°C, which is the range of temperature required for azo-initiators decomposition) after cooling to room temperature. To overcome this issue, photo-PISA has recently emerged as a versatile alternative due to its facility, rapidity (99% conversion within less than 1 hour) and ability to produce a broad range of nanostructures morphologies at room temperature. This approach can also afford temporal control of polymerization by switching the light "on" or "off", which facilitates the tracking of the polymerization progress and the isolation of nanostructures morphologies at defined conversion. 19 In addition, owing to its mild experimental conditions, the photo-PISA should ensure a good reproducibility of the nanostructures morphologies. In this present study, PHPMA is grafted from a dextran backbone (Scheme 1) to demonstrate the ability for a dispersion photo-PISA process to easily and rapidly prepare a broad set of advanced glyco-nanostructures. To the best of our knowledge, this work is the first report of a PISA using polysaccharide as steric stabilizer yielding high-ordered non-spherical morphologies.

First, the photosensistive chain transfer agent 4-(propylthiocarbonothioylthio)-4-cyanopentanoic acid (TTC, 1, Scheme 1) was synthesized (Fig. S1 †). 20 The intensity (I) of the UV source (365 nm) was then optimized by carrying out the RAFT homopolymerization of HPMA in DMSO using TTC, without using an exogenous photoinitiator. Indeed, thiocarbonylthio compounds are known to act simultaneously as initiators and chain transfer agents, given the fragmentation of the weak C-S bond under UV irradiation. 21 A very good control of the HPMA RAFT homopolymerization was observed with I=27 mW.cm -2

, as evidenced from the linear evolutions of both ln([M] 0 /[M] t ) versus irradiation time and molecular weight versus monomer conversion and by the low dispersities (Ð<1.2) of PHPMA (Fig. S2 † and S3 †). Furthermore, TTC displays a better photolytic stability under I=27 mW.cm -2 rather than higher one (I=53 mW.cm -2 ) (Fig. S4 † and S5 †). In the following, the UV irradiation intensity was fixed at 27 mW.cm -2 to perform PISA of dextran derivatives with HPMA grafts.

Scheme 1. Synthetic pathway of Dex-g N -PHPMA y -based glyco-nanostructures using aqueous photo-PISA process. N is the number average of PHPMA grafts per dextran chain. y is the number-average degree of polymerization ( ) of each PHPMA graft.

In a second step, the photo-macromolecular chain transfer agent Dex-TTC (2) based on dextran, was prepared through the partial esterification of some hydroxyl groups with TTC in the presence of N,N'-carbonyldiimidazole (CDI) in DMSO (Scheme 1). The functionalization yield (ζ) has been estimated using 1 H

NMR in DMSO-d 6 (see Fig. S6 † for the detail of calculation).

Here, 2.5 TTC were introduced per 100 glucopyranosic units meaning that Dex-TTC (2) contains about 5 TTC groups per dextran chain. Such low functionalization yield (ζ) has been preselected to prevent precipitation of the glycopolymers that will be prepared.

12a

As shown in Scheme 1, Dex-TTC was then used to investigate the in situ RAFT aqueous dispersion polymerization of HPMA under UV irradiation leading to amphiphilic Dex-g 5 -PHPMA Y glycopolymers, where 5 is the number-average of PHPMA grafts per dextran chain and Y is the number-average degree of polymerization ( ) of each graft. Various Dex-g 5 -PHPMA Y glycopolymers has then been synthesized by varying the targeted graft length ( ) and the final solids content (table 1). As evidenced from 1 H NMR analysis, a high conversion for HPMA (>90%) was reached within 10min to 60min of irradiation depending on the solids content (see Fig. S7 † and S8 †). A pretty good agreement between the theoretical ( (the) ) and the experimental ( (SEC) ) number average molecular weight was observed for all glycopolymers. SEC characterizations (Fig. S9 †) indicates that Dex-g 5 -PHPMA y displays relatively high dispersity (Ð). This is attributed to the large dispersity (Ð=1.8) of Dex-TTC macro-CTA used in the preparation of glycopolymers. SEC analysis of cleaved grafts (see Fig. S10 †) shows chromatograms with narrow dispersity (1.1), which indicates that the grafts grow uniformly and in a controlled way from the dextran backbone. Examples of photo-PISA kinetics investigation of HPMA at 5% w/w and 20% w/w solids content using Dex-TTC as the macro-CTA are presented in Fig. 1.

As shown in Fig. 1, whatever the solids content, the HMPA photo-PISA proceeds without any induction period, unlike its thermal analogue where an induction period of 50 min was reported. 15 In addition, a non-linear evolution of ln The photo-RAFT polymerization of HPMA was performed in DMSO, which is a good solvent for the Dex-g 5 -PHPMA y grafted glycopolymers, in order to check the consumption of the TTC in homogeneous medium (see Fig S12 †). In this condition, the slope of the ln([M] 0 /[M] t versus time remained linear, which means that all TTC were consummated from the first instances of the polymerization and that the number of the active species remains constant during polymerization. However, the increase of the rate of polymerization is due to a high local residual HPMA concentration, which helps at solvating growing water-insoluble PHPMA grafts. This finding is qualitatively consistent with observations previously reported by Zhang and coworkers 19a for PHPMA-based diblock copolymers using PEO as a macro-CTA. We note that for Dex-g 5 -PHPMA y grafted glycopolymers, the onset of self-assembly occurs when the size of PHPMA grafts reaches ( ) equal to 76 (i.e. PHPMA 76 ), which is smaller than the value ( = 120) reported for PEO-b-PHPMA diblock copolymers.

19a This indicates that growing PHPMA chains are better solubilized within diblock copolymers, and that the number of grafts has a considerable effect on the onset of self-assembly.

The influence of the PHPMA grafts length ( ) and of solids content on the glyco-nanostructures morphologies was systematically investigated by preparing various colloidal Dexg 5 -PHPMA y -based nano-objects at two solids contents (5% and 20% w/w) (see table 1 andS1). Crude aqueous colloidal solutions of Dex-g 5 -PHPMA y were first diluted, then characterized by Dynamic Light Scattering (DLS, Fig. 2) and observed by Transmission Electron Microscopy (TEM, Fig. 3) without any purification. Whatever the solids content, a single distribution of relaxation times over the whole scattering range (from q = 4.6 × 10 -4 -1 to 2.55 × 10 -3 -1

) was observed by DLS. Typical examples of autocorrelation functions are presented in Fig. S13 †. The relaxation time derived from the autocorrelation functions displayed a q 2 dependence (Fig. S14 †), which means that diffusive motions of the scatterers were probed. This allows estimating their hydrodynamic radius (R h ) using the Stokes-Einstein equation (Eq S1) since the samples were diluted enough prior to measurements to ensure that the interactions between the scatterers can be neglected.

