Temperature behavior of ferroelectric liquid-crystal thin films: A classicalXYsystem

Abstract

Freely suspended films of the material DOBAMBC ($p$-decyloxybenzylidene-$p^{\prime }$-amino 2-methyl butyl cinnamate), which has a layered ferroelectric liquid-crystalline phase (the chiral smectic $C$ phase), are created across a rectangular hole in a glass microscope cover slide. The films are quantized in thickness, being one, two, three, or more monomolecular (smectic) layers thick. In the tilted smectic $C$ phase, the films exhibit a net spontaneous electric polarization parallel to the smectic layers and in the plane of the film. A unique determination of the polarization, the Frank elastic constants, and the associated viscosities is made by comparing intensities of quasielastic Rayleigh-scattered light from orientational fluctuations of the molecular director in the presence and absence of an applied electric field. Measurements are performed on films three smectic layers thick as a function of temperature near the $C-A$ transition. The relevence of our results to the theories of the classical two-dimensional $\mathrm{XY}$ transition will be discussed.