Double layer theories Frumkin

Finally, it should be noted that non-Butler-Volmer behaviour may be observed in the analysis of cyclic voltammetric data. For example, particularly in the presence of low concentrations of supporting electrolyte, electron transfer kinetics of charged species may be significantly modified due to the double layer or Frumkin effects [79]. Under these conditions, (i) the potential experienced by the reactant at the point of closest approach to the electrode can be different from the applied potential, and (ii) an additional energy barrier for the approach of charged reactants to the electrode may exist. Corrections to account for Frumkin effects have been proposed. Deviations from Butler-Volmer behaviour may also be interpreted in terms of the Marcus theory [80]. A further interesting case of non-Butler-Volmer voltammetric characteristics is observed with semiconducting elecfrode materials [81]. 

The Frumkin theory of the effect of the electrical double layer on the rate of the electrode reaction is a gross simplification. For example, the electrode reaction does not occur only at the outer Helmholtz plane but also at a somewhat greater distance from the electrode surface. More detailed considerations indicate, however, that Eq. (5.3.20) can still be used to describe the effect of the electrical double layer as a good approximation. 

The values of k°a have been corrected for the double layer in a KC1 medium (as 2 data were available only in this medium) by applying the Frumkin theory. They are given in Table 6. 

The ka values in chloride, bromide, and percholate media have been corrected by applying the Frumkin theory for the double-layer... 

The k°a values in KF, KC1, and KBr have been corrected by applying the Frumkin theory for the double-layer correction as cf>2 data were available in the literature for these media. The k°t values obtained in Cl and Br media correspond to CdCl+ and CdBr complexes, respectively, as they correlate93 with corrected values... 

These modifications are known as the Frumkin double-layer corrections. They are useful when the electrolyte concentration is sufficiently low, so that fa can be calculated from Gouy-Chapman theory, and the uncertainty in the position of the reaction site is unimportant. Whenever possible, kinetic investigations should be carried out with a high concentration of supporting electrolyte, so that double-layer corrections can be avoided. 

As was mentioned in the introduction, Frumkin and his group [Kuchinsky et al. (107) and Frumkin et al. (10 )] proposed an electrochemical theory, according to which the adsorption of electrolytes by carbon would be determined by the electrical potential at the carbon-solution interface, and by the capacity of the double layer. At higher concentrations some physical adsorption of acid might occur in addition. 

Few outer-sphere electrode reactions have precursor-state concentrations that are measurable [21] so that it is usual to estimate wp and ws from double-layer models. The simplest, and by far the most commonly used, treatment is the Frumkin model embodied in eqns. (8) and (8a) whereby, as noted in Sect. 2.2, the sole contributor to wp and ws is presumed to be electrostatic work associated with transporting the reactant from the bulk solution to the o.H.p. at an average potential Gouy-Chapman (GC) theory [58],... 

Modem theory describing the structure of the EDL was developed by G. Gouy, D. Chapman. O. Stem, A. Frumkin, D. Graham and others, and is based on the analysis of the electrostatic interactions between ions in the double layer and comparison of these interactions with the intermolecular interactions and thermal motion of ions [11,17]. 

At first, however, it seemed that the slow discharge theory was irreconcilably at variance with experimental data since in solutions of pure acids the hydrogen overpotential was found to be independent of the acid concentration. This inconsistency was solved in Frumkin s classical work in which he took into consideration the effects of the double-layer structure on the discharge rate. The numerous studies by Frumkin and his coworkers, as well as the work of other electrochemists, that followed, have provided experimental proof of the limited rate of electrode reactions involving transfer of a charge across the metal-solution interface. 

The effect of the double layer on the kinetics is contained within the term xp[(oicn — ZQ)iFA(t>2lRT)], which is known as the Frumkin correction. It is the same for the forward and backward processes in compliance with transition state theory and the importance of the correction depends upon the magnitude and signs of olq, , Zq, and A02- If it is assumed that equilibrium prevails within the diffuse layer even when charge transfer occurs and that the diffusion layer is much thicker than the diffuse layer, then Gouy-Chapman theory can be used to calculate the dependence of 02 on the supporting electrolyte concentration (Equation (5.35)). The combination of these theoretical calculations with experimental o jE data allows the dependence of 02 on potential to be obtained, as shown in Fig. 5.9. The magnitude of A02 depends upon the position of the... 

In 1935, Frumkin and M. A. Proskumin [11] used ac measurements to measure the electric double layer capacitance. This permitted empirical values of the double layer capacitance to be compared rigorously with theory for the first time. The authors were successful because they carried out their experiments under conditions of exceptional cleanliness, such as glassware that had been acid-cleaned and water that had been multiply distilled. This work had an enormous impact internationally, because it demonstrated how reproducible measurements of the electrical double layer could be obtained. Indeed, Frumkin s experimental methods soon became legendary among western scientists. From that time forward, the ac method became the standard method of measuring interfacial capacitance. 

This equation is known as the Frumkin equation, expressing the Frumkin theory. It shows the corrections which have to be made to a current-potential curve because of the presence of the double layer. However, it has two drawbacks. The first is that the site of reaction is identified with the plane of closest approach. In solutions of several components there are several such planes and the reaction site need not necessarily coincide with any of them. The second drawback is that this theory was developed for a simple, one step reaction and cannot be applied generally. However, equation 4.107 does provide us with some understanding of the influence of the value of < o... 

Fig. 7, Differential ca acity of the double layer according to Stern s theory. Capacity of the molecular condenser 3B [iF for positive surface and 20 pF for negative surface. (Taken from A. Frumkin, Trans. Faraday Soc., 36 (1940) 126).

---