The Langmuir adsorption isotherms of over-potentially deposited hydrogen ͑OPD H͒ for the cathodic hydrogen evolution reaction ͑HER͒ at poly-Au and Rh/0.5 M H 2 SO 4 aqueous electrolyte interfaces have been studied using cyclic voltammetric and ac impedance techniques. The behavior of the phase shift (0°р Ϫ р 90°) for the optimum intermediate frequency can be linearly related to that of the fractional surface coverage (1 у у 0) of OPD H for the cathodic HER at the interfaces. The phase-shift profile ͑Ϫ vs. E͒ for the optimum intermediate frequency, i.e., the phase-shift method, can be used as a new electrochemical method to determine the Langmuir adsorption isotherm ͑ vs. E͒ of the OPD H for the cathodic HER at the interfaces. At the poly-Au/0.5 M H 2 SO 4 aqueous electrolyte interface, the equilibrium constant ͑K͒ and the standard free energy (⌬G ads ) of the OPD H are 2.3 ϫ 10 Ϫ6 and 32.2 kJ/mol, respectively. At the poly-Rh/0.5 M H 2 SO 4 aqueous electrolyte interface, K and ⌬G ads of the OPD H are 4.1 ϫ 10 Ϫ4 or 1.2 ϫ 10 Ϫ2 and 19.3 or 11.0 kJ/mol depending on E, respectively. In contrast to the poly-Au electrode interface, two different Langmuir adsorption isotherms of OPD H are observed at the poly-Rh electrode interface. The two different Langmuir adsorption isotherms of OPD H correspond to two different adsorption sites of OPD H on the poly-Rh electrode surface.

The phase-shift method and correlation constants, that is, unique electrochemical impedance spectroscopy (EIS) techniques for studying the linear relationship between the behavior (−φ vs E) of the phase shift (90° ≥ −φ ≥ 0°) for the optimum intermediate frequency and that (θ vs E) of the fractional surface coverage (0 ≤ θ ≤ 1), are proposed and verified to determine the Frumkin, Langmuir, and Temkin adsorption isotherms of overpotentially deposited hydrogen (OPD H) and related electrode kinetic and thermodynamic parameters of noble metals (alloys) in aqueous solutions. On Pt and Ir in 0.1 M KOH aqueous solution, the Frumkin and Temkin adsorption isotherms (θ vs E), equilibrium constants (K), interaction parameters (g), rates (r) of change of the standard free energy of OPD H with θ, and standard free energies (ΔG θ 0) of OPD H are determined using the phase-shift method and correlation constants. The Frumkin adsorption isotherm is more accurate, useful, and effective than the Temkin adsorption isotherm. At 0.2 < θ < 0.8, the negative (positive) values of the interaction parameter for the Frumkin (Temkin) adsorption isotherms of OPD H are determined. A lateral attraction or repulsion interaction between the adsorbed OPD H species appears. The duality of the lateral attraction and repulsion interactions is probably a unique feature of OPD H on Pt, Ir, and Pt−Ir alloys in aqueous solutions.

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