Abstract:
The elastic and capillary interactions between a pair of colloidal particles trapped on top of a nematic film are studied theoretically for large separations $d$. The elastic interaction is repulsive and of quadrupolar type, varying as $d^{-5}$. For macroscopically thick films, the capillary interaction is likewise repulsive and proportional to $d^{-5}$ as a consequence of mechanical isolation of the system comprised of the colloids and the interface. A finite film thickness introduces a nonvanishing force on the system (exerted by the substrate supporting the film) leading to logarithmically varying capillary attractions. However, their strength turns out to be too small to be of importance for the recently observed pattern formation of colloidal droplets on nematic films.

Abstract:
we compute the one-body probability density function of a dipolar and a quadrupolar colloid driven by an external ordering field. colloids with low structure in the absence of the external field, and with axially symmetric coupling potential are assumed. to compute the one-body probability density function, it is assumed that the dynamics of the colloid are given by the smoluchowski equation without hydrodynamic interactions. we use an appropiate homogeneous external field for each moment. the results for the one-body probability density function predict an axial nematic-like phase for the dipole moment, whereas a biaxial nematic-like phase is predicted for the quadrupole moment.

Abstract:
Three-body effective interactions emerging between parallel cylindrical rods immersed in a nematic liquid crystals are calculated within the Landau-de Gennes free energy description. Collinear, equilateral and midplane configurations of the three colloidal particles are considered. In the last two cases the effective triplet interaction is of the same magnitude and range as the pair one.

Abstract:
We exploit the long-ranged elastic fields inherent to confined nematic liquid crystals to assemble colloidal particles trapped at the liquid crystal interface into reconfigurable structures with complex symmetries and packings. Spherical colloids with homeotropic anchoring trapped at the interface between air and the nematic liquid crystal 5CB create quadrupolar distortions in the director field causing particles to repel and consequently form close-packed assemblies with a triangular habit. Here we report on complex, open structures organized via interactions with defects in the bulk. Specifically, by confining the nematic liquid crystal in an array of microposts with homeotropic anchoring conditions, we cause defect rings to form at well-defined locations in the bulk of the sample. These defects source elastic deformations that direct the assembly of the interfacially-trapped colloids into ring-like assemblies, which recapitulate the defect geometry even when the microposts are completely immersed in the nematic. When the surface density of the colloids is high, they form a ring near the defect and a hexagonal lattice far from it. Since topographically complex substrates are easily fabricated and liquid crystal defects are readily reconfigured, this work lays the foundation for a new, robust mechanism to dynamically direct assembly over large areas by controlling surface anchoring and associated bulk defect structure.

Abstract:
In an elegant paper, D. Nelson suggested a method to produce tetravalent colloids based on a tetrahedral configuration created on the surface of a spherical particle. It emerges from a two-dimensional nematic liquid crystal placed on a sphere due to the presence of four 1/2 disclinations, i.e., topological defects in the orientational order. In this paper we show that such a tetrahedral configuration also occurs in the wetting layers which form around spheres dispersed in a liquid crystal above the nematic-isotropic phase transition. Nematic wetting therefore offers an alternative route towards tetravalent colloids.

Abstract:
The implications of soft `patchy' interactions on the orientational disorder-order transition of strongly elongated colloidal rods and flat disks is studied within a simple Onsager-van der Waals density functional theory. The theory provides a generic framework for studying the liquid crystal phase behaviour of highly anisometric cylindrical colloids, which carry a distinct geometrical pattern of repulsive or attractive soft interactions localised on the particle surface. In this paper, we apply our theory to the case of charged rods and disks for which the local electrostatic interactions can be described by a screened-Coulomb potential. We consider infinitely thin rod-like cylinders with a uniform line charge and infinitely thin discotic cylinders with several distinctly different surface charge patterns. Irrespective of the backbone shape, the isotropic-nematic phase diagrams of charged colloids feature a generic destabilization of nematic order, a dramatic narrowing of the biphasic density region and a reentrant phenomenon upon reducing the electrostatic screening. At higher particle density the electrostatic repulsion leads to a complete suppression of nematic order in favour of spatially inhomogeneous liquid crystals.

Abstract:
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.

Abstract:
We investigated the physical properties of low concentration ferroelectric nematic colloids, using calorimetry, optical methods, infra-red spectroscopy and capacitance studies. The resulting colloids normally remain homogeneous, but the nematic orientational coupling is significantly amplified. In particular cases, the nematic orientation coupling increases by 10% for particle concentrations of 0.2%. A manifestation of the increased orientational order is that the clearing temperature of a nematic colloid increases up to 40 Celsius degrees compared to the pure LC host. A theoretical model is proposed in which the ferroelectric particles induce local dipoles whose effective interaction is proportional to the square of the orientational order parameter.

Abstract:
Calculamos la densidad de probabilidad de un cuerpo de un coloide dipolar y uno cuadrupolar controlados por un campo externo ordenador. Consideramos un coloide con poca estructura en ausencia del campo externo y con potencial de interacción axialmente simétrico. Para calcular la función de densidad de probabilidad suponemos que la dinámica del coloide esta dada por la ecuación de Smoluchowski sin interacciones hidrodinámicas. Usamos un campo homogeneo externo apropiado para cada momento. Los resultados, para la función de densidad de probabilidad de un cuerpo, predicen una fase axial tipo nemática para el dipolo, mientras que una fase biaxial tipo nemática se obtiene para el momento cuadrupolar.

Abstract:
Using extensive Monte Carlo (MC) simulations of colloids immersed in a nematic liquid crystal we compute an effective interaction potential via the local nematic director field and its associated order parameter. The effective potential consists of a local Landau-de Gennes (LdG) and a Frank elastic contribution. Molecular expressions for the LdG expansion coefficients are obtained via classical density functional theory (DFT). The DFT result for the LdG parameter $A$ is improved by locating the phase transition through finite-size scaling theory. We consider effective interactions between a pair of homogeneous colloids with Boojum defect topology. In particular, colloids attract each other if the angle between their center-of-mass distance vector and the far-field nematic director is about $30^{\circ}$ which settles a long-standing discrepancy between theory and experiment. Using the effective potential in two-dimensional MC simulations we show that self-assembled structures formed by the colloids are in excellent agreement with experimental data.