The phase-shift method for determining Langmuir adsorption isotherms of over-potentially deposited hydrogen for the cathodic H2 evolution reaction at poly-Re/aqueous electrolyte interfaces

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 H2 evolution reaction (HER), i.e., the phase-shift method, at poly-Re/0.5 M H2SO4 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 H2SO4 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 (ΔGadso=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 ΔGadso=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.