Computer simulation of chiral liquid crystal phases Part 5 Temperature dependence of the pitch of a cholesteric phase studied under self-determined boundary conditions

Abstract

The temperature dependence of the pitch was studied investigating a lattice model for a cholesteric phase using Monte Carlo (MC) computer simulations. To enable the formation of equilibrium helical structures self-determined boundary conditions have been applied using commensurable periodic images. The chiral molecules interacting as derived by van der Meer etal. were placed at the sites of a three-dimensional, simple cubic lattice with orientations confined to two dimensions. Starting from an isotropic phase, cholesteric phases were obtained on cooling down systems with lattice sizes 8 × 8 × 8, 12 × 12 × 12 and 16 × 16 × 16. The energy, specific heat, second and fourth rank order parameters have been calculated in order to localise the phase transition. The equilibrium pitch was obtained to be independent of the system size studied even for wavevectors incommensurable with the lattice. Interactions restricted to second order terms yielded a cholesteric phase with temperature-independent pitch. In agreement with mean field predictions a temperature dependence of the pitch was obtained taking into account fourth order terms.