Measured values of the phase shift (−
1. Introduction
To obtain an environmentally clean energy source, many experimental methods have been developed and used to study the adsorption of hydrogen for the cathodic H2 evolution reaction (HER) and hydroxide for the anodic O2 evolution reaction (OER) at noble and highly corrosion-resistant metal and alloy/aqueous solution interfaces [1−7]. The cathodic HER is one of the most extensively studied topics in electrochemistry, electrode kinetics, renewable and sustainable energy, etc. It is well known that underpotentially deposited hydrogen (UPD H) and overpotentially deposited hydrogen (OPD H) occupy different surface adsorption sites and act as two distinguishable electroadsorbed H species, and that only OPD H can contribute to the cathodic HER [2−7]. Similarly, one can interpret that underpotentially deposited deuterium (UPD D) and overpotentially deposited deuterium (OPD D) occupy different surface adsorption sites and act as two distinguishable electroadsorbed D species, and that only OPD D can contribute to the cathodic D2 evolution reaction (DER). However, there is not much reliable electrode kinetic data for OPD H and OPD D, i.e. the fractional surface coverage, interaction parameter, and equilibrium constant for the Frumkin adsorption isotherm, at the interfaces. Also, a quantitative relationship between the Temkin and Frumkin or Langmuir adsorption isotherms has not been developed to study the cathodic HER and DER. Thus, there is a technological need for a useful, effective, and reliable method to determine the Frumkin, Langmuir, and Temkin adsorption isotherms of OPD H and OPD D and related electrode kinetic and thermodynamic parameters. In the following discussions, H and D mean OPD H and OPD D, respectively.
Although the electrochemical Frumkin and Langmuir adsorption isotherms may be regarded as classical models and theories, it is preferable to consider the Frumkin and Langmuir adsorption isotherms for H and D rather than electrode kinetics and thermodynamics equations for H and D because these adsorption isotherms are associated more directly with the atomic mechanisms of H and D [8]. However, there is not much reliable information on the Frumkin and Langmuir adsorption isotherms of H for the cathodic HER and related electrode kinetic and thermodynamic data [1−7]. Furthermore, there is not much reliable information on the Frumkin and Langmuir adsorption isotherms of D for the cathodic DER and related electrode kinetic and thermodynamic data. Because, to the authors’ knowledge, the interaction parameter and equilibrium constant for the Frumkin adsorption isotherm of H and D cannot be experimentally and readily determined using other conventional methods [3,7].
To determine the Frumkin, Langmuir, and Temkin adsorption isotherms, the phase-shift method and correlation constants have been originally developed on the basis of relevant experimental results and data. The phase-shift method is a unique electrochemical impedance spectroscopy technique for studying the linear relationship between the phase shift (90° ≥ −
At first glance, it seems that there is no linear relationship between the −
The comments and replies on the phase-shift method are described elsewhere [30−34]. New ideas or methods must be rigorously tested, especially when they are unique, but only with pure logic and objectivity and through scientific procedures. 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 a unique feature of the faradaic resistance for the recombination step [35]. The validity and correctness of the phase-shift method should be discussed on the basis of numerical simulations with a single equation for −
In practice, the numerical calculation of equivalent circuit impedances of the noble and highly corrosion-resistant metal and alloy/solution interfaces is very difficult or impossible due to the superposition of various effects. However, it is simply determined by frequency analyzers, i.e. tools. Note that the phase-shift method and correlation constants are useful and effective tools for determining the Frumkin, Langmuir, and Temkin adsorption isotherms and related electrode kinetic and thermodynamic parameters.
This work is one of our continuous studies on the phase-shift method and correlation constants for determining the Frumkin, Langmuir, and Temkin adsorption isotherms. In this paper, as a selected example of the phase-shift method and correlation constants for determining the electrochemical adsorption isotherms, we present the Frumkin and Temkin adsorption isotherms of (H + D) for the cathodic (HER + DER) and related electrode kinetic and thermodynamic parameters of a Pt−Ir alloy/0.1 M LiOH (H2O + D2O) solution interface. These experimental results are compared with the relevant experimental data of the noble and highly corrosion-resistant metal and alloy/solution interfaces [11, 13, 16, 19−21, 23−29]. The interaction parameters, equilibrium constants, standard Gibbs energies of adsorptions, and rates of change of the standard Gibbs energies with
2. Experimental
2.1. Preparations
Taking into account the H+ and D+ concentrations [27] and the effects of the diffuse-double layer and pH [36], a mixture (1:1 volume ratio) of 0.1 M LiOH (H2O) and 0.1 M LiOH (D2O) solutions, i.e. 0.1 M LiOH (H2O + D2O) solution, was prepared from LiOH (Alfa Aesar, purity 99.995%) using purified water (H2O, resistivity > 18 MΩ · cm) obtained from a Millipore system and heavy water (D2O, Alfa Aesar, purity 99.8%). The p(H + D) of 0.1 M LiOH (H2O + D2O) solution was 12.91. This solution was deaerated with 99.999% purified nitrogen gas for 20 min before the experiments.
