Randles-Sevcik expression

The peak currents (7 and I ) are equal for a reversible process, and at 25 °C are described by the Randles-Sevcik expression ... 

Many years ago, a theoretical expression for the peak current for a reversible cyclic voltammogram was derived as a function of the scan rate to give the Randles-Sevcik expression [50] (Eq. n.1.11). According to this relationship, the dependence of the peak current. Ip, on scan rate, v, follows a characteristic square-root law, which provides a tell-tale sign of the presence of a diffusion-controlled process. 

Table II.1.2 Randles-Sevcik expressions (see Eq. II.1.15) for reversible electron transfer and commonly used electrode geometries [11, 63-65]...

Cyclic voltammograms for the case of a transition from reversible to irreversible characteristics are shown in Fig. II. 1.18. It can be seen that the peak current for the current response in the forward direction decreases as the peak is shifted to more positive potentials. The Randles-Sevcik expression for the irreversible electrochemical response is different to the reversible case by a factor 0.351/0.446 (see Fig. 11.1.18a) or 0.496(of) /0.446 taking account of the change in wave shape (Eq. II. 1.17). 

The analytical solution of the transient diffusion problem of selective anodic dissolution of a binary alloy in the potentiodynamic polarization mode allowed us to obtain the equations for the concentration profiles of an electronegative metal in an alloy, voltammograms as well as modified Randles-Sevcik expressions, taking into accoimt the mixed solid-liquid phase diffusion nature of the kinetic limitations of the process, equilibrium solid phase adsorption of the components, and surface roughness of an electrode. 

As reversible ion transfer reactions are diffusion controlled, the mass transport to the interface is given by Fick s second law, which may be directly integrated with the Nernst equation as a boundary condition (see, for instance. Ref. 230 232). A solution for the interfacial concentrations may be obtained, and the maximum forward peak may then be expressed as a function of the interfacial area A, of the potential scan rate v, of the bulk concentration of the ion under study Cj and of its diffusion coefficient D". This leads to the Randles Sevcik equation [233] ... 

Such an expression is called the Randles-Sevcik equation. 

In this equation a denotes the - transfer coefficient and n is the number of electrons transferred in the ratedetermining reaction step. All Randles-Sevcik-type expressions have in common a 7p oc s/d dependence which is indicative of diffusion control [iii]. 

The usual expressions for the current peak-height in cyclic voltammetry (CV) (such as the Randles-Sevcik equation) are simply inserted into Eq. (40) to obtain the corresponding DCVA relations. 

Oldham KB (1979) Analytical expressions for the reversible Randles-Sevcik function. J Electroanal Chem 105 373. 

The quantitative information regarding the concentration of electroactive(s) com-pound(s) can be obtained from the voltammogram using the Randles-Sevcik equation, for the case of a reversible reaction. This equation expresses the relationship between the peak current intensity /p (either anode or cathode) and the analyte concentration (C) at a given absolute temperature (T, in Kelvin or Rankine) and is given by... 

Provided Sevcik-Randles equation is valid for the first reduction peak, the logarithmic expression, if sweep rate and concentration are constant, can be written... 

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