Diffusion-driven rotation in cholesteric liquid crystals studied using molecular dynamics simulation of a mixture of the Gay–Berne fluid and the Lennard-Jones fluid

Abstract

Diffusion-driven rotation in cholesteric liquid crystals has been studied using molecular dynamics simulation. Then a chemical potential gradient parallel to the cholesteric axis induces a torque that rotates the director at a constant rate around this axis, besides driving a mass current. An equimolar mixture of Gay–Berne ellipsoids and Lennard-Jones spheres was used as the molecular model. In order to keep the system homogeneous, the color conductivity algorithm was used to apply a color field instead of a chemical potential gradient to drive a mass current. Then the particles are given a color charge that interacts with a color field in the same way as with an electric field, but these charges do not interact with each other. This algorithm is often used to calculate the mutual diffusion coefficient. In the above liquid crystal model, it was found that the color field induces a torque that rotates the director at a constant rate around the cholesteric axis in addition to driving a mass current. The phenomenon was quantified by calculating the cross-coupling coefficient between the color field and the director angular velocity. The results were cross-checked by using a director rotation algorithm to exert a torque to rotate the director at a constant rate. Besides rotation of the director, this resulted in a mass current parallel to the cholesteric axis. The cross-coupling coefficient between the torque and the mass current was equal to the cross-coupling coefficient between the color field and the director rotation rate within a statistical uncertainty of 10 percent, thus fulfilling the Onsager reciprocity relations. As a further cross-check, these cross-coupling coupling coefficients, the color conductivity, and the twist viscosity were calculated by evaluating the corresponding Green–Kubo relations. Finally, it was noted that the orientation of the cholesteric axis parallel to the color field is the one that minimizes the irreversible energy dissipation rate. This is in accordance with a theorem stating that this quantity is minimal in the linear regime of a nonequilibrium steady state.