The phase-shift method for determining Langmuir and Temkin adsorption isotherms of over-potentially deposited hydrogen for the cathodic evolution reaction at the poly- aqueous electrolyte interface

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 the poly-Pt/0.5 M H 2 SO 4 aqueous electrolyte interface has been verified using cyclic voltammetric, differential pulse voltammetric, and ac impedance techniques. The phase-shift method for determining the suitable adsorption isotherm (Langmuir, Frumkin, Temkin) of OPD H for the cathodic HER at the interface also has been proposed. At the poly-Pt/0.5 M H 2 SO 4 aqueous electrolyte interface, the Langmuir adsorption isotherm ( θ vs. E ) of OPD H, the equilibrium constant ( K = 1.3 × 10 - 4 ) for OPD H and the standard free energy ( Δ G ads 0 = 22.2 kJ / mol ) of OPD H are determined using the phase-shift method. At the same interface, the Temkin adsorption isotherm ( θ vs. E ) of OPD H, the equilibrium constant ( 1.3 × 10 - 3 ⩾ K ⩾ 1.3 × 10 - 5 with θ , i.e., 0 ⩽ θ ⩽ 1 ) for OPD H, and the standard free energy ( 16.5 ⩽ Δ G θ 0 ⩽ 27.9 kJ / mol with θ , i.e., 0 ⩽ θ ⩽ 1 ) of OPD H are also determined using the phase-shift method. At the intermediate values of θ , i.e., 0.2 < θ < 0.8 , the Langmuir and Temkin adsorption isotherms of OPD H for the cathodic HER at the interface are converted to each other. The equilibrium constant ( K 0 ) for the Temkin adsorption isotherm ( θ vs. E ) is ca. 10 times greater than that ( K ) for the corresponding Langmuir adsorption isotherm ( θ vs. E ). The interaction parameter ( g ) for the Temkin adsorption isotherm ( θ vs. E ) is ca. 4.6 greater than that ( g ) for the corresponding Langmuir adsorption isotherm ( θ vs. E ). These numbers (10 times and 4.6) can be taken as constant conversion factors between the corresponding adsorption isotherms (Temkin, Langmuir, Frumkin). The Temkin adsorption isotherm corresponding to the Langmuir or the Frumkin adsorption isotherm, and vice versa, can be effectively converted using the constant conversion factors. Both the phase-shift method and constant conversion factors can be effectively used as a new electrochemical method to determine the suitable adsorption isotherms (Langmuir, Frumkin, Temkin) of H for the cathodic HER in electrochemical systems.