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

Abstract:

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.