A linear relationship between the behavior (-phi vs. E) of the phase shift (0 degrees <= - phi <= 90 degrees) for the optimum intermediate frequency and that (theta vs. E) of the fractional surface coverage (1 >= theta >= 0) of over-potentially deposited hydrogen (OPD H) for the cathodic H-2 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 (0 vs. E) of OPD H, the equilibrium constant (K = 4.5 x 10(-7)) for OPD H, and the standard free energy (Delta G(ads)degrees, = 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, 0 vs. E of OPD H,K= 1.9 x 10(-6) for OPD H, and Delta G(ads)degrees = 32.6 kJ/mol of OPD H are also determined using the phase-shift method. The applicability of the Frumkin and Temkin adsorption isotherms (theta 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. (c) 2004 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.