Visual inspection of the samples (Fig. 2) shows that the turbidity of the final aqueous dispersions of glyco-nanostructures increases with the size of the PHPMA graft ( ), as well as with R h . We also note that the glyconanostructures display a relatively low PDI (<0.25) and a pretty good colloidal stability upon ageing since their sizes remain almost unchanged after 4 months (Fig. 2). The increase of the size of the nano-objects with the length of PHPMA grafts may be attributed to a change of the morphology of the nanostructures, which has been investigated by TEM measurements (Fig. 3). As shown in Fig. 3 a broad set of glyco-nanostructures morphologies has been achieved in situ including spherical micelles (Fig. 3A and3D), oblate micelles (in addition to the spherical micelles) (Fig. 3B), worm-like micelles (Fig. 3C and3E), and vesicles (Fig. 3F) depending on both grafts length ( ) and the solids content. Indeed, with short PHPMA grafts ( < 200), only spherical micelles were observed whatever the solids content. Oblate and worm-like micelles were observed by increasing the length of PHPMA grafts up to =370. Finally, at a high solids content (20% w/w), vesicular morphology was achieved with longer PHPMA grafts ( =410). Additional TEM images of various Dex-g 5 -PHPMA Y nanoobjects are available in Fig. S15 † to S20 †. To the best of our knowledge, this is the first time that such a broad set of highordered morphologies is observed with glycopolymers, especially oblate and worm-like morphologies. Such an evolution follows what has been previously reported by Armes and coworkers 15 with PEO-b-PHPMA copolymers prepared by thermal-induced PISA. It has been established that transition from spheres to oblate micelles was due to the fusion of spherical micelles into dimers and then trimers. Such theory is confirmed in our case, since Fig. 3B shows a coexistence of spherical and oblate micelles. Furthermore, for diblock copolymers the morphology sequence can be rationalized in terms of hydrophobic / hydrophilic blocks volume ratio. 22 For grafted glycopolymers such a rationale is more difficult to establish.

In summary and for the first time, we have demonstrated that glycopolymers could self-assemble into a broad set of advanced nanostructures morphologies, other than micelles and solid core-shell nanoparticles when using polymerization induced self-assembly (PISA) process. TEM observations and DLS measurements support an evolution of morphology of the glyco-nanostructures from spherical micelles to vesicles depending on both the glycopolymers concentration and the length of PHPMA grafts. A complete phase diagram and the influence of the number of grafts on the morphology of the glyco-nanostructures will be the subject of a future investigation. We believe that PISA process could be an efficient way for designing new smart biofriendly glyconanocarriers for drug/gene delivery or medical imaging.

MATERIALS AND METHODS

Materials. Dextran T 40 ( =32,000 g.mol -1 , Ð=1.4, determined by SEC-MALLS, see below) was purchased from Pharmacia Biotech and dried under reduced pressure at 100 °C for one night prior to use. 1-propanethiol (99%), carbone disulfide (>99%), iodine (99.8%), 4,4'-azobis(4cyanopentanoic acid) (98%), N,N'-carbonyldiimidazole (CDI) (97%), potassium tert-butoxide (95%), lithium chloride (99%), sodium thiosulfate, sodium sulfate, dimethylsulfoxide (DMSO) (≥99.9%), N,N-dimethylformamide (DMF) (99.8%), diethyl ether (Et 2 O), methanol (MeOH) and ethyl acetate (99%) were purchased from Sigma-Aldrich and used as received. 2-Hydroxypropyl methacrylate (HPMA) (98%) was purchased from ABCR, purified by dissolving the monomer in water, then washed with hexane to remove diacrylates. After saturation of the aqueous solution by NaCl, HPMA was extracted by Et 2 O to remove acrylic acid and dried over MgSO 4 (3 wt %).

Finally, Et 2 O was evaporated off under reduced pressure at room temperature.

Synthesis of 4-(propylthiocarbonothioylthio)-4-cyanopentanoic acid RAFT agent (TTC) (1, Figure S1).

TTC was synthesized using a modified procedure previously reported 1 . 1-propanethiol (3.4 g, 45 mmol) (1a, Figure S1) was added dropwise under nitrogen atmosphere at 5°C to a suspension of potassium tert-butoxide (5 g, 45 mmol) in anhydrous Et 2 O (100 mL) to provide a white slurry of potassium thiopropanate. After stirring the mixture for 20 min, carbon disulfide (3.4 g, 45 mmol) was introduced dropwise to the mixture at 0°C to provide a yellow precipitate of potassium-S-propyl trithiocarbonate, which was collected by filtration and used directly without purification. Afterwards, solid iodine (5.9 g, 23 mmol) was added portion-wise to a stirred suspension of potassium-S-propyl trithiocarbonate (8 g, 42 mmol) in anhydrous Et 2 O (200 mL).

After stirring the mixture for 2h at room temperature, the white solid of potassium iodide was filtered and the brown filtrate was washed three times with an aqueous solution of sodium thiosulfate to remove excess iodine, then dried over sodium sulfate. After evaporation of Et 2 O, a red oil of bis-(propanesulfyanyl thiocarbonyl)disulfide (4 g, 13.2 mmol) (1b, Figure S1) was obtained and characterized by 1 H NMR spectroscopy in CDCl 3 .

A solution of bis-(propanesulfyanyl thiocarbonyl) disulfide (2 g, 7 mmol) and 4,4'-azobis(4cyanopentanoic acid) (2.8 g, 10 mmol) in ethyl acetate (40 mL) was heated under reflux for 24h.

After removal of solvent, the crude product was solubilized in Et 2 O, washed five times with deionized water, and finally dried under vacuum to obtain an oily product. Propyl 2cyanopropan-2-yl-carbonotrithioate (2.6 g, 9.4 mmol) (1) was analyzed by 1 H NMR in CDCl 3 (Figure S1).

Synthesis of the macromolecular Chain Transfer Agent (Dex-TTC) (2, Figure S6). Dex-TTC containing 5 TTC groups per dextran chain, was prepared via the partial esterification of hydroxyl groups of dextran with carboxylic acid function of TTC in the presence of N,N'carbonyldiimidazole (CDI). CDI (0.3 g, 1.5 mmol) and TTC (0.4 g, 1.5 mmol) were dissolved in anhydrous DMSO (20 mL) and stirred at 40 °C for 6h to produce the activated acid imidazolide.

Afterwards, the acid imidazolide reaction mixture was added under nitrogen atmosphere to a solution of dextran (2g, 12.3 mmol glucopyranosic units) in DMSO previously prepared in a separate flask. The reaction was kept under stirring for 72h at 60°C. Finally, the crude product was precipitated in MeOH. Dex-TTC was collected by filtration, dried under reduced pressure (yield=80%), and then analyzed by 1 H NMR in DMSO-d 6 (Figure S6).

Photoinitiated RAFT homopolymerization of HPMA in DMSO.

In a dried schlenk flask, HPMA (2.5 g, 17.4 mmol) and TTC (16 mg, 0.058 mmol) were dissolved in dried DMSO (5.1 mL). The homogeneous mixture was purged with nitrogen for 10 min, sealed, and then irradiated with a UV lamp (365 nm) using suitable light intensity (4 mW/cm -2 , 27 mW/cm -2 , 45 mW/cm -2 or 53 mW/cm -2 ) at room temperature. Samples were taken under nitrogen at different time and the polymerization was quenched by exposure to air and addition of a small amount of hydroquinone. Crude product was then analyzed by and by SEC-MALLS in DMF at 50°C (Figures S2 andS3).

In-situ preparation of Dex-g 5 -PHPMA 260 -based nano-objects via aqueous photo polymerization-induced self-assembly.

In a typical experiment for the synthesis of Dex-g 5 -PHPMA 260 , HPMA (1.18 g, 8.2 mmol) and Dex-TTC (0.2 g, 1.2 mmol glucopyranosic units) were dissolved in a dried schlenk flask using a suitable volume of water to obtain a 5% w/w solids content (26.4 mL). The homogeneous mixture was purged with nitrogen for 10 min, sealed, and then irradiated at room temperature S9 with a UV lamp (365 nm, light intensity of 27 mW/cm -2 ) for 1h to achieve a full conversion. A small aliquot of the obtained dispersion was taken. One portion was freeze-dried and analyzed by 1 H NMR in DMSO-d 6 (Figure S7) and by SEC-MALLS in DMF/LiCl at 50°C (Figure S9). The other portion was characterized by TEM (Figures S15 to S20).

