The phase-shift method for determining adsorption isotherms of hydrogen in electrochemical systems

A linear relationship between the behavior (-ϕ-ϕ vs. E  ) of the phase shift (0∘⩽-ϕ⩽90∘0∘⩽-ϕ⩽90∘) for the optimum intermediate frequency and that (θθ vs. E  ) of the fractional surface coverage (1⩾θ⩾01⩾θ⩾0) of H for the cathodic H2 evolution reaction (HER), i.e., the phase-shift method, in electrochemical systems has been suggested and verified using cyclic voltametric, linear sweep voltametric or differential pulse voltametric, and ac impedance techniques. The Langmuir and Frumkin adsorption isotherms of under-potentially deposited hydrogen (UPD H) or over-potentially deposited hydrogen (OPD H) for the cathodic HER at noble and transition-metal (Pt, Ir, Rh, Re, Pd, Au, Pt–Rh alloy, Ni)/aqueous electrolyte interfaces have been studied using the phase-shift method. At the interfaces, the fractional surface coverage (θθ), equilibrium constant (K  ), and standard free energy (ΔGads0,ΔGθ0) of H (UPD H, OPD H) for the cathodic HER are determined using the phase-shift method. The applicability of the Temkin adsorption isotherm (θθ vs. E  ) of OPD H for the cathodic HER at noble and transition-metal (Ir, Re, Ni)/aqueous electrolyte interfaces also has been studied using the phase-shift method. The phase-shift method is a simple and efficient tool for determining the adsorption, electrode kinetic, and thermodynamic parameters (θθ, K  , ΔGads0,ΔGθ0) of H (UPD H, OPD H) for the cathodic HER in electrochemical systems. The phase-shift method can be effectively used as a new electrochemical method to determine adsorption isotherms (Langmuir, Frumkin, Temkin) of intermediates for sequential reactions in electrochemical systems.