Determination of the Adsorption Isotherms of Overpotentially Deposited Hydrogen on a Pt−Ir Alloy in H₂SO₄ Aqueous Solution Using the Phase-Shift Method and Correlation Constants

Abstract

The phase-shift method and correlation constants, which are unique electrochemical impedance spectroscopy techniques for studying the linear relationship between the phase shift (90° ≥ −φ ≥ 0°) versus electric potential (E) behavior for the optimum intermediate frequency and the fractional surface coverage (0 ≤ θ ≤ 1) vs E behavior, are proposed and verified to determine the Frumkin, Langmuir, and Temkin adsorption isotherms and related electrode kinetic and thermodynamic parameters. On a Pt−Ir [90:10 % (by weight)] alloy in 0.5 M H2SO4 aqueous solution, the Frumkin and Temkin adsorption isotherms (θ vs E), equilibrium constants [K = 3.3 · 10−5 exp(2.5θ) mol−1 for the Frumkin and K = 3.3 · 10−4 exp(−2.1θ) mol−1 for the Temkin adsorption isotherm], interaction parameters (g = −2.5 for the Frumkin and g = 2.1 for the Temkin adsorption isotherm), standard Gibbs energies of adsorption of overpotentially deposited (OPD) H [(25.6 ≥ ΔG θ 0 ≥ 19.4) kJ·mol−1 for K = 3.3 · 10−5 exp(2.5θ) mol−1 and 0 ≤ θ ≤ 1 and (20.9 < ΔG θ 0 < 24.0) kJ·mol−1 for K = 3.3 · 10−4 exp(−2.1θ) mol−1 and 0.2 < θ < 0.8], and rates of change of ΔG θ 0 of OPD H with θ (r = −6.2 kJ·mol−1 for g = −2.5 and r = 5.2 kJ·mol−1 for g = 2.1) have been determined and are compared using the phase-shift method and correlation constants. For 0.2 < θ < 0.8, a lateral attractive (g < 0) or repulsive (g > 0) interaction between the adsorbed OPD H species appears. On Pt, Ir, and Pt−Ir alloys in 0.5 M H2SO4 aqueous solution, the values of K for the Frumkin adsorption isotherms of OPD H decrease with increasing mass ratio of Ir. Negative values of g for the Frumkin adsorption isotherms of OPD H on the Pt, Ir, and Pt−Ir alloys in acidic and alkaline H2O and D2O solutions are experimentally and consistently determined. The duality of the lateral attractive and repulsive interactions is a unique feature of the adsorbed OPD H species on the Pt, Ir, and Pt−Ir alloys in acidic and alkaline H2O and D2O solutions.

Developments in Electrochemistry: The Phase-Shift Method and Correlation Constants for Determining the Electrochemical Adsorption Isotherms at Noble and Highly Corrosion-Resistant Metal/Solution Interfaces

“…Note that the following description of the phase-shift method for determining the Frumkin adsorption isotherm is similar to our previous papers due to use of the same method and procedures [27,28]. Fig.…”

“…Correspondingly, all of the simulations of the phase-shift method using Eq. (1) that appear in these comments (where C P does not include C D ) [30,32,34] are basically invalid or wrong [27,28]. All of the analyses of the effect of R P on −φ for intermediate frequencies are also invalid or wrong (see Supporting Information of Refs.…”

“…However, the objections to the phase-shift method do not fulfill these criteria. The objections to the phase-shift method are substantially attributed to a misunderstanding of the phase-shift method itself [27,28]. Note especially that all of the objections to the phase-shift method can be attributed to confusion regarding the applicability of related impedance equations for intermediate frequencies and…”

Review on the Determination of Frumkin, Langmuir, and Temkin Adsorption Isotherms at Electrode/Solution Interfaces Using the Phase-Shift Method and Correlation Constants

“…18). The comments and replies on the phase-shift method are briefly summarized elsewhere [18][19][20]. In recent, the validity of the phase-shift method has been qualitatively analyzed and verified by Garcia et al [22].…”

“…In this review article, we supplement and summarize the Frumkin, Langmuir, and Temkin adsorption isotherms of OPD H and OPD D and related electrode kinetic and thermodynamic parameters (θ vs. E, K, g, ∆G θ ○ , r) at noble metal (Pt, Ir, Pd, Au, Re) and alloy (Pt-Ir)/ normal (H 2 O) and heavy water (D 2 O) solution interfaces [9][10][11][12][13][14][15][16][17][18][19][20][21].…”