Correlation of Exchange Current Density j₀ and the Standard Potential of the Metal Electrodes EM⁰ for the Hydrogen Evolution Reaction (HER)
Authors: Parr Daniel Lee , Dadallagei Kasun , DeBie Sidney J. , Coduto Joshua R , Haas Christian D , Leddy Johna 
Published: May 2020

The hydrogen evolution reaction (HER) is critical technologically in electrochemically energy systems. HER is also important fundamentally as 2H⁺ + 2e ⇌ H₂ provides the standard reference potential E0
H = 0.000 V in thermodynamics and HER serves as a primary and critical test case for kinetics theory.
For HER electrocatalytic rates, the mechanism is historically broken down into three steps. The reaction sequence begins with adsorption and reduction of proton to form electrochemically adsorbed hydrogen. This is the Volmer step.
H⁺ + e ⇄ Hads    (Volmer)
After the first Hads is formed, H2 can be formed by two pathways. In the Heyrovsky pathway, a second proton undergoes electrochemical hydrogen adsorption at the same metal atom to form hydrogen gas.
Hads + H⁺ + e ⇄ H2    (Heyrovsky)
In the Tafel pathway, electrochemically adsorbed hydrogens on adjacent metal atoms react to form H2.
Hads + Hads ⇄ H2    (Tafel)
HER electrode kinetics measured as exchange current densities j₀ are evaluated in accord with the Volmer-Heyrovsky-Tafel scheme.
For HER at metal electrodes, log j₀ is known highly dependent on the metal of the electrodes with rates that vary > 10 orders of magnitude. HER data are evaluated according to these three steps, despite that properties of the metal are not explicit in the Volmer-Heyrovsky-Tafel scheme.
Here, properties of the metal electrode are introduced through the standard potential E0
M. For metal M0,
Mz+ + ze ⇌ M⁰    E0
M

Data for log j₀ are taken from a paper by Trasatti (Electroanalytical Chemistry and Interfacial Electrochemistry (1972) 39, 163-184). Trasatti grouped the 31 metal electrodes into d and sp metals. For the d metals (transition metals), log j₀ is well and linearly correlated with E0
M, whereas for the sp metals, little to no correlation is found.
Several points are considered.

Higher HER rates are observed at transition metal electrodes with more positive values of E0
M.

It is sketched that the initial step in the metal dependent HER process is release of electron(s) to form Mz+ immediately at the electrode surface.

Where formation of Mz+immediately at the electrode solution interface is the initial step, log j₀ is anticipated linearly dependent on E0
M.

The behavior is sketched within transition state or activated complex theory and is based on a transition state formed of electron(s) shared between the metal cation Mz+ and the proton H+.

Formation of the transition state [(1/z)Mz+⋯e⋯H+]‡ precedes the Volmer step, and where applicable, is a rate determining step.

Implications for overpotential η pinned by E0
M are considered.

This may account for the counter intuitive observation that higher log j₀ are found on metals such as Pt where E0
M is more positive.

A kinetic model is sketched where a component of the activation energy is set by F(E0
H-E0
M).

Finally, the process of proposing an electrode dependent transition state and evaluating the thermodynamic and kinetic consequences may yield a general method for modeling interfacial electron transfer and electrocatalysis. Such a process may introduces electrode specific properties into the rate expressions a priori.