Download Hi-Res ImageDownload to MS-PowerPointCite This:J. Phys. Chem. C 2020, 124, 7, 3988-4000

Full Model for the Two-Step Polarization Curves of Hydrogen Evolution, Measured on RDEs in Dilute Acid Solutions

María de Jesús Gálvez-Vázquez
María de Jesús Gálvez-Vázquez
Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
More by María de Jesús Gálvez-Vázquez
,
Vitali Grozovski
Vitali Grozovski
Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
More by Vitali Grozovski
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Noémi Kovács
Noémi Kovács
Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
Department of Physical Chemistry, Eötvös Loránd University of Budapest, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
More by Noémi Kovács
,
Peter Broekmann*
Peter Broekmann
Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
*E-mail: [email protected]. Tel: +41316314317 (P.B.).
More by Peter Broekmann
http://orcid.org/0000-0002-6287-1042
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Soma Vesztergom*
Soma Vesztergom
Department of Physical Chemistry, Eötvös Loránd University of Budapest, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
*E-mail: [email protected]. Tel: +36204612429 (S.V.).
More by Soma Vesztergom
http://orcid.org/0000-0001-7052-4553

Cite this: J. Phys. Chem. C 2020, 124, 7, 3988–4000

Publication Date (Web):January 18, 2020

https://doi.org/10.1021/acs.jpcc.9b11337

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Abstract

Polarization curves of the hydrogen evolution reaction (HER), recorded on rotating disk electrodes (RDEs) in mildly acidic solutions, usually show a “two step” behavior. That is, two exponentially rising segments (the first commonly assigned to H⁺, the second to water reduction) are separated by a limiting current plateau. Here, we devise an analytical model for the full polarization curve by assuming that HER proceeds according to a quasireversible two-electron reaction, H⁺ + H₂O + 2e^– ⇌ H₂ + OH^–, obeying the Erdey-Grúz–Volmer–Butler equation. Our model is able to reproduce the two step behavior of polarization curves and can also be used for the fitting of measured currents over a broad range of pH, rotation rate, and electrode potential, on both Au and on Pt. We show that the length of the limiting current plateaus measured on RDEs for HER is inversely related to the electrocatalytic activity of the electrode and that at a given rotation rate a linear relationship exists between the plateau length and the bulk solution pH. By analyzing this relationship, we can estimate kinetic parameters, even in cases where the transport performance of the RDE would otherwise not be sufficient to measure well-defined kinetic currents at low overpotentials.

Introduction

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The electrochemical hydrogen evolution reaction (HER) is regarded as a straightforward way of transferring electrical energy to a chemical one, enabling the storage of electricity gained from renewable sources like hydro and solar plants. (1) The development of efficient catalysts for HER has thus become a subject of intensive research. Hydrogen evolution gains, however, further importance, as HER is an almost inevitable side reaction of cathodic electrode processes occurring in aqueous environments. For example, in the electroreduction of CO₂ (2,3) or the deposition of base metals, (4−6) HER often appears as a parasitic reaction.

It is usually claimed (7) that in acidic solutions the overall hydrogen evolution reaction can be described as

(R1)

while in neutral or alkaline media the reaction is written as

(R2)

The exact mechanism of the above reactions, including the identification of the rate-determining step and the pH dependency, is still a matter of debate. While according to Reaction R2, HER can also occur, at a moderate rate, in solutions that are neutral or even alkaline, when hydrogen production is the primary goal of the electrode process, usually acidic conditions are applied.

Under acidic conditions, Reaction R1 is known to proceed quickly on certain transition metals (e.g., on platinum (8−14)) and less quickly on others (e.g., on gold (15−20)). The catalytic performance of these metals can be explained by Sabatier’s principle; (21) that is, the catalytic rate follows a volcano trend with the binding energy of the metal and hydrogen.

To obtain meaningful kinetics in acidic solutions, it is essential to compensate for the effect of mass transport, as it can have a decisive role in the observed current/overpotential characteristics, especially for kinetically facile reactions. (21) It is usually assumed (11,20) that experimentally measured currents for HER can be described, at least at certain overpotential intervals, by the Erdey-Grúz–Volmer–Butler equation:

(1)

While current/potential curves recorded at high transport rates on a gold rotating disk electrode (RDE) can be made subject to analysis based on eq 1, (20) on more facile catalysts like Pt, no kinetic currents can be determined due to the presence of severe diffusion hindrance even at vigorous stirring. As noted by Zheng et al. (14) and by the group of Gasteiger, (12,13) on a Pt surface, the rate of charge transfer becomes so fast (with respect to that of mass transfer) that essentially a thermodynamic equilibrium is established.

The pH dependency of the rate of HER is often related to a reactant switching from H⁺ to water molecule (from Reaction R1 to R2). (21−27) This reactant switching can be observed, for example, on the polarization curves of HER recorded at rotating disk electrodes (28) immersed into mildly acidic solutions, exhibiting a “two step” behavior, as shown by Figure 1.

Figure 1. Polarization curve of an RDE, showing two hydrogen evolution steps with an intermittent limiting current plateau section.

Figure 1 demonstrates that in mildly acidic conditions HER is kinetically controlled at low cathodic overpotentials, yielding cathodic currents that rise exponentially with the applied cathodic overpotential (“first kinetic control section”). At higher cathodic overpotentials, the mass transport of H⁺ becomes rate determining and a limiting current plateau is attained. Cathodic currents higher than the limiting current of H⁺ reduction can only be achieved by applying extremely negative potentials (see the “second kinetic control section” in Figure 1). At such potentials, it is usually assumed that apart from H⁺ reduction (Reaction R1), also the reduction of water molecules (Reaction R2) contributes to HER; thus, a further exponential increase of the cathodic current can be seen, following the limiting plateau section.

The described two step behavior of HER polarization curves was first noticed as early as 1956 by Nagel and Wendler (29) and it was studied more recently by the groups of Tobias, (22) Mayrhofer, (23,24) Bruckenstein, (30) Arenz, (31) Pereira, (32) and the present authors. (27) Finding an adequate model to describe the shape of the two step polarization curves is, however, difficult due to complications arising from an interplay of the mass transport of the diffusing species (H⁺ and OH^–) and a bulk chemical reaction, the autoprotolysis of water:

(R3)

To write proper kinetic equations for HER, Reactions R1–R3 all have to be taken into account, in a scheme suggested by Figure 2a. This was attempted before by Hessami and Tobias, (22) who used the equidiffusivity approximation (i.e., the assumption that the diffusion coefficients of H⁺ and OH^– ions are equal in the solution) to solve combined reaction–diffusion–convection equations to obtain pH profiles. The approach of Mayrhofer et al. (23,24) was based on a different, finite diffusion layer-based approximation, where the diffusion layer thickness was determined by a weighted average of the two diffusion coefficients. None of these two methods were concerned, however, about the kinetics of HER. In the work of Hessami and Tobias, (22) the pH profiles were parametrized by the current of HER (and no potential dependence of this current was analyzed), while in the works of Mayrhofer et al., (23,24) the approximation of full reversibility was used (that is, the authors assumed that the near-surface pH depends linearly on the applied potential, as dictated by Nernst’s equation).

Figure 2. Reaction schemes for HER. Two separate reactions are shown in (a) for acidic and neutral to alkaline solutions. A combined scheme is shown in (b) for near-neutral solutions. The autoprotolysis of water is part of both schemes.

In a recent work of our group, (27) we attempted to model HER by taking into account two strictly irreversible reactions, the reduction of H⁺ and that of water molecules, both following Erdey-Grúz–Volmer–Butler kinetics. In ref (27), we developed a digital simulation-based modeling approach to HER and we presented an approximative analytical model that could well describe polarization curves at various values of pH and rotation rates. In this model, we used an assumption that the diffusivity of OH^– ions exceeds that of H⁺ and that thus at high current densities the near-surface solution layer does not turn alkaline but neutral instead. The resulting model could be used to describe HER polarization curves measured on nickel electrodes.

The model described in ref (27) followed the reaction scheme shown in Figure 2a and it thus contained altogether four variable (fittable) kinetic parameters: two reaction rate and two charge-transfer coefficients, each describing the reduction of H⁺ and that of H₂O molecules, respectively. We noticed, however, a strong correlation between the fitted parameters, which suggested that the reduction of this model would still be possible.

In this present paper, we aim to develop an analytical model that can well describe the polarization curves of HER, recorded on rotating disk electrodes immersed into mildly acidic solutions, by taking into consideration a quasireversible charge-transfer reaction, which represents the combination or Reactions R1 and R2 and that contains an inherent coupling, as a result of autoprotolysis, Reaction R3, between the concentrations of H⁺ and OH^– ions. From a mathematical point of view, this model, represented by Figure 2b, is simpler than the one previously described, (27) as it contains only two variable kinetic parameters (a single reaction rate and a single charge-transfer coefficient).

In what follows, we will give a brief description of the model and then present how it can be used for the estimation of kinetic parameters of HER on two chosen model electrodes (gold and platinum). We will demonstrate that the different lengths of the limiting current plateaus observed on these metals can be used as a direct measure of electrocatalytic hindrance.

Theory

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Thermodynamic Considerations

Although Reactions R1 and R2 (the formation of H₂ either by the reduction of H⁺ ions or by that of water molecules) are seemingly different, from a thermodynamic point of view, both processes lead to the same equilibrium conditions. The standard potentials are E_R1^⊖ = 0 V and E_R2^⊖ = −0.8277 V vs standard hydrogen electrode (SHE) (33) and assuming equilibrium conditions, we can use Nernst’s equation to relate the potentials of electrode Reactions R1 and RR R2 to the a_H⁺ and a_OH^– activities of H⁺ and OH^– ions, respectively, as well as to the Φ_H₂ fugacity of hydrogen gas:

(2)

and

(3)

while from the equilibrium condition E_R1 = E_R2 it follows that

(4)

Assuming that the autoprotolysis of water, Reaction R3, exactly determines the product of H⁺ and OH^– activities as the ionic product of water K_w, we get to K_w = 1.019 × 10^–14 using the standard potential values mentioned before. It can thus be seen that Reactions R1–R3 are not independent from each other and they all have to be considered when describing the thermodynamics of hydrogen evolution. Somewhat contradicting this statement, in the formal kinetic treatment of HER, it is still common to treat Reactions R1 and R2 as separate processes, each valid in its respective pH regime. In what follows, we aim to develop a kinetic treatment that can describe hydrogen evolution on an electrode surface near which the pH shifts, depending on the applied electrode potential, from acidic to alkaline values.

