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.

The Mathematics of Diffusion

Introduction. Basic Equations. Approximations to Derivatives. Ordinary Differential Equations. The Explicit Method. Boundary Conditions. Unequal Intervals. The Commonly Used Implicit Methods. Other Methods. Adsorption. Effects Due to Uncompensated Resistance and Capacitance. Two-Dimensional Systems. Convection. Performance. Programming. Simulation Packages. Some Mathematical Proofs. Useful Procedures. Example Programs.

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Eine Näherungsmethode zur Auflösung Volterrascher Integralgleichungen

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Eine Näherungsmethode zur Auflösung Volterrascher Integralgleichungen