45884-AC6
Interactions and Structure in Nematic Colloids
Colloid-nematic dispersions have unique physical properties, and the colloidal particles exhibit a variety of structures, such as chains, lattices, and cellular forms. Colloidal particles and interfaces present in the system interact with molecules of the fluid (nematogens) and orient them with respect to their surfaces. The symmetry of these interactions depends on the surfactant treatment of the surfaces and defines the resulting nematic anchoring at a wall and at colloidal surfaces. Since nematics are critical systems, 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 potentials of mean force (PMF) and dispersion properties can be tuned or switched 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 equations of statistical mechanics which allows us to relate microscopic properties to mesoscopic structure and thermodynamic observables.
We have considered spherical colloids with up-down symmetry and obtained exact asymptotic forms for the colloid-colloid PMF. This reveals how the electrostatic analogy and other phenomenological concepts arise at the molecular level. In contrast to phenomenological approaches, our molecular theory does not assume particular boundary conditions (anchoring) at colloidal surfaces. For relevant molecular parameters, 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. We show that a simple van der Waals approximation gives a PMF that in some important aspects 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. In contrast, the more sophisticated 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, this 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 basic approach we have developed is flexible and can be readily applied to a broad range of physically interesting systems.
Intense experimental research of nematic colloids in the presence of walls and other interfaces is motivated by a variety of applications. The synergy of field and surface effects 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, we have shown that new forces appear, and that these forces can act over significant distances. The symmetry of the colloid-induced nematic distribution (the colloidal coat) 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.
Our molecular approach for the calculation of effective potentials can be readily applied to a wide range of physically important systems. These include patterned and nonspherical colloids, colloids trapped at interfaces, and nematic fluids in confined geometries such as droplets. The PMF obtained from microscopic theory will be used for mesoscale simulations to extract the structure and practically important observables of nematic colloid dispersions in different configurations.
