https://doi.org/10.1140/epje/i2003-10049-y
The effect of thermal fluctuations on Schulman area elasticity
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
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 
between the projected (frame) and the saturated areas. We show that thermal fluctuations modify the elastic energy of stretched surfaces (
), and dominate the elastic energy of compressed surfaces (
). When 
the elastic energy is not much affected by the fluctuations; the frame area at which the surface tension vanishes becomes smaller than 
and the area elasticity modulus increases.
© EDP Sciences, Società Italiana di Fisica, and Springer-Verlag, 2003
