Determination of Adsorption Isotherms of Hydroxide ata Platinum Electrode Interface Using the Phase-Shift Method and Correlation Constants

Abstract

The phase-shift method and correlation constants, i.e., the electrochemical impedance spectroscopy (EIS) techniques for studying linear relationships between the behaviors (<TEX>${\varphi}\;vs.\;E$</TEX>) of the phase shift (<TEX>$0^{\circ}{\leq}-{\varphi}{\leq}90^{\circ}$</TEX>) for the optimum intermediate frequency and those (<TEX>${\theta}\;vs.\;E$</TEX>) of the fractional surface coverage (<TEX>$1{\geq}{\theta}{\geq}0$</TEX>), have been proposed and verified to determine the Langmuir, Frumkin, and Temkin adsorption isotherms (<TEX>${\theta}\;vs.\;E$</TEX>) of H for the cathodic <TEX>$H_2$</TEX> evolution reaction (HER) at noble and transition-metal/aqueous solution interfaces. At the Pt/0.1 MKOH aqueous solution interface, the Langmuir, Frumkin, and Temkin adsorption isotherms (<TEX>${\theta}\;vs.\;E$</TEX>), equilibrium constants (<TEX>$K=5.6{\times}10^{-10}\;mol^{-1}\;at\;0{\leq}{\theta}<0.81$</TEX>, <TEX>$K=5.6{\times}10^{-9}{\exp}(-4.6{\theta})\;mol^{-1}\;at\;0.2<{\theta}<0.8$</TEX>, and <TEX>$K=5.6{\times}10^{-10}{\exp}(-12{\theta})\;mol^{-1}\;at\;0.919<{\theta}{\leq}1$</TEX>, interaction parameters (g = 4.6 for the Temkin and g = 12 for the Frumkin adsorption isotherm), rates of change of the standard free energy (<TEX>$r=11.4\;kJ\;mol^{-1}$</TEX> for g=4.6 and <TEX>$r=29.8\;kJ\;mol^{-1}$</TEX> for g=12), and standard free energies (<TEX>${\Delta}G_{ads}^0=52.8\;kJ\;mol^{-1}\;at\;0{\leq}{\theta}<0.81,\;49.4<{\Delta}G_{\theta}^0<56.2\;kJ\;mol^{-1}\;at\;0.2<{\theta}<0.8$</TEX> and <TEX>$80.1<{\Delta}_{\theta}^0{\leq}82.5\;kJ\;mol^{-1}\;at\;0.919<{\theta}{\leq}1$</TEX>) of OH for the anodic <TEX>$O_2$</TEX> evolution reaction (OER) are also determined using the phase-shift method and correlation constants. The adsorption of OH transits from the Langmuir to the Frumkin adsorption isotherm (<TEX>${\theta}\;vs.E$</TEX>), and vice versa, depending on the electrode potential (E) or the fractional surface coverage (<TEX>${\theta}$</TEX>). At the intermediate values of <TEX>${\theta}$</TEX>, i.e., <TEX>$0.2<{\theta}<0.8$</TEX>, the Temkin adsorption isotherm (<TEX>${\theta}\;vs.\;E$</TEX>) correlating with the Langmuir or the Frumkin adsorption isotherm (<TEX>${\theta}\;vs.\;E$</TEX>), and vice versa, is readily determined using the correlation constants. The phase-shift method and correlation constants are accurate and reliable techniques to determine the adsorption isotherms and related electrode kinetic and thermodynamic parameters. They are useful and effective ways to study the adsorptions of intermediates (H, OH) for the sequential reactions (HER, OER) at the interfaces.