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

Abstract

The phase-shift method and correlation constants, i.e., the unique electrochemical impedance spectroscopy (EIS) techniques for studying the linear relationship between the behavior (-φ vs E) of the phase shift (90°g -φ g 0°) for the optimum intermediate frequency and that (θ vs E) of the fractional surface coverage (0 e θ e 1), have been proposed and verified to determine the Langmuir, Frumkin, and Temkin adsorption isotherms of H and related electrode kinetic and thermodynamic parameters on noble metals (alloys) in aqueous solutions. On Ti in 0.5 M H 2 SO 4 aqueous solution, the Frumkin and Temkin adsorption isotherms (θ vs E), equilibrium constants (K ) 8.3 • 10 -12 exp(-6.6θ) mol -1 for the Frumkin, and K ) 8.3 • 10 -11 exp(-11.2θ) mol -1 for the Temkin adsorption isotherm), interaction parameters (g ) 6.6 for the Frumkin and g ) 11.2 for the Temkin adsorption isotherm), rates of change of the standard free energy (r ) 16.4 kJ • mol -1 for g ) 6.6 and r ) 27.8 kJ • mol -1 for g ) 11.2) of H with θ, and standard free energies [(63.2 e ∆G θ 0 e 79.6) kJ • mol -1 for K ) 8.3 • 10 -12 exp(-6.6θ) mol -1 and 0 e θ e 1 and (63.1 < ∆G θ 0 < 79.6) kJ • mol -1 for K ) 8.3 • 10 -11 exp(-11.2θ) mol -1 and 0.2 < θ < 0.8] of H are determined using the phaseshift method and correlation constants. At 0.2 < θ < 0.8, the Temkin adsorption isotherm correlating with the Frumkin adsorption isotherm, and vice versa, is readily determined using the correlation constants. The two different adsorption isotherms appear to fit the same data regardless of their adsorption conditions. 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 on highly corrosion-resistant metals in aqueous solutions.

Determination of Adsorption Isotherms of Overpotentially Deposited Hydrogen on Platinum and Iridium in KOH Aqueous Solution Using the Phase-Shift Method and Correlation Constants

“…However, as shown in Figures and , the two different adsorption isotherms, that is, the Temkin and Frumkin adsorption isotherms, appear to fit the same data at 0.2 < θ < 0.8 (also see Supplementary Figures 1 and 2 in the Supporting Information). This unique feature of the Temkin and Frumkin or Langmuir adsorption isotherms has been experimentally and consistently verified using the phase-shift method and correlation constants. − …”

“…The combination of ( R S , R F ) and ( C P , C D ) is equivalent to that of R ϕ and C ϕ . This is attributed to the reciprocal property of R F and C P . − As stated above, the unique feature and combination of R ϕ and C ϕ versus E , that is, Δ(−φ)/Δ E and Δθ/Δ E , most clearly appear at f o . The Gaussian profile and linear relationship between Δ(−φ)/Δ E and Δθ/Δ E for f o imply that only one Frumkin or Langmuir adsorption isotherm is determined on the basis of the relevant experimental results (see Figures to ).…”

“…The following limitations and conditions of the equivalent circuit elements for f o are summarized on the basis of the experimental data. − Both R S and C D are not constant. At θ ≈ 0, R S > R F and C D > C P , vice versa, and so forth.…”

“…The values of g and K o for the Temkin adsorption isotherm are approximately 4.6 and 10 times greater than those for the correlating Frumkin or Langmuir adsorption isotherm, respectively. This aspect is described elsewhere. ,, …”

“…The phase-shift method and correlation constants are unique electrochemical impedance spectroscopy (EIS) techniques for studying the linear relationship between the behavior (−φ vs E ) of the phase shift (90° ≥ −φ ≥ 0°) for the optimum intermediate frequency ( f o ) and that (θ vs E ) of the fractional surface coverage (0 ≤ θ ≤ 1) on noble metals (alloys) in aqueous solutions. − The behavior (θ vs E ) of the fractional surface coverage (0 ≤ θ ≤ 1) is well-known as the Frumkin or the Langmuir adsorption isotherm (θ vs E ). The phase-shift method and correlation constants are also proposed and verified to determine the Frumkin and Temkin adsorption isotherms and related electrode kinetic and thermodynamic parameters of highly corrosion-resistant metals in aqueous solutions. , …”