Here, a thermodynamic specification for the slope of log j0 versus 𝚽 is suggested as 𝛂F/RT, where 𝛂 is the transfer coefficient for heterogeneous electron transfer.
Electrochemical potentials for species i in phase j have been used to derive the rates of heterogeneous electron transfer within a transition state context for Butler Volmer kinetics (Bard and Faulkner).
The standard chemical potential, activity, and ion charge for species i are 𝝁i0,j, aij, and zi is the electrical potential is 𝝓j.
Extrapolation of the electrochemical potential to include 𝚽 and derive a rate expression for j0 yield:
- The electrode potential and the work function group into a common term.
- The slope of log j0 versus 𝚽 as 𝛂F/RT.
- An explanation of how Pt with the highest energetic cost to remove an electron 𝚽 yields the highest log j0 is presented.
At 25 oC, F/RT = (0.05916 V)-1. Within the electrochemical potential model for log j0 versus 𝚽, the slopes of 6.44 and 6.6 for the d and sp metals at room temperature yield 𝛂 of 0.381 and 0.39. Across 30 metals, 𝛂 is estimated the same. The value of 0.4 is common in measurements of 𝛂 found for the potential dependent term in Butler Volmer kinetics.
References
Trasatti, S. Work Function, Electronegativity, and Electrochemical Behavior of Metals. III. Electrolytic Hydrogen Evolution in Acid Solution. Electroanalytical Chemistry and Interfacial Electrochemistry 39, 163-184 (1972).
A.J. Bard and L. R. Faulkner, Electrochemical Methods, 1980, wiley and Sons, Chapter 2.
Acknowledgments
This work was supported by the National Science Foundation and the Army Research Office. The University of Iowa Obermann Center for Advanced Studies is acknowledged.