The Effect of Thermal Fluctuations on Schulman Area Elasticity

TL;DR

This paper investigates how thermal fluctuations influence the elastic properties of a two-dimensional surface, revealing different elastic regimes and the impact of fluctuations on surface tension and elasticity depending on area ratios.

Contribution

It introduces a comprehensive analysis of the interplay between elastic energy, curvature, and entropy in fluctuating surfaces, identifying regimes and effects of thermal fluctuations on elasticity.

Findings

Thermal fluctuations modify elastic energy in stretched surfaces.

Fluctuations dominate elastic energy in compressed surfaces.

Surface tension vanishes at smaller frame areas when fluctuations are considered.

Abstract

We study the elastic properties of a two-dimensional fluctuating surface whose area density is allowed to deviate from its optimal (Schulman) value. The behavior of such a surface is determined by an interplay between the area-dependent elastic energy, the curvature elasticity, and the entropy. We identify three different elastic regimes depending on the ratio $A_p/A_s$ between the projected (frame) and the saturated areas. We show that thermal fluctuations modify the elastic energy of stretched surfaces ($A_p/A_s> 1$), and dominate the elastic energy of compressed surfaces ($A_p/A_s< 1$). When $A_p\sim A_s$ the elastic energy is not much affected by the fluctuations; the frame area at which the surface tension vanishes becomes smaller than $A_s$ and the area elasticity modulus increases.