Beyond Poisson–Boltzmann: Numerical Sampling of Charge Density Fluctuations

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• 作者：Frédéric Poitevin ; Marc Delarue ; Henri Orland
• 刊名：Journal of Physical Chemistry B
• 出版年：2016
• 出版时间：July 7, 2016
• 年：2016
• 卷：120
• 期：26
• 页码：6270-6277
• 全文大小：457K
• 年卷期：0
• ISSN：1520-5207

文摘

We present a method aimed at sampling charge density fluctuations in Coulomb systems. The derivation follows from a functional integral representation of the partition function in terms of charge density fluctuations. Starting from the mean-field solution given by the Poisson–Boltzmann equation, an original approach is proposed to numerically sample fluctuations around it, through the propagation of a Langevin-like stochastic partial differential equation (SPDE). The diffusion tensor of the SPDE can be chosen so as to avoid the numerical complexity linked to long-range Coulomb interactions, effectively rendering the theory completely local. A finite-volume implementation of the SPDE is described, and the approach is illustrated with preliminary results on the study of a system made of two like-charge ions immersed in a bath of counterions.