Correlation of Exchange Current Density j₀ and the Standard Potential of the Metal Electrodes E0
M
: A Different View of the Hydrogen Evolution Reaction (HER)
Authors: Parr Daniel , Dadallagei Kasun Saweendra Rathnatunga , Debie Sidney , Coduto Joshua Richard , Haas Christian D , Leddy Johna 
Published: July 2021

Technologically, the hydrogen evolution reaction (HER) is the foundation of many electrochemical energy systems. Fundamentally, HER is important as 2H+ + 2e ⇌ H2 defines the standard reference potential E0
H
= 0.000 V in thermodynamics. All evolutions in kinetic theory are critically tested against HER.
In electrocatalysis, the HER mechanism is historically specified in three steps. The first step, Volmer, couples concerted adsorption and reduction of proton to form electrochemically adsorbed hydrogen.
H+ + e ⇄ Hads (Volmer) (1)
Once the first proton electroadsorbs, H2 forms by two parallel pathways. The Heyrovsky step proceeds as a second proton is electroadsorbed to the same metal atom and hydrogen gas desorbs from the common metal center.
Hads + H+ + e ⇄ H2 (Heyrovsky) (2)
In the Tafel step, electrochemically adsorbed hydrogen forms on an adjacent metal center and H2 desorbs.
Hads + Hads ⇄ H2 (Tafel) (3)
Commonly, HER electrode kinetics are evaluated according to the Volmer-Heyrovsky-Tafel scheme, where rate is measured as exchange current densities j₀.
For HER at metal electrodes, log j₀ depends strongly on the electrode metal where log j₀ falls between -3 for Pt, Re, and Pd and -12 for Hg. Although metals are not explicit in the Volmer-Heyrovsky-Tafel scheme, j₀ is evaluated in view of Steps (1) to (3).
Here, metal electrode properties are introduced as the standard potential E0
M
of the electrode metal. For metal cation reduction to metal M⁰,
Mz+ + ze ⇌ M⁰ E0
M

log j₀ values are cataloged in a paper by Trasatti (Electroanalytical Chemistry and Interfacial Electrochemistry 1972, 39, 163-184), where he partitioned 31 metal electrodes into d and sp metals. For the transition metals, the d metals, log j₀ is well and linearly correlated with E0
M
. For the sp metals, there is little to no correlation of log j₀ with E0
M
.
For the transition metals, several observations and a model sketch are noted.

HER rates as log j₀ increase with more positive values of E0
M
.

For the initial step of the metal dependent HER process, it is sketched that electron(s) release from M0 to form Mz+ immediately at the electrode surface.

For this initial step, formation of Mz+ immediately at the electrode solution interface yields log j₀ linearly dependent on E0
M
.

Within transition state or activated complex theory, a proposed transition state is formed of electron(s) shared between Mz+ and H+.

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

Overpotential η pinned by E0
M
may characterize the counter intuitive observation that rate (log j₀) increases as E0
M
is more positive.

This sketch of HER yields a kinetic model where a component of the activation energy is set by F(E0
H
-E0
M
).

The sketch of an electrode dependent transition state may pose a general approach to characterizing electrocatalysis and interfacial electron transfers. The proposed transition state introduces physical properties of specific electrode materials into the rate expressions a priori.