Dynamics of smectic elastomers

TL;DR

This paper investigates the low-frequency dynamics of smectic liquid crystal elastomers across various phases, comparing formulations and analyzing sound velocities and rheological behaviors.

Contribution

It introduces two formulations for analyzing smectic elastomers' dynamics and compares their results, providing new insights into phase-specific behaviors and sound velocities.

Findings

Dynamics of smectic-A elastomers are closely related to nematics.

Calculated sound velocities in biaxial smectic and smectic-C phases.

Discussed rheological behavior of smectic-C elastomers.

Abstract

We study the low-frequency, long-wavelength dynamics of liquid crystal elastomers, crosslinked in the smectic-$A$ phase, in their smectic-$A$, biaxial smectic and smectic-$C$ phases. Two different yet related formulations are employed. One formulation describes the pure hydrodynamics and does not explicitly involve the Frank director, which relaxes to its local equilibrium value in a non-hydrodynamic time. The other formulation explicitly treats the director and applies beyond the hydrodynamic limit. We compare the low-frequency, long-wavelength dynamics of smectic-$A$ elastomers to that of nematics and show that the two are closely related. For the biaxial smectic and the smectic-$C$ phases, we calculate sound velocities and the mode structure in certain symmetry directions. For the smectic-$C$ elastomers, in addition, we discuss in some detail their possible behavior in rheology experiments.