The effect of thermal fluctuations on Schulman area elasticity

O. Farago; P. Pincus

doi:10.1140/epje/i2003-10049-y

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2024 Impact factor 2.2

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: This email address is being protected from spambots. You need JavaScript enabled to view it.

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