The Landau–Khalatnikov Relaxation Mechanism in Smectic Liquid Crystals

Abstract

The idea proposed and implemented by Landau and Khalatnikov to describe the dispersion and absorption of sound in superfluid helium is applied to smectic liquid crystals. The order parameter Φ that describes the phase transition between an orthogonal smectic SmA and a tilted smectic SmC is a two-component complex scalar and in this sense resembles the order parameter of superfluid helium. The interaction of the sound waves propagating in a system with the order parameter Φ leads to a periodic modulation of the system’s physical characteristics and parameters (in particular, its temperature). However, the order parameter cannot follow the temperature oscillations induced by a sound wave due to the presence of spatial order parameter correlations (long-range ones near the phase transition). It is this delay that leads to a sound-frequency-dependent dynamic specific heat. In this paper, we calculate this dynamic specific heat for the SmA–SmC phase transition for the so-called de Vries smectics (SmdV), with a highly developed short-range order. In turn, we analyze the dependence of the dynamic specific heat on frequency and temperature and find the dispersion and absorption of sound near the SmdV–SmC phase transition.