Digital simulations dimensionless parameters

The real power of digital simulation techniques lies in their ability to predict current-potential-time relationships when the reactants or products of an electrode reaction participate in some intervening chemical reaction. These kinetic complications often result in a fairly difficult differential equation (when combined with the conditions for diffusion or convection encountered in electrochemical problems) that resists solution by ordinary means. Through simulation, however, the effect of any number of chemical steps may be predicted. In practice, it is best to limit these predictions to cases where the reactants and products participate in one or two rate-determining steps each independent step adds another dimensionless kinetics parameter that must be varied over the range of... 

In addition, one needs the appropriate i-E characteristic (i.e., for a reversible, totally irreversible, or quasireversible reaction). The resulting nonlinear integral equation must be evaluated numerically. Alternatively, the problem can be addressed by digital simulation techniques. Figures 8.3.1 and 8.3.2 illuminate the effects of different relative contributions of double-layer charging on if (at constant /) and on the E-t curves of a nemstian reaction. The charging contribution is represented there by the dimensionless parameter, K, defined as... 

The solution of this equation would then follow as described in Section 9.4. The modifications of the mass-transfer equations for the different cases generally follow those used in voltammetric methods as shown in Table 12.2.1. Appropriate dimensionless parameters are listed in Table 12.3.1. It is usually not possible to solve these equations analytically, so various approximations (e.g., the reaction layer approach, as described in Section 1.5.2), digital simulations, or other numerical methods must be employed. The behavior of systems at the RDE can be analyzed by means of the zone diagrams employed for voltammetry (Section 12.3) by redefining the parameter A. This is accomplished by re-... 

Figure 6 shows a selection of simulations resulting from digital computer solutions of the three ordinary differential equations which comprised the mathematical model after all assumptions were made. The parameters for this set of six curves of dimensionless temperature versus dimensionless time is the dimensionless rate constant for the reaction between chemisorbed reactants. The interesting point is that the model, relatively innocent and simple in appearance, can yield such complex oscillations, including an apparently chaotic state for case (c). Chang and Aluko have shown simulated complex oscillations from a similar model [61]. 

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