Computer simulation study of a nematogenic lattice model based on an elastic energy mapping of the pair potential

Director configurations in a nematic liquid crystal can be determined by mi nimizing its total elastic free energy, for given elastic constants and spe cific boundary conditions. In some cases, these configurations have been ob tained by numerical procedures where the elastic free energy density plays the same role as the overall potential energy in a standard Metropolis Mont e Carlo simulation. The interaction energies or potentials used in these st udies are short ranged but, in general, not pairwise additive, unless the t hree elastic constants are set to a common value, thus reducing the potenti al to that in the well-known Lebwohl-Lasher lattice model. On the other han d, we can construct, in different ways, a lattice model with pairwise addit ive interactions, which approximately reproduces the elastic free energy de nsity, where the parameters defining the pair potential are expressed as li near combinations of elastic constants. An anisotropic nematogenic pair int eraction of this kind, originally proposed by Gruhn and Hess (T. Gruhn and S. Hess, Z. Naturforsch. A51, 1 (1996)), has recently been investigated by one of us, using a Monte Carlo simulation (S. Romano, Int. J. Mod. Phys. B 12, 2305 (1998)). Here we propose another approximate procedure for the map ping, and study the resulting pair potential model with the aid of Monte Ca rlo simulations. The behaviour of the nematic phases formed by the two mode ls is compared together with the predictions of molecular held theory and t he properties of the Lebwohl-Lasher model.