Transport properties of cholesteric liquid crystals studied by molecular dynamics simulation

We have studied the transport properties of a cholesteric liquid crystal by molecular dynamics simulation. The molecules consist of six soft ellipsoid s of revolution, the axes of which are perpendicular to the line connecting their centres of symmetry. The angle between the symmetry axes of two adja cent ellipsoids is 7.5 degrees, so the molecules are twisted. At high densi ties they form a cholesteric phase where their twist axes are oriented arou nd the cholesteric axis and the symmetry axes of the ellipsoids are approxi mately parallel to the local director. We have been particularly interested in thermomechanical coupling or the Lehmann effect, which arises when a te mperature gradient parallel to the cholesteric axis induces a torque that r otates the director. The converse is also possible: rotation of the directo r can drive a heat current. The thermal conductivity, the twist viscosity, the cross-coupling coefficient between the temperature gradient and the tor que, and the cross-coupling coefficient between the director angular veloci ty and the heat current have been calculated by non-equilibrium molecular d ynamics simulation methods (NEMD) and by evaluation of the Green-Kubo relat ions from equilibrium simulations. Two ensembles have been utilized: the or dinary canonical ensemble and another ensemble where the director angular v elocity is constrained to be a constant of motion. All the methods give con sistent results for the twist viscosity and the thermal conductivity. The N EMD estimates of the cross-coupling coefficients agree within a relative er ror of 20%. This is consistent with the Onsager reciprocity relations that state that the two cross-coupling coefficients should be equal. The relativ e error of the Green-Kubo estimates is about 100% even though the order of magnitude is the same as that of the NEMD estimates.