Determination of the Langmuir and Temkin Adsorption Isotherms of H for the Cathodic H2Evolution Reaction at a Pt/KOH Solution Interface Using the Phase-Shift Method

Abstract

The phase-shift method for determining the Langmuir, Frumkin, and Temkin adsorption isotherms (<TEX>$\theta_H\;vs.\;E$</TEX>) of H for the cathodic <TEX>$H_2$</TEX> evolution reaction (HER) at a Pt/0.1 M KOH solution interface has been proposed and verified using cyclic voltammetric, differential pulse voltammetric, and electrochemical impedance techniques. At the Pt/0.1 M KOH solution interface, the Langmuir and Temkin adsorption isotherms (<TEX>$\theta_H\;vs.\;E$</TEX>), the equilibrium constants (<TEX>$K_H=2.9X10^{-4}mol^{-1}$</TEX> for the Langmuir and <TEX>$K_H=2.9X10^{-3}\exp(-4.6\theta_H)mol^{-1}$</TEX> for the Temkin adsorption isotherm), the interaction parameters (g=0 far the Langmuir and g=4.6 for the Temkin adsorption isotherm), the rate of change of the standard free energy of <TEX>$\theta_H\;with\;\theta_H$</TEX> (r=11.4 kJ <TEX>$mol^{-1}$</TEX> for g=4.6), and the standard free energies (<TEX>${\Delta}G_{ads}^{\circ}=20.2kJ\;mol^{-1}$</TEX> for <TEX>$k_H=2.9\times10^{-4}mol^{-1}$</TEX>, i.e., the Langmuir adsorption isotherm, and <TEX>$16.7<{\Delta}G_\theta^{\circ}<23.6kJ\;mol^{-1}$</TEX> for <TEX>$K_H=2.9\times10^{-3}\exp(-4.6\theta_H)mol^{-1}$</TEX> and <TEX>$0.2<\theta_H<0.8$</TEX>, i.e., the Temkin adsorption isotherm) of H for the cathodic HER are determined using the phase-shift method. At intermediate values of <TEX>$\theta_H$</TEX>, i.e., <TEX>$0.2<\theta_H<0.8$</TEX>, the Temkin adsorption isotherm (<TEX>$\theta_H\;vs.\;E$</TEX>) corresponding to the Langmuir adsorption isotherm (<TEX>$\theta_H\;vs.\;E$</TEX>), and vice versa, is readily determined using the constant conversion factors. The phase-shift method and constant conversion factors are useful and effective for determining the Langmuir, Frumkin, and Temkin adsorption isotherms of intermediates for sequential reactions and related electrode kinetic and thermodynamic data at electrode catalyst interfaces.