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

Isotopic Shifts of the Frumkin and Temkin Adsorption Isotherms of H and D at Pt/Alkaline Solution Interfaces: Analysis Using the Phase-Shift Method

“…The frequency responses of the equivalent circuit for all f shown in Figure 2a are essential for understanding the linear relationship and Gaussian profile between −ϕ vs E for f o and θ vs E. At very low frequencies, the equivalent circuit for all f shown in Figure 2a can be expressed as a series circuit of R S , R F , and R P . At very high frequencies, the equivalent circuit for all f shown in Figure 2a can be In Figure 2b, the impedance (Z) and phase shift (−ϕ) for intermediate frequencies are given by 16,18,23…”

“…This is the reason why the Langmuir adsorption isotherm has been used or modified, even though it has critical limitations. [14][15][16][17] Furthermore, there is not much reliable experimental data on the isotopic shifts of the Frumkin and Temkin adsorption isotherms of H and D for the HER and DER at the interfaces. 18 The phase-shift method developed by our group is a unique electrochemical impedance spectroscopy technique for studying the linear relationship between the phase shift (90°≥ −ϕ ≥ 0°) for the optimum intermediate frequency (f o ) vs potential (E) (i.e., −ϕ vs E for f o ) behavior and the fractional coverage (0 ≤ θ ≤ 1) for adsorption vs E (i.e., θ vs E) behavior of the intermediate (H, D) for the sequential reaction (HER, DER) at noble metal/solution interfaces.…”

“…18 The phase-shift method developed by our group is a unique electrochemical impedance spectroscopy technique for studying the linear relationship between the phase shift (90°≥ −ϕ ≥ 0°) for the optimum intermediate frequency (f o ) vs potential (E) (i.e., −ϕ vs E for f o ) behavior and the fractional coverage (0 ≤ θ ≤ 1) for adsorption vs E (i.e., θ vs E) behavior of the intermediate (H, D) for the sequential reaction (HER, DER) at noble metal/solution interfaces. 16,[18][19][20][21][22][23] The θ vs E behavior is well known as the Frumkin or Langmuir adsorption isotherm. At first glance, it might seem that there is no relationship between the −ϕ vs E for f o behavior and the θ vs E behavior, leading to objections, errors, and confusion on the phase-shift method (see Ref.…”

Dopant Effects of Gd3+ on the Electrochemical Pseudocapacitive Characteristics of Electroactive Mesoporous NiO Electrodes for Supercapacitors

“…The ion transfer rate and the interfacial reaction kinetics are not efficient enough at higher scan rate in which redox reaction undergoes limited diffusion. At fast charging/discharging rates, the components of the surface of the electrode are inaccessible, while the depletion or oversaturation of OH – occurs at the electrolyte/electrode interface, thus impeding the charge-transfer process and promoting increase in resistance . In contrast, at slow charging/discharging rates, electron transport may be coordinated with OH – , resulting in high pseudocapacitance/lower resistance.…”

“…At fast charging/ discharging rates, the components of the surface of the electrode are inaccessible, while the depletion or oversaturation of OH − occurs at the electrolyte/electrode interface, thus impeding the charge-transfer process and promoting increase in resistance. 74 In contrast, at slow charging/discharging rates, electron transport may be coordinated with OH − , resulting in high pseudocapacitance/lower resistance. As analyzed by CV measurement among four working electrode materials, Ni 0.98 Gd 0.02 O electrode exhibits a great deal of specific capacitance compared to the other three electrode materials; an analogous trend can also be seen in GCD profiles in Figure 10b, which may be due to the doping effect of Gd into NiO electrode material.…”