Kinetics of photoinitiated aqueous RAFT dispersion polymerization of Dex-g 5 -PHPMA 180 .

In a typical experiment for the synthesis of Dex-g 5 -PHPMA 180 , HPMA (0.8 g, 5.5 mmol) and Dex-TTC (0.2 g, 1.2 mmol glucopyranosic units) were dissolved in a dried schlenk flask and using a suitable volume of D 2 O to obtain a 5% w/w solids content (19 mL). The homogeneous mixture was purged with nitrogen for 10 min, sealed, and then irradiated with a UV lamp (365 nm, light intensity of 27 mW/cm -2 ) at room temperature. Samples were taken under nitrogen at different times and the polymerization was stopped by exposure to air and addition of a small amount of hydroquinone. Crude product was then analyzed by 1 H NMR in DMSO-d 6 and by SEC-MALLS in DMF at 50°C.

Cleavage of the PHPMA grafts from Dextran Backbone

In a typical experience of cleavage of PHPMA grafts from the glycopolymer Dex-g 5 -PHPMA 180 , 1 mL of the crude aqueous suspension (5% w/w solids content) was mixed with 2 mL of alkaline solution of NaOH (1 mol.L -1 ) for 24 hours at 50 °C to hydrolyze the ester functions linking grafts to dextran backbone. The white precipitate (PHPMA) that formed was recovered by centrifugation, washed 1 times with aqueous solution of HCl (1 mol.L-1) and two times with distillated water, dried overnight at 50 °C under vacuum, then analyzed by SEC-MALLS in DMF at 50°C (see Figure S…).

Polymer Analysis.

1 H NMR spectra of products were recorded on a Bruker Avance 300 apparatus (300, 13 MHz, 25°C) in CDCl 3 or DMSO-d 6 .

Size Exclusion chromatography (SEC).

The molecular weights were measured using a SEC in DMF/LiCl (flow rate of 1.0 mL min -1 ) at 50°C, equipped with Multi-Angle Laser Light Scattering (MALLS) detector (Mini Dawn Wyatt), differential refractometer detector (RID 10A, Shimadzu), HPLC pump (LC 20AD, Shimadzu), degazer AF (DGU -20A3R, Shimadzu), and three PLgel columns (100000, 1000, and 100 Å). Refractive index increments (dn/dc) of 0.01 was measured for all polymers (PHPMA, Dextran, Dex-TTC and Dex-g-PHPMA) in DMF/LiCl at 50°C using a differential refractometer from WYATT Technology (Optilab rEX and HELEOS-II).

Dynamic Light Scattering (DLS).

Hydrodynamic radii and size distribution of glycopolymers nano-objects were determined at 20°C using Dynamic Light Scattering. Samples were diluted 500-fold with water to produce 0.01% w/w solids content. Measurements were recorded using an ALV-5000 multitau correlator system in combination with a vertically polarized helium-neon laser with a wavelength of λ = 632.8 nm. The autocorrelation functions were analyzed in terms of relaxation time (t) distribution according to REPES routine. 2 Measurements were done at angles θ varying from 30° to 150° corresponding to scattering wave vectors q ranging from q = 4.6 × 10 -4 -1 to 2.55 × 10 -3 -1 . Z-average hydrodynamic radius (R h ) was estimated using the Stokes-Einstein relation (Eq-S1), where D 0 is diffusion coefficient determined from the slope of the q 2 dependence of relaxation rate (<Γ>=Dq 2 ), k B is the Boltzmann constant, T is experimental temperature and η s is the viscosity of the solvent (water).

(S1)

Turbidity measurement.

Evolution of the turbidity with conversion of PHPMA, during preparation of glyconanostructures via PISA process, was estimated by measuring transmittance of suspension at predefined time during UV-irradiation. Transmittance was measured at 600 nm using UVikon-XL spectrometer (Bio-Tech instruments) (see Figure S10).

Transmission Electron Microscopy (TEM).

The glycopolymers-based nano-objects were investigated by Transmission Electron Microscopy (TEM) using a microscope Philips CM200 operating at an accelerative voltage of 200kV. Images were recorded with a post-column camera Gatan MSC600. Samples were diluted 50-fold with water to produce 0.1% w/w solids content. A drop of the solution was adsorbed onto a copper grid for 30 s, and then blotted with filter paper to remove excess solution. A drop of uranyl S1).

  (a) Conversion of HPMA estimated by 1 H NMR analysis in DMSO-d6. (b) Number average molecular weight ( (SEC) ) and dispersity (Ð) estimated by SEC analysis in DMF/LiCl at 50°C. (c) Theoretical molecular weight calculated using Eq (1) : with g.mol -1 and kg.mol -1 . (d) Weight fraction of dextran in Dex-g 5 -PHPMAy calculated using Eq (2): , with g.mol -1 . conversion, indicates that PHPMA grafts have reached a critical length and became water-insoluble, which drove from now on the self-assembly of Dex-g5-PHPMAy glycopolymers. The onset of selfassembly was defined as the conversion of HPMA at which solution started to become turbid (see Fig S11 † for turbidity and hydrodynamic radius evolutions with conversion). Such polymerization rate profile, which is generally observed in homogeneous medium, could suggest a gradual consumption of the TTC up to its full consumption, which causes a change in activation rate and thus the increase of the polymerization rate.

Fig. 1 .

 1 Fig. 1. Kinetics of the aqueous HPMA photo-PISA performed at (■) 5% w/w and (▲)20% w/w solids content using Dex-TTC as the macro-CTA.[HPMA] 0 /[TTC] 0 =190/1.

Fig. 2 . 5 -

 25 Fig. 2. Evolution of hydrodynamic radius (R h ), PDI and visual inspection of the samples as a function of the grafts length ( . Dex-g 5 -PHPMA Y colloidal dispersions were prepared at 5% w/w solids content, by photo-PISA of HPMA using Dex-TTC as the macro-CTA.

Fig. 3 . 5 - 1 .

 351 Fig. 3. TEM images of a series of Dex-g 5 -PHPMA Y based glyconanostructures prepared by aqueous photo-PISA of HPMA using Dex-TTC as the macro-CTA, at room temperature and with two solids contents (5% and 20% w/w) and y as targets. Samples were observed at 1 mg.mL -1.

Figure S14 .

 S14 Figure S14. q² dependence of the relaxation rate () for various Dex-g 5 -PHPMA y nanostructures prepared by photo-PISA of HPMA in aqueous medium using Dex-TTC as the macro-CTA, at different conditions (see TableS1).

Figure S15 .

 S15 Figure S15. TEM images of Dex-g 5 -PHPMA 180 nanostructures prepared by photo-PISA of HPMA in aqueous medium using Dex-TTC as the macro-CTA, at 5% w/w solids content. The histogram was made from TEM images based on 100 nano-objects.

Figure S17 .

 S17 Figure S17. TEM images of Dex-g 5 -PHPMA 340 nanostructures prepared by photo-PISA of HPMA in aqueous medium using Dex-TTC as the macro-CTA, at 5% w/w solids content.

Figure S19 .

 S19 Figure S19. TEM images of Dex-g 5 -PHPMA 370 nanostructures prepared by photo-PISA of HPMA in aqueous medium using Dex-TTC as the macro-CTA, at 20% w/w solids content. The histogram was made from TEM images based on length (L) of 40 nano-objects.

