Bias Dependence of the Transition State of the Hydrogen Evolution Reaction

Abstract

The hydrogen evolution reaction (HER) is one of the most prominent electrocatalytic reactions of green energy transition. However, the kinetics across materials and electrolyte pH and the impact of hydrogen coverage at high current densities remain poorly understood. Here, we study the HER kinetics over a large set of nanoparticle catalysts in industrially relevant acidic and alkaline membrane electrode assemblies that are only operated with pure water humidified gases. We discover distinct kinetic fingerprints between the iron triad (Fe, Ni, Co), coinage (Au, Cu, Ag), and platinum group metals (Ir, Pt, Pd, Rh). Importantly, the applied bias changes not only the activation energy (E_A) but also the pre-exponential factor (A). We interpret these changes as entropic changes in the interfacial solvent that differ between acid and base and entropic changes on the surface due to a changing hydrogen coverage. Finally, we observe that anions can induce Butler-Volmer behavior for the coinage metals in acid. Our results provide a new foundation to understand HER kinetics and, more broadly, highlight the pressing need to update common understanding of basic concepts in the field of electrocatalysis.

Figure 1

Arrhenius analysis with membrane electrode assemblies. (a) The cell potential, η_Cell, of a H₂^1bar|X/C|CEM|Pt/C|H₂^1bar cell with a 2 mg cm^–2 Pt/C hydrogen oxidation reaction (HOR) reference gas diffusion electrode informs directly on hydrogen evolution reaction (HER) kinetics of 10–40 μg_metal cm^–2 carbon supported catalyst X/C (X = Ir, Pt, Pd, Rh, Co, Ni, Fe, Au, Cu, Ag) (green) on the acidic cation exchange membrane (orange) or alkaline anion exchange membrane (blue). The HOR overpotential is negligible due to fast HOR kinetics and 2 orders of magnitude higher loading than the HER electrode. (b) Arrhenius analysis provides the bias dependent pre-exponential factor and activation energy. The dashed lines display the least-squares fit for three exemplary potentials with R² > 0.99 for Pt/C.

Figure 2

Bias dependent pre-exponential factor and activation energy for the hydrogen evolution reaction in acid. (a, b) Pre-exponential factor (log A) vs activation energy (E_A) for the platinum group metals (PGMs) and iron triad (Fe, Co, Ni) in acid, respectively. For the iron triad only overpotentials larger (more negative) than the corrosion potentials are shown. The compensation slopes for all metals of the iron triad, Δlog A(η)·ΔE_A(η)⁻¹ ∼ 0.12–0.13 mol kJ^–1, and for metals of the PGMs, Δlog A(η)·ΔE_A(η)⁻¹ ∼ 0.06–0.09 mol kJ^–1, are strikingly similar within each metal group. (c) log A vs E_A for coinage metals in acid. In clear contrast to the d-metals, the bias increases the activation energy, but also the pre-exponential factor. The slope Δlog A(η)·ΔE_A(η)⁻¹ ∼ 0.37–0.41 mol kJ^–1 is again identical within and distinctly different to the other groups. All listed potentials are cathodic overpotentials. For all catalysts, a low loading of 5–50 μg_metal cm^–2 was used to limit the impact of mass transport and interfering kinetics of the internal reference electrode. Values are means and error bars reflect standard deviation for E_A (slope) and A (intercept) from Arrhenius analysis, based on five observations (temperatures). The gray diagonal lines in the background are iso-current lines at 65 °C.

Figure 3

Bias dependent pre-exponential factor and activation energy for the hydrogen evolution reaction in alkali. (a, b) log A vs E_A for PGMs and iron triad in alkali, respectively. The 3–4 nm PGM nanoparticles display a similar behavior as in acid, but with a higher E_A(η). Reference measurements on polycrystalline Pt foils in 0.1 M KOH (inset in (a)) result in the same compensation slope as for the other metals in base. (c) log A vs E_A for coinage metals in alkali with a very similar compensation slope as the d-band metals in alkali (panel (b)), but substantially lower compared to the slopes of the coinage metals in acid of Δlog A(η)·ΔE_A(η)⁻¹ ∼ 0.37–0.41 mol kJ^–1 (Figure 2c). All listed potentials are cathodic overpotentials. For all catalysts, a low loading of 5–50 μg_metal cm^–2 was used to limit the impact of mass transport and interfering kinetics of the internal reference electrode. Values are means and error bars reflect standard deviation for E_A (slope) and A (intercept) from Arrhenius analysis, based on five observations (temperatures). The gray diagonal lines in the background are iso-current lines at 65 °C, i.e., pairs of log A and E_A that result in the same current.

Figure 4

The absence of unifying HER kinetics. (a) Exemplary Tafel plots for the HER in acid at 65 °C. (b) Overview of log A vs E_A across metals from Figure 2 and 3 at low overpotentials with arrow direction based on two successive potentials, for the PGMs a slightly higher potential was chosen due to the impact of the reverse hydrogen oxidation reaction. Gray diagonal lines in the background are iso-current lines at 65 °C.

Figure 5

Impact of anion adsorption on the HER kinetics of Au nanoparticles. The Nafion-containing gas diffusion electrodes were used as prepared (pristine) or soaked for 12 h in 1 M HClO₄, H₂SO₄, and KCl prior to assembly. Subsequently, the GDEs were operated in the H₂ pump membrane electrode assembly that uses the reversible hydrogen oxidation reaction as counter and internal reference electrode. Strongly adsorbing anions (SO₄^2– and Cl^–) lead to a distinct change in the kinetics. At higher overpotentials, the pre-exponential factor saturates and the kinetics switch into a fast Butler–Volmer regime, where the reduction of the activation energy in the Boltzmann factor leads to rapid acceleration of the rates. In contrast, weakly adsorbing anions (ClO₄^–) lead to negligible change in the bias dependent kinetics compared to the pristine Nafion. Note, the absolute rate is substantially suppressed for ClO₄^–, which might be caused by nontrivial (co)ion-exchange. Bias dependent pre-exponential factor, log A(η), and activation energy, E_A(η), from Arrhenius analysis, based on five observations (temperatures). The gray diagonal lines in the background are iso-current lines at 65 °C, i.e., pairs of log A and E_A that result in the same current.

Figure 6

Bias dependent activation enthalpy and entropy compensation in electrocatalysis. Starting at low overpotentials, the excess charge and, thus, electric fields, at the solid–electrolyte interface increase, causing an increasing activation entropy for the solvation step, ΔS_sol(η), likely due to ion delocalization in the ordered hydrogen bond network. However, the increasing excess charge at the surface is penalized by an increasing activation energy, E_A(η). Once the water is ordered sufficiently, ion solvation becomes fast and the bias starts to reduce the activation enthalpy of the intermediates over the (capacitively charged) catalyst surface. This transition region in the kinetics is critical to speed up reactions and switch into the fast Butler–Volmer regime where activation energies decrease with bias. However, with increasing coverage of intermediates (green circles), the surface configurational entropy, ΔS_surf(η), decreases due to a change of the number of microstates on the surface. Here, different compensation slopes might reflect what are traditionally considered the Volmer or Heyrovsky rate-determining step.