Abstract:
This mini-review discusses the recent contribution of theoretical and computational physics as well as experimental efforts to the understanding of the behavior of colloidal particles in confined geometries and at liquid crystalline interfaces. Theoretical approaches used to study trapping, long- and short-range interactions, and assembly of solid particles and liquid inclusions are outlined. As an example, an interaction of a spherical colloidal particle with a nematic-isotropic interface and a pair interaction potential between two colloids at this interface are obtained by minimizing the Landau-de Gennes free energy functional using the finite-element method with adaptive meshes.

Abstract:
Combining molecular simulation, Onsager theory and the elastic description of nematic liquid crystals, we study the dependence of the nematic liquid crystal elastic constants and the zenithal surface anchoring coefficient on the value of the bulk order parameter.

Abstract:
Molecular simulations of a nematic liquid crystal confined in cylinder geometry with homeotropic anchoring have been carried out. The core structure of a disclination line defect of strength +1 has been examined, and comparison made with various theoretical treatments, which are presented in a unified way. It is found that excellent fits to the cylindrically-symmetrized order tensor profiles may be obtained with appropriate parameter choices; notwithstanding this, on the timescales of the simulation, the cylindrical symmetry of the core is broken and two defects of strength +1/2 may be resolved.

Abstract:
We use molecular dynamics to study the ordering of a nematic liquid crystal around a spherical particle or droplet. Homeotropic boundary conditions and strong anchoring create a hedgehog director configuration on the particle surface and in its vicinity; this topological defect is cancelled by nearby defect structures in the surrounding liquid crystal, so as to give a uniform director field at large distances. We observe three defect structures for different particle sizes: a quadrupolar one with a ring defect surrounding the particle in the equatorial plane; a dipolar one with a satellite defect at the north or south pole; and a transitional, non-equatorial, ring defect. These observations are broadly consistent with the predictions of the simplest elastic theory. By studying density and order-parameter maps, we are able to examine behaviour near the particle surface, and in the disclination core region, where the elastic theory is inapplicable. Despite the relatively small scale of the inhomogeneities in our systems, the simple theory gives reasonably accurate predictions of the variation of defect position with particle size.

Abstract:
We propose a simple and reliable method to measure the liquid crystal surface anchoring strength by molecular simulation. The method is based on the measurement of the long-range fluctuation modes of the director in confined geometry. As an example, molecular simulations of a liquid crystal in slab geometry between parallel walls with homeotropic anchoring have been carried out using the Monte Carlo technique. By studying different slab thicknesses, we are able to calculate separately the position of the elastic boundary condition, and the extrapolation length.

Abstract:
When a mixture is confined, one of the phases can condense out. This condensate, which is otherwise metastable in the bulk, is stabilized by the presence of surfaces. In a sphere-plane geometry, routinely used in atomic force microscope (AFM) and surface force apparatus (SFA), it can form a bridge connecting the surfaces. The pressure drop in the bridge gives rise to additional long-range attractive forces between them. Minimizing the free energy of a binary mixture we obtain the force-distance curves as well as the structural phase diagram of the configuration with the bridge. Numerical results predict a discontinuous transition between the states with and without the bridge and linear force-distance curves with hysteresis. We also show that similar phenomenon can be observed in a number of different systems, e.g. liquid crystals and polymer mixtures.

Abstract:
The Landau-de Gennes free energy is used to study theoretically the interaction of parallel cylindrical colloidal particles trapped at a nematic-isotropic interface. We find that the effective interaction potential is non-monotonic. The corresponding force-distance curves exhibit jumps and hysteresis upon approach/separation due to the creation/annihilation of topological defects. Minimization results suggest a simple empirical pair potential for the effective colloid-colloid interaction at the interface. We propose that the interface-mediated interaction can play an important role in self-organization and clustering of colloidal particles at such interfaces.

Abstract:
Some fluids exhibit anomalously low friction when flowing against a certain solid wall. To recover the viscosity of a bulk fluid, slip at the wall is usually postulated. On a macroscopic level, a large slip length can be explained as a formation of a film of gas or phase-separated `lubricant' with lower viscosity between the fluid and the solid wall. Here we justify such an assumption in terms of a prewetting transition. In our model the thin-thick film transition together with the viscosity contrast gives rise to large boundary slip. The calculated value of the slip length has a jump at the prewetting transition temperature which depends on the strength of the fluid-surface interaction (contact angle). Furthermore, the temperature dependence of the slip length is non-monotonous.

Abstract:
A correlation is established between the molecular structure and charge mobility of discotic mesophases of hexabenzocoronene derivatives by combining electronic structure calculations, Molecular Dynamics, and kinetic Monte Carlo simulations. It is demonstrated that this multiscale approach can provide an accurate ab-initio description of charge transport in organic materials.

Abstract:
Using the phenol-terminated polycarbonate blend as an example, we demonstrate that the hydrodynamic boundary conditions for a flow of an adsorbing polymer melt are extremely sensitive to the structure of the epitaxial layer. Under shear, the adsorbed parts (chain ends) of the polymer melt move along the equipotential lines of the surface potential whereas the adsorbed additives serve as the surface defects. In response to the increase of the number of the adsorbed additives the surface layer becomes thinner and solidifies. This results in a gradual transition from the slip to the no-slip boundary condition for the melt flow, with a non-monotonic dependence of the slip length on the surface concentration of the adsorbed ends.