Surface tension and deformations of membrane structures : relation to two-dimensional phase transitions

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Abstract
We analyse the thermal fluctuations of two types of flexible membranes : 1) Closed systems (such as the membrane of a biconcave red blood cell) where the chemical constituents of the membrane are fixed in number, but the membrane surface S is adjustable. 2) Open systems (such as bilayer films) where constituent molecules can be exchanged with a reservoir (at the outer surface of the rim). For the first case, the surface tension is zero; fluctuations are then very large, and limited only by certain anharmonic terms. We show that these terms can be analysed exactly - the problem being related to the spherical model of phase transitions. Although the anharmonic terms are strong, they do not modify the laws derived for the light scattering in the simpler harmonic model constructed earlier by one of us [1]. For the second case, there is a finite surface tension, and the fluctuations are much less pathological. This seems to agree with recent measurements by inelastic light scattering on black films by Grabowski and Cowen

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