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Soft Matter and Biological Physics

Eur. Phys. J. E 5, 423-439 (2001)

Two direct methods to calculate fluctuation forces between rigid objects embedded in fluid membranes

W. Helfrich1 and T.R. Weikl2

1  Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
2  Max-Planck-Institut für Kolloid- und Grenzflächenforschung, Am Mühlenberg, 14476 Golm, Germany


(Received 15 December 2000 )

The fluctuation-induced attractive interaction of rigid flat objects embedded in a fluid membrane is calculated for a pair of parallel strips and a pair of equal circular disks. Assuming flat boundary conditions, we derive the interaction from the entropy of the suppressed boundary angle fluctuation modes. Each mode entropy is computed in two ways: from the boundary angles themselves and from the mean-curvature mode functions. A formula for the entropy loss of suppressing one or more mean-curvature modes is developed and applied. For the pair of disks we recover the result of Goulian et al. and Golestanian et al. in a direct manner, avoiding any mappings by Hubbard-Stratonovitch transformations. The mode-by-mode agreement of the two computed entropies in both systems confirms an earlier claim that mean curvature is the natural measure of integration for fluid membranes.

82.70.Uv - Surfactants, micellar solutions, vesicles, lamellae, amphiphilic systems (hydrophilic and hydrophobic interactions).
87.16.Dg - Membranes, bilayers, and vesicles.
34.20.-b - Interatomic and intermolecular potentials and forces, potential energy surfaces for collisions.

© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001