The phase-shift method for determining Langmuir adsorption isotherms of over-potentially deposited hydrogen for the cathodic H 2 evolution reaction at poly-Re/aqueous electrolyte interfaces

Abstract

A linear relationship between the behavior (− ϕ vs. E) of the phase shift (0°⩽− ϕ⩽90°) for the optimum intermediate frequency and that ( θ vs. E) of the fractional surface coverage (1⩾ θ⩾0) of over-potentially deposited hydrogen (OPD H) for the cathodic H 2 evolution reaction (HER), i.e., the phase-shift method, at poly-Re/ 0.5 M H 2 SO 4 and 0.1 M KOH aqueous electrolyte interfaces has been suggested and verified using cyclic voltammetric, differential pulse voltammetric, and AC impedance techniques. At the poly-Re/ 0.5 M H 2 SO 4 aqueous electrolyte interface, the Langmuir adsorption isotherm ( θ vs. E) of OPD H, the equilibrium constant ( K=4.5×10 −7) for OPD H, and the standard free energy ( ΔG ads o =36.2 kJ/ mol) of OPD H are determined using the phase-shift method. At the poly-Re/ 0.1 M KOH aqueous electrolyte interface, θ vs. E of OPD H, K=1.9×10 −6 for OPD H, and ΔG ads o =32.6 kJ/ mol of OPD H are also determined using the phase-shift method. The applicability of the Frumkin and Temkin adsorption isotherms ( θ vs. E) of OPD H for the cathodic HER at the interfaces also has been studied using the phase-shift method. The phase-shift method experimentally provides the link between the microscopic system of the adsorption sites and process of OPD H on the atoms and the macroscopic system of the electrode kinetics and thermodynamics for OPD H at the interfaces. The phase-shift method can be effectively used as a new electrochemical method to determine or estimate adsorption isotherms of intermediates for sequential reactions in electrochemical systems.