Kinetic Considerations

As a first step, we have to write kinetic rate equations for HER that take both H⁺ and OH^– ions into account. Probably the most straightforward possibility of doing this is to sum Reactions R1 and R2, in a manner illustrated by Figure 2b, to get

(R4)

Reaction R4 contains the H⁺ (or the H₃O⁺) ion as a reactant and the OH^– ion as a product. Assuming that the reaction can proceed in both directions, the current density j yielded by the reaction can be expressed as a sum of cathodic (j_c) and anodic (j_a) terms:

(5)

Assuming that Reaction R4 follows the Erdey-Grúz–Volmer–Butler equation, the cathodic and anodic current densities may be formally expressed as

(6a)

and

(6b)

In eqs 6a and 6b, α_c and α_a are charge-transfer coefficients, k′ is a reaction rate coefficient, and the c⁰ terms stand for near-surface concentrations. The eqs 6a, 6b can be simplified by utilizing the usual assumption that α_a + α_c = n = 2 (the number of electrons involved in Reaction R4). (34) Further assuming that the near-surface concentrations of water and of H₂ molecules can be treated as unit constants—the latter, at least, in a solution saturated with H₂, assuming that the dissolved H₂ concentration shows no significant pH dependence—we can introduce another reaction rate coefficient k in place of k′ as

(7)

This turns eqs 6a and 6b into

(8a)

and

(8b)

In eqs 6a, 6b, 8a, and 8b, E° denotes a potential value where no net current flows in the case when c_H⁺⁰ = c_OH^–⁰. E° can thus be expressed as

(9)

using Nernst’s equation (where we again assumed a unity fugacity of H₂).

Provided that the activity coefficients of H⁺ and OH^– ions can both be considered unity and that the autoprotolysis Reaction R3 is fast enough so that it always maintains the equilibrium constraint that

(10)

independent of space and of time, eqs 8a, 8b can further be simplified to the following form:

(11a)

and

(11b)

where c^⊖ = 1 mol dm^–3 is the standard concentration.

Note that to get from eqs 6a and 6b to eqs 11a and 11b, we made use of eq 9, where, by definition, E_R1^⊖ = 0 V vs SHE. Thus, the electrode potential E, appearing in equation set 11a, 11b, is also to be referenced to SHE.

Equations 11a and 11b determine the current of the electrode reaction provided that the near-surface concentration of hydrogen ions, c_H⁺⁰, is known. On rotating disk electrodes (RDEs), stationary currents can be measured for HER and deriving a mathematical expression for c_H⁺⁰ becomes possible as described below.

Problem of Transport

Provided that (i) mass transfer occurs only by means of diffusion and convection and other means of transport (e.g., migration) can be ignored and (ii) that the diffusion coefficients D_H⁺ and D_OH^– are constants, independent of the concentrations and of spatial coordinates, the condition of stationarity can be expressed in the form of the following equation:

(12)

Here, v_z denotes the axial (z direction) component of the stationary fluid flow under the RDE that can be approximated (35) as

(13)

where a ≈ 0.51023, (28) ω denotes the angular velocity of rotation, and ν the kinematic viscosity of the solution.

If we now express the concentration of OH^– ions from eq 10 as

and plug this into eq 12, we arrive to a nonlinear ordinary differential equation, describing stationary H⁺ concentration profiles under the RDE. This equation has no analytical solution; assuming, however, that the diffusion coefficients of H⁺ and OH^– ions are equal—and this assumption is not uncommon— (22)the differential equation can be linearized in the form:

(14)

where

is the diffusion coefficient of H⁺ and OH^– ions (assumed to be equal) and the function

(15)

was introduced to describe the difference of H⁺ and OH^– concentrations as a function of the z distance measured from the electrode surface. Equation 14 is a linear, second-order ordinary differential equation with a known solution:

(16)

In eq 16, Δc⁰ and Δc^∞ denote near-surface (z = 0) and bulk (z → ∞) concentration differences (see eq 15) and Q_s(x) is the regularized incomplete gamma function (36) (with s = 1/3) defined as

(17)

From eq 16, the current density can be expressed as

(18)

where

(19)

is the generalized Nernstian diffusion layer thickness that contains the gamma function (36) defined by the integral

(20)

Modeling the Polarization Curve of an RDE

The current density expressed by eq 18 is equal to that given in eq 5, with the partial current densities defined by eqs 11a and 11b. This yields the following expression for c_H⁺⁰:

(21)

where the θ(α) function (a dimensionless, potential dependent, combined kinetic parameter) is defined as

(22)

Finally, the equation of a polarization curve recorded on an RDE can be expressed by combining eqs 18 and 21 to

(23)

Equation 23 is the final result of this theoretical treatment. It is an analytical formula for the current density of an RDE on which hydrogen is evolved at a given pH, rotation rate (f), and electrode potential (E). The parameters of this model are listed in Table 1, where it can be seen that the model relies only on two kinetic parameters, the k reaction rate coefficient and the α_c charge-transfer coefficient of Reaction R4. Note that the presented model is very robust, as it considers only the effect of charge transfer, that of mass transport occurring by diffusion and convection, and the effect of the autoprotolysis. Although no mechanistic details (such as those of H adsorption to the surface) are considered, we will see that this robust model delivers well when used for the fitting of experimentally obtained data.

Table 1. Description of Symbols Used

symbol	meaning	formula or typical value(s)
basic physicochemical parameters
pH^∞	pH of the bulk of the solution	3
f	rotation rate of the RDE	625 min^–1
k	reaction rate coefficient for Reaction R4	1 μm s^–1
α_c	charge-transfer coefficient for Reaction R4	1
T	temperature	298.15 K
	diffusion coefficient of H⁺ and OH^– ions, considered equal	10^–4 cm² s^–1
ν	kinematic viscosity of the solution	8.917 × 10^–7 m² s^–1
constants
F	Faraday’s constant	96 485.3 C mol^–1
R	Regnault’s constant	8.314 J mol^–1 K^–1
c^⊖	standard concentration	1 mol dm^–3
a	Kármán’s constant (28)	0.51023
Γ(1/3)	see eq 20	2.67894
E_R1^⊖	standard potential of Reaction R1	0 V vs SHE
E_R2^⊖	standard potential of Reaction R2	–0.8277 V vs SHE
K_w	autoprotolysis constant of water	1.019 × 10^–14
derived quantities
c_H⁺^∞	H⁺ concentration in the bulk of the solution	10^–pHc^⊖
Δc^∞	difference of H⁺ and OH^– concentrations in the bulk
ω	angular frequency of rotation	2πf
δ_N	generalized Nernstian diffusion layer thickness, see eq 19
θ(α)	combined kinetic parameter, see eq 22
c_H⁺⁰	near-surface H⁺ concentration, see eq 21
j	current density of the RDE, see eq 23
j_cat,H⁺	catalytic current density of H⁺ reduction, see eq 24
j₀	exchange current density, see eq 25
	limiting current density, see eq 26
j_cat,H₂O	catalytic current density of water splitting, see eq 29
j_rev	Nernstian (reversible) current density, see eq 31

Experimental

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The rotating disk electrodes used in this study were obtained from Metrohm (Herisau, Switzerland). The diameter of the disk electrodes was (3.00 ± 0.05) mm, embedded into a PEEK shaft of 10 mm outer diameter. The geometric surface area was used for calculating current densities. Prior to the experiments, the electrodes were dipped, for a few moments, into Caro’s acid and were then rinsed abundantly with ultrapure water (Milli-Q by Merck Millipore, R = 18.2 MΩ cm, used for the preparation of solutions as well).

The studied solutions of different pH were prepared by diluting calculated amounts of a 0.1 mol dm^–3 HClO₄ (70%, Merck, Suprapure) stock solution and solid NaClO₄ (99.99%, trace metals basis, Merck) with ultrapure water, by keeping the ionic strength at a fixed value of 0.1 mol dm^–3. The pH of the solutions was measured by a calibrated Metrohm 914 pH meter.

A lab-made three-electrode glass cell was used for the experiments. For measurements on Au, a large Au foil was used as a counter electrode, while for measurements on Pt, we applied a large surface area Pt foil. All measurements were carried out by using a Hg|Hg₂SO₄|K₂SO₄ (sat) reference electrode (Radiometer Analytical XR200, connected to the main chamber through a Luggin capillary). Electrode potentials in the paper are reported with reference to the standard hydrogen electrode (SHE); for the potential shift, the value of E_{Hg/Hg₂SO₄} = 650 mV was used.

Prior to measurements, the solution in the cell was deaerated with a pure Ar (5N, Alphagaz) flow for 15 min and saturated by hydrogen (5N, Alphagaz). The electrodes were submerged to the electrolyte solution without potential control, and the equilibrium potential E^eq was determined by measuring the open-circuit potential. Polarization curves presented in the paper were recorded point by point by steady-state current measurements at given electrode potentials and rotation rates, according to the following sequence (see Figure 3): the electrode potential and the rotation rate were set, and the current was measured until it reached a stationary value. Then, the potential was set back to E^eq and a rotation rate of f = 4500 min^–1 was applied for some seconds to remove any accumulated H₂ from the surface. The current measurement was then repeated with other potential and rotation rate settings. The measured data were IR-corrected postexperimentally—the solution resistance was determined by means of high-frequency impedance measurements. During all measurements, the solutions were kept saturated with H₂ by continuous but slow purging (that did not interfere with the hydrodynamics of rotation).

Figure 3. Experimental protocol for the measurement of HER polarization curves on RDEs. The stationary current of the RDE is measured at given electrode potential (E) and rotation rate (f) values (green periods). Between the measurements, the potential control is switched off and the RDE rotated quickly, to remove accumulated bubbles (red periods).

The measurements were automated by using an Autolab PGSTAT128N potentiostat in connection with a Metrohm Autolab rotator unit and by the application of the Nova v2.1 software.

Results

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Experimentally obtained polarization curves are shown in Figure 4 for both the gold and the platinum RDE. These curves were recorded in mildly acidic solutions (2.0 ≲ pH ≲ 3.6) and at different rotation rates (400 < f < 2500). As shown by the figures, the measured polarization curves can well be fitted using eq 23. Note that during the fitting we varied only three parameters (

, k, and α_c), while the other parameters were fixed at values listed in Table 1. Also note that the optimization was carried out by considering all data points shown either for gold or for platinum Figure 4 and not in a curve-by-curve manner. Even under such strict conditions, the calculated values (shown by the green curves) match reasonably well the measured ones (shown by the red dots).

Figure 4. Experimentally obtained polarization curves (red dots) on an Au (a) and on a Pt (b) RDE, showing a two step behavior. In each panel (at different values of pH), the cathodic current density increases as the rotation rate f is set to values of 400, 625, 900, 1225, 1600, 2025, and 2500 min^–1. The green curves are created by fitting the model described by eq 23 globally, that is, for all pH and rotation rate values, and by optimizing only three parameters (α_c, k, and ). Determined confidence intervals (at 95% statistical certainty) for the fitted parameters are α_c = 0.486 ± 0.067, and for gold and α_c = 0.643 ± 0.037, and for platinum. Other parameter values (not optimized) are shown in Table 1.

Optimized values of α_c, k, and

are given in the caption of Figure 4 for Au and Pt. As can be seen, the optimized

values match well with the diffusion coefficient of H⁺ ion known from the literature. (31) The determined values of α_c are also in good agreement with those found in the literature (37) and, as we will show later, the determined k and α values can be recombined to exchange current densities in the expected range for both gold (38) and platinum. (11)

A notable difference between the polarization curves of gold and platinum, as can be seen in Figure 4, is in the length of their limiting current plateaus, which is substantially shorter in the case of Pt. This, as we will see below, can be explained by the reaction rate coefficient k on platinum being 5 orders of magnitude higher compared with gold, and by that the determined α_c values for the two metals also differ.

