The phase-shift method for determining Langmuir adsorption isotherms of over-potentially deposited hydrogen for the cathodic H evolution reaction at poly-Re/aqueous electrolyte interfaces

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

“…8 show the four numerically calculated Langmuir adsorption isotherms of (H + D) corresponding to K = 5.3 × 10 , respectively. For 0.2 < θ < 0.8, all of the Langmuir adsorption isotherms are always parallel to each other [13,16,42]. Correspondingly, all of the slopes of the Langmuir adsorption isotherms, i.e.…”

“…Thus, the tedious experimental procedures presented there [e.g. 13,16,[19][20][21]27] have been used to verify or confirm the validity and correctness of the phase-shift method. This is discussed in more detail in the section on theoretical and experimental backgrounds of the phase-shift method.…”

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

“…In our previously published papers, [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] only Eq.…”

“…[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].…”

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

“…At first glance, it seems that there is no linear relationship between the (−ϕ vs. E) behavior for f o and the (θ vs. E) behavior at the interfaces. Thus, tedious experimental techniques and procedures [9][10][11][12][13] have been used to verify the validity and correctness of the phase-shift method. A new method must be rigorously tested, especially when it is unique, but only with pure logic and objectivity and through scientific procedures.…”