Randles-Sevcfk equation

In many cases, some property of the output of the simulation is described by a known analytical or empirically derived expression which can be used to test if the simulation output is correct. The peak current of a cyclic voltammogram is the largest current recorded on the forward sweep. For an electrode process with fully reversible electrode kinetics, the peak current of a voltammogram in amps (A) is given by the Randles-Sevcfk equation [7-9] for a one-electron reversible reduction process ... 

A second metric that can be tested is the forward peak potential relative to the formal potential of the couple, Ep — Aj ). This is the potential at which the peak current is observed to occur. For a reversible process, this is 28.5 mV which in dimensionless units is 6p = 1.11 at 298 K. By comparing the simulation s output with this peak position and with the Randles-Sevcfk equation for a range of values of a, we can test to see if it is correct. Figure 3.3 demonstrates how cyclic voltammetry varies with scan rate and Figure 3.4 demonstrates the agreement between simulated results and the Randles-Sevcfk equation. 

This equation expresses very clearly that the transition through linear and convergent diffusion mainly depends on the value of the sphericity parameter T, that is, on the electrode size, the time scale of the experiment and the diffusivity of the electroactive species. Indeed, in the limit of very fast scan rates, a, independently of the geometry of the electrode the voltammetry will show peaked response with a peak current given by the Randles-Sevcfk equation (see Figure 4.7) ... 

Case 4 behaviour, depicted in Figure 10.4(d), represents the extreme limit of Case 3, where the spacing between adjacent discs is very small, such that there is very strong overlap of neighbouring diffusion fields and d < fDt. In this case, diffusion is linear to the entire surface and the voltammetric response shows a well-defined peak. Perhaps surprisingly, in this limit, the peak current is given by the Randles-Sevcfk equation where A is the total geometric area of the electrode system (active and inert) it is the same as it would be were the entire surface electroactive ... 

A differential equation with these boundary conditions was solved independently by Augustin Sevcfk and John E. B. Randles in 1948. The expression obtained for the current is... 

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