Simulation of Cyclic Voltammetry Using Finite Difference Methods

cussed how cyclic voltammetry could be used to achieve a qualitative understanding of electrochemical mechanisms, particularly those that involve chemical reactions coupled to the electron transfer reaction(s). However, since the effects of mass transport, electron transfer kinetics and the kinetics of coupled chemical reactions on a cyclic voltammogram cannot generally be separated, the extraction of quantitative data from a cyclic voltammogram typically requires comparison of the experimental data with simulated data or predictions of a theoretical model. The simulated data are generated by software that requires input of the reaction mechanism, and the appropriate parameters. One approach that often has been used for calculation of theoretical voltammograms is the method of finite differences (2-5), which is the subject of this paper. Particular reference is made to DigiSim, the BAS simulation program for cyclic voltammetry. Finite difference methods require that the electrochemical experiment be discretized into space and time grids. The space grid is generated by dividing the solution in which concentration changes occur during the experiment into small, discrete volume elements. During the simulation, the concentrations of all the species involved in the electrochemical reaction are calculated for each of the volume elements (F1). Since these concentrations change during the experiment, the concentration calculation must be carried out at many time points during the experiments. Therefore, the electrochemical experiment is described by knowing the concentrations in all the volume elements at each of the selected time points. The accuracy of the simulation depends upon the size of the time and space grids; that is, the number of volume elements and the number of time points. Increasing these numbers increases the accuracy of the simulation, but also increases the time required for the simulation. The selection of these numbers (i.e., how the grids are set up) is discussed in more detail below. The other aspect discussed in this article is the method used for calculation of the concentrations (the explicit and implicit methods), and their advantages and disadvantages.