A standard three-electrode configuration was employed. A saturated calomel electrode (SCE) was used as the standard reference electrode. A platinum−iridium alloy wire (Johnson Matthey, 90:10 Pt/Ir mass ratio, 1.5 mm diameter, estimated surface area ca. 1.06 cm2) was used as the working electrode. A platinum wire (Johnson Matthey, purity 99.95%, 1.5 mm diameter, estimated surface area ca. 1.88 cm2) was used as the counter electrode. Both the Pt−Ir alloy working electrode and the Pt counter electrode were prepared by flame cleaning and then quenched and cooled sequentially in Millipore Milli-Q water and air.
2.2. Measurements
A cyclic voltammetry (CV) technique was used to achieve a steady state at the Pt−Ir alloy/0.1 M LiOH (H2O + D2O) solution interface. The CV experiments were conducted for 20 cycles at a scan rate of 200 mV · s−1 and a scan potential of (0 to −1.0) V vs. SCE. After the CV experiments, an electrochemical impedance spectroscopy (EIS) technique was used to study the linear relationship between the −
The CV experiments were performed using an EG&G PAR Model 273A potentiostat controlled with the PAR Model 270 software package. The EIS experiments were performed using the same apparatus in conjunction with a Schlumberger SI 1255 HF frequency response analyzer controlled with the PAR Model 398 software package. To obtain comparable and reproducible results, all of the measurements were carried out using the same preparations, procedures, and conditions at 298 K. The international sign convention is used: cathodic currents and lagged-phase shifts or angles are taken as negative. All potentials are given on the standard hydrogen electrode (SHE) scale. The Gaussian and adsorption isotherm analyses were carried out using the Excel and Origin software packages.
3. Results and discussion
3.1. Theoretical and experimental backgrounds of the phase-shift method
The equivalent circuit for the adsorption of (H + D) for the cathodic (HER + DER) at the Pt−Ir alloy/0.1 M LiOH (H2O + D2O) solution interface can be expressed as shown in Fig. 1a [27, 28, 37−39]. Taking into account the superposition of various effects (e.g. a relaxation time effect, a real surface area problem, surface absorption and diffusion processes, inhomogeneous and lateral interaction effects, an oxide layer formation, specific adsorption effects, etc.) that are inevitable under the experimental conditions, we define the equivalent circuit elements as follows:
The numerical derivation of
The frequency responses of the equivalent circuit for all
At intermediate frequencies, the impedance (
for the upper circuit in Fig. 1b or
for the lower circuit in Fig. 1b, where j is the imaginary unit (i.e. j2 = −1) and
In our previous papers [9−24], only Eq. (1) was used with a footnote stating that
The following limitations and conditions of the equivalent circuit elements for
3.2. Basic procedure and description of the phase-shift method
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].
