经典极限电流及以上的电化学薄膜
Electrochemical Thin Films At and Above the Classical Limiting Current
摘要：
我们研究了一个模型电化学薄膜在直流电流超过经典的扩散限制值。数学问题涉及稳定的Poisson-Nernst-Planck方程的二元电解质与非线性边界条件的反应动力学和斯特恩层电容，以及积分约束的阴离子的数量。在极限电流下，我们发现阴极处有一个嵌套的边界层结构，这是反应边界条件所要求的。在极限电流以上，阴离子的耗尽通常表征电池的阴极侧。在这个制度中，我们推导出领先的顺序渐近近似的（一）经典的散装空间电荷层和（二）另一个嵌套的高度带电的边界层在阴极。前者涉及一个精确的解决方案，能斯特-普朗克方程的一个单一的，未屏蔽的离子物种，这可能适用于更普遍的法拉第传导通过非常薄的绝缘膜。通过匹配展开，我们得到的电流-电压关系以及空间电荷制度。在整个分析过程中，我们强调斯特恩层电容对细胞行为的强烈影响。
英文摘要：
We study a model electrochemical thin film at dc currents exceeding the classical diffusion-limited value. The mathematical problem involves the steady Poisson-Nernst-Planck equations for a binary electrolyte with nonlinear boundary conditions for reaction kinetics and Stern-layer capacitance, as well as an integral constraint on the number of anions. At the limiting current, we find a nested boundary layer structure at the cathode, which is required by the reaction boundary condition. Above the limiting current, a depletion of anions generally characterizes the cathode side of the cell. In this regime, we derive leading-order asymptotic approximations for the (i) classical bulk space-charge layer and (ii) another, nested highly charged boundary layer at the cathode. The former involves an exact solution to the Nernst-Planck equations for a single, unscreened ionic species, which may apply more generally to Faradaic conduction through very thin insulating films. By matching expansions, we derive current-voltage relations well into the space-charge regime. Throughout our analysis, we emphasize the strong influence of the Stern-layer capacitance on cell behavior.
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