Sprik Michiel
Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, England, United Kingdom.
Phys Rev E. 2021 Feb;103(2-1):022803. doi: 10.1103/PhysRevE.103.022803.
Mobile charge in an electrolytic solution can in principle be represented as the divergence of ionic polarization. After adding explicit solvent polarization a finite volume of an electrolyte can then be treated as a composite nonuniform dielectric body. Writing the electrostatic interactions as an integral over electric-field energy density we show that the Poisson-Boltzmann functional in this formulation is convex and can be used to derive the equilibrium equations for electric potential and ion concentration by a variational procedure developed by Ericksen for dielectric continua [J. L. Ericksen, Arch. Rational Mech. Anal. 183, 299 (2007)AVRMAW0003-952710.1007/s00205-006-0042-4]. The Maxwell field equations are enforced by extending the set of variational parameters by a vector potential representing the dielectric displacement which is fully transverse in a dielectric system without embedded external charge. The electric-field energy density in this representation is a function of the vector potential and the sum of ionic and solvent polarization making the mutual screening explicit. Transverse polarization is accounted for by construction, lifting the restriction to longitudinal polarization inherent in the electrostatic potential based formulation of Poisson-Boltzmann mean field theory.
原则上，电解液中的移动电荷可表示为离子极化的散度。在加入明确的溶剂极化后，有限体积的电解质可被视为复合非均匀电介质体。将静电相互作用写成电场能量密度的积分形式，我们表明，在此公式中的泊松 - 玻尔兹曼泛函是凸的，并且可以通过埃里克森为电介质连续体开发的变分程序来推导电势和离子浓度的平衡方程[J. L. 埃里克森，《理性力学与分析档案》183, 299 (2007)AVRMAW0003 - 952710.1007/s00205 - 006 - 0042 - 4]。通过引入一个表示电位移的矢量势来扩展变分参数集，从而强制执行麦克斯韦场方程，该矢量势在没有嵌入外部电荷的电介质系统中是完全横向的。在此表示中，电场能量密度是矢量势以及离子和溶剂极化之和的函数，这使得相互屏蔽变得明确。通过构造考虑了横向极化，解除了泊松 - 玻尔兹曼平均场理论基于静电势公式中对纵向极化的限制。
