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Generalized Langevin-Debye model of the field dependence of tilt, birefringence, and polarization current near the de Vries smectic-A* to smectic-C* liquid crystal phase transition.

In chiral smectic-A (Sm-A) liquid crystals, an applied electric field induces a tilt of the optic axis from the layer normal. When these materials are of the de Vries type, the electroclinic tilt susceptibility is unusually large, with the field-induced director reorientation accompanied by a substantial increase in optical birefringence with essentially no change in the smectic layer spacing. In order to account for the observed electro-optic behavior, we assume that the molecular orientation distribution in the Sm-A has two degrees of freedom: azimuthal orientation and tilt of the molecular long axis from the layer normal, with the tilt confined to a narrow range of angles. We present a generalized Langevin-Debye model of the response of this orientational distribution to applied field that gives a field-induced optic axis tilt, birefringence, and polarization dependence that agrees well with experimental measurements and reproduces the double-peaked polarization current response characteristic of a first-order Sm-A(*)-Sm-C(*) transition. Additionally, we find that the measured field-induced polarization and the Langevin-Debye model predictions can be quantitatively described as pre-transitional behavior near the tricritical point of a recently published generalized 3D XY model of interacting hard rods confined to reorient on a cone in the presence of an applied field.