Mechanistic Analysis of Hydrogen Evolution Reaction on Stationary Polycrystalline Gold Electrodes in H₂SO₄ Solutions

An impedance model based on the Volmer–Heyrovsky–Tafel mechanism was developed to study the kinetics of the hydrogen evolution reaction on polycrystalline gold electrodes at moderate overpotentials in aqueous H₂SO₄ (0.5 and 1.0 M) solutions. The model was optimized on data from potentiodynamic polarization and electrochemical impedance spectroscopy, and model parameters were extracted. Consistent with expectations, the magnitude of the impedance data indicated a higher rate of hydrogen evolution at lower pH. Also, the fractional surface coverage of adsorbed hydrogen (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi>H</mi><mi>a</mi><mi>d</mi><mi>s</mi></mrow></msub></mrow></semantics></math></inline-formula>) increases with increasing overpotential but the small value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi>H</mi><mi>a</mi><mi>d</mi><mi>s</mi></mrow></msub></mrow></semantics></math></inline-formula> indicates only weak adsorption of H on gold. Tafel slopes and exchange current densities were estimated to be in the range of 81–124 mV/dec, and 10⁻⁶ and 10⁻⁵ A/cm² in H₂SO₄ (0.5 and 1.0 M), respectively. The results show that the model accounts well for the experimental data, such as the steady-state current density. Sensitivity analysis reveals that the electrochemical parameters (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>α</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo> </mo><msub><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo> </mo><msubsup><mrow><mi>k</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>0</mn></mrow></msubsup><mo>,</mo><mo> </mo><msubsup><mrow><mi>k</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow><mrow><mn>0</mn></mrow></msubsup><mo>,</mo><mo> </mo><msubsup><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><mo> </mo><mi>k</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>0</mn></mrow></msubsup><mo>)</mo></mrow></semantics></math></inline-formula> associated with the kinetics of the hydrogen evolution reaction have a major impact on the calculated impedance but the standard rate constant for hydrogen oxidation reaction (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mrow><mi>k</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow><mrow><mn>0</mn></mrow></msubsup><mo>)</mo></mrow></semantics></math></inline-formula> does not strongly affect the calculated impedance.