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Charged dielectric spheres interacting in electrolytic solution: A linearized Poisson–Boltzmann equation model
The Journal of Chemical Physics ( IF 4.4 ) Pub Date : 2021-09-21 , DOI: 10.1063/5.0056120
Sergii V Siryk 1 , Artemi Bendandi 2 , Alberto Diaspro 2 , Walter Rocchia 1
Affiliation  

We present an analytical theory of electrostatic interactions of two spherical dielectric particles of arbitrary radii and dielectric constants, immersed into a polarizable ionic solvent (assuming that the linearized Poisson–Boltzmann framework holds) and bearing arbitrary charge distributions expanded in multipolar terms. The presented development entails a novel two-center re-expansion analytical theory that expands upon and improves the existing ones, bypassing the conventional expansions in modified Bessel functions. On this basis, we develop a specific matrix formalism that facilitates the construction of asymptotic expansions in ascending order of Debye screening terms of potential coefficients, which are then employed to find exact closed-form expressions for the total electrostatic energy. In particular, this work allows us to explicitly and precisely quantify the k-screened terms of the potential coefficients and mutual interaction energy. Specific cases of monopolar and dipolar distributions are described in particular detail. Comprehensive numerical examples and tests of series convergence and the relative balance of leading and higher-order terms of the mutual interaction energy are presented depending on the inter-particle distance and particles’ radii. The results of this work find application in soft matter modeling and, in particular, in computational biophysics and colloid science, where the availability of increasingly larger experimental structures at the atomic-level resolution makes numerical treatment challenging and calls for more efficient expressions and an increased range of validity.

中文翻译:

带电介电球在电解液中相互作用:线性化 Poisson-Boltzmann 方程模型

我们提出了两个具有任意半径和介电常数的球形介电粒子的静电相互作用的分析理论,它们浸入可极化的离子溶剂(假设线性化泊松-玻尔兹曼框架成立)并带有以多极形式扩展的任意电荷分布。所提出的发展需要一种新颖的双中心再展开分析理论,该理论扩展并改进了现有理论,绕过了修正贝塞尔函数中的常规展开。在此基础上,我们开发了一种特定的矩阵形式主义,它有助于以潜在系数的德拜筛选项的升序构造渐近展开式,然后将其用于找到总静电能量的精确闭式表达式。特别是,势系数和相互作用能的k筛选项。特别详细地描述了单极和偶极分布的具体情况。根据粒子间距离和粒子半径,给出了级数收敛的综合数值例子和测试,以及相互作用能的前导项和高阶项的相对平衡。这项工作的结果在软物质建模中得到了应用,特别是在计算生物物理学和胶体科学中,在原子级分辨率下越来越大的实验结构的可用性使得数值处理具有挑战性,并需要更有效的表达和增加有效范围。
更新日期:2021-09-21
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