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.

Director/barycentric rotation in cholesteric droplets under temperature gradient

“…15 Based on the symmetry argument, Leslie had predicted that in chiral LCs whose mirror symmetry was broken, any transport current could directly cause unidirectional molecular rotation. [15][16][17] The prediction was later veried by experimental observations such as the director rotation driven by direct currents in cholesteric droplets [18][19][20] and the gaspermeation-driven molecular precessions in smectic C* lms. [21][22][23] Recently, the missing heat-current-driven Lehmann effect was nally reproduced and quantitatively analyzed by Oswald et al [24][25][26] In their experiments, two types of samples were used; cholesteric droplets coexisting with the isotropic phase and the bulk cholesterics sandwiched by glass substrates.…”

Formation of a columnar liquid crystal in a simple one-component system of particles

“…[6][7][8] These simulations have so far followed the phenomenological paradigm that dominated the science of liquid crystals for decades, whereby the structural anisotropy of liquid crystals was assumed to be determined by the anisometric shape of a molecule. Respectively, the shapes of the constituent particles in the models of liquid crystals have been designed to imitate the shapes of the molecules in the respective mesogens: the smectic phases have been simulated using rod-like particles, [9][10][11][12] and models of columnar liquid crystals 8,[13][14][15][16] commonly used flat discotic particles or oblate ellipsoids.…”

Formation of the smectic-Bcrystal from a simple monatomic liquid

“…Systems of elongated molecules interacting via Gay-Berne (GB) potential [8][9][10][11] have been found successful in reproducing the liquid-crystal phase behaviour in a variety of simulation experiments. These models were also exploited for calculating transport properties of the liquid crystals [12]. Moreover, it was proved possible to reduce the models of anisotropically interacting GB particles to hard spherocylinders [13,14], which appears to indicate the entropic origin of the LC phases due to geometry of excluded volume.This experience poses a question of conceptual interest for the statistical mechanics of condensed matter: how far further can the particle models successfully reproducing the basic features of smectic phases be simplified?…”