The effect of thermal fluctuations on Schulman area elasticity

O. Farago; P. Pincus

doi:10.1140/epje/i2003-10049-y

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2023 Impact factor 1.8

Soft Matter and Biological Physics

Eur. Phys. J. E (2003) 11: 399-408
https://doi.org/10.1140/epje/i2003-10049-y

The effect of thermal fluctuations on Schulman area elasticity

O. Farago¹^,2^* and P. Pincus¹^,2

¹ Materials Research Laboratory, University of California, CA 93106, Santa Barbara, USA
² Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), 373-1 Kusong-dong, Yusong-gu, 305-701, Taejon, South Korea

^* e-mail: farago@mrl.ucsb.edu

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 $A_{\rm p}/A_{\rm s}$ between the projected (frame) and the saturated areas. We show that thermal fluctuations modify the elastic energy of stretched surfaces ( $A_{\rm p}/A_{\rm s} > 1$ ), and dominate the elastic energy of compressed surfaces ( $A_{\rm p}/A_{\rm s} < 1$ ). When $A_{\rm p}\sim A_{\rm s}$ the elastic energy is not much affected by the fluctuations; the frame area at which the surface tension vanishes becomes smaller than $A_{\rm s}$ and the area elasticity modulus increases.