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

Abstract The transfer coefficient α is a quantity that is commonly employed in the kinetic investigation of electrode processes. In the 3 rd edition of the IUPAC Green Book, the cathodic transfer coefficient α c is defined as –( RT / nF )( d ln k c /d E ), 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 )( d ln| j c |/d E ), 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 α 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 α c , or their release to the electrode in the case of α 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 α c and α a has led researchers to provide unwarranted mechanistic interpretations of electrode reactions. In fact, the only directly measurable experimental quantity is d ln| j |/d E , which can be made dimensionless upon multiplication by RT / F , yielding ( RT / F )( d ln| j |/d E ). One common source of misinterpretation consists in setting this experimental quantity equal to αn , according to the above definition of the transfer coefficient, and in trying to estimate n from αn , upon ascribing an arbitrary value to α , 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 α c = –( RT / F )( d ln| j c |/d E ) and α a = ( RT / F )( d ln j a /d E ), which are independent of any mechanistic consideration.