Discussion

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General Behavior of the Model; Polarization Curve Segments

As could be seen in Figure 4, the model function given by eq 23 can describe well the two step behavior of HER polarization curves. For the parameter values listed in Table 1, a calculated polarization curve is shown in Figure 5 (thick gray curve).

Figure 5. Polarization curve (thick gray) calculated using eq 23 and the parameter values of Table 1, shown in two different representations: with linear axis scaling in (a) and on a Tafel plot in (b). The three different segments of the curves, marked by the dashed lines, can be approximated by eqs 24–30, as discussed in the text. The contour map in the background of (a) shows the variation of pH as a function of the distance measured from the electrode surface at each disk potential. (Details of calculating pH profiles using the presented model are discussed later, cf. to Figure 9).

First of all, it can be seen that the modeled polarization curves clearly exhibit three distinct parts: (i) a starting exponential rise, assigned to the charge-transfer-controlled reduction of H⁺ ions denoted by j_cat,H⁺ and plotted by a dashed red curve in Figure 5; (ii) an almost horizontal plateau section (j_lim), shown by a dashed black line, where the current is limited by the rate of transport of H⁺; and, finally, (iii) another exponential rise that we may assign to a charge-transfer-controlled reduction of H₂O, denoted by j_cat,H₂O and is shown by the green dashed curve in Figure 5.

The model is able to describe a smooth transition between the aforementioned limiting cases. Formulae for the current density for each limiting case can be derived as follows.

Catalytic Current of H⁺ Reduction, j_cat,H⁺

In this limiting case, the current is controlled by the catalytic reduction of (i.e., charge transfer to) H⁺ ions. If the cathodic potential is far enough from the equilibrium potential E^eq (where the rate of the opposite reaction, hydrogen oxidation, is negligible) but still not very negative (so that the transport of H⁺ ions still does not become rate limiting), current can be determined by assuming that ω → ∞ and that

. This turns eq 23 into

(24)

The current density calculated from eq 24 is plotted by the red dashed curve in Figure 5. As shown by the Tafel representation in Figure 5b, this section of the polarization curve is characterized by a Tafel slope of

. Equation 24 is also useful for expressing the exchange current density j₀ by evaluation at

(25)

The variation of exchange current densities on pH is shown for gold and platinum in Figure 6. These data agree well with values found in the literature. (11,38)

Figure 6. Exchange current densities j₀ in the studied pH range, calculated by using eq 25, based on the kinetic parameters determined by nonlinear fitting in Figure 4 for gold and platinum.

Limiting Current of H⁺ Reduction, j_lim

In this limiting case, shown by the black dashed line in Figure 5, the current density is governed solely by the transport of H⁺ ions from the bulk of the solution to the electrode surface. A formula for the limiting current

can be provided within the framework of the presented model by assuming that the near-surface concentration difference of H⁺ and OH^– ions (Δc⁰) equals zero in eq 18. Then

(26)

where for fairly acidic solutions, we can assume that Δc^∞ ≈ c_H⁺^∞ and thus

(27)

The Tafel slope corresponding to this flat plateau is, as shown in Figure 5b, ∞.

Case of Mixed Charge-Transfer/Transport Control for H⁺ Reduction

It can be shown that in this region of mixed control, where the gray curve in Figure 5 already leaves j_cat,H⁺ but still does not attain the limiting current plateau, our model yields current densities that fully match those calculated from the Koutecký–Levich equation (39) and thus for this “first transition” section of the polarization curve

(28)

Charge-Transfer-Controlled H₂O Reduction

When the potential is very negative, a series expansion of the current, as given by eq 23, around −∞ for the term

to the first order yields the following equation

(29)

Note that, as expected, this equation is independent of c_H⁺^∞. This current is shown by the dashed green curve in Figure 5; as seen in the Tafel representation, Figure 5b, the corresponding Tafel slope is

Mixed Charge-Transfer Control of H₂O Reduction and Transport Control of H⁺ Reduction

It can be shown that at the potential regime between these two segments, i.e., in the “second transition section”, the current can be described by the equation

(30)

In what follows, we will analyze the effect of varying certain parameters (α_c and k) on the calculated polarization curves.

Parameter Dependencies

Dependence on α_c

Polarization curves calculated based on eq 23 show a strong dependence on the value of the charge-transfer coefficient α_c, as illustrated by Figure 7a,b.

Figure 7. Effect of varying the parameters α_c (a, b) and k (c, d) on the calculated polarization curves. Values assumed are shown on the graph; other parameters are given in Table 1. Polarization curves are shown in two different representations: with linear axis scaling (a, c) and on a Tafel plot (b, d).

With respect to the definition of the charge-transfer coefficient α_c, we emphasize that since the presented model is built on Reaction R4, a two-electron reaction, we assumed that α_c + α_a = 2; (34) thus, based on this definition, α_c = 1 represents symmetry.

Note in Figure 7b that the Tafel slopes of the first and second exponentially increasing segments are

and

, in accordance with what was said earlier about these segments. Also note that as a result of the two differing Tafel slopes, the length of the transport-limited plateau is heavily influenced by the value of α_c: smaller α_c values result in longer plateaus.

Dependence on k

The dependence of the polarization curves on the reaction rate coefficient k is illustrated by Figure 7c,d. Note that as shown by the figure, the polarization curves tend toward a reversible curve (indicated in Figure 7c,d by a dashed blue line) if we increase the value of k. Indeed, in the k → ∞ limit, the current of eq 23 reduces to

(31)

Note that we get to this very same expression of the reversible current if we solve eq 12 by assuming that the value of Δc₀ is determined by Nernst’s equation (that is, if we utilize a Nernstian boundary condition). As expected, eq 31 contains no kinetic parameters as it is a consequence of thermodynamic and transport-related considerations.

Note in Figure 5 that the “first steps” of the polarization curves calculated for finite k values tend to achieve the reversibility limit quite easily. In the case of α_c = 1, the first steps of the polarization curves calculated for k ≥ 10^–2 m s^–1 are practically indistinguishable from the reversible current. This agrees well with the experimental observations and the argumentation of Gasteiger et al. who have warned that in such cases no conclusions with respect to the kinetics of HER should be drawn from RDE experiments. (12) We note, however, that for the “second step” of the polarization curves, it takes far higher (in fact, unrealistically high, k ≥ 1 m s^–1) rate coefficients to match the reversibility case. This finding offers a new perspective for the interpretation of RDE polarization curves, as will be discussed below.

Kinetic Parameters from Plateau Lengths

As we saw before, HER polarization curves exhibit plateaus of different lengths when measured on metals of different electrocatalytic activities (Figure 4); this behavior is reproduced by the presented model. Although the fitting of the whole model to a set of measurements is computationally not difficult—eq 23 is, after all, an analytical expression—and fitting the full model is always favorable, it seems worthy to analyze plateau lengths and, in particular, their dependence on the pH, in the hope that this analysis will make kinetic parameters accessible more easily.

As the term plateau length is, however, not well-defined, it seems easier to introduce the concept of breakdown overpotential (η_br) as a quantity of similar meaning. We define η_br, as illustrated by Figure 8a, as the overpotential at which the measured current, following the second current step, reaches the value of 2j_lim.

Figure 8. (a) Concept of the breakdown overpotential η_br illustrated on a polarization curve. (b) Dimensionless breakdown overpotentials plotted as a function of pH for gold and platinum, determined from measured data (dots). The lines were created by linear fitting to the measured data, using a pH² weighting. The acquired slopes and intercepts were used according to eq 32 to calculate the kinetic parameters shown in Table 2. Chosen rotation rate: 625 min^–1.

Keeping in mind that

, we can obtain the following formula for the value of η_br from eq 30:

(32)

That is, following a standard Levich analysis for the determination of

, we can plot the normalized breakdown potentials (measured at a chosen, fixed rotation rate) as a function of pH; we can then perform linear fitting to these data (shown in Figure 8b for a rotation rate of 625 min^–1 for gold and platinum) and determine α_c and k values from the slope and intercept. As shown in Table 2, the results are acceptable but not as reliable as those of full-model fitting.

Table 2. Kinetic Parameters of HER on Pt and on Au, in Mildly Acidic Solutions^a

system			α_c
Au	Figure 4	–5.10 ± 0.26	0.486 ± 0.067
	Figure 8	–5.2 ± 1.4	0.50 ± 0.11
Pt	Figure 4	0.024 ± 0.050	0.643 ± 0.037
	Figure 8	0.2 ± 1.6	0.63 ± 0.16

^{^a}

Parameters were determined either by the fitting of the full model to all measured data, Figure 4, or by plotting limiting current plateau lengths as a function of pH, Figure 8.

pH Profiles

The presented model may not only be found useful to fit HER polarization curves but it may also give predictions on how the local pH changes in the vicinity of a rotating electrode at which H₂ evolves. The basis of such predictions is eq 16. In it, expressing Δc⁰ with the aid of the current density j by using eq 23, we arrive to the following equation describing the variation of the concentration differences of H⁺ and OH^– as a function of the distance measured from the electrode surface:

(33)

Concentration difference profiles, calculated based on eq 33, are shown in Figure 9a. Provided that pH^∞ is known, eq 33 permits the direct calculation of pH profiles as well; for that we need to recall the definition of Δc in eq 15. The pH(z) profile can then be calculated as

(34)

Some example pH profiles are shown in Figure 9b.

Figure 9. (a) Normalized concentration difference profiles as a function of the normalized distance, for some chosen values of the normalized current density (shown in the figure). (b) An example for pH profiles calculated for various normalized current values, assuming that pH^∞ = 3.

It follows from eqs 33 and 18 that as the cathodic current increases, pH values measured in the vicinity of the electrode will rise. Exactly at j = j_lim, the pH at the electrode surface reaches neutrality (pH⁰ ≈ 7). When a cathodic current density higher than j_lim is forced through the electrode surface, the near-electrode solution region gets alkaline, yet at a given distance, the pH drops suddenly to acidic values (see Figure 9b).

The distance at which the aforementioned drop occurs (i.e., the distance of the neutrality point z_neut) depends on how much the current density exceeds the limiting current density and it can be expressed as

(35)

where we denoted by Q_s^–1(x) the inverse of the regularized incomplete gamma function Q_s(x), defined by eq 17.

In Figure 10, z_neut is plotted as a function of the normalized current density

. The z_neut quantity can be interpreted as a measure of how deep the near-electrode solution layer becomes alkaline, as shown by Figure 9. Note in Figure 10 that true alkalination (i.e., the appearance of a pH ≳ 7 region) can only occur if

and that at high current densities, the depth of alkalination can exceed the diffusion layer thickness δ_N.

Figure 10. Full black curve: the distance of neutrality (normalized to the diffusion layer thickness δ_N) as a function of the current density normalized to . Note that the function, eq 35, is not defined for . Dashed gray curve: an estimate for the neutrality distance based on an analytical solution assuming that D_OH^– ≫ D_H⁺. (27)

Concluding Remarks; Comparison to Other Works

The presented model seems suitable to describe polarization curves of HER measured at two electrodes of different electrocatalytic activities (Au and Pt). The extracted parameters are in agreement with some shown in the literature before, (11,20) yet at this point, we would like to emphasize limitations of the treatment and to make a brief comparison to earlier works on the topic of HER.