In situ Glyco-nanostructures Formulation via Photo- Polymerization Induced Self-Assembly

	Khalid Ferji,*	a Pierre Venturini,

b Franck Cleymand, b Christophe Chassenieux, c Jean-Luc Six, a

Table 1 .

 1 The first one observed at low conversion (X < 40%), which is characterized by a small slope of the ln([M] 0 /[M] t versus time, is related to growing grafts that remained soluble. RAFT polymerization proceeds then in a homogeneous aqueous medium. The Second domain, which is characterized by a higher slope, observed above 40% of Characteristics of Dex-g 5 -PHPMA Y glyco-nanostructures prepared by photo-PISA of HPMA in aqueous medium using Dex-TTC as the macro-CTA, at different solids content.

	Entry	Solids content	Irradiation time	Dex-g	5 -PHPMA y	[HPMA] 0 /[TTC] 0	X (a) (%)	(SEC) (Kg.mol (b) -1 )	(the) (Kg.mol (c) -1 )	Ð	(b)	f dextran	(d)
	A B C D E F	5 % 20 %	60 min 10 min	Dex-g Dex-g Dex-g Dex-g Dex-g Dex-g	5 -PHPMA 180 5 -PHPMA 260 5 -PHPMA 340 5 -PHPMA 105 5 -PHPMA 370 5 -PHPMA 410	190/1 281/1 370/1 110/1 370/1 422/1	95 93 92 95 100 97	144 217 252 90 273 297	163 221 280 109 300 330	1.6 1.6 1.7 1.8 2.0 1.7	0.22 0.16 0.13 0.35 0.12 0.11

([M]

0 /[M] t )

versus time, which displays two time domains, was observed for both solids content.

Acknowledgements

The authors thank O. Fabre for NMR characterization, C. Sejil for SEC characterization and J.-C. Sivault for UV lamp development.

Conflicts of interest

There are no conflicts to declare.

Supporting information

In situ Glyco-nanostructures Formulation via Photo-Polymerization Induced Self-Assembly Khalid Ferji, *,a E-mail: khalid.ferji@univ-lorraine.fr acetate solution (0.5 wt%) was soaked on the sample-loaded grid for 30 s, and then blotted with filter paper to remove excess stain.

S19

Table S1. Characteristics of Dex-g 5 -PHPMA y nanostructures prepared by photo-PISA of HPMA in aqueous medium using Dex-TTC as the macro-CTA, at different solids content (HPMA + Dex-TTC).

Entry

Figure S13

. Autocorrelation functions and size distributions recorded at scattering wave vectors q of 1.7x10 7 m -1 for different Dex-g 5 -PHPMA y nanostructures prepared by photo-PISA of HPMA in aqueous medium using Dex-TTC as the macro-CTA, at different conditions (see Table S1).


M Hadded

A Hmima

T Maurer

A Chehaidar
email: abdallah.chehaidar@fss.rnu.tn

J Plain

Theoretical investigation of optical properties of optimal architectures of magnetoplasmonic nanoparticles in human tissue for potential applications in photothermal therapy

Keywords:

The absorption and scattering efficiencies of light by a single magnetoplasmonic nanoparticle, based on magnetite and gold, embedded in human tissue are analyzed theoretically in the framework of Finite-Difference-Time-Domain method and Lorenz-Mie theory. We consider separately three different architectures for the magnetoplasmonic nanoparticle: rectangular three-layer gold/magnetite/gold nanobar, circular three-layer gold/magnetite/gold nanoring and magnetite/gold core/shell nanosphere. We address the influence of particle sizes and magnetite-layer and gold-layer thicknesses on the optical response of such nanostructures. Particular attention is paid to the effectiveness of these designed nanostructures in photothermal therapy. Our simulation shows that these hybrid nanostructures support the famous localized surface plasmon resonance mode of gold, which manifests itself in the absorption spectrum by an intense peak whose spectral position can be adjusted to be in the first and second NIR-biological windows. The magnitude of the resonant absorption peak as well as that of the corresponding scattering peak vary from one nanostructure to another and, for the same nanostructure, change with its characteristic sizes. The three-layer nanobars as well as the three-layer nanorings can support significant absorption accompanied by significant scattering of light into both NIR-biological windows. For core/shell nanospheres, the low scattering efficiency of light within the second NIR-biological window, together with their large sizes, limit the usefulness of these nanostructures in photothermal therapy operating in the first NIR-biological window only.

Introduction

Nanoparticles continue to attract more and more attention from researchers worldwide, because of their peculiar physico-chemical properties, and especially because of their wide range of potential applications.

The properties of nanoparticles are critically dependent on their morphology, size and material composition. The optical properties of nanoparticles, in particular, have aroused particular interest from physicists as well as technologists. This interest is due to their unique properties, in particular significant enhancements of the electromagnetic field resulting in a strong scattering and absorption of light. These optical resonances have paved the way for many applications based on scattering and/or absorption of light [START_REF] Salata | Applications of nanoparticles in biology and medicine[END_REF][START_REF] Rehman | Super absorption of solar energy using a plasmonic nanoparticle based CdTe solar cell[END_REF][START_REF] Tiguntseva | Resonant silicon nanoparticles for enhancement of light absorption and photoluminescence from hybrid perovskite films and metasurfaces[END_REF][START_REF] Serpone | Application of nanoparticles in the photocatalytic degradation of water pollutants[END_REF][START_REF] Choi | Current achievements of nanoparticle applications in developing optical sensing and imaging techniques[END_REF][START_REF] Nguyen | Iron oxide and gold based magnetoplasmonic nanostructures for medical applications: a review[END_REF]. Among these applications we distinguish the photothermal therapy used in cancer medicine to destroy cancer cells [START_REF] Jaque | Nanoparticles for photothermal therapies[END_REF][START_REF] Abadeer | Recent progress in cancer thermal therapy using gold nanoparticles[END_REF][START_REF] Multari | Magnetoplasmonic nanoparticles for photothermal therapy[END_REF][START_REF] Yang | Gold nanoparticle based photothermal therapy: development and application for effective cancer treatment[END_REF]. This application is based on a class of noble metal nanoparticles called plasmonic nanoparticles. These metallic particles are distinguished by their conduction electrons assimilated to a free electron gas. Excited by light, the free electrons at the surface undergo collective oscillations at specific frequencies called resonant frequencies. A resonant collective oscillation of free electrons on the nanoparticle surface is called localized surface plasmon resonance (LSPR). These resonances result in strong extinction of the light (absorption and scattering). The part of electromagnetic energy absorbed by the metallic nanoparticle is converted into heat by the Joule effect; the illuminated plasmonic nanoparticle is then assimilated to a point source of heat. Inserted into human tissue, the plasmonic nanoparticle illuminated at a given LSPR frequency causes the diseased cell to burn and therefore its destruction.

