Capacitive deionization (CDI) for water treatment, which relies on the capture of charged species to sustain the electrical double layers (EDLs) established within porous electrodes under an applied electrical potential, can be enhanced by the chemical attachment of fixed charged groups to the porous electrode electrodes (ECDI). It has recently been demonstrated that further improvements in capacity and energy storage can be gained by functionalization of the electrode surfaces with redox polymers in which the charge on the electrodes can be modulated through Faradaic reactions under different cell voltages in a pseudo-capacitive process that can be called “Faradaic CDI” (FaCDI). Here, we extend recent mathematical models developed for the characterization of CDI and ECDI systems to incorporate the redox mediated contributions by allowing for the variable chemical charges generated by reactions in FaCDI. The lumped model developed here assumes the spacer channel is well-mixed with uniform electrosorption in each electrode. We demonstrate that the salt adsorption performance characterization of the fixed chemical charge ECDI and variable chemical charge FaCDI materials can be unified within a common theoretical framework based on the point of zero charge (PZC) of the electrode material. In the latter case the PZC is determined by the equilibrium potentials of the redox couples immobilized on the porous electrodes. The new model is able to predict the experimentally observed enhanced and inverted performance of CDI cells, and illuminates the benefit of choosing redox active materials for water treatment applications. The deionization performance of FaCDI cells is shown to be superior to that of CDI and ECDI systems with equilibrium adsorption capacities 50 to 100% higher than attained with CDI systems, and at smaller cell voltages, depending on the redox potentials of the Faradaic moieties.

用于水处理的电容去离子（CDI）依赖于捕获带电物质，以在施加电势的情况下维持在多孔电极内建立的双电层（EDL），可通过将固定的带电基团化学连接到多孔材料上来增强电极（ECDI）。最近已经证明，通过用氧化还原聚合物对电极表面进行功能化可以进一步提高容量和能量存储，其中可以通过伪电容法在不同电池电压下通过法拉第反应调节电极上的电荷，从而可以被称为“法拉第CDI”（FaCDI）。这里，我们扩展了为表征CDI和ECDI系统而开发的最新数学模型，以通过允许FaCDI中的反应产生的可变化学电荷来纳入氧化还原介导的贡献。此处开发的集总模型假设间隔物通道混合均匀，并且每个电极中的电吸附均匀。我们证明固定化学电荷ECDI和可变化学电荷FaCDI材料的盐吸附性能表征可以在基于电极材料零电荷点（PZC）的通用理论框架内统一。在后一种情况下，PZC由固定在多孔电极上的氧化还原对的平衡电势确定。新模型能够预测通过实验观察到的CDI细胞的增强和反向性能，并阐明了为水处理应用选择氧化还原活性材料的好处。FaCDI电池的去离子性能优于CDI和ECDI系统，其平衡吸附能力比CDI系统高50至100％，并且在较小的电池电压下，取决于法拉第部分的氧化还原电势。