The Calculus of Boundary Variations and the Dielectric Boundary Force in the Poisson–Boltzmann Theory for Molecular Solvation
The Calculus of Boundary Variations and the Dielectric Boundary Force in the Poisson–Boltzmann Theory for Molecular Solvation
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DOI：
10.1007/s00332-021-09749-7
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发表时间：
2020-10
影响因子：
3
通讯作者：
Bo Li;Zhengfang Zhang;Shenggao Zhou
中科院分区：
文献类型：
--
作者：
Bo Li;Zhengfang Zhang;Shenggao Zhou
在带电分子在水溶液中溶剂化的连续介质模型中，离子溶液静电学的经典Poisson-Boltzmann(PB)理论被推广到包括溶质点电荷和分隔高介电质和低介电溶质的介电边界。在这样的设置下，我们构造了有效的离子浓度的静电自由能泛函。泛函允许唯一的极小元，其对应的静电势是非线性介质边界PB方程边值问题的唯一解。该最小自由能相对于介质边界变化的负第一变化定义了介质边界力的法向分量。与溶质-溶剂界面张力和范德华相互作用力一起，这种边界力驱动带电分子体系达到稳定的平衡，如变分隐式溶剂模型所描述的那样。我们发展了边界变分理论，并导出了介质边界力的显式公式。我们的结果与分子水平的预测一致，即静电作用力从高介电性的水溶液指向低介电性的带电分子。我们的分析方法是通用的，因为它不依赖于任何变分原理。
In a continuum model of the solvation of charged molecules in an aqueous solvent, the classical Poisson–Boltzmann (PB) theory for the electrostatics of an ionic solution is generalized to include the solute point charges and the dielectric boundary that separates the high-dielectric solvent from the low-dielectric solutes. With such a setting, we construct an effective electrostatic free-energy functional of ionic concentrations. The functional admits a unique minimizer whose corresponding electrostatic potential is the unique solution to the boundary-value problem of the nonlinear dielectric boundary PB equation. The negative first variation of this minimum free energy with respect to variations of the dielectric boundary defines the normal component of the dielectric boundary force. Together with the solute–solvent interfacial tension and van der Waals interaction forces, such boundary force drives an underlying charged molecular system to a stable equilibrium, as described by a variational implicit-solvent model. We develop an-theory for boundary variations and derive an explicit formula of the dielectric boundary force. Our results agree with a molecular-level prediction that the electrostatic force points from the high-dielectric aqueous solvent to the low-dielectric charged molecules. Our method of analysis is general as it does not rely on any variational principles.