Propagation and attenuation of sound near the smectic-A—smectic-Cphase transition in liquid crystals

Anomalous contributions to the sound attenuation on the smectic-$A$ side of the smectic-$A$ —smectic-$C$ phase transition are found by generalizing the Landau-Ginzburg theory. Terms coupling the smectic-$C$ order parameter to the density and to the gradient of the layer spacing are incorporated and are found, to second order near the transition, to enhance certain of the viscosities which determine the acoustic attenuation. The anomalous attenuation depends on the angle between the propagation direction and layer normal, with the degree of anisotropy governed by the sensitivity of the transition temperature to changes in the layer spacing for constant density. The dispersion in the sound velocity near this transition is also considered.