大交流电压下电解质的强非线性动力学
Strongly nonlinear dynamics of electrolytes in large ac voltages
摘要：
我们研究了一个模型微型电化学电池的响应，以一个大的交流电压的频率相媲美的逆细胞弛豫时间。为了揭示基本的物理学，我们考虑了限制在平行板阻挡电极之间的对称二元电解质的最简单的可能模型，忽略了任何横向不稳定性或流体流动。我们分析所产生的一维问题，通过匹配的渐近展开在薄双层的极限和扩展以前的工作到强非线性制度，其特征在于两个新的功能-显着的盐耗尽在电极附近的电解质，在非常大的电压，击穿的准平衡结构的双层。前者导致“交流电容脱盐”的预测，因为有一个时间平均转移的盐从散装的双层，通过振荡扩散层。后者与瞬态扩散限制相关，其驱动空间电荷层的形成和崩溃，即使在没有任何净法拉第电流通过电池的情况下。我们还预测，空间效应的有限离子尺寸（超越稀溶液理论）的行为，以抑制强非线性制度的限制，浓缩电解质，离子液体和熔融盐。除了模型问题，我们的薄双层简化方程，一致有效的匹配渐近展开的基础上，提供了一个有用的数学框架来描述额外的非线性响应大交流电压，如法拉第反应，电渗不稳定性，和感应电荷电动现象。
英文摘要：
We study the response of a model micro-electrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow. We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two novel features - significant salt depletion in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasi-equilibrium structure of the double layers. The former leads to the prediction of "ac capacitive desalination", since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and collapse of space-charge layers, even in the absence of any net Faradaic current through the cell. We also predict that steric effects of finite ion sizes (going beyond dilute solution theory) act to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena.
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