Unconventional elasticity in smectic-A elastomers

TL;DR

This paper investigates the unique elastic properties of smectic-A elastomers, predicting a phase transition under strain that explains experimental observations and exploring the electroclinic effect in chiral variants.

Contribution

It introduces a theoretical model linking strain-induced phase transitions to elastic behavior and electroclinic effects in smectic-A elastomers, aligning with experimental data.

Findings

Strain above 3% induces a transition to a smectic-C-like state.

The model predicts changes in elastic modulus and layer tilt under strain.

Electroclinic effect causes significant lateral electrostriction in chiral smectic-A* elastomers.

Abstract

We study two aspects of the elasticity of smectic-$A$ elastomers that make these materials genuinely and qualitatively different from conventional uniaxial rubbers. Under strain applied parallel to the layer normal, monodomain smectic-$A$ elastomers exhibit a drastic change in Young's modulus above a threshold strain value of about 3%, as has been measured in experiments by Nishikawa and Finkelmann [Macromol. Chem. Phys. {\bf 200}, 312 (1999)]. Our theory predicts that such strains induce a transition to a smectic-$C$-like state and that it is this transition that causes the change in elastic modulus. We calculate the stress-strain behavior as well as the tilt of the smectic layers and the molecular orientation for strain along the layer normal, and we compare our findings with the experimental data. We also study the electroclinic effect in chiral smectic-$A^\ast$ elastomers. According to experiments by Lehmann {\em et al}. [Nature {\bf 410}, 447 (2001)] and K\"{o}hler {\em et al}. [Applied Physics A {\bf 80}, 381 (2003)], this effect leads in smectic-$A^\ast$ elastomers to a giant or, respectively, at least very large lateral electrostriction. Incorporating polarization into our theory, we calculate the height change of smectic-$A^\ast$ elastomer films in response to a lateral external electric field, and we compare this result to the experimental findings.