Nematic fluid structure in wall-field geometry

Contact theorems for anisotropic fluids near a hard wall

In this paper, from the Born-Green-Yvon equation, we formulate a general expression for the contact value of the singlet distribution function for anisotropic fluids near a hard wall. This expression consists of two separate contributions. One is related to the bulk partial pressure for a given orientation of the molecules. The second is related to the anchoring phenomena and is characterized by the direct interaction between the molecules and the wall. Given this relation, we formulate the contact theorems for the density and order parameter profiles. The results are illustrated by the case of a nematic fluid near a hard wall.

Wall-colloid interaction in nematic solvents: external field effects

We propose a molecular theory of colloid-wall interactions in nematic media that predicts a new effective force acting on colloidal particles in the presence of an external field. In contrast to the so-called 'image' interaction that is always repulsive at long distances, the force identified here can be attractive or repulsive, depending on the type of anchoring at the wall and colloidal surfaces. The effective force on a colloidal particle decreases with distance s from the wall as exp(-s/ξ), where ξ is a magnetic (electric) coherence length. At weak fields the force is proportional to (Σ/ξ)(3) for 'quadrupolar' colloids and to (Σ/ξ)(2) for 'dipoles', where Σ is the colloidal diameter. A brief discussion of recent experiments in the light of our findings is presented.

Bridging the gap between phenomenology and microscopic theory: asymptotes in nematic colloids

The Ornstein-Zernike equation is applied to nematic colloids with up-down symmetry to determine how the electrostatic analogy and other phenomenological results appear in molecular theory. In contrast to phenomenological approaches, the molecular theory does not assume particular boundary conditions (anchoring) at colloidal surfaces. For our molecular parameters the resulting anchoring appears to be realistic, neither rigid nor infinitely weak. For this case, the effective force between a colloidal pair at large separation remains essentially constant over the entire region of nematic stability. We show that a simple van der Waals approximation gives a potential of mean force that in some important aspects is similar to the phenomenological results obtained in the limit of weak anchoring; at large separations the potential varies as Sigma8, where Sigma is the colloidal diameter. In contrast, the more sophisticated mean spherical approximation yields a Sigma6 dependence consistent with phenomenological calculations employing rigid boundary conditions. We show that taking proper account of the correlation (or magnetic coherence) length xi inherent in the nematic sample is essential in an analysis of the Sigma dependence. At infinite xi the leading Sigma dependence is Sigma6, but this shifts to Sigma8 when xi is finite. The correlation length also influences the orientational behavior of the effective interaction. The so-called quadrupole interaction that determines the long-range behavior at infinite xi transforms into a superposition of screened "multipoles" when xi is finite. The basic approach employed in this paper can be readily applied to a broad range of physically interesting systems. These include patterned and nonspherical colloids, colloids trapped at interfaces, and nematic fluids in confined geometries such as droplets.

Nematic-fluid structure in wall-field geometry. II. The direct correlation function

An explicit expression for the wall-nematic direct correlation function (DCF) is obtained for any orientation of the wall with respect to an external orienting field. It is found that inside the surface of the wall, the DCF rapidly tends to a function of the nematogen orientation and depends only on parameters of the bulk fluid. We suggest that the wall-nematic DCF can be used as an ansatz for the colloid-nematic DCF in dilute nematic colloids. The reliability of this ansatz is investigated at different field strengths in both isotropic and nematic regions. Our calculations for spherical colloidal particles show that this approximation is valid for colloidal particles that are large, but well within the physically realistic size range. The ansatz could also be applied to nonspherical colloidal particles.

Colloidal interactions in nematic fluids

Microscopic theory is used to obtain effective interactions between colloidal particles in nematic fluids subjected to an external orienting field. It is shown that the field can dramatically change the effective intercolloidal interactions without altering the symmetry of the director configuration around a single particle. Our calculations suggest that a rich variety of colloidal structures can be promoted by varying the external field.

Colloid-induced structure in liquid crystal media

The structural perturbations induced by colloidal particles immersed in a model nematic subjected to an external field are calculated employing integral equation methods. Maps of the density-orientational distribution about a colloidal particle are obtained, and these provide a microscopic picture of the colloid's nematic coat. We focus on colloidal particles that favor homeotropic anchoring, but planar anchoring cases are also considered. The range and structure of the nematic coat is shown to be significantly influenced by the nature of the anchoring, the size of the colloidal particle, the range and strength of the colloid-nematogen interaction, and the external field strength. All of these factors are discussed.