Randles-Sevcik function

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

According to Eq. (1) the steady-state current across a micro-ITIES is proportional to the bulk concentration of the transferred species. Thus, the micro-ITIES can function as an amperometric ion-selective sensor. Similarly, the peak current in a linear sweep voltam-mogram of ion egress from the micropipette obeys the Randles-Sevcik equation. Both types of measurements can be useful for analysis of small samples [18a]. 

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] ... 

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. 

The observed voltammetry is then a superposition of currents from different Faradaic processes and so care must be taken in discussing peak currents . These are not usually meaningful when compared to a baseline of zero current. Hence, the use of the Randles-Sevcik equations to analyse peak currents in either of the above cases will result in significant errors. As a further point, it should be noted that the size and potential of the reverse peak vary as a function of the switching potential, as highlighted in Fig. 4.3 (unless, for a reversible redox couple, the switching potential is beyond a certain threshold). 

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