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Volume 86, Issue 2 (Feb 2014)

Issues

Definition of the transfer coefficient in electrochemistry (IUPAC Recommendations 2014)

Rolando Guidelli
  • Corresponding author
  • Department of Chemistry “Ugo Schiff”, University of Florence, Via della Lastruccia 3, 50014 Sesto Fiorentino (Firenze), Italy
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/ Richard G. Compton
  • Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, UK
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/ Juan M. Feliu
  • Department of Physical Chemistry, University of Alicante, Ap. De Correos, 99, 03080, Alicante, Spain
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/ Eliezer Gileadi / Jacek Lipkowski
  • Department of Chemistry and Biochemistry, University of Guelph, 50 Stone Road East, Guelph, Ontario, N1G 2W1, Canada
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/ Wolfgang Schmickler
  • Institute of Theoretical Chemistry, University of Ulm,Albert Einstein Allee 11, D-89069 Ulm, Germany
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/ Sergio Trasatti
Published Online: 2014-02-05 | DOI: https://doi.org/10.1515/pac-2014-5025

Abstract

The transfer coefficient α is a quantity that is commonly employed in the kinetic investigation of electrode processes. An unambiguous definition of the transfer coefficient, independent of any mechanistic consideration and exclusively based on experimental data, is proposed. The cathodic transfer coefficient αc is defined as –(RT/F)(dln|jc|/dE), where jc is the cathodic current density corrected for any changes in the reactant concentration on the electrode surface with respect to its bulk value, E is the applied electric potential, and R, T, and F have their usual significance. The anodic transfer coefficient αa is defined similarly, by simply replacing jc with the anodic current density and the minus sign with the plus sign. This recommendation aims at clarifying and improving the definition of the transfer coefficient reported in the 3rd edition of the IUPAC Green Book.

Keywords: electrode kinetics; IUPAC Physical and Biophysical Chemistry Division; symmetry factor; Tafel slope; transfer coefficient

1 Preamble

The task group recommends the definition of the transfer coefficient given in the next section. This is followed by a brief section that summarizes the reasons why this definition differs from that presently reported in the 3rd edition of IUPAC Green Book [1] and in some textbooks [2–5], and also from the different definition reported in the IUPAC Gold Book [6]. The task group has also produced a comprehensive technical report where the rationale behind the recommended definition is thoroughly described. The technical report immediately precedes this recommendation [7].

2 Definition

The anodic transfer coefficient αa and the cathodic transfer coefficient αc are defined by the following equations:

In these equations, ja and jc are the anodic and cathodic current densities, respectively, corrected for any changes in the reactant concentration at the electrode surface with respect to its bulk value; incidentally, the symbols lnja and ln|jc| imply that the argument of the logarithm is of dimension one, obtained by division with the corresponding unit, e.g., lnja meaning ln(ja/A m–2), and similarly for the other quantities |jc|, ka, and kc. E is the applied electric potential, R is the gas constant, T is the thermodynamic temperature, and F is the Faraday constant. In practice, αa and αc are defined as the reciprocal of the corresponding Tafel slopes, dE/dlnja and –dE/dln|jc|, made dimensionless by the multiplying factor RT/F. Both the transfer coefficient and the Tafel slope are determined at constant temperature and pressure.

3 Rationale behind the recommended definition

The definition of the cathodic transfer coefficient as recommended herein differs from that reported in the IUPAC Green Book, αc= -(RT/nF)(dlnkc/dE), in two points: (1) the electroreduction rate constant kc is replaced by the cathodic current density jc corrected for any changes in the reactant concentration at the electrode surface with respect to its bulk value; (2) the number n of electrons is removed. For the sake of simplicity, the following considerations will refer to the cathodic transfer coefficient αc, but they can be readily extended to the anodic transfer coefficient αa; it is just sufficient to replace the minus sign by the plus sign in front of the definition of the transfer coefficient, the cathodic current density jc by the anodic current density ja, and the release of electrons from the electrode by their uptake.

With respect to the first change, the rate constant kc differs from the current density jc by a constant multiplying factor. Since this constant factor vanishes when differentiating the logarithm of kc to obtain αc, strictly speaking, the first change is irrelevant. Nonetheless, the determination of kc requires a correction for any change in the reactant concentration at the electrode surface, which in turn depends on the particular electrochemical perturbation imposed on the system. In some cases, the equations adopted to determine the rate of change of lnkc with potential are roughly approximate, and they may also account for diffuse layer effects by using the Frumkin correction factor [8, 9]. It is, therefore, deemed more convenient not to bind the definition of the transfer coefficient to the more or less rigorous equations used to determine kc, by simply referring to the current density jc “corrected for any changes in the reactant concentration at the electrode surface with respect to its bulk value”. In this way, the unavoidable amount of arbitrariness involved in this correction is manifest, instead of being hidden in the procedure adopted to determine kc.