Many experimental studies have shown that gold nanoparticles are promising and typical noble metal photothermal agents [START_REF] Yu | Gold nanorods: electrochemical synthesis and optical properties[END_REF][START_REF] Kim | Photochemical synthesis of gold nanorods[END_REF][START_REF] Schwartzberg | Synthesis, characterization, and tunable optical properties of hollow gold nanospheres[END_REF][START_REF] Storti | One-pot synthesis of gold nanoshells with high photon-to-heat conversion efficiency[END_REF][START_REF] Skrabalak | Gold nanocages: synthesis, properties, and applications[END_REF][START_REF] Xia | Gold nanocages: from synthesis to theranostic applications[END_REF][START_REF] Kumar | High-yield synthesis and optical response of gold nanostars[END_REF][START_REF] Liu | A plasmonic gold nanostar thernostic probe fir in vivo tumor imaging and photothermal therapy[END_REF]. Five types of gold nanoparticles were synthesized and entered the preclinical testing phase, namely gold nanorods [START_REF] Yu | Gold nanorods: electrochemical synthesis and optical properties[END_REF][START_REF] Kim | Photochemical synthesis of gold nanorods[END_REF], gold nanospheres [START_REF] Schwartzberg | Synthesis, characterization, and tunable optical properties of hollow gold nanospheres[END_REF], gold nanoshells [START_REF] Storti | One-pot synthesis of gold nanoshells with high photon-to-heat conversion efficiency[END_REF], gold nanocages [START_REF] Skrabalak | Gold nanocages: synthesis, properties, and applications[END_REF][START_REF] Xia | Gold nanocages: from synthesis to theranostic applications[END_REF] and gold nanostars [START_REF] Kumar | High-yield synthesis and optical response of gold nanostars[END_REF][START_REF] Liu | A plasmonic gold nanostar thernostic probe fir in vivo tumor imaging and photothermal therapy[END_REF]. These findings have stimulated numerous theoretical studies dedicated to the design of gold-based plasmonic nanoparticles that best meet the optimal requirements of the PTT technique and also at an affordable cost [START_REF] Tsai | Au nanorod design as light-absorber in the first and second biological Near-Infrared windows for in vivo photothermal therapy[END_REF][START_REF] Sikdar | Effect of number density on optimal design of gold nanoshells for plasmonic photothermal therapy[END_REF][START_REF] Ghosh | Calculated thickness dependent plasmonic properties of gold nanobars in the visible to near-infrared light regime[END_REF][START_REF] Tuersun | Optimization of nonspherical gold nanoparticles for photothermal therapy[END_REF][START_REF] Chehaidar | Scattering and absorption of light by homogeneous BiFeO3 and hybrid BiFeO3/Au core/shell spherical nanoparticles: a computational study[END_REF][START_REF] Chaabani | Comparative theoretical study of the optical properties of slicon/gold, silica/gold core/shell and gold spherical nanoparticles[END_REF][START_REF] Xue | Optimization of optical absorption of colloids of SiO 2 @Au and Fe 3 O 4 @Au nanoparticles with constraints[END_REF][START_REF] Brullot | Magnetic-plasmonic nanoparticles for the life sciences: calculated optical properties of hybrid structures[END_REF][START_REF] Hadilou | An optimal architecture of magneto-plasmonic core-shell nanoparticles for potential photothermal applications[END_REF]. The dominant idea in these works is to design a hybrid nanostructure made up of gold and metallic, dielectric or magnetic material. A nanoparticle composed of gold and magnetic material is called a gold-based magnetoplasmonic nanoparticle. To our knowledge, the only structural models conceived for this kind of nanoparticles are of the core-magnetic/shell-plasmonic type cut in spherical, ellipsoidal and nanorod shapes [START_REF] Xue | Optimization of optical absorption of colloids of SiO 2 @Au and Fe 3 O 4 @Au nanoparticles with constraints[END_REF][START_REF] Brullot | Magnetic-plasmonic nanoparticles for the life sciences: calculated optical properties of hybrid structures[END_REF][START_REF] Hadilou | An optimal architecture of magneto-plasmonic core-shell nanoparticles for potential photothermal applications[END_REF].

In our present work, we propose other structural models for magnetoplasmonic nanoparticles formed by a layer of magnetite sandwiched between two gold layers (gold/magnetite/gold) and cut in the form of rectangular nanobar and circular nanoring. We are also re-examining the spherical Fe 3 O 4 /Au core/shell nanostructure. We analyze numerically the light absorption and scattering efficiencies of an individual magnetoplasmonic nanoparticle embedded in human tissue in the absence of an external static magnetic field. We address the influence of particle sizes and magnetite-layer and gold-layer thicknesses on the scattering and absorption cross-sections of such nanostructures. In addition, we discuss the efficacy of these nanoparticles in photothermal therapy.

Structural design and calculation method

In our present study, we are interested in the optical response of a single nanoparticle embedded in human tissue irradiated by a light wave, as illustrated schematically in Fig. 1 (a). The host medium is assumed to be unbounded and non-absorbent, and the light wave is assimilated to a plane electromagnetic wave polarized along x-axis and propagating along the z-axis. We are interested in hybrid nanoparticles composed of two different materials, one of which is magnetic such as magnetite (Fe 3 O 4 ) and the other a noble metal such as gold (Au). In addition, we have limited ourselves to relatively simple model nanostructures, namely rectangular nanobars, circular nanorings with rectangular cross-section, and nanospheres; a schematic representation of the different nanostructures is shown in Fig. 1(b). The three-layer Au/ Fe3O4/Au nanobars are characterized by a length ℓ, a width w, a goldlayer thickness t 1 and a magnetite-layer thickness t 2 . Au/Fe3O4/Au nanorings with three concentric layers are characterized by an internal radius r 1 , an external radius r 2 , a magnetite-layer thickness t 1 and a goldlayer thickness t 2 . Concentric core/shell nanospheres are characterized by a core radius r 1 and a global particle radius r 2 .

The optical response of the nanoparticle is characterized by two dimensionless quantities, so-called scattering efficiency Q sca and absorption efficiency Q abs . These two quantities represent, respectively, the total electromagnetic power scattered in all the space outside the nanoparticle and that absorbed by the material constituting the nanoparticle, divided by its geometric cross-section normal to the direction of propagation of the incident light. The problem then consists in solving the famous Maxwell's equations in electric field E → and magnetic field H → at any point in space, taking into account the passage relations or even the continuity relations at the interfaces. For a spherical nanoparticle an analytical solution of Maxwell's equations is available thanks to the theory of Lorenz-Mie well documented in the book of Bohren and Huffman [START_REF] Bohren | Absorption and Scattering of Light by Small Particles[END_REF]. According to this theory the scattering and absorption efficiencies of light by a spherical nanoshell are given by Ref. [START_REF] Bohren | Absorption and Scattering of Light by Small Particles[END_REF]:

Q sca = 2 x 2 ∑ ∞ n=1 (2n + 1) ( |a n | 2 + |b n | 2 ) (1)
Q abs = 2 x 2 ∑ ∞ n=1 (2n + 1)Re(a n + b n ) -Q sca (2)
where Redenotes the real part of a complex quantity, a n and b n are the Mie coefficients, and x = 2πr 2 /λ is the size parameter at wavelength λ.

The theoretical expressions of the Mie coefficients for a spherical core/ shell nanoparticle embedded in a non-absorbent matrix are developed in our recent work [START_REF] Chehaidar | Scattering and absorption of light by homogeneous BiFeO3 and hybrid BiFeO3/Au core/shell spherical nanoparticles: a computational study[END_REF]. Using commercial MATLAB software, we have computed numerically the Mie coefficients and hence the scattering and absorption efficiencies. For nanobar and nanoring shaped nanoparticles, an analytical solution of Maxwell's equations is unfortunately not available; numerical methods are then used. In our present investigation, we have used the Finite-Difference-Time-Domain method (FDTD) [START_REF] Inan | Numerical Electromagnetics: the FDTD Method[END_REF] integrated in the commercial Lumerical software.

