Nous nous sommes intéressés aux instabilités que développent les coques minces de cristal liquide smectique. Ces coques sont obtenues à partir de doubles émulsions d’un cristal liquide SmA (8CB) dans une solution aqueuse. Contrairement aux coques nématiques bien étudiées [1], les coques smectiques présentent une texture très particulière consistant en une structure de parois de courbures, hiérarchique, bien organisée, qui évolue fortement avec l’épaisseur de la coque [2]. Nous montrons que cette instabilité ne relève pas de la frustration topologique rencontrée par le directeur sur une sphère, mais de frustrations géométriques subies par des couches smectiques minces déposées sur des surfaces fortement courbées lorsque l’ancrage est planaire [3]. A l’aide d’une formulation semi-géométrique, nous avons modélisé cette instabilité et expliqué quantitativement les mécanismes de formation de cette texture [4].

NEMATIC LIQUID CRYSTALS OF CARBON NANOTUBES AND GRAPHENE

In a seminal work, [1] D. R. Nelson proposed that nematic coatings could be used to promote localized functionalization on colloidal particles. Topological defects are indeed necessarily present on genus-0 surfaces and it could be possible to attach ligands to them. Such a realization, however, still remains an experimental challenge. As a first step, the fabrication of thin nematic shells from double emulsions drops was reported a few years ago in Ref. [2]. Since then, the equilibrium structure of the topological defects on a sphere has been studied in details both theoretically and experimentally. It not only depends strongly on the homogeneity of the shell thickness [3,4] but also on the nematic elastic constants [4,5]. The defects structure on a nematic shell can therefore be finely controlled. As a next step, we have recently examined, both experimentally and theoretically, how a small number of solid particles can be trapped on nematic shells[6]. We have used water/5CB/water double emulsions produced by microfluidics techniques. The anchoring of the nematic at the water-5CB interface is strongly planar due to the presence of polyvinyl alcohol in aqueous solutions. The colloids are silica beads treated with silane to provide a homeotropic alignment. We especially have examined how the particles interact with the topological defects, where they get trapped, and how the equilibrium textures depend on their size. A great diversity of defect structures and patterns, different from the ones known in simple nematic shells, can be observed. I will describe their main features and explain how they result from the competition between elasticity and capillarity effects, during the formation of the shells. I will show how this last mechanism can be used to control the position of ligands on a spherical shell.

The fabrication of novel materials with revolutionary technological applications, such as photonic crystals with large band gaps or metamaterials, could perhaps be based on colloidal particles. However, common particles lack the ability to interact along specic directions, which is needed to build colloidal crystals with desired structures. A possibility is to use either anisotropic building blocks, or to induce tunable directionality and controllable valence of building blocks [1]. Liquid crystal shells oer a way to induce controllable valence by using double emulsions of nematic liq- uid crystal in a host liquid [2,3]. The nematic liquid crystal is an anisotropic medium with local orientational order that exhibits topological singularities (defects). And it is by functionalizing these singularities with linkers, that one could induce directional interactions and bonds between the colloidal particles. Here, we study theoretically and experimentally, the behaviour of microspheres trapped to a spher- ical nematic shell [4]. We demonstrate dierent { director and defect { organizations around a sin- gle particle, such as congurations where the colloidal particle is accompanied by an escaped

Liquid crystal shells offer an elegant way for imprinting well defined interaction sites on a sphere, since a set of symmetrically positioned topological defects naturally decorate the ground states of these systems. These defects are a consequence of a fascinating interplay between topology and energy that arises when an ordered system is confined to a space with curvature. The prospect of using these nematic shells as nano or micro-sized superatoms creates an avenue for the fabrication of new materials with revolutionary technological applications. In this talk, I will show recent advances in the topic. Microfluidic techniques have enabled the experimental realization of nematic shells [1]. A precise control in the defect architecture has been achieved by tuning parameters such as shell thickness, anchoring of the liquid crystal at the boundaries, or the type of liquid crystal phase considered [2-4]. A number of different defect structures have been engineered, including the sp, sp2 and sp3 symmetries of carbon atoms, which have enormous potential for photonic applications [2]. On the other hand, the functionalization of defects with ligands, capable to establish directional bonds between shells, has just started to be explored experimentally. A promising alternative has recently been proposed, consisting in exploiting attractive elastic interactions between defects and small beads embedded in the liquid crystal [5].

In many aspects, colloids behave as big atoms [1]; however, the usual absence of directionality in the interaction between colloids has limited the complexity of the structures that they can spontaneously form [2]. As a result, low-coordination structures, common in atomic and molecular systems, are rare in the colloidal domain. One way to address this is to exploit the anisotropy that spontaneously arises when a colloidal particle is coated by a nematic liquid crystal. In this spherical geometry, the orientational molecular order of the nematic liquid crystal is disrupted by the presence of singularities or topological defects, which appear symmetrically organized on the particle surface. These topological defects are not only mathematic concepts, but also high energy spots suitable for chemical attack that could be functionalized with ligands and act as attractive patches between particles [3,4]. The number and arrangement of these defects can vary, providing flexibility for tuning directional interactions. We have recently shown that these defects can be engineered to emulate the linear, trigonal and tetrahedral geometries of sp, sp2, and sp3carbon bonds [5]. These symmetries represent just a small sample of the variety of configurations that we can generate by tuning parameters such as shell geometry, temperature, or symmetry of the liquid crystal phase, which has revealed a vast playground for the formation of complex colloidal superlattices [5,6].

In this course, I will review the different uses of liquid crystals to fabricate nanomaterials and to create specific structures at submicron scales. Three main topics will be discussed.  The fabrication of nanostructured materials with original and tunable optical properties is a major trend in the liquid crystal field. For example, recent progress in the synthesis of mesogenic nanoparticles now allows the self-assembly of monodisperse nanoparticles within large scales. The resulting materials are potentially useful for photonics applications.  The liquid crystal elasticity can also be used to create specific structures or to localize particles in chosen places (for example nanowires between two defined points).  In bulk composites, the presence of anisotropic nanoparticles has two main consequences. The properties of the liquid crystal can be greatly changed by a small amount of doping. Liquid cristallinity can also be used to transfer anisotropic properties of nanoparticles at the macroscopic scale. Each of these topics will be discussed through several examples, after a brief introduction and a rapid presentation of the physics of liquid crystals.