Figure 2 compares the phase-shift curves (−
The intermediate frequency of 1.259 Hz, shown as a vertical solid line on the −
|
− |
|
Δ(− |
Δ |
−0.659 | 84.7 | ~ 0 | ~ 0 | ~ 0 |
−0.684 | 84.0 | 0.00830 | 0.08304 | 0.08304 |
−0.709 | 79.4 | 0.06287 | 0.54567 | 0.54567 |
−0.734 | 60.8 | 0.28351 | 2.20641 | 2.20641 |
−0.759 | 26.6 | 0.68921 | 4.05694 | 4.05694 |
−0.784 | 7.7 | 0.91340 | 2.24199 | 2.24199 |
−0.809 | 2.6 | 0.97390 | 0.60498 | 0.60498 |
−0.834 | 1.3 | 0.98932 | 0.15421 | 0.15421 |
−0.859 | 0.7 | 0.99644 | 0.07117 | 0.07117 |
−0.884 | 0.6 | 0.99763 | 0.01186 | 0.01186 |
−0.909 | 0.4 | ~ 1 | 0.02372 | 0.02372 |
The procedure and description of the phase-shift method for determining the Frumkin adsorption isotherm of (H + D) at the interface are summarized in Table 1. The values of −
The Gaussian profile shown in Fig. 4b is illustrated on the basis of Δ(−
3.3. Frumkin, Langmuir, and Temkin adsorption isotherms
The derivation and interpretation of the practical forms of the electrochemical Frumkin, Langmuir, and Temkin adsorption isotherms are described elsewhere [41−43]. The Frumkin adsorption isotherm assumes that the Pt−Ir alloy surface is inhomogeneous or that the lateral interaction effect is not negligible. It is well known that the Langmuir adsorption isotherm is a special case of the Frumkin adsorption isotherm. The Langmuir adsorption isotherm can be derived from the Frumkin adsorption isotherm by setting the interaction parameter to be zero. The Frumkin adsorption isotherm of (H + D) can be expressed as follows [42]
where
At the Pt−Ir alloy/0.1 M LiOH (H2O + D2O) solution interface, the numerically calculated Frumkin adsorption isotherms using Eq. (4) are shown in Fig. 5. Curves a, b, and c in Fig. 5 show the three numerically calculated Frumkin adsorption isotherms of (H + D) corresponding to
At intermediate values of
Figure 6 shows the determination of the Temkin adsorption isotherm corresponding to the Frumkin adsorption isotherm shown in curve b of Fig. 5. The dashed line labeled b in Fig. 6 shows that the numerically calculated Temkin adsorption isotherm of (H + D) using Eq. (7) is
3.4. Applicability of the Frumkin, Langmuir, and Temkin adsorption isotherms
Figure 7 shows the applicability of ranges of
Figures 8 and 9 show the applicability of the Langmuir and Temkin adsorption isotherms at the same potential ranges, respectively. Figs. 8 and 9 also show that the Langmuir and Temkin adsorption isotherms are not applicable to the adsorption of (H + D) at the interface.
At extreme values of
interface | adsorbate |
|
|
Ref. |
Pt−Ir alloy |
H+D | −2.2 | 5.3 × 10−5 exp(2.2 |
− |
Pt−Ir alloy |
H | −2.2 | 8.6 × 10−5 exp(2.2 |
27 |
Pt−Ir alloy |
D | −2.3 | 2.1 × 10−5 exp(2.3 |
27 |
Pt−Ir alloy |
H | −2.5 | 3.3 × 10−5 exp(2.5 |
28 |
Pt−Ir alloy |
OH | 0.6 | 5.4 × 10−9 exp(−0.6 |
26 |
Pt−Ir alloy |
OH+OD | 2.7 | 3.9 × 10−9 exp(−2.7 |
26 |
Pt−Ir alloy |
H | −2.5 | 3.1 × 10−5 exp(2.5 |
20 |
Pt−Ir alloy |
OH | 1.8 | 4.7 × 10−10 exp(−1.8 |
20 |
Pt/0.1 M KOH (H2O) | H | −2.4 | 1.2 × 10−4 exp(2.4 |