Results and discussion

The simulation of the absorption and scattering efficiencies of light by the nanostructures under consideration requires as input data the complex refractive indices as well as the permeabilities of the various component materials, namely surrounding medium, gold and magnetite. As we mentioned before, human tissue is assumed to be a non-absorbent medium, which amounts to assigning it a pure real refractive index. In reality, this approximation is not valid for the whole electromagnetic spectrum, but it does apply in a few intervals, in particular in the wavelength ranges 650 -950 nmand 1000 -1350 nmcalled first and second biological Near-Infrared windows [START_REF] Smith | Second window for in vivo imaging[END_REF]. Experimental measurements have shown that the refractive index of human tissue disperses little in the optical domain. In our calculations we have taken a single value of 1.44 [START_REF] Tsai | Au nanorod design as light-absorber in the first and second biological near-infrared windows for in vivo photothermal therapy[END_REF] along the wavelength range under consideration. Values of the complex refractive indices measured for bulk crystalline Fe 3 O 4 [START_REF] Querry | Optical Constants[END_REF], and bulk crystalline gold [START_REF] Johnson | Optical constants of the noble metals[END_REF] were used. The missing data were interpolated from the available experimental data by cubic spline interpolation method. For gold, the complex refractive index was corrected for the nanoparticle size [START_REF] Nehl | Scattering spectra of single gold nanoshells[END_REF]. The refractive indices n and the extinction coefficients κ for the materials considered here are shown as curves in Fig. 2 over the 200-1400 nm wavelengths range. The surrounding medium and gold are non-magnetic in nature, and thus have the same permeability as vacuum. Magnetite on the other hand is a magnetic material, and its magnetism manifests itself in the presence of an applied magnetic field and also in the low frequency range. In our case, the applied magnetic field of the incident light is extremely weak and in addition acts in the high frequency domain (the optical domain). Thus, we have assumed that the permeability of magnetite is the same as that of vacuum.

Besides the optical properties of the materials composing the target nanoparticle, the simulation of its optical response also requires its characteristic sizes as input data. Remember that the main objective of our simulations is to determine the characteristic sizes of the proposed nanostructures giving rise to resonant absorptions of light in the two biological NIR-windows. For core/shell nanospheres the calculation is fast thanks to the Lorenz-Mie theory. Thus, we have treated all the particle-diameters ranging from 2 to 500 nm, and all the shell-thickness fractions between 0 and 1. Regarding now the three-layer Au/Fe 3 O 4 /Au nanostructures, the calculations are carried out by the numerical FDTD method which is time-consuming, and it is therefore necessary to select a few sizes. In any case, the sizes of these nanoparticles should not exceed 100 nm to facilitate their penetration into human tissues. For the Au/ Fe 3 O 4 /Au nanobars, we started with the sizes of the pure gold nanobars previously reported by Ghosh et al. [START_REF] Ghosh | Calculated thickness dependent plasmonic properties of gold nanobars in the visible to near-infrared light regime[END_REF], namely a length of 100 nm, a width of 60 nm and a thickness of 10 nm. We then examined the effect of the aspect ratio defined by the length/width ratio, and furthermore the effect of the thicknesses of the gold layer and of the magnetite layer; here it should be noted that we have limited ourselves to gold-layer thicknesses of less than 10 nm because we are seeking to reduce the cost of the nanostructures in question. Regarding now Au/Fe 3 O 4 /Au nanorings, the choice of the overall size is in fact arbitrary but must not exceed 100 nm, as mentioned above.

The results of our simulations will now be presented and discussed. We start with the three-layer Au/Fe 3 O 4 /Au nanobars, then the threelayer Au/Fe 3 O 4 /Au nanorings and finally the Fe 3 O 4 /Au core/shell nanospheres.

Three-layer Au/Fe 3 O 4 /Au nanobars

We started by computing the absorption spectra of pure gold nanobars to ensure the proper functioning of our FDTD code. Fig. 3 shows the results of our FDTD calculations for gold nanobars of length 100 nm, width 60 nmand different thicknesses t (between 8 and 60 nm) embedded in a homogeneous medium of refractive index 1.25. As can be seen from this figure, our FDTD simulation well reproduces the results reported by Ghosh et al. [START_REF] Ghosh | Calculated thickness dependent plasmonic properties of gold nanobars in the visible to near-infrared light regime[END_REF] using the finite element method. As expected, the spectra show a resonant absorption peak attributed to the LSPR mode of gold. For a perfect rectangular nanobar, this peak is found to shift from the visible towards the NIR by reducing its thickness; more quantitatively, it shifts from 600 nmfor t = 60 nmto 980 nmfor t = 8 nm. In addition, its magnitude is also thickness dependent where it increases while decreasing the thickness for a fixed length and width; more quantitatively, the maximum absorption efficiency of ~3 for t = 60 nm jumps to the value ~7 for t = 8 nm.

The scattering and absorption spectra simulated for three-layer Au/ Fe 3 O 4 /Au nanobars, 100 nm long and 60 nm wide, embedded in human tissue, are shown in Fig. 4. The results relate to six nanobars, three of which have a gold layer of thickness 5 nm and the other three have a gold layer 10 nm thick; for each gold layer thickness, three thicknesses of the magnetite layer were considered: 10, 20 and 30 nm. For comparison, this figure also shows the scattering and absorption spectra of pure gold nanobars of thicknesses 5 and 10 nm. The Q sca and Q abs spectra of the Au/Fe 3 O 4 /Au three-layer nanobar have the same shape as those of a pure gold nanobar; they are dominated by the LSPR peak of gold. The spectral position, magnitude and linewidth of the LSPR peak in Au/ Fe 3 O 4 /Au three-layer nanobars differ from those relating to the LSPR peak in pure gold, and are dependent on the thickness of the magnetite separation layer. The spectral shift of the LSPR peak in the sandwich nanobar with respect to its counterpart in the gold nanobar is manifested in both directions. A blue shift occurs for a magnetite layer of thickness less than 20 nm practically, and a red shift for greater thicknesses. The linewidth of the LSPR peak is found to increase by increasing the thickness of the magnetite layer. In absorption, the intensity of the LSPR peak in the Au/Fe 3 O 4 /Au nanobar can never exceed that of the LSPR peak in the monolayer-gold nanobar. It can be, however, in the light scattering; this opportunity is achieved with a very thin magnetite separation layer. At this level, one may wonder if rectangular nanobars, whether pure gold or three-layer Au/Fe 3 O 4 /Au, are effective in PTT whatever the thickness of the gold layer. Here it must be remembered that PTT requires plasmonic agents with high NIR light absorption efficiency to effectively burn cancer cells, but at the same time these agents must be good light scatterers in order to be able to image the target cells or tissues before, during and after the therapy. According to Fig. 4, this requirement rules out nanobars with gold layers of thicknesses smaller than 10 nm. In this context, we can also affirm the superiority of three-layer Au/Fe 3 O 4 /Au nanobars over pure gold nanobars.