An important issue, to which we would like to direct the readers attention, is the equidiffusivity assumption that we utilized. This assumption, although not unprecedented in the literature (see the works of Tobias as an example (22)), poses some limitations to the validity of our analysis. Avoiding use of the assumption is, unfortunately, not possible, as it is required for eq 12 to be analytically solvable. The equidiffusivity assumption means that we consider the diffusion coefficients of H⁺ and OH^– ions equal, appearing as a common coefficient

in our equations. We are aware (and the reader should also be) that this approximation is only valid on an order of magnitude level (while in reality, D_H⁺ is supposed to be about 2 times higher than D_OH^–). The equidiffusivity assumption, as also pointed out by Tobias, (22) renders the concentration of OH^– at and under the disk surface to be underestimated. That the model equations can still be used to obtain good apparent fits of the measured polarization curves is probably attributed to the fact that currents measured at high cathodic overpotentials show only a moderate (order of 1/3) dependence on

(cf. eq 29).

At this point, it seems worthy to make a comparison between the model presented here and one of our previous attempts at modeling polarization curves of HER. In ref (27), we constructed analytical approximations to an otherwise digital simulation-based model where we assumed that the diffusion coefficient of OH^– is not only equal to but actually much higher than that of H⁺. This assumption also led to a fittable model function, but it predicted that the near-surface solution region, instead of getting alkaline, would get neutral up to a certain depth. Of course, under these circumstances, the “distance of neutrality” was higher than the one obtained here: instead of the formation of a thin alkaline layer, we assumed the formation of a thicker, however, neutral layer. In Figure 10, we show a comparison between the two approaches.

A further difference between the model presented here and the one we described before (27) is that while the previous one was dealing with two irreversible reactions (namely, the reduction of H⁺ ions and that of water molecules), the present model is built on a combined, quasireversible, reaction (Reaction R4). The present model thus performs better compared with the previous one in two ways: (i) it provides good fits with only two (instead of four) kinetic parameters, and (ii) it is also able to model a quasiequilibrium (that is, the k → ∞ case). Although within the framework of the present model it is still possible to distinguish two reactions (see our discussion of polarization curve segments assigned to H⁺ reduction and to water splitting), we emphasize here that such distinctions are all but arbitrary and the treatment presented here is built on a single charge-transfer reaction, Reaction R4.

In comparison to the models of some other authors, (22−24) a clear advantage of the model presented here is that it contains kinetic parameters and does not rely on the use of the Nernstian boundary condition. This condition would predict that the near-surface pH is exactly determined by, and directly proportional to, the electrode potential. Instead of using a Dirichlet (i.e., Nernstian) boundary condition, our model utilizes a Neumann condition (40) and thus allows the calculation of kinetic currents.

Although the model seems to fit experimental data on a broad scale (Figure 4), here we would like to draw the attention of the readers to another limitation, which arises from the very fact that we assumed the validity of the Erdey-Grúz–Volmer–Butler equation for Reaction R4. We thus ignored any effects related to surface kinetics and that the parameters k and α_c can be potential dependent. (41) This simplification was, however, necessary to describe the experimentally observed two step behavior of HER, visible at high cathodic overpotentials. Consequently, the k and α_c parameters that we determined here can be considered valid primarily at high overpotential. Although some variations of these parameters may occur—and this is probably responsible for the fits of Figure 4 not being perfect at low overpotentials—the overall fits are still satisfactory.

Conclusions

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We have developed a new model that is able to describe HER as it occurs on RDEs immersed into mildly acidic solutions, where the polarization curves show a two step behavior. The model is centered around a single reaction, Reaction R4, that contains both H⁺ ions (as a reactant) and OH^– ions (as a product). We assumed that the Erdey-Grúz–Volmer–Butler equation applies for this reaction and that the diffusion coefficient of the two reacting species (H⁺ and OH^–) are equal. On the basis of these assumptions, we managed to solve the differential equations governing the system; the resulting analytical model could be used for the fitting of experimentally obtained polarization curves. By varying only three model parameters, we achieved good fits over a relatively broad range of pH and rotation rates for both Au and Pt RDEs.

A very important implication of the model is that the plateau lengths seen on RDE polarization curves are (inversely) related to electrocatalytic activity. We showed that at fixed rotation rates, a linear relationship exists between the plateau length and the bulk solution pH. By analyzing this relationship, we can get a good estimate of the kinetic parameters k and α_c, even in cases where the transport performance of the RDE is not sufficient to measure well-defined kinetic currents using the standard Koutecký–Levich analysis. (12,41)

Within the presented framework, it is also possible to model the variation of pH as a function of distance measured from the electrode surface. This result may become useful if we study HER as a side reaction of, for example, metal deposition processes where local pH rises can have unwanted effects on the deposit.

Author Information

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Corresponding Authors
- Peter Broekmann - Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland; http://orcid.org/0000-0002-6287-1042; Email: [email protected]
- Soma Vesztergom - Department of Physical Chemistry, Eötvös Loránd University of Budapest, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary; http://orcid.org/0000-0001-7052-4553; Email: [email protected]
Authors
- María de Jesús Gálvez-Vázquez - Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
- Vitali Grozovski - Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
- Noémi Kovács - Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland; Department of Physical Chemistry, Eötvös Loránd University of Budapest, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
Notes
The authors declare no competing financial interest.

Acknowledgments

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Support by the CTI Swiss Competence Center for Energy Research (SCCER Heat and Electricity Storage) is gratefully acknowledged. P.B. acknowledges financial support from the Swiss National Foundation (grant No. 200020–172507). S.V. acknowledges support from the National Research, Development and Innovation Office of Hungary (NKFIH grant Nos. PD124079 and K129210). M.d.J.G.-V. and N.K. acknowledge the financial support by the Swiss Government Excellence Scholarships for Foreign Scholars (ESKAS).