25 |
Pt/0.5 M H2SO4 (H2O) | H | −2.4 | 3.5 × 10−5 exp(2.4 |
21 |
Ir/0.1 M KOH (H2O) | H | −2.4 | 9.4 × 10−5 exp(2.4 |
25 |
Ir/0.5 M H2SO4 (H2O) | H | −2.4 | 2.7 × 10−5 exp(2.4 |
21 |
Pd/0.5 M H2SO4 (H2O) | H | 1.4 | 3.3 × 10−5 exp(−1.4 |
19 |
Au/0.5 M H2SO4 (H2O) | H | 0 |
2.3 × 10−6 | 13 |
Re/0.1 M KOH (H2O) | H | 0 |
1.9 × 10−6 | 16 |
Re/0.5 M H2SO4 (H2O) | H | 0 |
4.5 × 10−7 | 16 |
Ni |
H | 10 | 1.3 × 10−1 exp(−10 |
11 |
Ni |
H | 7.4 | 3.6 × 10−4 exp(−7.4 |
29 |
Ni |
H | 5.3 | 4.1 × 10−9 exp(−5.3 |
29 |
Ti/0.5 M H2SO4 (H2O) | H | 6.6 | 8.3 × 10−12 exp(−6.6 |
23 |
Zr/0.2 M H2SO4 (H2O) | H | 3.5 | 1.4 × 10−17 exp(−3.5 |
24 |
interface | adsorbate |
|
|
Ref. |
Pt−Ir alloy |
H+D | 2.4 | 5.3 × 10−4 exp(−2.4 |
− |
Pt−Ir alloy |
H | 2.4 | 8.6 × 10−4 exp(−2.4 |
27 |
Pt−Ir alloy |
D | 2.3 | 2.1 × 10−4 exp(−2.3 |
27 |
Pt−Ir alloy |
H | 2.1 | 3.3 × 10−4 exp(−2.1 |
28 |
Pt−Ir alloy |
OH | 5.2 | 5.4 × 10−8 exp(−5.2 |
26 |
Pt−Ir alloy |
OH+OD | 7.3 | 3.9 × 10−8 exp(−7.3 |
26 |
Pt−Ir alloy |
H | 2.1 | 3.1 × 10−4 exp(−2.1 |
20 |
Pt−Ir alloy |
OH | 6.4 | 4.7 × 10−9 exp(−6.4 |
20 |
Pt/0.1 M KOH (H2O) | H | 2.2 | 1.2 × 10−3 exp(−2.2 |
25 |
Pt/0.5 M H2SO4 (H2O) | H | 2.2 | 3.5 × 10−4 exp(−2.2 |
21 |
Ir/0.1 M KOH (H2O) | H | 2.2 | 9.4 × 10−4 exp(−2.2 |
25 |
Ir/0.5 M H2SO4 (H2O) | H | 2.2 | 2.7 × 10−4 exp(−2.2 |
21 |
Pd/0.5 M H2SO4 (H2O) | H | 6 | 3.3 × 10−4 exp(−6 |
19 |
Au/0.5 M H2SO4 (H2O) | H | 4.6 | 2.3 × 10−5 exp(−4.6 |
13 |
Re/0.1 M KOH (H2O) | H | 4.6 | 1.9 × 10−5 exp(−4.6 |
16 |
Re/0.5 M H2SO4 (H2O) | H | 4.6 | 4.5 × 10−6 exp(−4.6 |
16 |
Ni |
H | 14.6 | 1.3 exp(−14.6 |
11 |
Ni |
H | 12 | 3.6 × 10−3 exp(−12 |
29 |
Ni |
H | 9.9 | 4.1 × 10−8 exp(−9.9 |
29 |
Ti/0.5 M H2SO4 (H2O) | H | 11.2 | 8.3 ×10−11 exp(−11.2 |
23 |
Zr/0.2 M H2SO4 (H2O) | H | 8.1 | 1.4 × 10−16 exp(−8.1 |
24 |
3.5. Standard Gibbs energy of adsorption
Under the Frumkin adsorption conditions, the relationship between the equilibrium constant (
For the Pt−Ir alloy/0.1 M LiOH (H2O + D2O) solution interface, use of Eqs. (6) and (8) shows that ∆
4. Comparisons
4.1. Mixture solution
Curves a, b, and c in Fig. 10 show the
interface | adsorbate | ∆ |
|
Ref. |
Pt−Ir alloy |
H+D | 24.4 ≥ ∆ |
−5.5 | − |
Pt−Ir alloy |
H | 23.2 ≥ ∆ |
−5.5 | 27 |
Pt−Ir alloy |
D | 26.7 ≥ ∆ |
−5.7 | 27 |
Pt−Ir alloy |
H | 25.6 ≥ ∆ |
−6.2 | 28 |
Pt−Ir alloy |
OH | 47.2 ≤ ∆ |
1.5 | 26 |
Pt−Ir alloy |
OH+OD | 48.0 ≤ ∆ |
6.7 | 26 |
Pt−Ir alloy |
H | 25.7 ≥ ∆ |
−6.2 | 20 |
Pt−Ir alloy |
OH | 53.2 ≤ ∆ |
4.5 | 20 |
Pt/0.1 M KOH (H2O) | H | 22.4 ≥ ∆ |
−6.0 | 25 |
Pt/0.5 M H2SO4 (H2O) | H | 25.4 ≥ ∆ |
−6.0 | 21 |
Ir/0.1 M KOH (H2O) | H | 23.0 ≥ ∆ |
−6.0 | 25 |
Ir/0.5 M H2SO4 (H2O) | H | 26.1 ≥ ∆ |
−6.0 | 21 |
Pd/0.5 M H2SO4 (H2O) | H | 25.6 ≤ ∆ |
3.5 | 19 |
Au/0.5 M H2SO4 (H2O) | H | 32.2 | 0 |
13 |
Re/0.1 M KOH (H2O) | H | 32.6 | 0 |
16 |
Re/0.5 M H2SO4 (H2O) | H | 36.2 | 0 |
16 |
Ni |
H | 5.1 ≤ ∆ |
24.8 | 11 |
Ni |
H | 19.6 ≤ ∆ |
18.4 | 29 |
Ni |
H | 47.8 ≤ ∆ |
13.1 | 29 |
Ti/0.5 M H2SO4 (H2O) | H | 63.2 ≤ ∆ |
16.4 | 23 |
Zr/0.2 M H2SO4 (H2O) | H | 96.1 ≤ ∆ |
