Electrostatic potential inside ionic solutions confined by dielectrics: a variational approach
Electrostatic potential inside ionic solutions confined by dielectrics: a variational approach
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DOI：
10.1039/b105176h
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发表时间：
2001-01-01
影响因子：
3.3
通讯作者：
Melchionna, S
中科院分区：
文献类型：
--
作者：
Allen, R;Hansen, JP;Melchionna, S
本文提供了一个教学介绍的变分制定的自由电荷之间的静电相互作用接近的电介质界面。构造了一个泛函，它在最小化时产生满足静电学通常定律的极化电荷密度h（r）。当界面尖锐时，体电荷密度的初始泛函退化为表面极化电荷密度的泛函。首先示出的变分过程提供了一个优雅的系统的解决方案的情况下，非常简单的几何形状，其中解析解是众所周知的。数值实现的变分过程中使用足够的网格进行测试，对精确的结果，在应用该方法的角度，几何上更复杂的情况下，如离子通道通过膜，这是远远超出了分析处理。接触是与生物分子的溶剂化的相关工作，基于极化本身的功能。简要讨论了这两种配方的相对优点和缺点。
This paper provides a pedagogical introduction to a variational formulation of electrostatic interactions between free charges close to a dielectric interface. A functional is constructed which, upon minimization, yields a polarization charge density h(r) which satisfies the usual laws of electrostatics. The initial functional of a volume charge density is shown to reduce to a functional of a surface polarization charge density when the interface between dielectrics is sharp. The variational procedure is first shown to provide an elegant systematic solution in cases with very simple geometries, for which analytic solutions are well known. Numerical implementations of the variational procedure using adequate grids are tested against exact results, in the perspective of applying the method to geometrically more complex situations, like ion channels through membranes, which are well beyond analytic treatment. Contact is made with related work on the solvation of biomolecules, based on a functional of the polarization itself. The relative advantages and shortcomings of the two formulations are briefly discussed.