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Soft Matter and Biological Physics

Eur. Phys. J. E 3, 149-157

Effect of thermal undulations on the bending elasticity and spontaneous curvature of fluid membranes

H.A. Pinnow - W. Helfrich

Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany
Wolfgang.Helfrich@physik.fu-berlin.de

Received 19 April 1999 and in Received in final form 7 January 2000

Abstract
We amplify previous arguments why mean curvature should be used as measure of integration in calculating the effective bending rigidity of fluid membranes subjected to a weak background curvature. The stiffening of the membrane by its fluctuations, recently derived for spherical shapes, is recovered for cylindrical curvature. Employing curvilinear coordinates, we then discuss stiffening for arbitrary shapes, confirm that the elastic modulus of Gaussian curvature is not renormalized in the presence of fluctuations, and show for the first time that any spontaneous curvature also remains unchanged.

PACS
68.10.Et Interface elasticity, viscosity, and viscoelasticity - 82.65.Dp Thermodynamics of surfaces and interfaces

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