Bazant Martin Z
Department of Chemical Engineering and Department of Mathematics, Massachusetts Institute of Technology, Cambridge 02139, MA, USA.
Faraday Discuss. 2023 Oct 12;246(0):60-124. doi: 10.1039/d3fd00108c.
A general theory of coupled ion-electron transfer (CIET) is presented, which unifies Marcus kinetics of electron transfer (ET) with Butler-Volmer kinetics of ion transfer (IT). In the limit of large reorganization energy, the theory predicts normal Marcus kinetics of "electron-coupled ion transfer" (ECIT). In the limit of large ion transfer energies, the theory predicts Butler-Volmer kinetics of "ion-coupled electron transfer" (ICET), where the charge transfer coefficient and exchange current are connected to microscopic properties of the electrode/electrolyte interface. In the ICET regime, the reductive and oxidative branches of Tafel's law are predicted to hold over a wide range of overpotentials, bounded by the ion-transfer energies for oxidation and reduction, respectively. The probability distribution of transferring electron energies in CIET smoothly interpolates between a shifted Gaussian distribution for ECIT (as in the Gerischer-Marcus theory of ET) to an asymmetric, fat-tailed Meixner distribution centered at the Fermi level for ICET. The latter may help interpret asymmetric line shapes in x-ray photo-electron spectroscopy (XPS) and Auger electron spectroscopy (AES) for metal surfaces in terms of shake-up relaxation of the ionized atom and its image polaron by ICET. In the limit of large overpotentials, the theory predicts a transition to inverted Marcus ECIT, leading to a universal reaction-limited current for metal electrodes, dominated by barrierless quantum transitions. Uniformly valid, closed-form asymptotic approximations are derived that smoothly transition between the limiting rate expressions for ICET and ECIT for metal electrodes, using simple but accurate mathematical functions. The theory is applied to lithium intercalation in lithium iron phosphate (LFP) and found to provide a consistent description of the observed current dependence on overpotential, temperature and concentration. CIET theory thus provides a critical bridge between quantum electrochemistry and electrochemical engineering, which may find many other applications and extensions.
本文提出了一种耦合离子-电子转移（CIET）的通用理论，该理论将电子转移（ET）的马库斯动力学与离子转移（IT）的巴特勒-沃尔默动力学统一起来。在重组能较大的极限情况下，该理论预测了“电子耦合离子转移”（ECIT）的正常马库斯动力学。在离子转移能量较大的极限情况下，该理论预测了“离子耦合电子转移”（ICET）的巴特勒-沃尔默动力学，其中电荷转移系数和交换电流与电极/电解质界面的微观性质相关。在ICET区域，预计塔菲尔定律的还原和氧化分支在很宽的过电位范围内成立，分别由氧化和还原的离子转移能量界定。CIET中转移电子能量的概率分布在ECIT的移位高斯分布（如ET的格里舍尔-马库斯理论）到ICET的以费米能级为中心的不对称、肥尾迈克斯纳分布之间平滑插值。后者可能有助于根据ICET对电离原子及其镜像极化子的振激弛豫来解释金属表面的X射线光电子能谱（XPS）和俄歇电子能谱（AES）中的不对称线形。在过电位较大的极限情况下，该理论预测向反向马库斯ECIT的转变，导致金属电极的通用反应限制电流，由无障碍量子跃迁主导。利用简单但精确的数学函数，推导出了在金属电极的ICET和ECIT的极限速率表达式之间平滑过渡的统一有效、封闭形式的渐近近似。该理论应用于磷酸铁锂（LFP）中的锂嵌入，发现它能对观察到的电流对过电位、温度和浓度的依赖性提供一致的描述。因此，CIET理论为量子电化学和电化学工程之间提供了一座关键的桥梁，可能会有许多其他应用和扩展。
