Frumkin corrections

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). 

By means of the Frumkin correction, identical Tafel diagrams for different media are obtained. 

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 Frumkin epoch in electrochemistry [i-iii] commemorates the interplay of electrochemical kinetics and equilibrium interfacial phenomena. The most famous findings are the - Frumkin adsorption isotherm (1925) Frumkin s slow discharge theory (1933, see also - Frumkin correction), the rotating ring disk electrode (1959), and various aspects of surface thermodynamics related to the notion of the point of zero charge. His contributions to the theory of polarographic maxima, kinetics of multi-step electrode reactions, and corrosion science are also well-known. An important feature of the Frumkin school was the development of numerous original experimental techniques for certain problems. The Frumkin school also pioneered the experimental style of ultra-pure conditions in electrochemical experiments [i]. A list of publications of Frumkin until 1965 is available in [iv], and later publications are listed in [ii]. 

The classical version of Frumkin correction includes the initial procedure of Zq determination [iii] from the dependence of current density on the supporting electrolyte concentration at constant electrode charge. 

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]. 

The apparent rate constant k was expressed [60] by an equation which is equivalent to the classical Frumkin correction ... 

Provided the exponential term in Eq. (113), called the Frumkin correction, is invariant with E, that is, when electrode potential, both are constant and characterize the R/P electron transfer independently of the electrode potential. Otherwise kf is preferred. In the following we nevertheless use k for simplicity in the formulations. 

Conducting (via electrons or via permeation of electroactive species) adsorbed species usually introduce small disturbances in electrochemical behavior compared with the former class. Yet obviously the diffuse layer is extremely affected vis-a-vis the bare electrode. Thus the rate constants k° may be modified to a high degree because of large changes in the Frumkin correction. Such effects may easily explain, at least on a qualitative basis, the well-known dependence of k° on the size of the supporting electrolyte cation (reductions) or anion (oxidations), as well as on ionic additives [89]. 

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. 

This important relationship, in which the exponential term is sometimes called the Frumkin correction, allows the calculation of the true (or corrected) standard rate constant from the apparent one k. In a similar way, a true exchange current, can be defined as in (3.4.6) ... 

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

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... 

The Frumkin correction in Eq. (24) reduces the EDL structure effect to its single characteristic, i/ i potential, whde real reactants represent a distribution of electric charges. A recent development has taken into account this distribution in the calculation of the work term, so that it depends on the whole profile of the potential across the EDL. Besides, the presence of the reactant perturbs this potential profile in the vicinity of the species (a kind of discreteness-of-charge effects [48] discussed in Sect. 2.1.11.3), due to both the field created by its charges and the cavity effects arising from the replacement of solvent molecules in the volume occupied by the solute species [63, 64]. 

The foregoing discussion of hydrogen overtension should be regarded more as an exercise in the use of the MD theory rather than as a strict and complete treatment for which space is not available here. We shall, however, come back to the problem in section (11.12) where we discuss the so-called Frumkin correction. 

In our opinion no Frumkin correction should here be made when the approach process H (c) is assumed to have an... 

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... 

Fig. 5.10 The effect of the Frumkin correction on the ideal Tafel plot (-...

We saw that formal kinetic equations apart from kinetic parameters also contain surface concentrations Cj of electrically active species. It follows from the material presented in previous chapters that differs from the corresponding bulk values because a diffusion layer with certain concentration profiles forms at the electrode surface. Moreover, another reason due to which surface concentrations change is adsorption phenomena, which form a certain structure called a double electrode layer (DEL) at the boundary metal solution. It is clear that in kinetic equations, it is necessary to use local concentrations of reactants and products, that is, concentrations in that region of DEL where electrically active particles are located. The second effect produced by DEL is related to the fact that a potential in the localization of the electrically active complex (EAC) differs from the electrode potential. Therefore, activation energy of the electrochemical process does not depend on the entire jump of the potential at the boundary but on its part only, which characterizes the change in the potential in the reaction zone. In this connection, the so-called Frumkin correction appears in the electrochemical kinetic equations, which is related to the evaluation of the local potential i// [1]. 

In the context of classical electrochemistry, this convention implies that Frumkin corrections (Schmickler, 1996) to the electrochemical kinetics of interfacial faradaic reactions are either negligible or constant. How good is this simplifying assumption It is justified at the hydrogen anode, where the overpotential is generally small. At the cathode, where the interfacial potential drop varies significantly with the value of the... 

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