References

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Durst, J.; Siebel, A.; Simon, C.; Hasché, F.; Herranz, J.; Gasteiger, H. A. New insights into the electrochemical hydrogen oxidation and evolution reaction mechanism. Energy Environ. Sci. 2014, 7, 2255– 2260, DOI: 10.1039/C4EE00440J
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New insights into the electrochemical hydrogen oxidation and evolution reaction mechanism
Durst, J.; Siebel, A.; Simon, C.; Hasche, F.; Herranz, J.; Gasteiger, H. A.
Energy & Environmental Science (2014), 7 (7), 2255-2260CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
The effect of pH on the hydrogen oxidn. and evolution reaction (HOR/HER) rates is addressed for the first time for the three most active monometallic surfaces: Pt, Ir, and Pd carbon-supported catalysts. Kinetic data were obtained for a proton exchange membrane fuel cell (PEMFC; pH ≈ 0) using the H2-pump mode and with a rotating disk electrode (RDE) in 0.1 M NaOH. Our findings point toward: (i) a similar ≈100-fold activity decrease on all these surfaces when going from low to high pH; (ii) a reaction rate controlled by the Volmer step on Pt/C; and (iii) the H-binding energy being the unique and sole descriptor for the HOR/HER in alk. electrolytes. Based on a detailed discussion of our data, we propose a new mechanism for the HOR/HER on Pt-metals in alk. electrolytes.
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Zheng, J.; Sheng, W.; Zhuang, Z.; Xu, B.; Yan, Y. Universal Dependence of Hydrogen Oxidation and Evolution Reaction Activity of Platinum-group Metals on pH and Hydrogen Binding Energy. Sci. Adv. 2016, 2, e1501602 DOI: 10.1126/sciadv.1501602
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Universal dependence of hydrogen oxidation and evolution reaction activity of platinum-group metals on pH and hydrogen binding energy
Zheng, Jie; Sheng, Wenchao; Zhuang, Zhongbin; Xu, Bingjun; Yan, Yushan
Science Advances (2016), 2 (3), e1501602/1-e1501602/9CODEN: SACDAF; ISSN:2375-2548. (American Association for the Advancement of Science)
Understanding how pH affects the activity of hydrogen oxidn. reaction (HOR) and hydrogen evolution reaction (HER) is key to developing active, stable, and affordable HOR/HER catalysts for hydroxide exchange membrane fuel cells and electrolyzers. A common linear correlation between hydrogen binding energy (HBE) and pH is obsd. for four supported platinum-group metal catalysts (Pt/C, Ir/C, Pd/C, and Rh/C) over a broad pH range (0 to 13), suggesting that the pH dependence of HBE is metal-independent. A universal correlation between exchange c.d. and HBE is also obsd. on the four metals, indicating that they may share the same elementary steps and rate-detg. steps and that the HBE is the dominant descriptor for HOR/HER activities. The onset potential of CO stripping on the four metals decreases with pH, indicating a stronger OH adsorption, which provides evidence against the promoting effect of adsorbed OH on HOR/HER.
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Pentland, N.; Bockris, J. O. M.; Sheldon, E. Hydrogen Evolution Reaction on Copper, Gold, Molybdenum, Palladium, Rhodium, and Iron. J. Electrochem. Soc. 1957, 104, 182, DOI: 10.1149/1.2428530
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Hydrogen-evolution reaction on copper, gold, molybdenum, palladium, rhodium, and iron. Mechanism and measurement technique under high-purity conditions
Pentland, N.; Bockris, J. O'M.; Sheldon, E.
Journal of the Electrochemical Society (1957), 104 (), 182-94CODEN: JESOAN; ISSN:0013-4651.
Various aspects of technique in measurements of electrode kinetics under conditions where competing reactions due to the presence of trace impurities in the soln. are important are examd. The kinetics of the H-evolution reaction in acid and alkaline solns. on several transition metals has been examd. with special reference to the low c.-d. region. Inferences concerning the rate-detg. step in the reaction 2H+ + 2e0- → H2 are drawn. In general, there is a tendency for the metals examd. in acid soln. to have a rate-controlling electrochem. desorption reaction and for those in alk. soln. to have a rate-detg. discharge step.
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Ives, D. J. G. Some Abnormal Hydrogen Electrode Reactions. Can. J. Chem. 1959, 37, 213– 221, DOI: 10.1139/v59-028
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Some abnormal hydrogen electrode reactions
Ives, D. J. G.
Canadian Journal of Chemistry (1959), 37 (), 213-21CODEN: CJCHAG; ISSN:0008-4042.
cf. C.A. 51, 1498a; 52, 6976c. The reasonably normal behavior of the H overvoltage with H or N as the sweeping gas on a Au electrode in pre.ovrddot.electrolyzed 0.1N HCl was changed on prolonged annealing of the Au electrode at temps. below 800°. On restoration of the annealed Au electrode to the soln. it showed a rest potential of 400 mv., insensitivity to the substitution of N for H, enhanced cathodic overpotentials increasing with time, and curved Tafel plots of varying but excessively high gradients. Thermally deactivated Au was not capable of atomizing mol. H or catalyzing the recombination of H atoms and formed a "nonequil. H electrode." The dependence of open-circuit potential and prolonged growth of overpotential on cathodization time independent of c.d. above a min. value suggests that H atoms penetrate the Au lattice. Pt electrodes poisoned with Hg showed a similar behavior on cathodic polarization with rest potentials increasing from 350 to 625 mv. with increasing degrees of poisoning. The presence of a cathodic product with reducing properties was demonstrated by the imprint of W blue by bringing the Pt cathode in contact with a WO3 target. It is suggested that the results justify consideration of the desorption of the H2+ ion as a transition step in the H evolution reaction mechanism.
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Brug, G. J.; Sluyters-Rehbach, M.; Sluyters, J. H.; Hemelin, A. The Kinetics of the Reduction of Protons at Polycrystalline and Monocrystalline Gold Electrodes. J. Electroanal. Chem. Interfacial Electrochem. 1984, 181, 245– 266, DOI: 10.1016/0368-1874(84)83633-3
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The kinetics of the reduction of protons at polycrystalline and monocrystalline gold electrodes
Brug, G. J.; Sluyters-Rehbach, M.; Sluyters, J. H.; Hamelin, A.
Journal of Electroanalytical Chemistry and Interfacial Electrochemistry (1984), 181 (1-2), 245-66CODEN: JEIEBC; ISSN:0022-0728.
The redn. of H+ from 1M HClO4 and 1M NaClO4 solns. at polycryst. and single-crystal faces of very pure Au electrodes was studied by detg. the forward rate const. (k1) as a function of potential and of H+ concn. The techniques applied are d.c. and impedance measurements both with a step-wise variation of d.c. potential (duration 4 s), and d.c. measurements with a continuous potential variation. The consistency of the results was extensively tested and was very satisfactory. Plots of ln kf vs. potential are curved and exhibit limiting slopes corresponding to values for the operational transfer coeffs. of α = 1 at pos. and α = 0.5 at neg. potentials. This behavior is discussed in terms of mech. models described in the literature, and also an alternative mechanism is tentatively proposed. An increase in the rate consts. is obsd. when the purity of the Au is less. The slight differences in the rate consts. obsd. at single-crystal faces of the same purity but with different crystallog. orientation are discussed.
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Conway, B. E.; Bai, L. State of Adsorption and Coverage by Overpotential-Deposited H in the H₂ Evolution Reaction at Au and Pt. Electrochim. Acta 1986, 31, 1013– 1024, DOI: 10.1016/0013-4686(86)80017-2
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State of adsorption and coverage by overpotential-deposited hydrogen in the molecular hydrogen evolution reaction at gold and platinum
Conway, B. E.; Bai, L.
Electrochimica Acta (1986), 31 (8), 1013-24CODEN: ELCAAV; ISSN:0013-4686.
By means of potential decay measurements using a digital data acquisition and computer processing system, accurate values of overvoltage decay rates, dη/dt, may be obtained from which the pseudocapacitance and coverage behavior of overvoltage-deposited (OPD) H species in the cathodic H evolution reaction (HER)at Au electrodes may be quant. derived as a function of η. The behavior of the HER at Au is of interest in that an unusual Tafel slope value of 2.3 RT/F is exhibited in acid soln. while the value of alk. solns. is the more familiar value of ∼2.32 RT/F. Anal. of the overvoltage relaxation behavior on open-circuit, following interruption of cathodic polarization currents, gives an almost const. and small interfacial capacitance corresponding to a double-layer capacitance. Steady-state OPD H coverage (θ) is hence quite small (θH < 0.3%). The Tafel slope value of 2.3 RT/F requires, however, a potential-dependent H coverage detd. by an H electrosorption step almost at equil. but with θH small. The rate-detg. step is suggested to be surface diffusion to preferred desorption sites. Comparative results are presented for the HER at activated Pt where, contrary to the behavior of Au, a large pseudocapacitance for OPD H is derived that may be assocd. with some surface hydride formation, the possibility ofreadsorption of H from a boundary layer supersatd. with H having been minimized by electrode rotation at a sufficiently high rate of 3600 rpm.
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Khanova, L. A.; Krishtalik, L. I. Kinetics of the hydrogen evolution reaction on gold electrode. A new case of the barrierless discharge. J. Electroanal. Chem. 2011, 660, 224– 229, DOI: 10.1016/j.jelechem.2011.01.016
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Kinetics of the hydrogen evolution reaction on gold electrode. A new case of the barrierless discharge
Khanova, Larisa A.; Krishtalik, Lev I.
Journal of Electroanalytical Chemistry (2011), 660 (2), 224-229CODEN: JECHES; ISSN:1873-2569. (Elsevier B.V.)
Kinetics of hydrogen evolution reaction on the electrodeposited gold electrode is studied. In semi-logarithmic coordinates, polarization curves consist of two linear segments with Tafel slopes 0.06 V at lower overpotentials and 0.12 V at the higher ones. The kinetics in the higher-slope region depends on the soln. pH and the ψ 1-potential (effects of the ionic strength and of the presence of the surface-active tetrabutylammonium cation) as it is predicted by the theory of the ordinary slow discharge. In the lower-slope region, overpotential does not depend on pH and ψ 1-potential; this is in full accordance with the theory of the barrierless discharge. We nevertheless analyze also several alternatives to the theory of barrierless discharge for the explanation of the low-slope region, but we show that they are not consistent with the exptl. data.
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Kahyarian, A.; Brown, B.; Nesić, S. Mechanism of the Hydrogen Evolution Reaction in Mildly Acidic Environments on Gold. J. Electrochem. Soc. 2017, 164, H365– H374, DOI: 10.1149/2.1061706jes
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Mechanism of the Hydrogen Evolution Reaction in Mildly Acidic Environments on Gold
Kahyarian, Aria; Brown, Bruce; Nesic, Srdjan
Journal of the Electrochemical Society (2017), 164 (6), H365-H374CODEN: JESOAN; ISSN:0013-4651. (Electrochemical Society)
Despite numerous studies studying the kinetics of the H evolution reaction (HER) on a Au surface in acidic solns., the underlying mechanism of this reaction have remained controversial to date. The existing mechanisms are reevaluated and are inadequate in explaining the steady state polarization behavior of the H evolution reaction in an extended cathodic potentials and mildly acidic pH range. A mechanism including a surface diffusion step of Hads alongside the Volmer, Heyrovsky, and Tafel elementary steps, best describes the exptl. data obtained in acidic perchlorate solns. up to pH 5, while the rate detg. step changes both with pH and electrode potential. This overall HER mechanism was further verified using a comprehensive math. model based on the proposed elementary steps, where a satisfactory agreement with exptl. results was obtained.
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Obata, K.; Stegenburga, L.; Takanabe, K. Maximizing Hydrogen Evolution Performance on Pt in Buffered Solutions: Mass Transfer Constrains of H₂ and Buffer Ions. J. Phys. Chem. C 2019, 123, 21554– 21563, DOI: 10.1021/acs.jpcc.9b05245
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Maximizing Hydrogen Evolution Performance on Pt in Buffered Solutions: Mass Transfer Constrains of H2 and Buffer Ions
Obata, Keisuke; Stegenburga, Liga; Takanabe, Kazuhiro
Journal of Physical Chemistry C (2019), 123 (35), 21554-21563CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
