The Langmuir adsorption isotherms of under-potentially deposited hydrogen (UPD H) and over-potentially deposited hydrogen (OPD H) for the cathodic H-2 evolution reaction (HER) at poly-Ir/0.5 M H2SO4 and 0.05 M KOH aqueous electrolyte interfaces have been studied using cyclic voltammetric, differential pulse voltammetric, and ac impedance techniques. The behavior of the lagged phase shift (0degrees less than or equal to - phi less than or equal to 90degrees) for the optimum intermediate frequency can be linearly related to that of the fractional surface coverage (1 greater than or equal to 0 greater than or equal to 0) of H (UPD H, OPD H) for the cathodic HER at the interfaces. A linear relationship between the phase-shift profile (-phi vs. E) for the optimum intermediate frequency and the Langmuir adsorption isotherm (0 vs. E) of H (UPD H, OPD H), i.e., the phase-shift method, can be used as a new electrochemical method to determine or estimate the fractional surface coverage (0), equilibrium constant (K), and standard free energy (DeltaG(ads)(0) of H (UPD H, OPD H) for the cathodic HER at the interfaces. At the poly-Ir/0.5 M H2SO4 aqueous electrolyte interface, K and DeltaG(ads)(0), of the OPD H for the cathodic HER are 9.9 x 10(-5) and 22.8 kj/mol, respectively. At the poly-Ir/0.05 M KOH aqueous electrolyte interface. K and DeltaG(ads)(0) of the UPD H for the cathodic HER are 3.9 and -3.4 kJ/mol, respectively. At the poly-Ir/0.05 M KOH ads aqueous electrolyte interface, K and DeltaG(ads)(0) of the OPD H for the cathodic HER are 5.8 x 10(-4) and 18.5 kj/mol, respectively. ad The two different Langmuir adsorption isotherms for H (UPD H, OPD H) correspond to two different adsorption sites of H (UPD H, OPD H) on the poly-Ir electrode surface. The two different adsorption sites of UPD H and OPD H act as two distinguishable electroadsorbed H species. The phase-shift method is a simple and efficient tool for determining the adsorption, electrode kinetic, and thermodynamic parameters (theta, K,DeltaG(ads)(0)) of H (UPD H, OPD H) for the cathodic HER at the interfaces. (C) 2004 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.