Thermomechanical coupling, heat conduction and director rotation in cholesteric liquid crystals studied by molecular dynamics simulation

Abstract

The lack of a centre of inversion in a cholesteric liquid crystal allows linear cross couplings between thermodynamic forces and fluxes that are polar vectors and pseudovectors, respectively. This makes it possible for a temperature gradient parallel to the cholesteric axis to induce a torque that rotates the director, a phenomenon known as the Lehmann effect or thermomechanical coupling. The converse is also possible: a torque applied parallel to the cholesteric axis rotates the director and drives a heat flow. In order to study this phenomenon, nonequilibrium molecular dynamics simulation algorithms and Green-Kubo relations evaluated by equilibrium molecular dynamics simulation have been used to calculate the Leslie coefficient, i.e. the cross coupling coefficient between the temperature gradient and the director angular velocity, for a model system composed of soft prolate ellipsoids of revolution interacting via the Gay-Berne potential augmented by a chiral interaction potential causing the formation of a cholesteric phase. It is found that the Leslie coefficient is two orders of magnitudes smaller than other transport coefficients such as the heat conductivity and the twist viscosity, so that very long simulations are required to evaluate it. The Leslie coefficient decreases with the pitch but it has not been possible to determine the exact functional dependence of this coefficient on the pitch. Since very long simulations have been performed to evaluate the Leslie coefficient, very accurate values have been obtained for the twist viscosity and the heat conductivity as a by-product and it is found that they are very similar to the values of the corresponding quantities in the achiral nematic phase that arises when the pitch goes to infinity.