Although the electrochem. H evolution reaction (HER) on a Pt electrode is among the most studied electrocatalytic reactions, its reaction mechanism and exchange c.d. are still under debate. Particularly on the Pt catalyst, its facile reaction kinetics and lack of effective methods to compensate mass transport make it difficult to isolate kinetic and diffusion contributions. This study focuses on the quant. description of mass transfer constraints arising from both H2 and phosphate buffer ions using a Pt electrocatalyst in near-neutral pH regions, which are overlooked in the literature despite the relevance to various (photo-) electrochem. reactions for H2O splitting and CO2 redn. The established HER model that uses H+ as a reactant quant. breaks down the obsd. overpotentials with diffusion contributions of both H and buffer species while the intrinsic kinetics on Pt exhibits negligible contribution. The significance of electrolyte engineering, i.e., the optimization of the electrolyte identity and molality, is confirmed to det. the overall HER performance. To maximize the HER performance on Pt at ambient temp., the phosphate-buffer electrolyte should be adjusted to a pH close to pKa of the buffer that effectively minimizes the pH gradient and to the adequate molality of the buffer (typically ∼0.5 M phosphates) that H2 diffusion is maximized, which is related with H2 soly. and soln. viscosity. At pH far from pKa, concn. overpotential of buffer ion dominates the overall performance, which requires highly dense buffer (>1.5 M phosphates) to minimize the pH gradient.
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Hessami, S.; Tobias, C. W. In-Situ Measurement of Interfacial pH Using a Rotating Ring-Disk Electrode. AIChE J. 1993, 39, 149– 162, DOI: 10.1002/aic.690390115
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In-situ measurement of interfacial pH using a rotating ring-disk electrode
Hessami, Sholeh; Tobias, Charles W.
AIChE Journal (1993), 39 (1), 149-62CODEN: AICEAC; ISSN:0001-1541.
A nonintrusive technique for the in-situ measurement of interfacial pH and current efficiency was developed. A ring electrode, operated potentiometrically at open-circuit, is used to measure the pH change at a rotating disk electrode. The technique takes advantage of the well-characterized hydrodynamics at the rotating disk electrode and has the added advantage that the pH probe, the ring electrode, is not interfering with the flow field and the current distribution on the disk. To det. the pH at the disk electrode by measuring the potential of the ring, the radial transport of hydronium ions across the insulating gap and on the ring is analyzed taking into account the effect of homogeneous dissocn. reactions of H2O and metal-hydroxide ion complexes. Shifts in the ring potential caused by H supersatn. and ohmic drop are also evaluated. A platinized ring electrode in a H-satd. electrolyte provides a stable and reproducible H+-sensor with a Nernstian response to the changes in the bulk pH. Performance of the ring is evaluated by generating H2 at the disk electrode from a dil. acid soln., in the absence of other electrochem. reactions. The technique is then applied to det. the interfacial pH of Ni, Fe, and Ni-Fe alloy electrodeposition with concurrent H2 evolution. This method was also used to measure the current efficiency of Ni electrodeposition in a fast, nonintrusive, and in-situ manner.
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Katsounaros, I.; Meier, J. C.; Klemm, S. O.; Topalov, A. A.; Biedermann, U. P.; Auinger, M.; Mayrhofer, K. J. J. The Effective Surface pH during Reactions at the Solid-Liquid interface. Electrochem. Commun. 2011, 13, 634– 637, DOI: 10.1016/j.elecom.2011.03.032
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The effective surface pH during reactions at the solid-liquid interface
Katsounaros, Ioannis; Meier, Josef C.; Klemm, Sebastian O.; Topalov, Angel A.; Biedermann, P. Ulrich; Auinger, Michael; Mayrhofer, Karl J. J.
Electrochemistry Communications (2011), 13 (6), 634-637CODEN: ECCMF9; ISSN:1388-2481. (Elsevier B.V.)
In this work the activity of protons directly at the solid-liq. interface during a heterogeneous reaction is demonstrated without introducing any pH measurement device, in non-buffered and buffered solns. Due to a simple approach we can exptl. demonstrate the relation between reaction rate and surface pH directly from the cyclic voltammograms. Clearly, the pH at a solid-liq. interface can be quite different from the bulk in unbuffered or insufficiently buffered solns. even at moderate reaction rates, in particular in the pH range of 4 to 10. However, at the given mass-transport conditions, well controlled by a rotating disk electrode, a buffer concn. of 10- 2 M is already sufficient to pin the surface pH to the bulk value at reaction rates of up to 1 mA cm- 2.
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Auinger, M.; Katsounaros, J. C.; Meier, I.; Klemm, S. O.; Biedermann, P. U.; Topalov, A. A.; Rohwerder, M.; Mayrhofer, K. J. J. Near-surface ion distribution and buffer effects during electrochemical reactions. Phys. Chem. Chem. Phys. 2011, 13, 16384– 16394, DOI: 10.1039/c1cp21717h
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Near-surface ion distribution and buffer effects during electrochemical reactions
Auinger, Michael; Katsounaros, Ioannis; Meier, Josef C.; Klemm, Sebastian O.; Biedermann, P. Ulrich; Topalov, Angel A.; Rohwerder, Michael; Mayrhofer, Karl J. J.
Physical Chemistry Chemical Physics (2011), 13 (36), 16384-16394CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
The near-surface ion distribution at the solid-liq. interface during the Hydrogen Oxidn. Reaction (HOR)/Hydrogen Evolution Reaction (HER) on a rotating platinum disk electrode is demonstrated in this work. The relation between reaction rate, mass transport and the resulting surface pH-value is used to theor. predict cyclic voltammetry behavior using only thermodn. and diffusion data obtained from the literature, which were confirmed by exptl. measurements. The effect of buffer addn. on the current signal, the surface pH and the ion distribution is quant. described by anal. solns. and the fragility of the surface pH during reactions that form or consume H+ in near-neutral unbuffered solns. or poorly buffered media is highlighted. While the ideal conditions utilized in this fundamental study cannot be directly applied to real scenarios, they do provide a basic understanding of the surface pH concept for more complex heterogeneous reactions.
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Shinagawa, T.; García-Esparza, A. T.; Takanabe, K. Insight on Tafel Slopes from a Microkinetic Analysis of Aqueous Electrocatalysis for Energy Conversion. Sci. Rep. 2015, 5, 13801 DOI: 10.1038/srep13801
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Insight on Tafel slopes from a microkinetic analysis of aqueous electrocatalysis for energy conversion
Shinagawa Tatsuya; Garcia-Esparza Angel T; Takanabe Kazuhiro
Scientific reports (2015), 5 (), 13801 ISSN:.
Microkinetic analyses of aqueous electrochemistry involving gaseous H2 or O2, i.e., hydrogen evolution reaction (HER), hydrogen oxidation reaction (HOR), oxygen reduction reaction (ORR) and oxygen evolution reaction (OER), are revisited. The Tafel slopes used to evaluate the rate determining steps generally assume extreme coverage of the adsorbed species (θ≈0 or ≈1), although, in practice, the slopes are coverage-dependent. We conducted detailed kinetic analyses describing the coverage-dependent Tafel slopes for the aforementioned reactions. Our careful analyses provide a general benchmark for experimentally observed Tafel slopes that can be assigned to specific rate determining steps. The Tafel analysis is a powerful tool for discussing the rate determining steps involved in electrocatalysis, but our study also demonstrated that overly simplified assumptions led to an inaccurate description of the surface electrocatalysis. Additionally, in many studies, Tafel analyses have been performed in conjunction with the Butler-Volmer equation, where its applicability regarding only electron transfer kinetics is often overlooked. Based on the derived kinetic description of the HER/HOR as an example, the limitation of Butler-Volmer expression in electrocatalysis is also discussed in this report.
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Strmcnik, D.; Uchimura, M.; Wang, C.; Subbaraman, R.; Danilovic, N.; van der Vliet, D.; Paulikas, A. P.; Stamenkovic, V. R.; Markovic, N. M. Improving the Hydrogen Oxidation Reaction Rate by Promotion of Hydroxyl Adsorption. Nat. Chem. 2013, 5, 300– 306, DOI: 10.1038/nchem.1574
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Improving the hydrogen oxidation reaction rate by promotion of hydroxyl adsorption
Strmcnik, Dusan; Uchimura, Masanobu; Wang, Chao; Subbaraman, Ram; Danilovic, Nemanja; van der Vliet, Dennis; Paulikas, Arvydas P.; Stamenkovic, Vojislav R.; Markovic, Nenad M.
Nature Chemistry (2013), 5 (4), 300-306CODEN: NCAHBB; ISSN:1755-4330. (Nature Publishing Group)
The development of hydrogen-based energy sources as viable alternatives to fossil-fuel technologies has revolutionized clean energy prodn. using fuel cells. However, to date, the slow rate of the hydrogen oxidn. reaction in alk. environments has hindered advances in alk. fuel cell systems. Here, we address this by studying the trends in the activity of the hydrogen oxidn. reaction in alk. environments. We demonstrate that it can be enhanced more than fivefold compared to state-of-the-art platinum catalysts. The max. activity is found for materials (Ir and Pt0.1Ru0.9) with an optimal balance between the active sites that are required for the adsorption/dissocn. of H2 and for the adsorption of hydroxyl species (OHad). We propose that the more oxophilic sites on Ir (defects) and PtRu material (Ru atoms) electrodes facilitate the adsorption of OHad species. Those then react with the hydrogen intermediates (Had) that are adsorbed on more noble surface sites.
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Grozovski, V.; Vesztergom, S.; Láng, G. G.; Broekmann, P. Electrochemical Hydrogen Evolution: H⁺ or H₂O Reduction? A Rotating Disk Electrode Study. J. Electrochem. Soc. 2017, 164, E3171– E3178, DOI: 10.1149/2.0191711jes
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Electrochemical Hydrogen Evolution: H+ or H2O Reduction? A Rotating Disk Electrode Study
Grozovski, Vitali; Vesztergom, Soma; Lang, Gyozo G.; Broekmann, Peter
Journal of the Electrochemical Society (2017), 164 (11), E3171-E3178CODEN: JESOAN; ISSN:0013-4651. (Electrochemical Society)
The authors study the effect of H+ and OH- diffusion on the H evolution reaction in unbuffered aq. electrolyte solns. of mildly acidic pH values. The cathodic polarization curves measured on a Ni rotating disk electrode in these solns. can be modeled by assuming two irreversible reactions, the redn. of H+ and of H2O mols., both following Erdey-Gra´a´u´z-Volmer-Butler kinetics. The redn. of H+ yields a transport-limited and thus, rotation rate-dependent current at not very neg. potentials. At more cathodic potentials the polarization curves are dominated by the redn. of H2O and no mass transfer limitation seems to apply for this reaction. Although prima facie the two processes may seem to proceed independently, by the means of finite-element digital simulations a strong coupling (due to the recombination of H+ and OH- to H2O mols.) exists between them. The authors also develop an anal. model that can well describe polarization curves at various values of pH and rotation rates. The key indication of both models is that hydroxide ions can have an infinite diffusion rate in the proximity of the electrode surface, a feature that can be explained by assuming a directed Grotthuss-like shuttling mechanism of transport.
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Vesztergom, S. Encyclopedia of Interfacial Chemistry: Surface Science and Electrochemistry;Wandelt, K., Ed.; Elsevier: Amsterdam, 2018; pp 421– 444.
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Nagel, K.; Wendler, F. Die Wasserstoffelektrode als zweifache Elektrode. Z. Elektrochem. 1956, 60, 1064– 1072, DOI: 10.1002/bbpc.19560600924
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The hydrogen electrode as a two-fold electrode
Nagel, K.; Wendler, F.
Zeitschrift fuer Elektrochemie und Angewandte Physikalische Chemie (1956), 60 (), 1064-72CODEN: ZEAPAA; ISSN:0372-8323.
The H electrode is considered as an example of double-equil. electrodes, involving the reactions H+ + e- → 1/2H2 (α) and H2O + e- → 1/2H2 + OH- (β) together with the equil. H+ + OH- .dblharw. H2O. Thermodynamic properties and kinetics of this system of reactions are derived. The relations between the stationary electrode reaction currents iα and iβ, the total current i, the polarization Δg of the electrode, and the overvoltages Δgα and Δgβ of the electrode reactions are discussed. Stationary current vs. polarization curves are derived for the special case of pure concn. overvoltage and are compared with exptl. curves. The theoretical development also permits insight into more complex electrode processes.
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Kanzaki, Y.; Tokuda, K.; Bruckenstein, S. Dissociation Rates of Weak Acids Using Sinusoidal Hydrodynamic Modulated Rotating Disk Electrode Employing Koutecky-Levich Equation. J. Electrochem. Soc. 2014, 161, H770– H779, DOI: 10.1149/2.0221412jes
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Dissociation rates of weak acids using sinusoidal hydrodynamic modulated rotating disk electrode employing koutecky-levich equation
Kanzaki, Yasushi; Tokuda, Koichi; Bruckenstein, Stanley
Journal of the Electrochemical Society (2014), 161 (12), H770-H779, 10 pp.CODEN: JESOAN; ISSN:0013-4651. (Electrochemical Society)
