High-resolution x-ray study of a smectic-A—smectic-Cphase transition

Abstract

We report measurements of the tilt angle $\Phi$ and the planar spacing $d_C$ near the second-order $\mathrm{Sm}C-\mathrm{Sm}A$ transition in $4-n-\mathrm{pentyl}-\mathrm{phenylthiol}-4^{\prime }-n-\mathrm{octyloxybenzoate} \left(8\mathrm{}\overline{S}5\right)$. We find that the ratio $\frac{\Phi }{invcos}\left(\frac{d_C}{d_A}\right)$ is constant (1.2 ± 0.1) through the $C$ phase, supporting a simple molecular-tilt model for the transition. For $5\times {10}^{-3\mathrm{}}>1-\frac{T}{T_c}>3\mathrm{}\times {10}^{-5\mathrm{}}$, $\Phi$ exhibits mean-field behavior. A simple Ginzburg-criterion argument indicates that the true critical region should be unobservably small for most $A-C$ transitions.