Electrostatics of multilamellar vesicles: Legendre expansion and reaction-field Brownian dynamics

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Abstract
An analytic expression for the electrostatic potential of a point charge within a concentric multilayered dielectric medium is derived in terms of a Legendre expansion. A novel Brownian dynamics algorithm for solving the Poisson equation for the reaction-field potential of charges near dielectricinterfaces is presented. To test both the computed and analytic solutions, the reaction-field potential and self-energy of a charge within a liposome are calculated and compared.