The hydrogen evolution reaction of HCOOH, CH3COOH, and C2H5COOH solns. consists of two different redn. processes depending on the evaluated potential region; (1) independent redn. of RCOOH and (2) simultaneous redn. of RCOOH and H2O. The redn. of each carboxylic acid generates an apparent convective diffusion-controlled limiting current. The first achievement of the present study is that by using a rotating disk electrode (RDE) and a sinusoidal hydrodynamic modulated-rotating disk electrode (SHM), it was elucidated that the additive property of the redn. currents of RCOOH and H2O was not effective, and the convective-diffusion current was successfully distinguished from the total current. The second achievement is the successful anal. of the rotation-speed dependency of the limiting current in RDE and SHM using a modified theory of the Koutecky-Levich equation. The slopes of the plots for each carboxylic acid increased in the following sequence: RDE, SHM (p = 0.05), and SHM (p = 0.24), which is consistent with the theory. The dissocn. rates of the carboxylic acids and the reverse recombination rate were calcd.
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31
Wiberg, G. K. H.; Arenz, M. On the Influence of Hydronium and Hydroxide Ion Diffusion on the Hydrogen and Oxygen Evolution Reactions in Aqueous Media. Electrochim. Acta 2015, 159, 66– 70, DOI: 10.1016/j.electacta.2015.01.098
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31
On the influence of hydronium and hydroxide ion diffusion on the hydrogen and oxygen evolution reactions in aqueous media
Wiberg, Gustav Karl Henrik; Arenz, Matthias
Electrochimica Acta (2015), 159 (), 66-70CODEN: ELCAAV; ISSN:0013-4686. (Elsevier Ltd.)
We present a study concerning the influence of the diffusion of H+ and OH- ions on the hydrogen and oxygen evolution reactions (HER and OER) in aq. electrolyte solns. Using a rotating disk electrode (RDE), it is shown that at certain conditions the obsd. current, i.e., the reaction rate, does not depend on the kinetics but on diffusion properties; In fact we demonstrate how studying these reactions in 0.1 M non-buffered aq. electrolytes with pH-values ranging between pH 1 to pH 13, the diffusion coeffs. of H+ and OH- ions can be detd. Within the exptl. error limits, we found no pH dependency on the diffusion coeffs. for any of the investigated ions.
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Carneiro-Neto, E. B.; Lopes, M. C.; Pereira, E. C. Simulation of Interfacial pH Changes during Hydrogen Evolution Reaction. J. Electroanal. Chem. 2016, 765, 92– 99, DOI: 10.1016/j.jelechem.2015.09.029
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32
Simulation of interfacial pH changes during hydrogen evolution reaction
Carneiro-Neto, Evaldo B.; Lopes, Mauro C.; Pereira, Ernesto C.
Journal of Electroanalytical Chemistry (2016), 765 (), 92-99CODEN: JECHES; ISSN:1873-2569. (Elsevier B.V.)
This work investigates the possibility of interfacial pH changes during a hydrogen evolution reaction using a finite elements simulation approach. This reaction is a common side step obsd. in many electrochem. systems, such as electrodeposition or corrosion. To develop a general approach, different mechanisms, i.e., Volmer/Tafel and Volmer/Heyrovsky´, were investigated. It is obsd. that for V-H mechanism the interfacial pH change increases 4.2 pH units for those cases where the bulk pH is 5.0. Therefore, in this case, the instant pH at the interface become alk., although the bulk is still acidic, which could justify parallel reactions such as metal hydroxide formation in metal electrodeposition. Besides, the interfacial pH changes and the corresponding pH profiles were calcd. under several exptl. conditions including the compn. of the metallic electrode, the bulk soln. pH and the total buffer concn. ([HA] + [A-]).
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Vanýsek, P. CRC Handbook of Chemistry and Physics, 93rd ed.; Haynes, W. M., Ed.; Chemical Rubber Company: Boca Raton FL, 2012.
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Guidelli, R.; Compton, R. G.; Feliu, J. M.; Gileadi, E.; Lipkowski, J.; Schmickler, W.; Trasatti, S. Defining the Transfer Coefficient in Electrochemistry: An Assessment (IUPAC Technical Report). Pure Appl. Chem. 2014, 86, 245– 258, DOI: 10.1515/pac-2014-5026
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Defining the transfer coefficient in electrochemistry: An assessment (IUPAC Technical Report)
Guidelli, Rolando; Compton, Richard G.; Feliu, Juan M.; Gileadi, Eliezer; Lipkowski, Jacek; Schmickler, Wolfgang; Trasatti, Sergio
Pure and Applied Chemistry (2014), 86 (2), 245-258CODEN: PACHAS; ISSN:0033-4545. (Walter de Gruyter, Inc.)
The transfer coeff. α is a quantity that is commonly employed in the kinetic study of electrode processes. In the 3rd edition of the IUPAC Green Book, the cathodic transfer coeff. αc is defined as -(RT/nF)(dlnkc/dE), where kc is the electroredn. rate const., E is the applied potential, and R, T, and F have their usual significance. This definition is equiv. to the other, -(RT/nF)(dln|jc|/dE), where jc is the cathodic c.d. cor. for any changes in the reactant concn. at the electrode surface with respect to its bulk value. The anodic transfer coeff. αa is defined similarly, by simply replacing jc with the anodic c.d. ja and the minus sign with the plus sign. This definition applies only to an electrode reaction that consists of a single elementary step involving the simultaneous uptake of n electrons from the electrode in the case of αc, or their release to the electrode in the case of αa. However, an elementary step involving the simultaneous release or uptake of more than one electron is regarded as highly improbable in view of the abs. rate theory of electron transfer of Marcus; the hardly satisfiable requirements for the occurrence of such an event were examd. Also, the majority of electrode reactions do not consist of a single elementary step; rather, they are multistep, multi-electron processes. The uncrit. application of the above definitions of αc and αa led researchers to provide unwarranted mechanistic interpretations of electrode reactions. In fact, the only directly measurable exptl. quantity is dln|j|/dE, which can be made dimensionless upon multiplication by RT/F, yielding (RT/F)(dln|j|/dE). One common source of misinterpretation consists in setting this exptl. quantity equal to αn, according to the above definition of the transfer coeff., and in trying to est. n from αn, upon ascribing an arbitrary value to α, often close to 0.5. The resulting n value is then identified with the no. of electrons involved in a hypothetical rate-detg. step or with that involved in the overall electrode reaction. A few examples of these unwarranted mechanistic interpretations are reported. In view of the above considerations, it is proposed to define the cathodic and anodic transfer coeffs. by the quantities αc= -(RT/F)(dln|jc|/dE) and αa= (RT/F)(dlnja/dE), which are independent of any mechanistic consideration.
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Haghighat, S.; Dawlaty, J. M. pH Dependence of the Electron-Transfer Coefficient: Comparing a Model to Experiment for Hydrogen Evolution Reaction. J. Phys. Chem. C 2016, 120, 28489– 28496, DOI: 10.1021/acs.jpcc.6b10602
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pH Dependence of the Electron-Transfer Coefficient: Comparing a Model to Experiment for Hydrogen Evolution Reaction
Haghighat, Shima; Dawlaty, Jahan M.
Journal of Physical Chemistry C (2016), 120 (50), 28489-28496CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
The empirical electron-transfer coeff. α is a valuable electrochem. observable that bridges the thermodn. and kinetics of redox reactions. For reactions that involve protons, the value of α is expected to be pH-dependent. However, even for the simplest redox processes, the nature of this dependency remains unclear. Toward clarifying this problem, the authors follow two goals. First, the authors calc. the electron-transfer coeff. α and its pH dependence based on a model 2-dimensional potential energy surface that was studied by Koper and Schmickler for proton redn. According to the model, α is pH-independent for high-pH values and pH-dependent for low-pH values, with α increasing as the pH is lowered. Second, the authors report the authors' exptl. measured α for H evolution on several electrode materials over a wide pH range. Several features of the data show similarities to the predictions of the model. The data show different behavior in two distinct pH regions. In the acidic region, a linearly increasing α with decreasing pH and in the basic side a pH-independent α are obsd. for several electrodes. However, certain predictions of the model, in particular the transition pH between the two regions, do not seem consistent with the data, which the authors propose likely arises due to mass-transfer limitations of the rate. The authors hope that this work will help better understand the pH dependence of interfacial electron-proton transfer reactions and, in particular, inspire further work to isolate mass-transfer limitations from interfacial chem. effects in measuring and interpreting the electron-transfer coeff.
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38
Nørskov, J. K.; Bligaard, T.; Logadottir, A.; Kitchin, J. R.; Chen, J. G.; Pandelov, S.; Stimming, U. Trends in the Exchange Current for Hydrogen Evolution. J. Electrochem. Soc. 2005, 152, J23– J26, DOI: 10.1149/1.1856988
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Trends in the exchange current for hydrogen evolution
Norskov, J. K.; Bligaard, T.; Logadottir, A.; Kitchin, J. R.; Chen, J. G.; Pandelov, S.; Stimming, U.
Journal of the Electrochemical Society (2005), 152 (3), J23-J26CODEN: JESOAN; ISSN:0013-4651. (Electrochemical Society)
A d. functional theory database of hydrogen chemisorption energies on close packed surfaces of a no. of transition and noble metals is presented. The bond energies are used to understand the trends in the exchange current for hydrogen evolution. A volcano curve is obtained when measured exchange currents are plotted as a function of the calcd. hydrogen adsorption energies and a simple kinetic model is developed to understand the origin of the volcano. The volcano curve is also consistent with Pt being the most efficient electrocatalyst for hydrogen evolution.
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The use of a rotating disk electrode in the study of electrochemical kinetics and electrolytic processes
Koutecky, J.; Levich, V. G.
Zhurnal Fizicheskoi Khimii (1958), 32 (), 1565-75CODEN: ZFKHA9; ISSN:0044-4537.
cf. C.A. 49, 1447e. Rotating disk electrodes were preferable to Hg drop electrodes in the study of reactions on electrodes involving kinetic and catalytic processes. The reactions on disk electrodes proceeded as stationary processes which permitted the formulation of reactions, even if they were complicated. Moreover, the properties of the solns. and the angular rotation velocities could be varied within wide limits with disk electrodes, while only the pH and the compn. of the soln. can be varied with the Hg drop electrode. The limiting diffusion currents were calcd. for typical cases on the assumption that the diffusion coeffs. (D) of the reacting substances were equal, because they frequently are very close. When D1 ≠ D2, the calcns. are no more complex in principle but require longer computations.
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Kucernak, A. R.; Zalitis, C. General Models for the Electrochemical Hydrogen Oxidation and Hydrogen Evolution Reactions: Theoretical Derivation and Experimental Results under Near Mass-Transport Free Conditions. J. Phys. Chem. C 2016, 120, 10721– 10745, DOI: 10.1021/acs.jpcc.6b00011
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General Models for the Electrochemical Hydrogen Oxidation and Hydrogen Evolution Reactions: Theoretical Derivation and Experimental Results under Near Mass-Transport Free Conditions
Kucernak, Anthony R.; Zalitis, Christopher
Journal of Physical Chemistry C (2016), 120 (20), 10721-10745CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
Full derivations of Heyrovsky-Volmer (HV), Tafel-Volmer (TV), Heyrovsky-Tafel (HT), and Heyrovsky-Tafel-Volmer (HTV) mechanisms under steady state conditions are provided utilizing a new theor. framework which allows better understanding of each of the mechanistic currents and part currents. Simple and easily implemented equations are presented, which provide both the hydrogen coverage and electrochem. current as a function of overpotential and relevant kinetic parameters. It is shown how these responses are governed by a set of dimensionless parameters assocd. with the ratio of electrokinetic parameters. For each of the different mechanisms, an "atlas" of Hads coverage with overpotential and corresponding c.d. is provided, allowing an understanding of all possible responses depending on the dimensionless parameters. Anal. of these mechanisms provides the limiting reaction orders of the exchange c.d. for protons and bimol. hydrogen for each of the different mechanisms, as well as the possible Tafel slopes as a function of the mol. symmetry factor, β. Only the HV mechanism is influenced by pH, whereas the TV, HT, and HTV mechanisms are not. The cases where the equations simplify to limiting forms are discussed. Anal. of the exchange c.d. from exptl. data is discussed, and it is shown that fitting the linear region around the equil. potential underestimates the true exchange c.d. for all of the mechanisms studied. Furthermore, ests. of exchange c.d. via back-extrapolation from large overpotentials are also shown to be highly inaccurate. Anal. of Tafel slopes is discussed along with the mechanistic information which can and cannot be detd. The new models are used to simultaneously fit 16 exptl. responses of Pt/C electrodes in acid toward the hydrogen evolution reaction (her)/hydrogen oxidn. reaction (hor) as a function of η, pH, p(H2), and temp., using a consistent set of electrokinetic parameters. Examples of implementation of the equations as both computable document format and Excel spreadsheets are provided.
