Digital simulations techniques

The convolution-deconvolution voltammetry, combined with digital simulation techniques, was applied [36] to determine the electrochemical and chemical parameters for the Cd(II)/Cd(Hg) system in aqueous NaNOs solution. The agreement between experimental and theoretical data indicated that the reduction mechanism at the mercury electrode proceeds via consisting in chemical step (C) followed by charge transfer step (E)-so-called CE mechanism [37]. 

To model this method using digital simulation techniques, one need only change the electrode boundary conditions after some predetermined number of time iterations (representing tf) have taken place. The electrode boundary conditions become... 

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... 

Dimerizations, which yield nonlinear partial differential equations if treated rigorously, may be handled with ease using digital simulation techniques. In this case the reaction... 

Digital simulation techniques allow the conclusion that the cyclic voltammetry data is consistent with mechanism that is first order in CO and first order in... 

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... 

Note that this equation is the same as (12.3.29). This limiting current holds only in the region of small (o. When A (= b C lcS) becomes small, the behavior approaches the mass-transfer-controlled limiting current. Results of a digital simulation of the catalytic case (83) are shown in Figure 12.4.3. Other treatments of the ErCj case at the RDE, as well as variations of this mechanism, have also appeared (84-86). The treatment of the Ej-CJ case for the RRDE by digital simulation techniques showed that the results (i.e., plots of Nk vs. XKT) are indistinguishable from those of the Ej-Ci case for first- or pseudo-first-order reactions (83). 

The above discussion assumes the condition [S] Ks- When the dependence of [S] on the catalytic current is to be studied, the bulk concentration of S, [S], must be lowered. Under such conditions, however, no steady-state current is observed on CVs as shown by curve (b). This is because the substrate depression occurs in the vicinity of the electrode surface, and no steady state is attained. A digital simulation technique [12] would be the most straightforward way to analyze such nonsteady-state currents or [Sj dependence of the catalytic current [13-15]. Substrate depression can be avoided when two enzyme reactions are coupled in mediated bioelectrocatalysis in such a way that S in the first enzyme reaction is regenerated from the product P by the second enzyme reaction to keep the S/P ratio constant [16]. Under such conditions, the steady-state limiting current can be given by [16,17]... 

In the investigation of electrochemical mechanisms, the use of digital simulation techniques opens new routes to the determination of kinetic parameters that would be difficuh to obtain otherwise [1,2]. Within our electrochemical studies of hydride complexes, we have recognized, by cyclic voltammetry, the possible involvement of several redox couples with one or more... 

X = 00 and the initial conditions will be expressed by the usual equations. In order to obtain ic and id. Equations (4) and (5) have been solved by a digital simulation technique. ... 

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