Frumkin, double layer correction

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. 

The effect of the phospholipids on the rate of ion transfer has been controversial over the last years. While the early studies found a retardation effect [6-8], more recent ones reported that the rate of ion transfer is either not retarded [9,10] or even enhanced due to the presence of the monolayer [11 14]. Furthermore, the theoretical efforts to explain this effect were unsatisfactory. The retardation observed in the early studies was explained in terms of the blocking of the interfacial area by the phospholipids, and therefore was related to the size of the transferring ion and the state of the monolayer [8,15]. The enhancement observed in the following years was attributed to electrical double layer effects, but a Frumkin-type correction to the Butler Volmer (BV) equation was found unsuitable to explain the observations [11,16]. Recently, Manzanares et al. showed that the enhancement can be described by an electrical double layer correction provided that an accurate picture of the electrical double layer structure is used [17]. This theoretical approach will be the subject of Section III.C. 

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... 

When an ion from the supporting electrolyte (e.g.. Cl or I ) is specifically adsorbed, 02 is perturbed from the value calculated strictly from diffuse double-layer corrections. Specific adsorption of an anion will cause 02 to be more negative, while specific adsorption of a cation will cause 02 to be more positive. In principle, these effects could be taken into account using the Frumkin correction factor however, the location of the plane of closest approach for the reacting species and the actual potential at the OHP often cannot be defined, and qualitative, rather than quantitative, explanations of these effects are usually given. Specific adsorption of an ion may also result in blocking of the electrode surface, as discussed in Section 13.6, and may inhibit the reaction, independent of the 02 effect. Consider the case of the polarographic reduction of CrO at the DME. Because z = — 2, the rate of reaction is very sensitive to 02 effects (68). The addition of quaternary... 

Looking back one can easily notice that before mid 1960s the thermodynamics of adsorption phenomena on platinum was considered mostly in terms of temperature dependence. This traditional approach was not specific for electrochemical thermodynamics, but there was no serious basis to involve other parameters. Another remarkable point is discussion exclusively in terms of hydrogen adsorption, imder more or less transparently formulated assumption of complete charge transfer with formation of uncharged adatom. It is shghtly strange future surface thermodynamics was outlined already in 1936, and its principal point was the interplay of ionic and atomic adsorption, but even 30 years later ionic contribution was still accounted only as very formal subtraction (double layer correction). When the idea of this interplay was first presented by Frumkin in more comprehensive form, it met immediately Breiter s support. ... 

An interesting conflict arises between the implications of MD electrode kinetics and the derivation of what has become to be known as Frumkin s double-layer correction. Frumkin s derivation has remained essentially unchanged over the years between its first presentation in 1933 and, for instance, that of 1961 in Advances in Electrochemistry and Electrochemical Engineering. It can be summarized as follows, for the case of hydrogen overtension and assuming ideality ... 

When analyzing kinetic data for ion-transfer reactions, some groups used different corrections such as the Frumkin correction for the double-layer effects, or the Levich correction for the double-layer corrections under Nernst-Planck transport as proposed by Samec et al. [102]. These corrections have been thoroughly discussed by Murtomaki et al. who have clearly shown that the Frumkin correction can be used for equilibrium measurements, and the Levich correction must be used under faradaic conditions [103]. 

In the crudest approximation, the effect of the efectrical double layer on electron transfer is taken into account by introduction of the electrostatic energy -e /i of the electron in the acceptor into the free energy of the transition AF [Frumkin correction see Eq. (34.25)], so that corrected Tafel plots are obtained in the coordinates In i vs. e(E - /i). Here /i is the average electric potential at the site of location of the acceptor ion. It depends on the concentration of supporting electrolyte and is small at large concentrations. Such approach implies in fact that the reacting ion represents a probe ion (i.e., it does not disturb the electric held distribution). 

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... 

In the treatment of the kinetics of the electron transfer illustrated in Section 4.1, it has been assumed that the propulsive force for the electron transfer was the electrochemical potential E i.e. a quantity directly related to 4>M — < >s). However, since the solvated ions cannot enter the inner layer of the double layer (IHP), the true propulsive force should be < )M — standard rate constant, k°, and the exchange current, i0, should become respectively ... 

