Defining the transfer coefficient in electrochemistry: An assessment (IUPAC Technical Report)

The transfer coefficient alpha is a quantity that is commonly employed in the kinetic investigation of electrode processes. In the 3rd edition of the IUPAC Green Book, the cathodic transfer coefficient alpha(c) is defined as (RT/nF)(dlnk(c)/dE), where k(c) is the electroreduction rate constant, E is the applied potential, and R, T, and F have their usual significance. This definition is equivalent to the other, -(RT/nF)(dln vertical bar j(c)vertical bar/dE), where j(c) is the cathodic current density corrected for any changes in the reactant concentration at the electrode surface with respect to its bulk value. The anodic transfer coefficient alpha(a) is defined similarly, by simply replacing j(c) with the anodic current density j(a) and the minus sign with the plus sign. It is shown that this definition applies only to an electrode reaction that consists of a single elementary step involving the simultaneous uptake of n electrons from the electrode in the case of alpha(c), or their release to the electrode in the case of alpha(a). However, an elementary step involving the simultaneous release or uptake of more than one electron is regarded as highly improbable in view of the absolute rate theory of electron transfer of Marcus; the hardly satisfiable requirements for the occurrence of such an event are examined. Moreover, the majority of electrode reactions do not consist of a single elementary step; rather, they are multistep, multi-electron processes. The uncritical application of the above definitions of alpha(c) and alpha(a) has led researchers to provide unwarranted mechanistic interpretations of electrode reactions. In fact, the only directly measurable experimental quantity is dln vertical bar j vertical bar/dE, which can be made dimensionless upon multiplication by RT/F, yielding (RT/F)(dln vertical bar j vertical bar/dE). One common source of misinterpretation consists in setting this experimental quantity equal to an, according to the above definition of the transfer coefficient, and in trying to estimate n from an, upon ascribing an arbitrary value to alpha, often close to 0.5. The resulting n value is then identified with the number of electrons involved in a hypothetical rate-determining step or with that involved in the overall electrode reaction. A few examples of these unwarranted mechanistic interpretations are reported. In view of the above considerations, it is proposed to define the cathodic and anodic transfer coefficients by the quantities alpha(c) = -(RT/F)(dln vertical bar j(c)vertical bar/dE) and alpha(a) = (RT/F) (dlnj(a)/dE), which are independent of any mechanistic consideration.