A continuum theory of chiral smectic C liquid crystals

We formulate a nonlinear continuum theory of flow of chiral smectic C liquid crystals (C*) involving molecular director, layer order parameter, polarization vector, flow velocity, and hydrostatic pressure fields. In addition to chiral orientational ordering, smectic C* phases also present positional ordering, with molecular centers of mass arranged in one dimensional layers. The nonzero tilt angle of the molecular director with respect to the layer normal together with the chirality is responsible for the ferroelectric nature of the phase. This results in a stronger coupling with applied electric fields than the dielectric nematic. We apply the model to study the molecular reorientation dynamics in homeotropic geometry under the influence of an applied electric field. The switching process between states with opposite polarization is understood by the traveling wave solution of the system. We prove existence and uniqueness of the traveling wave and show that the predicted switching time is smaller than that when the flow effect is neglected. We also obtain bounds on the speed of switching and an optimality condition on the parameters of the problem. Numerical simulations confirm the predictions of the analysis.