Abstract Electrodialysis, reverse electrodialysis, and related electrochemical processes are increasingly important technologies for water purification and renewable energy generation and storage, respectively. The electrical efficiency of these processes is directly related to the permselectivity of the ion exchange membranes (IEMs) – defined as the extent to which the membrane permits the passage of counter-ions (ions of opposite charge to the membrane, e.g., cations for cation exchange membrane) while blocking passage of co-ions. Permselectivity is not a material constant, but rather depends on the concentration and composition of the electrolyte solutions in contact with the IEM. Thus, even though permselectivity is routinely measured at standardized conditions (usually 0.5 M/0.1 M NaCl or KCl), the practical utility of such data is limited because we lack an accurate, quantitative way of using it to predict permselectivity under relevant process conditions. Moreover, the concentration dependence of IEM permselectivity has historically been studied primarily by evaluating the performance of (reverse) electrodialysis stacks rather than individual membranes, which has made it difficult to relate the concentration dependence of permselectivity to specific membrane characteristics. In this study, we measured the permselectivity of four commercial IEMs in six different concentration gradients employing 4 M and 0.5 M NaCl as the high salt concentration. We then constructed a predictive model of membrane permselectivity based on the extended Nernst-Planck equation and investigated how accounting for convection and electrostatic effects (via Manning's counter-ion condensation theory) affected model accuracy. We demonstrate that accurate, quantitative predictions of IEM permselectivity as a function of external salt concentrations are possible and require knowledge of only four easily measured membrane properties: water uptake, water permeability, charge, and thickness.

中文翻译：

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离子交换膜选择性渗透率的浓度依赖性建模和验证：对流和曼宁反离子凝聚理论的意义

摘要 电渗析、反电渗析和相关的电化学过程分别是水净化和可再生能源生产和储存越来越重要的技术。这些过程的电效率与离子交换膜 (IEM) 的选择性渗透率直接相关 - 定义为膜允许反离子（与膜具有相反电荷的离子，例如阳离子对阳离子）通过的程度交换膜），同时阻止共离子通过。选择性渗透率不是材料常数，而是取决于与 IEM 接触的电解质溶液的浓度和组成。因此，即使在标准化条件（通常为 0.5 M/0.1 M NaCl 或 KCl）下常规测量渗透选择性，这些数据的实际效用是有限的，因为我们缺乏一种准确、定量的方法来使用它来预测相关工艺条件下的渗透选择性。此外，IEM 选择性渗透性的浓度依赖性历来主要通过评估（反向）电渗析堆栈的性能而不是单个膜的性能来研究，这使得很难将选择性渗透性的浓度依赖性与特定的膜特性联系起来。在这项研究中，我们使用 4 M 和 0.5 M NaCl 作为高盐浓度，测量了四种商业 IEM 在六种不同浓度梯度下的渗透选择性。然后，我们基于扩展的 Nernst-Planck 方程构建了一个膜选择性渗透率的预测模型，并研究了对流和静电效应（通过曼宁的反离子冷凝理论）如何影响模型精度。我们证明了作为外部盐浓度函数的 IEM 渗透选择性的准确、定量预测是可能的，并且只需要了解四种易于测量的膜特性：吸水率、透水率、电荷和厚度。