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Spherical dielectric boundaries

Rapidly convergent expressions for the Green's function of the Poisson equation for spherically symmetric systems, where the dielectric constant varies discontinuously in the radial direction, were derived. These expressions were used in Monte Carlo simulations of various electrolyte systems, and their efficiency was assessed. The simulations were performed on six types of systems having either (i) a uniform surface charge distribution, (ii) a uniform volume charge distribution, or (iii) mobile ions, which were neutralized by mobile counterions. With only the leading term of the expansion included, a precision of the polarization energy of 0.005kT or better was achieved, which is smaller than the statistical uncertainty of a typical simulation. The inclusion of the dielectric inhomogeneity lead to a 2.5-fold increase of the computational effort, which is modest for this type of model. The ion density distributions were investigated for different dielectric conditions. These spatial distributions were discussed in terms of the importance of (i) the direct mean-field Coulomb interaction, (ii) the surface charge polarization at the dielectric discontinuity, and/or (iii) the change in the attractive Coulomb correlations. Moreover, the accuracy of a splitting theory, based on dividing the electrostatic interaction into long and short wavelength contributions and applying different approximations on the two contributions, has been assessed against simulation results. The splitting theory works best for the case where the dielectric constant of the confining sphere is equal to or less than that of the surrounding medium.

People: Leo Lue (University of Strathclyde) and (Per Linse).