The phase-shift method and correlation constants for determining adsorption isotherms of hydrogen at a palladium electrode interface

The Frumkin and Temkin adsorption isotherms ( θ vs. E) of over-potentially deposited hydrogen (OPD H) for the cathodic H 2 evolution reaction (HER) and related electrode kinetic and thermodynamic parameters at a Pd/0.5 M H 2 SO 4 aqueous solution interface are determined using the phase-shift method and correlation constants. The Frumkin and Temkin adsorption isotherms ( θ vs. E), equilibrium constants ( K = 3.3 × 10 - 5 exp ( - 1.4 θ ) mol - 1 for the Frumkin and K = 3.3 × 10 - 4 exp ( - 6 θ ) mol - 1 for the Temkin adsorption isotherm), interaction parameters ( g = 1.4 for the Frumkin and g = 6 for the Temkin adsorption isotherm), rates of change of the standard free energy of OPD H with θ ( r = 3.5 kJ mol - 1 for g = 1.4 and r = 14.9 kJ mol - 1 for g = 6 ), and standard free energies ( 25.6 ⩽ Δ G θ 0 ⩽ 29.0 kJ mol - 1 for the Frumkin and 22.8 < Δ G θ 0 < 31.8 kJ mol - 1 for the Temkin adsorption isotherm) of OPD H are determined using the phase-shift method and correlation constants. At the intermediate values of θ , i.e., 0.2 < θ < 0.8 , the Temkin adsorption isotherm ( θ vs. E) correlating with the Frumkin or the Langmuir adsorption isotherm ( θ vs. E), and vice versa, is readily determined using the correlation constants. The phase-shift method and correlation constants are unique, useful, and effective ways to determine the Langmuir, Frumkin, and Temkin adsorption isotherms ( θ vs. E) of intermediates for sequential reactions and related electrode kinetic and thermodynamic parameters (K, g, r, Δ G θ 0 ) at interfaces.