Lipid membranes with an edge

Details Lipid membranes with an edge Lipid membranes with an edge

2002-03-15

arxiv.org/abs/cond-mat/0203335v1

Physics

Condensed Matter

Soft Condensed Matter

8 pages

Scientific paper

10.1103/PhysRevE.66.021607

Consider a lipid membrane with a free exposed edge. The energy describing this membrane is quadratic in the extrinsic curvature of its geometry; that describing the edge is proportional to its length. In this note we determine the boundary conditions satisfied by the equilibria of the membrane on this edge, exploiting variational principles. The derivation is free of any assumptions on the symmetry of the membrane geometry. With respect to earlier work for axially symmetric configurations, we discover the existence of an additional boundary condition which is identically satisfied in that limit. By considering the balance of the forces operating at the edge, we provide a physical interpretation for the boundary conditions. We end with a discussion of the effect of the addition of a Gaussian rigidity term for the membrane.

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