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Colloid-nematic dispersions have unique physical properties, with the colloidal particles exhibiting an interesting variety of structures. Colloidal particles present in the system interact with molecules of the fluid (nematogens) and orient them with respect to the colloidal surfaces. The symmetry of these interactions depends on the surfactant treatment of the surfaces, and defines the resulting nematic anchoring at the interface. Colloidal particles in nematic solvents can experience strong, nematic- mediated interactions with each other and with surfaces. These effective interactions are highly sensitive to the direction and strength of electric and magnetic fields. Consequently, the colloid-colloid potentials of mean force can be tuned by controlling external fields, leading to variety of physical phenomena. Our recent work has focused on understanding these phenomena based on microscopic theory. We use the basic methods of statistical mechanics to relate microscopic properties to mesoscopic structure, and thermodynamic observables.

We have obtained exact asymptotic forms for the colloid-colloid potential of mean force, which reveal how the electrostatic analogy and other phenomenological concepts arise at the molecular level. In contrast to phenomenological approaches, our  theory does not assume particular boundary conditions (anchoring) at colloidal surfaces, and the anchoring obtained is physically realistic, neither rigid nor infinitely weak. The effective force between a colloidal pair at large separation remains essentially constant over the entire region of nematic stability. For spherical colloidal particles with up-down symmetry,  a simple van der Waals approximation gives a potential of mean force that  is similar to the phenomenological results obtained in the  weak anchoring limit; at large separations the potential varies as D⁸, where D is the colloidal diameter. The more accurate mean spherical approximation yields a D⁶ dependence consistent with phenomenological calculations employing rigid boundary conditions. We show that taking proper account of the correlation length x , which is inversely proportional to the electric (or magnetic) field, is essential in an analysis of the diameter dependence. At infinite x the leading dependence is D⁶, but shifts to D⁸ when  x is finite. The correlation length, and hence external fields, also influences the orientational behavior of the effective interaction. The so-called “quadrupolar” interaction that determines the long-range behavior at zero field transforms into a superposition of screened “multipoles” when the field is finite.

The synergy of field and surface effects in nematic colloids creates interesting possibilities for manipulating colloidal particles of micron and submicron size. We have developed a molecular theory of effective, field-dependent, wall-colloid interactions in nematic media. If the preferred nematic orientation imposed by the wall does not coincide with the director dictated by the external field, new forces appear, and these forces can act over significant distances. The symmetry of the colloid-induced nematic distribution  determines the diameter dependence of the wall-colloid interaction. The effective force decreases with the distance,  s,  from the wall as (D/x)³ exp(-s/x) for “quadrupolar” colloids and as (D/x)² exp(-s/x) for “dipoles”. The effect is most significant at moderate fields. Our results give a clear indication of the strength and direction of the external field required to optimize wall-colloid interactions. These forces can be designed to be attractive or repulsive depending on the type of anchoring at the wall and colloidal surfaces. For example, quadrupolar colloids with planar anchoring are attracted to walls with planar anchoring and repelled from the walls with perpendicular anchoring. Dipolar colloids with wall-ward hedgehogs are attracted to walls with planar anchoring and repelled from those with perpendicular anchoring.

The basic molecular approach we have developed is flexible, and can be applied to a range of physically interesting systems. These include patterned and nonspherical colloids, colloids trapped at interfaces, and nematic fluids in confined geometries.