Elasticity of smectic liquid crystals with focal conic domains

TL;DR

This study investigates the elastic properties of smectic liquid crystals with focal conic domains, revealing a universal scaling relation between shear modulus and FCD size linked to surface tension, akin to layered systems with defects.

Contribution

It demonstrates a universal scaling law relating shear modulus and FCD size in smectic liquid crystals, connecting surface tension to layered system behaviors.

Findings

Shear modulus G' scales with FCD size L as G' ~ c5_{eff}/L.

Effective surface tension c5_{eff} scales as rac{1}{2} \, \sqrt{KB}.

Universal rheological behavior observed across layered systems with defects.

Abstract

We study the elastic properties of thermotropic smectic liquid crystals with focal conic domains (FCDs). After the application of the controlled preshear at different temperatures, we independently measured the shear modulus G' and the FCD size L. We find out that these quantities are related by the scaling relation G' ~ \gamma_{eff}/L where \gamma_{eff} is the effective surface tension of the FCDs. The experimentally obtained value of \gamma_{\rm eff} shows the same scaling as the effective surface tension of the layered systems \sqrt{KB} where K and B are the bending modulus and the layer compression modulus, respectively. The similarity of this scaling relation to that of the surfactant onion phase suggests an universal rheological behavior of the layered systems with defects.