8.7 | 24 |
interface | adsorbate | ∆ |
|
Ref. |
Pt−Ir alloy |
H+D | 19.9 < ∆ |
6.0 | − |
Pt−Ir alloy |
H | 18.7 < ∆ |
6.0 | 27 |
Pt−Ir alloy |
D | 22.2 < ∆ |
5.7 | 27 |
Pt−Ir alloy |
H | 20.9 < ∆ |
5.2 | 28 |
Pt−Ir alloy |
OH | 44.0 < ∆ |
12.9 | 26 |
Pt−Ir alloy |
OH+OD | 45.9 < ∆ |
18.1 | 26 |
Pt−Ir alloy |
H | 21.1 < ∆ |
5.2 | 20 |
Pt−Ir alloy |
OH | 50.7 < ∆ |
15.9 | 20 |
Pt/0.1 M KOH (H2O) | H | 17.8 < ∆ |
5.5 | 25 |
Pt/0.5 M H2SO4 (H2O) | H | 20.8 < ∆ |
5.5 | 21 |
Ir/0.1 M KOH (H2O) | H | 18.3 < ∆ |
5.5 | 25 |
Ir/0.5 M H2SO4 (H2O) | H | 21.5 < ∆ |
5.5 | 21 |
Pd/0.5 M H2SO4 (H2O) | H | 22.8 < ∆ |
14.9 | 19 |
Au/0.5 M H2SO4 (H2O) | H | 28.7 < ∆ |
11.4 | 13 |
Re/0.1 M KOH (H2O) | H | 29.2 < ∆ |
11.4 | 16 |
Re/0.5 M H2SO4 (H2O) | H | 32.7 < ∆ |
11.4 | 16 |
Ni |
H | 6.6 < ∆ |
36.2 | 11 |
Ni |
H | 19.9 < ∆ |
29.8 | 29 |
Ni |
H | 47.0 < ∆ |
24.6 | 29 |
Ti/0.5 M H2SO4 (H2O) | H | 63.1 < ∆ |
27.8 | 23 |
Zr/0.2 M H2SO4 (H2O) | H | 94.4 < ∆ |
20.1 | 24 |
4.2. Correlation constants between the adsorption isotherms
Curves a, b, c, and d in Fig. 8 show the four numerically calculated Langmuir adsorption isotherms of (H + D) corresponding to
In addition, we have experimentally and consistently found and confirmed that the equilibrium constants (
In this work, one can also confirm that the values of
4.3. Negative and positive values of the interaction parameters for the Frumkin adsorption isotherms
A negative value of
In contrast to Table 2, Table 3 shows that only the lateral repulsive interaction (
4.4. Equilibrium constants
In the acidic H2O solutions, the values of
The lateral interaction between the adsorbed H, D, (H + D), OH, or (OH + OD) species cannot be interpreted by the value of
5. Conclusions
The Frumkin and Temkin adsorption isotherms (
The lateral attractive interaction (
The phase-shift method and correlation constants are the most accurate and efficient techniques to determine the Frumkin, Langmuir, and Temkin adsorption isotherms and the related electrode kinetic and thermodynamic parameters of the noble and highly corrosion-resistant metal and alloy/H2O and D2O solution interfaces. They are useful and effective in facilitating selection of optimal electrode materials to yield electrochemical systems of maximum hydrogen, deuterium, and oxygen evolution performances. We expect that numerical simulations with a single equation for −
Acknowledgments
The authors would like to thank Dr. Mu S. Cho (First President of Kwangwoon University, Seoul, Republic of Korea) for supporting the EG&G PAR 273A potentiostat/galvanostat, Schlumberger SI 1255 HF frequency response analyzer, and software packages. The section on theoretical and experimental backgrounds of the phase-shift method was reprinted with permission from Journal of Chemical & Engineering Data 55 (2010) 5598−5607. Copyright 2010 American Chemical Society. The authors wish to thank the American Chemical Society. This work was supported by the Research Grant of Kwangwoon University in 2012.
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