Anisotropic short range potentials for solutes in nematic liquid crystals

Abstract

Recently, it has been suggested that the orientational order of solutes dissolved in nematic liquid crystals results from short range forces which depend on the size and shape of the solute molecule and from the interaction between the molecular quadrupole moment and the average electric field gradient experienced by the molecule. In this paper, we model the size and shape-dependent short range potential by assuming that the contribution to the potential from each surface element of a cavity representing the molecule depends on the orientation of the surface element with respect to the director. We have tried a variety of potentials based on this assumption, and we report here the ones which yielded the best agreement between theory and experiment. One of the potentials is obtained by integrating, along the director, the circumference of a slice cut through the molecule perpendicular to the director; better fits are obtained by adding a term which depends on a Hooke's law elastic distortion of the liquid crystal solvent. Another potential depends on the surface area of a cavity formed from the projections onto a plane perpendicular to the director and onto walls parallel to it. These models are used to fit the experimental order parameters of a collection of 46 molecules dissolved in a special mixture where the ordering is dominated by the size and shape potential. We attribute the superior quality of the resulting fits to the fact that these potentials depend in a more sensitive manner on the details of the geometry of the molecules than previously used ones.