Anomalous elasticity in nematic and smectic elastomer tubule

TL;DR

This paper investigates how thermal fluctuations cause scale-dependent elastic properties in nematic and smectic elastomer tubules, revealing a universal anomalous elasticity similar to that in smectic liquid crystals, with potential experimental detectability.

Contribution

It identifies and characterizes the anomalous elasticity in tubule phases of nematic and smectic elastomers, establishing their universality class and highlighting the power-law anomaly for physical membranes.

Findings

Elastic moduli become scale-dependent due to thermal fluctuations.

Anomalous elasticity is in the same universality class as d-dimensional smectics.

Power-law anomaly in physical tubules (D=2) may be experimentally observable.

Abstract

We study anomalous elasticity in the tubule phases of nematic and smectic elastomer membranes, which are flat in one direction and crumpled in another. These phases share the same macroscopic symmetry properties including spontaneously-broken in-plane isotropy and hence belong to the same universality class. Below an upper critical value $D_c =3$ of the membranes' intrinsic dimension D, thermal fluctuations renormalize the elasticity with respect to elastic displacements along the tubule axis so that elastic moduli for compression along the tubule axis and for bending the tubule axis become length-scale dependent. This anomalous elasticity belongs to the same universality class as that of d-dimensional conventional smectics with D taking on the role of d. For physical tubule, D=2, this anomaly is of power-law type and thus might by easier to detect experimentally than the logarithmic anomaly in conventional smectics.