Response theory, reaction-diffusion process

This mechanism is denoted as an EC mechanism (Testa and Reinmuth, 1961 Bott, 1997). Thus homogeneous kinetic terms may be combined with the expressions for diffusion and convection [i.e. a modified version of (18)] to give the temporal variation of the concentration of a species in an electrode reaction mechanism. In order to model the voltammetric response associated with this mechanism, a knowledge of , a, ko and k is required, or deduced from a theoretical-experimental comparison, and the set of concentrationtime equations for species A, B and C must be solved subject to the constraints of the Butler-Volmer equation and the experimental design. Considerable simplification of the theory is achieved if the kinetics for the forward and reverse processes associated with the E step are fast, which is a good approximation for many organic reactions. Section 7 describes the approaches used to solve the equations associated with electrode reaction mechanisms, thus enabling theoretical simulation of voltammetric responses to be achieved. 

The deviations of the impedance responses [23,28, 30,32, 59,64,66,69,71, 76,120,123,132,144-146] predicted by the theories have been explained by taking into account different effects, such as interactions between redox sites [30, 136], ionic relaxation processes [95], distributions of diffusion coefficients [28], migration [65, 118, 125, 132], film swelling [64, 137], slow reactions with solution species [22,138], nonuniform film thickness [23], inhomogeneous oxida-tion/reduction processes [123], etc. 

Another approach to TG/SC experiments does not rely on the mediator feedback [56]. The reactant galvanostatically electrogenerated at the tip diffuses to the substrate and undergoes the reaction of interest at its surface. The substrate current is recorded as a function of either time or the tip/ substrate separation distance (approach cnrves). The theory for transient responses, steady-state TG/SC approach curves, and polarization cnrves (i.e., 4 vs. E ) was generated solving the diffnsion problem numerically (an explicit finite difference method was used). The substrate process was treated as a first-order irreversible reaction, and the effects of its rate constant and the experimental parameters were illnstrated by families of the dimensionless working curves (Figure 5.11). 

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