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

Abstract

Director con® gurations in a nematic liquid crystal can be determined by minimizing its total elastic free energy, for given elastic constants and speci® c boundary conditions. In some cases, these con® gurations have been obtained by numerical procedures where the elastic free energy density plays the same role as the overall potential energy in a standard Metropolis Monte Carlo simulation. The interaction energies or potentials used in these studies 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 that in the well-known Lebwohl± Lasher lattice model. On the other hand, we can construct, in di erent ways, a lattice model with pairwise additive interactions, which approximately reproduces the elastic free energy density, where the parameters de® ning the pair potential are expressed as linear combinations of elastic constants. An anisotropic nematogenic pair interaction 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 mapping, and study the resulting pair potential model with the aid of Monte Carlo simulations. The behaviour of the nematic phases formed by the two models is compared together with the predictions of molecular ® eld theory and the properties of the Lebwohl± Lasher model.

Basis Function Sampling: A New Paradigm for Material Property Computation

“…3(b) match identically with previous investigations based on long-wavelength director fluctuations [42]. [44] splits the elastic constants of bend, twist and splay deformations (diagrams at left). The elastic ratios of these coefficients (determined by BFS) for a model representing paraazoxyanisole (PAA) are given in the plot at right, with the expected ratios recovered as temperature is quenched toward zero [30].…”

“…4 we show that our method also captures the elastic ratios associated with generalized LL models; the model considered here was derived to describe para-azoxyanisole (PAA) in the limit of zero temperature [30,44]. Our simulations clearly obtain the correct elastic anisotropy at low T * , with logarithmic growth in both ratios approaching the isotropic-nematic transition.…”

Theoretical study of molecular ordering in a nematic liquid crystal

“…It is the molecular anisotropy which is held responsible for the longrange orientational order of thermotropic liquid crystals, be they formed from rod-or disc-like molecules. However, for many years it was not clear what were the roles played by anisotropic repulsive and attractive forces in determining liquid crystal behaviour [3]. Thus, the success of MaiereSaupe theory of nematics seemed to suggest that it is the attractive forces which are dominant, but less successful hard particle theories have also contributed to our understanding of liquid crystals.…”

“…Of particular interest is the study of hard ellipsoids which revealed that for both rods and discs the system will exhibit nematic behaviour provided the shape anisotropy is sufficiently large. The inability of hard ellipsoids to form smectic or columnar phases is of special importance, but it should be noted that systems of other hard objects have been found to form such translationally ordered phases [3,5].…”

Ordering of Mesogenic Compounds in a Dielectric Medium at the Nematic-Isotropic Transition Temperature - A Comparative Study

“…In the recent years there has been increasing interest in stable phases mediating the transition between different liquid crystalline phases (Rananavare et al, 1994;Rao et al, 1996;Srinivasulu et al, 1997;Potukuchi et al, 1998;Kumar et al, 2000). Further, computer simulation is finding an increasingly influential role for understanding liquid-crystal phases (Wilson and Allen, 1991;Bates and Luckhurst, 1997); Luckhurst and Romano, 1999;Blatch and Luckhurst, 2000;Sarman, 2000). However, it is essential to study simple models in some depth in order to understand the forces responsible for mesophase formation.…”