Determination of the Adsorption Isotherms of Hydrogen and Deuterium Isotopes on a Pt−Ir Alloy in LiOH Solutions 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 alloy (90:10 mass ratio) in 0.1 M LiOH (H2O) and 0.1 M LiOH (D2O) solutions, the Frumkin and Temkin adsorption isotherms (θ vs E), equilibrium constants (K), interaction parameters (g), standard Gibbs energies (ΔG θ °) of hydrogen (H) and deuterium (D) adsorption, and rates of change (r) of ΔG θ ° of H and D with θ have been determined and are compared using the phase-shift method and correlation constants. The value of K decreases in going from H2O to D2O. The values of K for both H and D increase with increasing E and θ. Over the θ range (i.e., 1 ≥ θ ≥ 0), the value of K for H is 3.7 to 4.1 times greater than that for D. For 0.2 < θ < 0.8, a lateral attractive (g < 0) or repulsive (g > 0) interaction between the adsorbed H or D species appears. The duality of the lateral attractive and repulsive interactions is a unique feature of the adsorbed H and D species on Pt, Ir, and Pt−Ir alloys in acidic and alkaline H2O and D2O solutions.

Determination of the Frumkin and Temkin Adsorption Isotherms of Hydrogen at Nickel/Acidic and Alkaline Aqueous Solution Interfaces Using the Phase-Shift Method and Correlation Constants

“…1(a). [23][24][25][26][33][34][35] Taking into account the superposition of various effects (relaxation time effects, real surface area problems, surface absorption and diffusion processes, inhomogeneous and lateral interaction effects, oxide layer formation, specific adsorption effects, etc.) that are inevitable under the experimental conditions, we define the equivalent circuit elements as follows: R S is the real solution resistance; R F is the real resistance due to the Faradaic resistance (R φ ) for the discharge step and superposition of various effects; R P is the real resistance due to the Faradaic resistance (R R ) for the recombination step and superposition of various effects; C P is the real capacitance due to the adsorption pseudocapacitance (C φ ) for the discharge step and superposition of various effects; and C D is the real double-layer capacitance.…”

“…(1) that appear in these comments (where C P does not include C D ) 27,29,31) are basically invalid or wrong. 25,26) 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. 25 and 26).…”

“…[27][28][29][30][31] The objections to the phase-shift method are substantially attributed to a misunderstanding of the phase-shift method itself. 25,26) 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 a unique feature of the Faradaic resistance for the recombination step [1]. The validity and correctness of the phase-shift method should be discussed on the basis of simulations with a single equation…”

Determination of the Frumkin and Temkin Adsorption Isotherms of Underpotentially Deposited Hydrogen at Pt Group Metal Interfaces Using the Standard Gibbs Energy of Adsorption and Correlation Constants

“…7,8) The Frumkin and Temkin adsorption isotherms of UPD H and electrode kinetic data (θ vs. E, g, K) have never been determined using ∆G θ o with θ (0 ≤ θ ≤ 1) and the correlation constants.…”

“…7,8,11,12) These factors (ca. 4.6 and 10) can be taken as correlation constants between the Temkin and Frumkin or Langmuir adsorption isotherms.…”