Determination of Adsorption Isotherms of Hydrogen on Zirconium in Sulfuric Acid Solution Using the Phase-Shift Method and Correlation Constants

The phase-shift method and correlation constants, i.e., the unique electrochemical impedance spectroscopy (EIS) techniques for studying the linear relationship between the behavior ($-{\varphi}$ vs. E) of the phase shift ($90^{\circ}{\geq}-{\varphi}{\geq}0^{\circ}$) for the optimum intermediate frequency and that ($\theta$ vs. E) of the fractional surface coverage ($0{\leq}{\theta}{\leq}1$), have been proposed and verified to determine the Langmuir, Frumkin, and Temkin adsorption isotherms of H and related electrode kinetic and thermodynamic parameters at noble metal (alloy)/aqueous solution interfaces. At a Zr/0.2 M ${H_2}{SO_4}$ aqueous solution interface, the Frumkin and Temkin adsorption isotherms ($\theta$ vs. E), equilibrium constants (K = $1.401{\times}10^{-17}\exp(-3.5{\theta})mol^{-1}$ for the Frumkin and K = $1.401{\times}10^{-16}\exp(8.1{\theta})mol^{-1}$ for the Temkin adsorption isotherm), interaction parameters (g = 3.5 for the Frumkin and g = 8.1 for the Temkin adsorption isotherm), rates of change of the standard free energy (r = $8.7\;kJ\;mol^{-1}$ for g = 3.5 and r = $20\;kJ\;mol^{-1}$ for g = 8.1) of H with $\theta$, and standard free energies ($96.13{\leq}{\Delta}G^0_{\theta}{\leq}104.8\;kJ\;mol^{-1}$ for K = $1.401{\times}10^{-17}\exp(-3.5{\theta})mol^{-1}$ and $0{\leq}{\theta}{\leq}1$ and ($94.44<{\Delta}G^0_{\theta}<106.5\;kJ\;mol^{-1}$ for K = $1.401{\times}10^{-16}\exp(-8.1{\theta})mol^{-1}$ and $0.2<{\theta}<0.8$) of H are determined using the phase-shift method and correlation constants. At 0.2 < $\theta$ < 0.8, the Temkin adsorption isotherm correlating with the Frumkin adsorption isotherm, and vice versa, is readily determined using the correlation constants. The phase-shift method and correlation constants are probably the most accurate, useful, and effective ways to determine the adsorption isotherms of H and related electrode kinetic and thermodynamic parameters at highly corrosion-resistant metal/aqueous solution interfaces.