Colloidal particles dispersed in a liquid crystal (LC) lead to distortions of the director field. The distortions are responsible for long-range effective colloidal interactions whose asymptotic behaviour is well understood. The short-distance behaviour depends on the structure and dynamics of the topological defects nucleated near the colloidal particles and a full nonlinear theory is required to describe it. Spherical colloidal particles with strong planar degenerate anchoring nucleate a pair of antipodal surface topological defects, known as boojums. We use the Landau-de Gennes theory to resolve the mesoscopic structure of the boojum cores and to determine the pairwise colloidal interactions. We compare the results in three (3D) and two (2D) spatial dimensions for spherical and disc-like colloidal particles, respectively. The corresponding free energy functionals are minimized numerically using finite elements with adaptive meshes. Boojums are always point-like in 2D, but acquire a rather complex structure in 3D, which depends on the combination of the anchoring potential, the radius of the colloid, the temperature and the LC elastic anisotropy. We identify three types of defect cores in 3D that we call single, double and split-core boojums, and investigate the associated structural transitions. The split-core structure is favoured by low temperatures, strong anchoring and small twist to splay or bend ratios. For sufficiently strong anchoring potentials characterized by a well-defined uniaxial minimum, the split-core boojums are the only stable configuration. In the presence of two

The interaction between two disks immersed in a 2D nematic is investigated (i) analitically using the tensor order parameter formalism for the nematic configuration around isolated disks and (ii) numerically using finite element methods with adaptive meshing to minimize the corresponding Landau-de Gennes free energy. For strong homeotropic anchoring, each disk generates a pair of defects with one-half topological charge responsible for the 2D quadrupolar interaction between the disks at large distances. At short distance, the position of the defects may change, leading to unexpected complex interactions with the quadrupolar repulsive interactions becoming attractive. This short range attraction in all directions is still anisotropic. As the distance between the disks decreases their preferred relative orientation with respect to the far-field nematic director changes from oblique to perpendicular.PACS numbers: 77.84.Nh Liquids, emulsions, and suspensions; liquid crystals -61.30.cz Theory and models of liquid crystal structure -61.30.Jf Defects in liquid crystals.

Colloidal crystals belong to a new class of materials with unusual properties in which the big challenge is to grow large-scale structures of a given symmetry in a well-controlled and inexpensive way. Recently, template-assisted crystallization was successfully exploited experimentally in the case of colloidal particles dispersed in isotropic fluids. In liquid crystal (LC) colloids, particles are subjected to long-range anisotropic elastic forces originating from the anisotropic deformation of the underlying order parameter. These effective interactions are easily tunable by external electric or magnetic fields, light, temperature, or confinement and, thus, provide additional handles for better control of colloidal assembly. Here we use the coupling between microsculptured bounding surfaces and LC elasticity in order to guide the self-assembly of large-scale colloidal structures. We present explicit numerical calculations of the free energy landscape of colloidal particles in the presence of convex protrusions modeled as squared pyramids comparable to the size of the particles. We show the existence of strong trapping potentials that are able to efficiently localize the colloidal particles and withstand thermal fluctuations. Three-dimensional optical imaging experiments support the theoretical predictions.

We investigate nematic wetting and filling transitions of crenellated surfaces (rectangular gratings) by numerical minimization of the Landau-de Gennes free energy as a function of the anchoring strength, for a wide range of the surface geometrical parameters: depth, width, and separation of the crenels. We have found a rich phase behavior that depends in detail on the combination of the surface parameters. By comparison to simple fluids, which undergo a continuous filling or unbending transition, where the surface changes from a dry to a filled state, followed by a wetting or unbinding transition, where the thickness of the adsorbed fluid becomes macroscopic and the interface unbinds from the surface, nematics at crenellated surfaces reveal an intriguingly rich behavior: in shallow crenels only wetting is observed, while in deep crenels, only filling transitions occur; for intermediate surface geometrical parameters, a new class of filled states is found, characterized by bent isotropic-nematic interfaces, which persist for surfaces structured on large scales, compared to the nematic correlation length. The global phase diagram displays two wet and four filled states, all separated by first-order transitions. For crenels in the intermediate regime re-entrant filling transitions driven by the anchoring strength are observed.

Abstract:We study wetting and filling of patterned surfaces by a nematic liquid crystal. We focus on three important classes of periodic surfaces: triangular, sinusoidal and rectangular. The results highlight the similarities and differences of nematic wetting of these surfaces and wetting by simple fluids. The interplay of geometry, surface and elastic energies can lead to the suppression of either filling or wetting. The periodic rectangular surface displays re-entrant transitions, with a sequence dry-filled-wetfilled, in the relevant region of parameter space.

We consider the interaction between two-dimensional nematic colloids and planar or sculpted walls. The elastic interaction between colloidal disks and flat walls, with homeotropic boundary conditions, is always repulsive. These repulsions may be turned into strong attractions at structured or sculpted walls, with cavities that match closely the shape and size of the colloids. This key-lock mechanism is analyzed in detail for colloidal disks and spherocylindrical cavities of various length to depth ratios, by minimizing the Landau-de Gennes free energy functional of the nematic orientational order parameter. We find that the attractions occur only for walls with cavities within a small range of the colloidal size and a narrow range of orientations with respect to the cavity's symmetry axis.

Close to sinusoidal substrates, simple fluids may undergo a filling transition, in which the fluid passes from a dry to a filled state, where the interface remains unbent but bound to the substrate. Increasing the surface field, the interface unbinds and a wetting transition occurs. We show that this double-transition sequence may be strongly modified in the case of ordered fluids, such as nematic liquid crystals. Depending on the preferred orientation of the nematic molecules at the structured substrate and at the isotropic-nematic interface, the filling transition may not exist, and the fluid passes directly from a dry to a complete-wet state, with the interface far from the substrate. More interestingly, in other situations, the complete wetting transition may be prevented, and the fluid passes from a dry to a filled state, and remains in this configuration, with the interface always attached to the substrate, even for very large surface fields. Both transitions are observed only for a same substrate in a narrow range of amplitudes.

We propose the use of topographic modulation of surfaces to select and localize particles in nematic colloids. By considering convex and concave deformations of one of the confining surfaces we show that the colloid-flat surface repulsion may be enhanced or switched into an attraction. In particular, we find that when the colloidal particles have the same anchoring conditions as the patterned surfaces, they are strongly attracted to concave dimples, while if they exhibit different anchoring conditions they are pinned at the top of convex protrusions. Although dominated by elastic interactions the first mechanism is reminiscent of the depletion induced attraction or of the key-lock mechanism, while the second is specific to liquid crystal colloids. These long-ranged, highly tunable, surface-colloid interactions contribute for the development of template-assisted assembly of large colloidal crystals, with well defined symmetries, required for applications.