We now turn our attention to the effect of the aspect ratio, defined as the length to width ratio (ℓ/w), on the spectra of the absorption and scattering efficiencies of a rectangular nanobar embedded in human tissue. We have thus examined two sets of rectangular nanobars with predefined thicknesses of the gold and magnetite layers. For the first set, we have fixed the width at 60 nm and vary the length between 60 and 100 nm by a step of 20 nm. For the second, it is the length which is fixed (at 100 nm) but the width varies between 10 and 60 nm by a step of 10 nm. The results of our simulations are reported in Fig. 5 for three-layer Au/Fe 3 O 4 /Au nanobars having a gold-layer thickness of 10 nm and a magnetite-layer thickness of 20 nm. It is clear from this figure that the LSPR peak strongly depends on the aspect ratio of the nanobar. For a fixed width w at 60 nm, the LSPR peak in three-layer Au/Fe 3 O 4 /Au nanobar blushifts and its magnitude decreases by decreasing its length from ℓ = 100 nm to ℓ = w. Now, for a fixed length ℓ at 100 nm, the LSPR peak of the Au/Fe 3 O 4 /Au nanobar redshifts remarkably with a magnitude which increases in absorption but decreases in scattering when the width w decreases from 60 to 10 nm. Although the 100 nm long and 10 and 20 nm wide nanobars are good light absorbers, they are unfortunately not suitable for PTT, as they weakly scatter light and therefore do not allow imaging. Nanobars with widths between 30 and 60 nm absorb light less effectively than the previous ones, but on the other hand, they scatter light better and therefore are more suitable for PTT. The linewidth of the LSPR peak seems to be insensitive to the aspect ratio of the nanobar.

Three-layer Au/Fe 3 O 4 /Au nanorings

We now move on to the second type of nanostructures proposed in this work, namely circular three-layer Au/Fe 3 O 4 /Au nanorings. Remember that the two layers of gold have the same thickness. In Fig. 6 Fig. 4. Computed absorption and scattering spectra for a single three-layer Au/Fe 3 O 4 /Au nanobar embedded in human tissue with gold-layer thickness of 10 nm (top panels) and 5 nm (lower panels) and different magnetite-layer thicknesses. The length and the width of the rectangular nanobar are maintained fix at 100 and 60 nm, respectively.

we expose the light absorption and scattering efficiency spectra computed for two sets of nanorings having as common characteristics an internal radius r 1 = 30 nm and an external radius r 2 = 50 nm: the first set is formed by nanorings having a gold layer 5 nm thick and a magnetite layer 10, 20 and 30 nm thick; the second set is formed by nanorings having a gold layer 10 nm thick and a magnetite layer 10, 20 and 30 nm thick. For comparison, this figure also shows the spectra computed for pure gold nanorings. The optical spectra of Au/Fe 3 O 4 /Au nanoring have the same overall appearance as those relating to pure gold nanoring; they are dominated by the LSPR peak of gold. Three-layer nanorings are able to absorb light along the optical domain and more specifically in the first and second biological NIR windows. The spectral position, magnitude and linewidth of the LSPR peak in three-layer Au/ Fe 3 O 4 /Au nanorings differ from those relating to the LSPR peak in pure gold nanoring, and are dependent on the thickness of the magnetite separation layer. The spectral shift of the LSPR peak in the sandwich nanoring with respect to its counterpart in the pure gold nanoring is manifested towards blue regardless of the thickness of the gold layers and for the thickness values of the magnetite-layer considered here. It is almost zero for 50 nm thick magnetite layer and increases monotically with increasingly thin ones. For sandwich nanorings with gold layers of thicknesses 10 and 20 nm, the magnitude of the absorption efficiency is almost identical to that corresponding to pure gold nanorings, while the magnitude of the scattering efficiency is much improved, especially with very thin magnetite layers. It should be noted that the light scattering efficiency by Au/Fe 3 O 4 /Au nanorings with 10 nm thick gold layers is low compared to that of nanorings with thicker gold layers. For nanorings with gold layers 5 nm thick, the magnitude of the scattering efficiency is worse; in the best case it does not exceed the value 0.1. The linewidth of the LSPR peak is found to increase by increasing the thickness of the manganite layer.

In addition to the thicknesses of the gold and magnetite layers, the nanoring provides additional geometric parameters namely its internal and external radii (r 1 and r 2 , respectively), also allowing the adjustment of the characteristics of the LSPR peak. Indeed, this is what can be seen in Fig. 7 showing absorption and scattering efficiency spectra computed for two sets of Au/Fe 3 O 4 /Au nanorings having layers of gold and magnetite 10 nm thick, an external radius r 2 = 25 nm for the first set and 50 nm for the second, but different values for the internal radius r 1 . It is important to note from this figure, that the small nanorings can be good absorbers of NIR light but they are poor scatteres of this light; the larger nanorings, on the other hand, can be both good absorbers and scatteres of NIR light. In addition, we note the wide spectral margin, going from visible to mid-infrared, offered by the variation of the internal radius of the nanoring. However, the requirement of efficient absorption and efficient scattering of NIR light in PTT limits the choice of inner and outer radii to few values. In this context, nanorings with an external radius of 25 nm are discarded, and among the nanorings with an external radius of 50 nm only the one with an internal radius of 20 nm seems to be the most suitable.

Fe 3 O 4 /Au core/shell nanospheres

As mentioned above, the optical response of Fe 3 O 4 /Au core/shell nanospheres in an aqueous medium has been theoretically investigated by Brullo et al. [START_REF] Brullot | Magnetic-plasmonic nanoparticles for the life sciences: calculated optical properties of hybrid structures[END_REF] and Hadilou et al. [START_REF] Hadilou | An optimal architecture of magneto-plasmonic core-shell nanoparticles for potential photothermal applications[END_REF]. None of these works reported absorption in the second biological NIR-window, which seems a bit strange to us. So we reconsider here this type of nanostructure and we analyze by Lorenz-Mie theory its optical response for wider ranges of particle diameter and shell thickness.

The absorption and scattering efficiencies of a single Fe 3 O 4 /Au core/ shell spherical nanoparticle embedded in human tissue are plotted in two-dimensional color maps as function of the outer diameter D( = 2r 2 ), the vacuum wavelength λ, and for different gold-shell thickness fractions t f ( = (r 2 -r 1 ) /r 2 ). The results obtained for t f = 0.1, 0.25 and 0.5 are shown in Fig. 8. For comparison, results for pure gold nanosphere are also shown in this figure. Our simulation results are given for particle diameters in the 2-400 nm range and for wavelengths in the 200-1400 nm range.

A global observation of these color maps shows that Fe 3 O 4 /Au core/ shell nanospheres differ from pure gold nanospheres, with respect to absorption and scattering of light, only for gold-shell thickness fractions t f less than 0.5. In addition, this difference becomes more and more obvious with increasingly small shell thickness fractions. A detailed observation of these maps shows that the pure gold nanosphere exhibits a resonant absorption corresponding to the LSPR located in the range of wavelengths 520-580 nm for particle diameters in the range 40-80 nm. The optimal absorption resonance is centered on λ = 544 nmand corresponds to particle diameter D = 60 nm. It should be noted that the useful absorption spectral range of pure gold nanosphere is located in the visible range where the phenomena of light absorption by the constituents of human tissue are manifested. Now for the core/shell nanospheres with a gold-shell thickness fraction t f < 0.5, the Q abs color maps highlight absorption resonances in the spectral domain where the gold particle does not absorb; precisely, beyond 600 nm. These resonant modes form a diffuse branch in the wavelength-diameter plane. The distribution of the magnitude of the resonance modes on the branch is not uniform; it is maximum in the barycenter of the branch and gradually decreases towards its edges. Such branch covers a finite spectral domain, and manifests itself in a finite range of particle sizes as well. For t f = 0.25 for example, this branch is spread over the 700-800 nm wavelength range and the 25-125 nm diameter range, with a barycenter located at λ = 729 nm and a particle diameter D = 70 nm. By decreasing the gold-shell thickness fraction, this branch redshifts and at the same time pushes slightly towards larger particle diameters. More quantitatively, for t f = 0.1, this branch covers the 960-1120 nm wavelength range and the 50-200 nm diameter range, with a barycenter located at λ = 1028 nm and a particle diameter D = 116 nm.

