High-resolution x-ray study of the nematic–smectic-Aand smectic-A–smectic-Ctransitions in liquid-crystal–aerosil gels

The effects of dispersed aerosil nanoparticles on two of the phase transitions of the thermotropic liquid-crystal material 4-$n$-pentylphenylthiol-${4}^{\ensuremath{'}}$-$n$-octyloxybenzoate $(8\ifmmode\bar\else\textasciimacron\fi{}S5)$ have been studied using high-resolution x-ray diffraction techniques. The aerosils hydrogen bond together to form a gel which imposes a weak quenched disorder on the liquid crystal. The smectic-$A$ fluctuations are well characterized by a two-component line shape representing thermal and random-field contributions. An elaboration on this line shape is required to describe the fluctuations in the smectic-$C$ phase; specifically the effect of the tilt on the wave-vector dependence of the thermal fluctuations must be explicitly taken into account. Both the magnitude and the temperature dependence of the smectic-$C$ tilt order parameter are observed to be unaffected by the disorder. This may be a consequence of the large bare smectic correlation length in the direction of modulation for this transition. These results show that the understanding developed for the nematic to smectic-$A$ transition for octylcyanobiphenyl and octyloxycyanobiphenyl liquid crystals with quenched disorder can be extended to quite different materials and transitions.