Elastic Constants and Pair Potentials for Nematogenic Lattice Models

Abstract

Director configurations in nematic Liquid Crystals can be determined by minimizing their elastic free-energy density, on the basis of elastic constants and of specific boundary conditions; in some published cases, this has been obtained by numerical procedures where the elastic free-energy density plays the same role as the overall potential energy in a standard Monte Carlo simulation. The "potentials" used in these papers are short-ranged but, in general, not pairwise additive, unless the three elastic constants are set to a common value, thus reducing the potential to the well-known Lebwohl–Lasher lattice model.On the other hand, one can construct, possibly in different ways, a lattice model with pairwise additive interactions, approximately reproducing the elastic free-energy density, where parameters defining the pair potential are expressed as linear combinations of elastic constants; a nematogenic pair interaction of this kind, originally proposed by Gruhn and Hess (T. Gruhn and S. Hess, Z. Naturforsch.A51, 1 (1996)), has been investigated here by Monte Carlo simulation with periodic boundary conditions, i.e. aimed at the resulting bulk behavior.