paper

Interface mediated interactions between particles -- a geometrical approach

arXiv:cond-mat/0506019 · doi:10.1103/PhysRevE.72.061407

Abstract

Particles bound to an interface interact because they deform its shape. The stresses that result are fully encoded in the geometry and described by a divergence-free surface stress tensor. This stress tensor can be used to express the force on a particle as a line integral along any conveniently chosen closed contour that surrounds the particle. The resulting expression is exact (i.e., free of any "smallness" assumptions) and independent of the chosen surface parametrization. Additional surface degrees of freedom, such as vector fields describing lipid tilt, are readily included in this formalism. As an illustration, we derive the exact force for several important surface Hamiltonians in various symmetric two-particle configurations in terms of the midplane geometry; its sign is evident in certain interesting limits. Specializing to the linear regime, where the shape can be analytically determined, these general expressions yield force-distance relations, several of which have originally been derived by using an energy based approach.

18 pages, 7 figures, REVTeX4 style; final version, as appeared in Phys. Rev. E. Compared to v2 several minor mistakes, as well as one important minus sign in Eqn. (18a) have been cured. Compared to v1, this version is significantly extended: Lipid tilt degrees of freedom for membranes are included in the stress framework, more technical details are given, estimates for the magnitude of forces are made

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