Consider a system in which a potential difference AV, in general different from the equilibrium potential between the two phases A 0, is applied from an external source to the phase boundary between two immiscible electrolyte solutions. Then an electric current is passed, which in the simplest case corresponds to the transfer of a single kind of ion across the phase boundary. Assume that the Butler-Volmer equation for the rate of an electrode reaction (see p. 255 of [18]) can also be used for charge transfer across the phase boundary between two electrolytes (cf. [16, 19]). It is mostly assumed (in the framework of the Frumkin correction) that only the potential difference in the compact part of the double layer affects the actual charge transfer, so that it follows for the current density in our system that... 

The double-layer influence on the electrode reaction of Zn(II)/Zn(Hg) on DME in NaNOs solutions was studied in the concentration range from 0.01 to 1 M, using dc and ac polarography [30]. The apparent rate constants of the Zn(II)/Zn(Hg) system increase with dilution of the NaN03 supporting electrolyte. However, after the Frumkin correction, the rate constant was virtually independent of the supporting electrolyte concentration. 

The static - double-layer effect has been accounted for by assuming an equilibrium ionic distribution up to the positions located close to the interface in phases w and o, respectively, presumably at the corresponding outer Helmholtz plane (-> Frumkin correction) [iii], see also -> Verwey-Niessen model. Significance of the Frumkin correction was discussed critically to show that it applies only at equilibrium, that is, in the absence of faradaic current [vi]. Instead, the dynamic Levich correction should be used if the system is not at equilibrium [vi, vii]. Theoretical description of the ion transfer has remained a matter of continuing discussion. It has not been clear whether ion transfer across ITIES is better described as an activated (Butler-Volmer) process [viii], as a mass transport (Nernst-Planck) phenomenon [ix, x], or as a combination of both [xi]. Evidence has been also provided that the Frumkin correction overestimates the effect of electric double layer [xii]. Molecular dynamics (MD) computer simulations highlighted the dynamic role of the water protrusions (fingers) and friction effects [xiii, xiv], which has been further studied theoretically [xv,xvi]. 

All these findings may point to limitations of the classical Frumkin model for correction of the double-layer influence on electrode kinetics in nonaqueous solvents, although it works well in aqueous solution. In the present author s opinion these rather surprising results may follow from some kind of compensation effects. For instance, ion-pair formation in these solutions by decreasing the effective charge of the reactant could reduce the double-layer effect. 

We conclude that, in view of the unequivocal existence of the diffuse double layer at the ITIES, the Frumkin-type correction appears to be a plausible working hypothesis, though its unambiguous proof has not been provided yet. A more advanced approach, which relies on solving the Nernst-Planck equation in the space charge region, has been developed by Matsuda and Delahay [164]. 

In mixed (0.8 - x) M NaClO4 + x M NaF supporting electrolyte the electroreduction of Cd(II) was also studied by Saakes etal. [25]. The kinetic parameters were analyzed using CEE mechanism. The obtained chemical rate constants at both steps, fcg 1 and fcg 2, decreased with increasing NaF concentration. The data were corrected for nonspecific double-layer effect (Frumkin correction). The interpretation of CEE mechanism with parallel pathways connected with coexisting cadmium complexes was presented. 

TABLE 13.7.2 Double-Layer Data for Mercury Electrode in NaF Solutions and Frumkin Correction Factors for Several Cases"... 

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]. 

This has been done in the works by Frumkin and Nikolaeva-Fedorovich et al., which will be discussed in Section 4.3. In particular. Figure 25 in that section suggests that the marked differences in the kinetics of persulfate reduction on various metals are associated with the differences in the structure of the double layer on these metals. After the data are corrected for the lAi effect, the rate of the process on most diverse metals becomes the same. 

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... 

Figure 2.5 demonstrates the difference in driven potential between a well-supported and weakly supported solution. The consequent difference in the perceived rate of reaction is given by the Frumkin correction as calculated from the difference in driving forces (indicated in the figure), as well as altered concentrations in the double layer. The derivation is discussed in Problem 2.10. 

In 1939, while carrying out ac measurements in dilute electrolyte solutions, Frumkin and M. A. Vorsina [12] discovered an unexpected minimum in the differential capacitance curves of mercury. They correctly associated this minimum with the behavior of the diffuse part of the double layer in the vicinity of the zero charge potential. 

In 1933, Fmmkin [14] became the first person to relate the rate of an electrode process to the stmcture of the double layer, by taking into account an effect which he called the psi-prime (i/rj) effect (now universally referred to as the Frumkin correction ). Thus, a close relationship was established between the two great divisions of electrochemistry, namely the double layer and electrode kinetics. 

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