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- W1910361549 abstract "We investigate the statistical-mechanical basis and the numerical accuracy of the Smoluchowski-Poisson-Boltzmann (SPB) approximation for describing ion diffusion in non-uniform electrolytes. The many-particle generalized Smoluchowski equation is formally reduced to a hierarchy of coupled n-particle equations. A closure relation, called the Instantaneous Relaxation Approximation (IRA), is used to decouple the equation for the one-particle self-propagator. Introducing also a mean field approximation (MFA), we recover the SPB equation. The accuracy of the IRA and MFA is quantitatively assessed for a model system consisting of two parallel uniformly charged plates with an intervening solution containing point ions in a dielectric medium. This is done by comparing diffusion propagators, survival probabilities and mean first passage times obtained by (1) solving the many-particle generalized Smoluchowski equation by the stochastic dynamics simulation technique (2) numerically solving the one-particle Smoluchowski equation with the exact (simulated) equilibrium potential of mean force, and (3) analytically solving the SPB equation. The IRA is found to be a useful approximation, whereas the MFA can lead to substantial error for systems with strong Coulomb coupling, as in the case of polyvalent counterions. Provided with a realistic potential of mean force, the one-particle Smoluchowski equation thus yields an accurate description of ion diffusion in non-uniform electrolytes." @default.
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- W1910361549 date "1986-04-20" @default.
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- W1910361549 title "Ion diffusion at charged interfaces" @default.
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- W1910361549 doi "https://doi.org/10.1080/00268978600100801" @default.
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