Orientational order of near D(3h) solutes in nematic liquid crystals. II. Description via Gay-Berne model with embedded quadrupoles.

We perform Monte Carlo simulations of a mixture of soft ellipsoids with embedded quadrupoles as a model of various chloro- and methyl-substituted benzenes dissolved in nematic liquid crystals. We find that oblate Gay-Berne ellipsoids with multiple embedded quadrupoles qualitatively reproduce the trend in the order parameter asymmetry experimentally observed in NMR spectra. The trend is opposite to what is expected on the basis of the interaction of the solute's quadrupole with the solvent's average electric field gradient "felt" by dissolved dihydrogen molecules. We identify the specific minimum of the solute-solvent interaction energy landscape that may produce the unexpected sign of the order parameter asymmetry that is seen in the experiment and the simulation.

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.

Tracer diffusion in hard sphere fluids from molecular to hydrodynamic regimes.

Molecular dynamics is employed to investigate tracer diffusion in hard sphere fluids. Reduced densities (rho*=rhosigma(3), sigma is the diameter of bath fluid particles) ranging from 0.02 to 0.52 and tracers ranging in diameter from 0.125sigma to 16sigma are considered. Finite-size effects are found to pose a significant problem and can lead to seriously underestimated tracer diffusion constants even in systems that are very large by simulation standards. It is shown that this can be overcome by applying a simple extrapolation formula that is linear in the reciprocal cell length L(-1), allowing us to obtain infinite-volume estimates of the diffusion constant for all tracer sizes. For higher densities, the range of tracer diameters considered spans diffusion behavior from molecular to hydrodynamic regimes. In the hydrodynamic limit our extrapolated results are clearly consistent with the theoretically expected slip boundary conditions, whereas the underestimated values obtained without extrapolation could easily be interpreted as approaching the stick limit. It is shown that simply adding the Enskog and hydrodynamic contributions gives a reasonable qualitative description of the diffusion behavior but tends to overestimate the diffusion constant. We propose another expression that fits the simulation results for all densities and tracer diameters.

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.

Nematic fluid structure in wall-field geometry.

We describe an integral equation method for obtaining the distribution of a nematic fluid near a wall and interacting with a uniform orienting field. Complete density-orientational profiles are calculated for a model nematic with different wall-particle interactions and different orientations of the wall with respect to the field. For orienting walls we identify particular long-range correlations that are responsible for reorientation of the bulk nematic at zero external field. These correlations become stronger as the wall-particle interaction is increased in range; they become longer ranged as the orienting field is weakened. Special attention is focused on systems where the wall-particle interaction favors orientations perpendicular to the surface. The local director orientation can vary discontinuously with the distance from the surface when the orienting influences of the field and the wall are antagonistic. At high densities smectic-like structures appear. Adsorption phenomena are also discussed. For inert hard walls, the ordered fluid avoids the surface, and a surface layer where the particles tend to orient perpendicular to the bulk director appears. Experimentally, this might be seen as wetting of the wall by a less-ordered fluid.

Surface-induced ordering of nematics in an external field: the strong influence of tilted walls.

Microscopic theory is used to investigate surface-induced order in a model nematic subjected to an external orienting field. The wall-particle interaction tends to orient particles perpendicular to the surface. It is shown that if the wall is tilted at approximately 45 degrees to the field, the reorientational effects can be an order of magnitude larger than those observed for perpendicular or parallel orientations. The surprising observation is associated with the breaking of a particular bulk symmetry. A possible practical application of the tilted geometry is briefly discussed.

Model fluid in a porous medium: results for a Bethe lattice.

We consider a lattice gas with quenched impurities or "quenched-annealed binary mixture" on the Bethe lattice. The quenched part represents a porous matrix in which the (annealed) lattice gas resides. This model features the three main factors of fluids in random porous media: wetting, randomness, and confinement. The recursive character of the Bethe lattice enables an exact treatment, whose key ingredient is an integral equation yielding the one-particle effective field distribution. Our analysis shows that this distribution consists of two essentially different parts. The first one is a continuous spectrum and corresponds to the macroscopic volume accessible to the fluid, the second is discrete and comes from finite closed cavities in the porous medium. Those closed cavities are in equilibrium with the bulk fluid within the grand canonical ensemble we use, but are inaccessible in real experimental situations. Fortunately, we are able to isolate their contributions. Separation of the discrete spectrum facilitates also the numerical solution of the main equation. The numerical calculations show that the continuous spectrum becomes more and more rough as the temperature decreases, and this limits the accuracy of the solution at low temperatures.

Possible new phase of antagonistic nematogens in a disorienting field.

A simple model is proposed for nematogenic molecules that favor perpendicular orientations as well as parallel ones. (Charged rods, for example, show this antagonistic tendency.) When a small disorienting field is applied along z, a low-density phase N- of nematic order parameter S(z)<0 coexists with a dense biaxial nematic N(b). (At zero field, N- becomes isotropic and N(b) uniaxial.) But at stronger fields, a new phase N+4, invariant under pi/2 rotations around the field axis, appears in between N- and N(b). Prospects for finding the N+4 phase experimentally are briefly discussed.

Nematic model in the presence of a finite disorienting field: integral equation approach.

A fluid of uniaxial particles in a disorienting field is considered as a simple model of biaxial nematics. The model stability with respect to the spontaneous formation of a biaxial phase is investigated by means of the integral equation method. The orientational instability condition is obtained explicitly and turns into known results for the limiting cases of zero and of infinite fields. It is shown that the biaxiality induced by small fields can expand considerably the region of spontaneously ordered fluid and could be useful to obtain mesomorphic phases in nonmesogens. The effect of small disorienting fields is more pronounced in systems with short-range anisotropic interactions between particles.