The second change, consisting in the removal of the number n, is based on the following considerations. From a purely experimental point of view, what can be directly measured is the slope of the plot of E against –ln|jc| (provided this slope is constant over a current range of at least one order of magnitude), i.e., the so-called Tafel slope, or its reciprocal, –dln|jc|/dE. According to the recommended definition of the cathodic transfer coefficient αc, its value is obtained by simply multiplying the directly measurable quantity –dln|jc|/dE by RT/F, to make it dimensionless. According to the definition in the 3rd edition of the Green Book, this quantity is regarded as equal to the product, αn, of the two distinct quantities α and n; one is, therefore, faced with the necessity of estimating both quantities separately, on the basis of some mechanistic considerations. This may generate misleading conclusions. A frequently adopted approach consists in regarding a priori αc as equal to a symmetry factor β = 0.5 in order to extract a value of n, which is then identified with the number of electrons involved in the rate-determining step of the electrode process. If n is close to an integer, it is rounded off to this integer, thus allowing for a deviation of β from the 0.5 value. The β value may indeed deviate from 0.5 to some extent, and it may also vary with potential over a sufficiently broad potential range. This approach is formally correct only if the electrode process consists of a single elementary step involving the simultaneous release of n electrons from the electrode to the reactant. In many cases, an electrode process consists of a sequence of consecutive (or even parallel) elementary electron-transfer steps and chemical steps. Under these conditions, the above approach can still be regarded as formally correct only if the first elementary step of the sequence determines the rate of the whole process and involves the simultaneous release of n electrons from the electrode.

There is a further restriction imposed on this approach by the Marcus theory of electron transfer, first formulated in 1956 [10–12]. In view of this theory and of the subsequent quantum mechanical theory of the kinetics of the elementary act of an electrochemical process in polar liquids developed by Levich, Dogonadze, Kuznetsov, and others [13], it is now clear that the simultaneous transfer of more than one electron to or from an electrode is highly improbable. Nowadays, only a few of the previously cited examples of simultaneous transfer of two electrons between species in solution can be regarded as possible. In view of this further restriction, equating the experimental quantity -(RT/F)(dlnkc/dE) to a product αn from which the n value is extracted by setting a priori α ≈ 0.5 can lead to an acceptable result only if n turns out to be equal to unity. When the n value obtained by this approach is greater than unity, identifying n with the number of electrons involved in an unspecified rate-determining step is unwarranted. Equally unwarranted is the identification of n with the number of electrons involved in the overall electrode reaction as written, a number commonly denoted in the literature by the same symbol. Thus, e.g., in a multistep electrode process consisting of a series of consecutive elementary steps, the electrode kinetics is only affected by the rate-determining step and by the steps that precede it, while it is blind to the subsequent steps, which may well involve further electron transfers.

The definition of the transfer coefficient as recommended herein is based exclusively on a directly determined experimental quantity, independent of any mechanistic consideration on the electrode process under investigation. In particular, it does not require a priori assumptions about the α value required to estimate the multiplying factor n. Conversely, the αc value directly obtained from the expression -(RT/F)(dln|jc|/dE) can be profitably compared a posteriori with values of this quantity calculated for different electrode reaction mechanisms in order to sort that (or those) in best agreement with the experimental αc value. Determining the reaction mechanism remains a quite demanding task, but the definition as proposed herein at least prevents an unjustified a priori assumption on the n value from invalidating the mechanism from the very beginning. Finally, it should be mentioned that the present definition of the transfer coefficient is not new, and has been reported in textbooks [14–16] and monographs [17] and adopted by many electrochemists for the elucidation of the mechanism of electrode processes.

Membership of sponsoring body

Membership of the IUPAC Physical and Biophysical Chemistry Division Committee for the period 2012–2013 was as follows:

President: K. Yamanouchi (Japan); Vice President: R. Marquardt (France); Secretary: A. Wilson (USA); Past President: A. McQuillan (New Zealand); Titular Members: K. Bartik (Belgium); A. Friedler (Israel); A. Goodwin (USA); R. Guidelli (Italy); A. Russell (UK); J. Stohner (Switzerland); Associate Members: V. Barone (Italy); A. Császár (Hungary); V. Kukushkin (Russia); V. Mišković-Stanković (Serbia); Á. Mombrú Rodríguez (Uruguay); X. S. Zhao (China); National Representatives: K. Bhattacharyya (India); J. Cejka (Czech Republic); S. Hannongbua (Thailand); M. Koper (Netherlands); A. J. Mahmood (Bangladesh); O. Mamchenko (Ukraine); J. Mdoe (Tanzania); F. Quina (Brazil); N. Soon (Malaysia); V. Tomišić (Croatia).

Sponsoring body: IUPAC Physical and Biophysical Chemistry Division: see more details on p. 247.

Republication or reproduction of this report or its storage and/or dissemination by electronic means is permitted without the need for formal IUPAC or De Gruyter permission on condition that an acknowledgment, with full reference to the source, along with use of the copyright symbol ©, the name IUPAC, the name De Gruyter, and the year of publication, are prominently visible. Publication of a translation into another language is subject to the additional condition of prior approval from the relevant IUPAC National Adhering Organization and De Gruyter.

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About the article

Corresponding author: Rolando Guidelli, Department of Chemistry “Ugo Schiff”, University of Florence, Via della Lastruccia 3, 50014 Sesto Fiorentino (Firenze), Italy, e-mail:


Published Online: 2014-02-05

Published in Print: 2014-02-01


Citation Information: Pure and Applied Chemistry, ISSN (Online) 1365-3075, ISSN (Print) 0033-4545, DOI: https://doi.org/10.1515/pac-2014-5025.

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