We study the influence of the dispersed aerosil particle concentration on the soft and Goldstone mode dynamics across the smectic-$A$–smectic-$C^{*}$ phase transition using dielectric spectroscopy. We use CE8 liquid crystal filled with aerosils of concentrations ${x=m}_s{/(m}_s{+m}_{\mathrm{LC}})=0.025,0.05,0.1,$ and $0.15,$ where $m_s$ and $m_{\mathrm{LC}}$ stand for masses of aerosil and liquid crystal, respectively. In dispersions with $x<\mathrm{}0.15\mathrm{}$ the characteristic Goldstone frequency temperature dependence $f_G\mathrm{}\left(T\right)\mathrm{}$ is almost bulklike in contrast to the corresponding soft mode dependence $f_s\mathrm{}\left(T\right).$ For $x>\mathrm{}0\mathrm{}$ the degeneracy of the modes at the $\mathrm{Sm}A-\mathrm{Sm}{C}^{*}$ transition temperature is lifted. With increasing x the modes’ intensities gradually decrease and the critical effective coefficient $\gamma$ tentatively approaches the value characterizing the three-dimensional $\mathrm{XY}$ universality class. For $x=0.15,$ a drastic change in behavior is observed. The Goldstone mode is completely suppressed and the $f_s\mathrm{}\left(T\right)\mathrm{}$ dependence begins to deviate from the Arrhenius behavior. A simple phenomenological approach is used in the explanation of results.

• Received 27 May 2002

DOI:https://doi.org/10.1103/PhysRevE.66.041702