Computer simulation studies of anisotropic systems. Part 25.—Chiral nematics, the Dzyaloshinsky–Moriya model

Abstract

A Monte Carlo computer simulation study of a model chiral nematogen has been undertaken. The chiral molecules are confined to the sites of a simple cubic lattice with their long axes in the xy plane and the helix axis along the z direction. The intermolecular interaction takes the form proposed by van der Meer et al. which is the simplest possible for chiral nematogens. For the lattice model the chiral part proves to be equivalent to the Dzyaloshinsky–Moriya model used to explain the weak antiferromagnetism in certain transition-metal oxides. To ensure that the periodic images are commensurate with the particles in the simulation box we have developed twisted boundary conditions. The chiral model exhibits a chiral nematic phase with a helical wavevector which is independent of temperature. This behaviour is entirely expected because the chiral term can be removed from the pair potential by a helical transformation with a constant wavevector. We have studied the transformed chiral model in detail in the vicinity of the order–disorder phase transition. In particular we have determined the internal energy and the heat capacity to locate the transition which is found to be second order or higher. The long-range order parameters, T₂ and T₄, have been evaluated together with the second- and fourth-rank angular correlation coefficients which characterise the short-range order. The spatial-director fluctuations have also been calculated to establish the extent of the monodomain formed. Finally, the properties simulated for the transformed chiral model are compared with those of its achiral analogue.