Abstract

Electrodiffusion coefficient and diffusion permeability of an ion-exchange membrane have been calculated as the kinetic coefficients of the Onsager matrix in terms of the thermodynamics of nonequilibrium processes and on the basis of the cell model proposed previously by the author for charged membranes. The membrane is assumed to consist of an ordered set of spherical porous charged particles placed into spherical shells filled with a binary electrolyte solution. Boundary value problems have been analytically solved to determine the diffusion permeability and electrodiffusion coefficient of such a membrane under the Kuwabara boundary condition imposed on the cell surface. The consideration has been realized within the framework of small deviations of system parameters from their equilibrium values under action of external fields. Different particular cases of the obtained exact analytical equations have been studied including the case of a binary symmetric electrolyte and an ideally selective membrane. It has been shown that, as electrolyte concentration increases, the cationic membrane electrodiffusion coefficient, which governs diffusion current density at a preset electrolyte concentration difference or salt flux density at a preset electric potential difference, may, similarly to the specific conductivity, either monotonically increase from zero (with or without an inflection point in a curve), or decrease after reaching a maximum at low electrolyte concentrations. As the electrolyte concentration grows, the behavior of the integral diffusion permeability coefficient (in the absence of current) depends on the relation between the physicochemical and geometric parameters of the system and may vary from a monotonic growth or a monotonic decrease throughout the concentration range to a drop of an extremal dependence with reaching a maximum or a minimum. This behavior has been confirmed experimentally.

中文翻译：

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离子交换膜的细胞模型。电扩散系数和扩散渗透率

摘要

离子交换膜的电扩散系数和扩散渗透率已根据非平衡过程的热力学计算为 Onsager 矩阵的动力学系数，并基于作者先前为带电膜提出的细胞模型。假定该膜由一组有序的球形多孔带电粒子组成，这些粒子置于填充有二元电解质溶液的球壳中。边界值问题已被解析解决，以确定这种膜在施加在细胞表面上的桑原边界条件下的扩散渗透率和电扩散系数。该考虑是在外部场作用下系统参数与其平衡值的小偏差框架内实现的。已经研究了获得的精确分析方程的不同特殊情况，包括二元对称电解质和理想选择性膜的情况。已经表明，随着电解质浓度的增加，与比电导率类似，控制预设电解质浓度差下的扩散电流密度或预设电势差下的盐通量密度的阳离子膜电扩散系数可能会单调增加从零（曲线中有或没有拐点），或在低电解质浓度下达到最大值后降低。随着电解质浓度的增加，积分扩散渗透系数的行为（在没有电流的情况下）取决于系统的物理化学和几何参数之间的关系，并且可能会在整个浓度范围内从单调增长或单调减少到极值依赖性的下降而变化达到最大值或最小值。这种行为已被实验证实。