Diffuse charge and Faradaic reactions in porous electrodes
Diffuse charge and Faradaic reactions in porous electrodes
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DOI：
10.1103/physreve.83.061507
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发表时间：
2011-06-23
影响因子：
2.4
通讯作者：
Bazant, Martin Z.
中科院分区：
文献类型：
--
作者：
Biesheuvel, P. M.;Fu, Yeqing;Bazant, Martin Z.
在电化学系统中广泛使用多孔电极代替平板电极，以提高离子和电子的存储容量，改善质量和电荷的传输，并提高反应速率。现有的多孔电极理论作了一些简化的假设：（1）电荷转移速率仅取决于电极基体和孔溶液之间的局部静电势差，而不考虑电极基体和孔溶液之间形成的双电层（DL）结构;（ii）电荷转移速率通常不仅在基质-孔界面的纳米级处等同于盐转移速率，而且在通过电极孔的宏观尺度上也是如此。在本文中，我们扩展了多孔电极理论，包括广义Frumkin-Butler-Volmer模型的法拉第反应动力学，假设电荷转移穿过分子斯特恩层之间的电子传导矩阵相和平面的离子扩散部分的DL最接近。这是一个优雅的和纯粹的局部描述的电荷转移速率，它自洽地确定表面电荷，不需要考虑参考电极或比较与全球平衡。对于DL的描述，我们考虑两个自然限制：（i）与宏观孔尺寸相比，用于薄DL的经典Gouy-Chapman-Stern模型，例如，对于高孔隙率金属泡沫（大孔> 50 nm）和（ii）对于强重叠DL的修改的Donnan模型，例如，多孔活性炭颗粒（微孔< 2 nm）。我们的理论是有效的电解质中的两个离子是移动的，它占电压和浓度的差异，不仅在整个电极的宏观尺度上，而且在本地规模的DL。该模型是足够简单的，使我们能够得到分析近似的稳态和早期瞬态。我们还提出了数值解来验证分析，并说明响应于施加电压的离子密度，孔隙电位，表面电荷和反应速率的演变。
Porous electrodes instead of flat electrodes are widely used in electrochemical systems to boost storage capacities for ions and electrons, to improve the transport of mass and charge, and to enhance reaction rates. Existing porous electrode theories make a number of simplifying assumptions: (i) The charge-transfer rate is assumed to depend only on the local electrostatic potential difference between the electrode matrix and the pore solution, without considering the structure of the double layer (DL) formed in between; (ii) the charge-transfer rate is generally equated with the salt-transfer rate not only at the nanoscale of the matrix-pore interface, but also at the macroscopic scale of transport through the electrode pores. In this paper, we extend porous electrode theory by including the generalized Frumkin-Butler-Volmer model of Faradaic reaction kinetics, which postulates charge transfer across the molecular Stern layer located in between the electron-conducting matrix phase and the plane of closest approach for the ions in the diffuse part of the DL. This is an elegant and purely local description of the charge-transfer rate, which self-consistently determines the surface charge and does not require consideration of reference electrodes or comparison with a global equilibrium. For the description of the DLs, we consider the two natural limits: (i) the classical Gouy-Chapman-Stern model for thin DLs compared to the macroscopic pore dimensions, e.g., for high-porosity metallic foams (macropores > 50 nm) and (ii) a modified Donnan model for strongly overlapping DLs, e.g., for porous activated carbon particles (micropores < 2 nm). Our theory is valid for electrolytes where both ions are mobile, and it accounts for voltage and concentration differences not only on the macroscopic scale of the full electrode, but also on the local scale of the DL. The model is simple enough to allow us to derive analytical approximations for the steady-state and early transients. We also present numerical solutions to validate the analysis and to illustrate the evolution of ion densities, pore potential, surface charge, and reaction rates in response to an applied voltage.