Smectic ordering in liquid-crystal–aerosil dispersions. I. X-ray scattering

Abstract

Comprehensive x-ray scattering studies have characterized the smectic ordering of octylcyanobiphenyl (8CB) confined in the hydrogen-bonded silica gels formed by aerosil dispersions. For all densities of aerosil and all measurement temperatures, the correlations remain short range, demonstrating that the disorder imposed by the gels destroys the nematic (N) to smectic-$A$ $\left(\mathrm{Sm}A\right)$ transition. The smectic correlation function contains two distinct contributions. The first has a form identical to that describing the critical thermal fluctuations in pure 8CB near the $N-\mathrm{Sm}A$ transition, and this term displays a temperature dependence at high temperatures similar to that of the pure liquid crystal. The second term, which is negligible at high temperatures but dominates at low temperatures, has a shape given by the thermal term squared and describes the static fluctuations due to random fields induced by confinement in the gel. The correlation lengths appearing in the thermal and disorder terms are the same and show a strong variation with gel density at low temperatures. The temperature dependence of the amplitude of the static fluctuations further suggests that nematic susceptibility becomes suppressed with increasing quenched disorder. The results overall are well described by a mapping of the liquid-crystal–aerosil system onto a three-dimensional $\mathrm{XY}$ model in a random field with disorder strength varying linearly with the aerosil density.