Excluded-Volume Short-Range Repulsive Potential for Tetrahedral Molecules

Abstract

Tetrahedral symmetry in nematic liquid crystals has been studied for several years, since the seminal paper by Fel [1]. Amongst statistical theories of nematic liquid crystals, a molecular mean-field model has proven to be quite effective in predicting phase sequences for thermotropic biaxial nematic molecules endowed with D_2h symmetry, as a function of the parameters entering their interaction potential [2,3]. This model has highlighted the role of a partially repulsive quadrupolar potential of mean torque in promoting condensed phases. It has been shown that the quadrupolar approximation to the excluded-volume interaction between hard spherocuboids can be written precisely as the superposition of two London interactions: one repulsive and one attractive [4]; furthermore, polar steric interactions have been shown to be capable of inducing orientationally ordered states possibly unexpected [5]. By adapting a numerical code available to the scientific community, we evaluate the analytical excluded volume function for non-convex tetrahedral molecules, modelled as chains of tangent hard spheres. Since this function is overly complicated, we expand it over a suitable set of Symmetry Adapted Wigner Functions (SAWFs).

Keywords:

• Excluded volume
• nematic liquid crystal
• symmetry adapted
• tetrahedral symmetry
• Wigner rotation functions

Acknowledgments

This work was partly supported by a Grant for Progetto Giovani 2008 by the GNFM (Gruppo Nazionale per la Fisica Matematica), Italy and supported in part under Grant N202 169 31/3455 of the Polish Ministry of Science and Higher Education.