The Effect of Thermal Fluctuations on Schulman Area Elasticity

Details The Effect of Thermal Fluctuations on Schulman Area Elasticity The Effect of Thermal Fluctuations on Schulman Area Elasticity

2003-07-29

arxiv.org/abs/cond-mat/0307710v1

Eur. Phys. J. E, 11 (2003) 399

Physics

Condensed Matter

Statistical Mechanics

12 pages, to appear in Euro. Phys. J. E

Scientific paper

10.1140/epje/i2003-10049-y

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.

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