Study of the pitch of fluids of electrostatically chiral anisotropic molecules: mean-field theory and simulation

Abstract

An analytical expression is derived for the pitch of a system of electrostatically chiral hard Gaussian overlap (HGO) particles. The calculations are performed for a planar geometry, i.e. the HGO particles are confined in a plane perpendicular to the helical axis and they are oriented in the direction of the local nematic director of a given plane. The chiral contribution between molecules is described in terms of the pseudo tensor introduced by Goossens [W.J. Goossens, Mol. Cryst. Liq. Cryst., 12, 237 (1971)]. The contribution of hard-body repulsion is treated using the Parsons–Lee [J.D. Parsons, Phys. Rev. A, 19, 1225 (1979); S.D. Lee, J. Chem. Phys., 87, 4972 (1987)] theory for the freely rotating rods in the limit of perfect local nematic alignment (planar geometry), while the mean-field approximation is used to account for the contribution due to the chiral dispersion interactions. This provides one of the first truly microscopic descriptions of the explicit dependence of the torque-field, twist-elastic constant, and the pitch of the chiral nematic phase on the molecular parameters and thermodynamic variables. The pitch of the chiral HGO fluid exhibits a significant dependence on the temperature (chiral strength), aspect ratio, and density of the system. The most interesting result is that the pitch increases with increasing packing fraction (corresponding to a weaker effective chiral interaction) even when a decrease in the nearest neighbour distance tends to increase the chiral contribution to the energy. Monte Carlo simulation data for the pitch of a freely rotating system of chiral hard spherocylinders obtained with a method previously developed by the authors [S. Varga and G. Jackson, Chem. Phys. Lett., 377, 6 (2003)] are fully consistent the predictions of the theoretical calculations.