As can be seen from the available maps shown in Fig. 8, the maximum absorption efficiency at the barycenter of a branch depends on the gold-shell thickness fraction t f . This observation is made clearer in Fig. 9 showing the absorption efficiency spectra computed for the [26] and Hadilou et al. [START_REF] Hadilou | An optimal architecture of magneto-plasmonic core-shell nanoparticles for potential photothermal applications[END_REF], we clearly understand why they did not report absorption resonances in the second biological NIR-window. It is also important to note from the shape of the absorption spectra reported in Fig. 9, that the absorption of light in the first biological NIR-window is selective and works well with near monochromatic sources, while that in the second window spreads out over a wide spectral band and is therefore suitable with polychromatic sources. So far, Fe 3 O 4 /Au core/shell nanospheres appear to be effective in PTT. It now remains to see their light scattering efficiency, part of which is absorbed by the nanoparticle in question. For this, we had the idea of superimposing on each Q sca color map the hand-drawn outline of the corresponding absorption resonance branch (shown in dashed white line) as well as its barycenter (reported by a black cross). It can be seen that the lower half of the resonant absorption branch corresponds to a virtually zero scattering efficiency. On the other hand, the upper half of the absorption branch, including the optimum mode at the barycenter, is associated with resonant scattering modes. The magnitude of these resonant scattering modes is low at the barycenter of the absorption branch, and gradually increases away from this towards large diameters. Thus, our simulation highlights a threshold size for each gold-shell thickness fraction below which the Fe3O4-core/Au-shell nanospheres do not scatter NIR light and therefore do not operate in PTT coupled with imaging. This threshold size corresponds to the absorption mode at the barycenter of the resonant absorption branch. More quantitatively, the threshold sizes evaluated for the thickness fractions examined in our present work are reported in Fig. 9. We can then deduce that the Fe 3 O 4 -core/Au-shell nanospheres operating in the second biological NIR-window must be much larger than 100 nm, thus greatly exceeding the optimal sizes (10-100 nm) used in PTT of cancer cells [START_REF] Chen | Gold nanoparticles: from nanomedicine to nanosensing[END_REF].

Conclusion

In this paper we have presented the results of numerical simulations of light absorption and scattering efficiencies by a magnetoplasmonic nanoparticle, based on magnetite and gold, embedded in human tissue, intended to be used as PTT agents. Three different architectures have been considered for the magnetoplasmonic nanoparticle: rectangular three-layer Au/Fe 3 O 4 /Au nanobar, circular three-layer Au/Fe 3 O 4 /Au nanoring and Fe 3 O 4 /Au core/shell nanosphere. Our simulation shows that these hybrid nanostructures support the famous LSPR mode of gold, which is reflected in the absorption spectrum by an intense peak whose spectral position can be adjusted to be in the first and second biological NIR-windows. The magnitude of the resonant absorption peak as well as that of the corresponding scattering peak vary from one nanostructure to another and, for the same nanostructure, change with its characteristic sizes. The three-layer nanobars as well as the three-layer nanorings can support significant absorption accompanied by significant scattering of light into both biological NIR-windows with a largest characteristic size not exceeding 100 nm. Significant scattering of NIR light accompanying significant resonant absorption by the core/shell nanospheres is much less evident than in the previous two cases, especially in the second NIRbiological window where the useful size of the nanoparticle exceeds the optimal sizes used in PTT. We are thus making available to the scientific and technological communities, two new magnetoplasmonic nanostructures that prove to be potential candidates for application in PTT therapy coupled with imaging and operating efficiently in both biological NIR-windows.

Fig. 1 .

 1 Fig. 1. (a) Schematic representation of the problem of scattering and absorption of light by a nanoparticle embedded in human tissue. (b) Drawings of the three gold-magnetite magnetoplasmonic nanostructures considered in the present study: three-layer Au/Fe 3 O 4 /Au rectangular nanobar (left), three-layer Au/ Fe 3 O 4 /Au circular nanoring (middle) and Fe 3 O 4 /Au core/shell nanosphere (right).

Fig. 2 .

 2 Fig. 2. The refractive index n and the extinction coefficient κ of bulk Fe 3 O 4 (left), and gold nanoparticle (right).

Fig. 3 .

 3 Fig. 3. Computed absorption spectra for gold nanobars of width w = 60 nm, length ℓ = 100 nm and various thicknesses t embedded in homogeneous medium of refractive index 1.25; the computation is performed using FDTD method.

Fig. 5 .

 5 Fig. 5. Computed absorption and scattering efficiency spectra for a single three-layer Au/Fe 3 O 4 /Au nanobar embedded in human tissue for different aspect ratios ℓ/ w: (top panels) the width w is set at 60 nm, (lower panels) the length ℓ is set at 100 nm. The gold-layer and the magnetite-layer thicknesses are set at 10 and 20 nm, respectively.

Fig. 6 .

 6 Fig. 6. Computed absorption and scattering spectra for a single three-layer Au/Fe 3 O 4 /Au nanoring embedded in human tissue with gold-layer thickness of 20 nm (top panels) and 10 nm (lower panels) and different magnetite-layer thicknesses. The internal and external radii of the nanoring are set at 30 and 50 nm, respectively.

Fig. 7 .

 7 Fig. 7. Computed absorption and scattering efficiency spectra for a single three-layer Au/Fe 3 O 4 /Au nanoring embedded in human tissue with external radii of 25 nm (top panels) and 50 nm (lower panels) and different internal radii. The gold-layer and the magnetite-layer thicknesses are set at 10 nm.

  Fe 3 O 4 -core/Au-shell nanospheres supporting the resonance modes at the barycentres of the branches for gold-shell thickness fractions ranging from 0.05 to 0.4 in a step of 0.05. From this figure, it can also be noted that the Fe 3 O 4 /Au core/shell nanospheres embedded in human tissue are capable of absorbing light in the two biological NIR-windows. The first biological window involves nanospheres with a gold-shell thickness fraction t f of between 0.35 and 0.125 and a particle diameter D of between 25 and 190 nm, while the second window corresponds to t f of between 0.1 and 0.05 and a particle diameter D of between 70 and 300 nm. If we now come back to the overall sizes and shell thicknesses of Fe 3 O 4 /Au core/shell nanospheres considered in the works of Brullo et al.

Fig. 8 .

 8 Fig. 8. The absorption efficiency Q abs (top) and scattering efficiency Q sca (bottom) of a single Fe 3 O 4 /Au core/shell nanosphere embedded in human tissue, as a function of the nanoparticle diameter D, the incident light wavelength λ, and for different shell thickness fractions t f . The white dashed line added to the Qsca color map represents the outline of the corresponding resonant absorption branch, and the black cross identifies the mode at its barycenter.

Fig. 9 .

 9 Fig. 9. Computed absorption efficiency spectra for a single Fe 3 O 4 /Au nanosphere embedded in human tissue, supporting the most intense resonance mode for different gold-shell thickness fractions t f . The shaded areas delimit the first (in cyan) and the second (in pink) biological NIR-windows.

Author contribution

Maha Hadded: Plain have contributed equally to this work. Abdelhamid Hmima: Plain have contributed equally to this work. Thomas Maurer: Plain have contributed equally to this work. Abdallah Chehaidar: Plain have contributed equally to this work. Jérôme Plain: have contributed equally to this work.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.