The Mathematics of Diffusion
The Mathematics of Diffusion
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DOI：
10.1007/978-1-4613-4145-1_3
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发表时间：
1977
期刊：
影响因子：
--
通讯作者：
D. Macdonald
中科院分区：
文献类型：
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作者：
D. Macdonald
如果由于反应的固有动力学性质或由于大的过电位，电极表面处的电子交换反应足够快，则总反应进行的速率由反应物向电极表面的传输速率或产物从电极表面的传输速率决定。在低过电位下，或者对于本质上慢的电极过程，当求解系统的扩散方程时，必须考虑表面处的电极反应的动力学。在其他情况下，化学反应可能在电荷转移反应之前或之后，在这些情况下，有必要修改扩散方程以识别这些“动力学”过程对系统整体瞬态响应的贡献。由于这种类型的系统的瞬态响应的理论描述需要的表面浓度和通量的时间依赖性，有必要详细考虑各种方法来解决菲克扩散定律。
If the electron exchange reaction at the surface of an electrode is sufficiently fast, either due to the inherent kinetic properties of the reaction or due to large overpotentials, then the rate at which the overall reaction will proceed is determined by the rate of transport of reactant to, or products from, the electrode surface. At low overpotentials, or for intrinsically slow electrode processes, it is necessary to take into account the kinetics of the electrode reaction at the surface when solving the diffusion equation for the system. In other instances, chemical reactions may precede or follow the charge transfer reaction, and in these cases it is necessary to modify the diffusion equations to recognize the contributions from these “kinetic” processes to the overall transient response of the system. Since the theoretical description of the transient responses of systems of this type requires the time dependences of surface concentrations and fluxes, it is necessary to consider in detail various methods for solving Fick’s laws of diffusion.