Optical properties of antiferroelectric liquid crystals in free-standing films.

Abstract

A theoretical explanation of the results of ellipsometric measurements, performed some time ago by Bahr and co-workers [Ch. Bahr, D. Fliegner, C. J. Booth, and J. W. Goodby, Phys. Rev. E 51, R3823 (1995)] on free-standing films of antiferroelectric liquid crystal (R)-1-methylheptyl-4-(4\ensuremath{'}-$n$-dodecyloxybiphenyl-4-$\mathrm{yl}$ carbonyloxy)-3-fluorobenzoate (in the following 12F1M7), is given within a discrete phenomenological model of antiferroelectric liquid crystals. The structure of the smecti-${C}_{\ensuremath{\alpha}}$ (Sm-${C}_{\ensuremath{\alpha}}$) phase is described as an incommensurate phase, an average dielectric tensor, in general biaxial, is determined and the ellipsometric parameter $\ensuremath{\Delta}$ is found for two orientations of the film structures, defined by external electric field. Results are in agreement with observations: we show that temperature induced changes of the structure of the Sm-${C}_{\ensuremath{\alpha}}$ phase, as derived from the model, lead to the oscillatory dependence of the ellipsometric parameters ${\ensuremath{\Delta}}_{\ensuremath{-}}$ and ${\ensuremath{\Delta}}_{+}$ on temperature.