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Abstract
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Figure 1
Figure 1. Polarization curve of an RDE, showing two hydrogen evolution steps with an intermittent limiting current plateau section.
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Figure 2
Figure 2. Reaction schemes for HER. Two separate reactions are shown in (a) for acidic and neutral to alkaline solutions. A combined scheme is shown in (b) for near-neutral solutions. The autoprotolysis of water is part of both schemes.
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Figure 3
Figure 3. Experimental protocol for the measurement of HER polarization curves on RDEs. The stationary current of the RDE is measured at given electrode potential (E) and rotation rate (f) values (green periods). Between the measurements, the potential control is switched off and the RDE rotated quickly, to remove accumulated bubbles (red periods).
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Figure 4
Figure 4. Experimentally obtained polarization curves (red dots) on an Au (a) and on a Pt (b) RDE, showing a two step behavior. In each panel (at different values of pH), the cathodic current density increases as the rotation rate f is set to values of 400, 625, 900, 1225, 1600, 2025, and 2500 min^–1. The green curves are created by fitting the model described by eq 23 globally, that is, for all pH and rotation rate values, and by optimizing only three parameters (α_c, k, and ). Determined confidence intervals (at 95% statistical certainty) for the fitted parameters are α_c = 0.486 ± 0.067, and for gold and α_c = 0.643 ± 0.037, and for platinum. Other parameter values (not optimized) are shown in Table 1.
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Figure 5
Figure 5. Polarization curve (thick gray) calculated using eq 23 and the parameter values of Table 1, shown in two different representations: with linear axis scaling in (a) and on a Tafel plot in (b). The three different segments of the curves, marked by the dashed lines, can be approximated by eqs 24–30, as discussed in the text. The contour map in the background of (a) shows the variation of pH as a function of the distance measured from the electrode surface at each disk potential. (Details of calculating pH profiles using the presented model are discussed later, cf. to Figure 9).
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Figure 6
Figure 6. Exchange current densities j₀ in the studied pH range, calculated by using eq 25, based on the kinetic parameters determined by nonlinear fitting in Figure 4 for gold and platinum.
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Figure 7
Figure 7. Effect of varying the parameters α_c (a, b) and k (c, d) on the calculated polarization curves. Values assumed are shown on the graph; other parameters are given in Table 1. Polarization curves are shown in two different representations: with linear axis scaling (a, c) and on a Tafel plot (b, d).
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Figure 8
Figure 8. (a) Concept of the breakdown overpotential η_br illustrated on a polarization curve. (b) Dimensionless breakdown overpotentials plotted as a function of pH for gold and platinum, determined from measured data (dots). The lines were created by linear fitting to the measured data, using a pH² weighting. The acquired slopes and intercepts were used according to eq 32 to calculate the kinetic parameters shown in Table 2. Chosen rotation rate: 625 min^–1.
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Figure 9
Figure 9. (a) Normalized concentration difference profiles as a function of the normalized distance, for some chosen values of the normalized current density (shown in the figure). (b) An example for pH profiles calculated for various normalized current values, assuming that pH^∞ = 3.
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Figure 10
Figure 10. Full black curve: the distance of neutrality (normalized to the diffusion layer thickness δ_N) as a function of the current density normalized to . Note that the function, eq 35, is not defined for . Dashed gray curve: an estimate for the neutrality distance based on an analytical solution assuming that D_OH^– ≫ D_H⁺. (27)
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This article references 41 other publications.
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  Ritzert, Nicole L.; Moffat, Thomas P.
  Journal of Physical Chemistry C (2016), 120 (48), 27478-27489CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
  The interaction between electrodeposition of Ni and electrolyte breakdown, namely, the H evolution reaction (HER) via H3O+ and H2O redn., was studied under well-defined mass transport conditions using ultramicroelectrodes (UMEs) coupled with optical imaging, generation/collection scanning electrochem. microscopy, and preliminary microscale pH measurements. For 5 mmol/L NiCl2 + 0.1 mol/L NaCl, pH 3.0, electrolytes, the voltammetric current at modest overpotentials, i.e., between -0.6 and -1.4 V vs. Ag/AgCl, was distributed between metal deposition and H3O+ redn., with both reactions reaching mass transport-limited current values. At more neg. potentials, an unusual sharp current spike appeared upon the onset of H2O redn. that was accompanied by a transient increase in H2 prodn. The peak potential of the current spike was a function of both [Ni(H2O)6]2+(aq.) concn. and pH. The sharp rise in current was ascribed to the onset of autocatalytic H2O redn., where electrochem. generated OH- species induce heterogeneous nucleation of Ni(OH)2(ads) islands, the perimeter of which is reportedly active for H2O redn. As the layer coalesces, further metal deposition is quenched while H2O redn. continues, albeit at a decreased rate as fewer of the most reactive sites, e.g., Ni/Ni(OH)2 island edges, are available. At potentials <-1.5 V vs. Ag/AgCl, H2O redn. is accelerated, leading to homogeneous pptn. of bulk Ni(OH)2·xH2O within the nearly hemispherical diffusion layer of the UME.
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6. 6
  Wu, J.; Wafula, F.; Branagan, S.; Suzuki, H.; van Eisden, J. Mechanism of Cobalt Bottom-Up Filling for Advanced Node Interconnect Metallization. J. Electrochem. Soc. 2019, 166, D3136– D3144, DOI: 10.1149/2.0161901jes
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  Mechanism of cobalt bottom-up filling for advanced node interconnect metallization
  Wu, J.; Wafula, F.; Branagan, S.; Suzuki, H.; van Eisden, J.
  Journal of the Electrochemical Society (2019), 166 (1), D3136-D3141CODEN: JESOAN; ISSN:0013-4651. (Electrochemical Society)
  A mechanism of Co bottom-up trench fill for advanced node interconnect metalization was studied. The mechanism in question employs a single additive which suppresses Co plating and directly impacts the plating rate. H, generated simultaneously during plating by electrolysis, reacts with the suppressor via H redn., and the product of this reaction is a deactivated form of the suppressor. The local plating rate is governed by the relative concns. of the activated/deactivated forms. Cyclic voltammetry (CV) shows that the suppressor deactivation is impacted by electrochem. potential, suppressor concn., rotation rate, and pH, all of which may be controlled to generate bottom up fill in interconnects. Such impacts were confirmed on the plating of patterned coupons. This H redn.-induced deactivation mechanism provides a theor. explanation for bottom-up plating in a single additive bath, and the factors that may impact the bottom-up filling.
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7. 7
  Horányi, G. Electrochemical Dictionary;Bard, A. J.; Scholz, F.; Inzelt, G., Eds.; Springer Verlag: Heidelberg, 2008; p 343.
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  There is no corresponding record for this reference.
8. 8
  Bockris, J. O. M.; Ammar, I. A.; Huq, A. K. M. S. The Mechanism of the Hydrogen Evolution Reaction on Platinum, Silver and Tungsten surfaces in Acid Solutions. J. Phys. Chem. A. 1957, 61, 879– 886, DOI: 10.1021/j150553a008
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  8
  The mechanism of the hydrogen-evolution reaction on platinum, silver, and tungsten surfaces in acid solutions
  Bockris, J. O'M.; Ammar, I. A.; Huq, A. K. M. S.
  Journal of Physical Chemistry (1957), 61 (), 879-86CODEN: JPCHAX; ISSN:0022-3654.
  cf. C.A. 51, 7899c. The parameters of the H-evolution reaction on Pt were detd. as a function of c.d., pH, salt addn., mode of electrode prepn., aging, and degree of pre.ovrddot.electrolysis; and as a function of c.d. and degree of pre.ovrddot.electrolysis for W and Ag. On Pt, Tafel slopes (b) and exchange currents (i0) varied with mode of prepn., that in air giving a slope of 2.303 RT/F compared with the more usually observed slope of 2.303RT/2F; anodic activation gave high and reproducible i0 values. Aging decreased i0 and extended the c.d. range in which b = 2.303RT/F. Successive increase of pre.ovrddot.electrolysis caused i0 to increase to a limiting value. Anodic activation occurred only at a c.d. in excess of 10-2 amp./sq.cm. and was independent of the amt. of current passed and subsequent reduction. The stoichiometric no. (ν) was unity. On W and Ag, Tafel lines had 2 distinct slopes; ν = 1 in 0.1 to 0.4N soln. There was no intrinsic screening effect due to a Luggin capillary. Previous work on Pt in pure solns. indicating b in excess of 2.303RT/F was reinterpreted in terms of partial diffusion control. Anodic activation on Pt was due to both mech. cleaning and oxidation. The limiting c.d. for activation is that at which H depolarization is negligible. Tafel slopes of RT/F were consistent with migration of H atoms over the surface as rate-detg. Calcn. of the rate of change of the potential of the layer of ions in contact with the electrode with that of the electrode indicated that near the electrocapillary max. Tafel slopes can be changed to lower values.
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9. 9
  Bagotzky, V. S.; Osetrova, N. V. Investigations of Hydrogen Ionization on Platinum with the Help of Micro-Electrodes. J. Electroanal. Chem. Interfacial Electrochem. 1973, 43, 233– 249, DOI: 10.1016/S0022-0728(73)80494-2
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  There is no corresponding record for this reference.
10. 10
  Tavares, M. C.; Machado, S. A. S.; Mazo, L. H. Study of Hydrogen Evolution Reaction in Acid Medium on Pt Microelectrodes. Electrochim. Acta 2001, 46, 4359– 4369, DOI: 10.1016/S0013-4686(01)00726-5
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  10
  Study of hydrogen evolution reaction in acid medium on Pt microelectrodes
  Tavares, M. C.; Machado, S. A. S.; Mazo, L. H.
  Electrochimica Acta (2001), 46 (28), 4359-4369CODEN: ELCAAV; ISSN:0013-4686. (Elsevier Science Ltd.)
  This work describes the use of a Pt UME in the study of the hydrogen evolution reaction in 0.5M H2SO4. A nonlinear fitting procedure was employed to analyze polarization curves obtained at several temps. (25-75°). The results revealed that the traditionally accepted model described by a Volmer-Tafel route fails to fit the obtained exptl. data. In this sense, a new model is proposed involving the Volmer-Heyrovsky mechanism, being the Heyrovsky reaction rate detg. step. To achieve the best fit between exptl. and calcd. data, the kinetic equations had to be proposed with a small value of the transfer coeff. (β<0.2). This unusual value was assocd. with an activationless process, which can also justify the limiting kinetic current (not diffusional) obsd. Trying to get further insight into this possibility, the polarization studies were also performed on a surface modified by underpotentially deposited copper. With a degree of coverage ≤0.8, the only obsd. effect on the polarization curves was a shift towards minor current values. This shift can be completely justified by the blocking of surface area. A change in mechanism was not obsd. albeit the Cu UPD eliminated the pairs of neighbor active sites necessary to the Volmer-Tafel pathway.
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11. 11
  Neyerlin, K. C.; Gu, W.; Jorne, J.; Gasteiger, H. A. Study of the Exchange Current Density for the Hydrogen Oxidation and Evolution Reactions. J. Electrochem. Soc. 2007, 154, B631– B635, DOI: 10.1149/1.2733987
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  11
  Study of the Exchange Current Density for the Hydrogen Oxidation and Evolution Reactions
  Neyerlin, K. C.; Gu, Wenbin; Jorne, Jacob; Gasteiger, Hubert A.
  Journal of the Electrochemical Society (2007), 154 (7), B631-B635CODEN: JESOAN; ISSN:0013-4651. (Electrochemical Society)
  The exchange c.d. for the H oxidn./evolution reactions was detd. in a p exchange membrane fuel cell. Ultralow Pt-loaded electrodes (0.003 mg Pt/cm2) were used to obtain measurable kinetic overpotential signals (50 mV at 2 A/cm2). Using the Butler-Volmer equation, the exchange c.d. was 235-600 mA/cm2 Pt and the transfer coeff. was 0.5-1. Due to the fast kinetics, no measurable voltage losses are predicted for pure-H2/air p exchange membrane fuel cell applications when lowering the anode Pt loadings from its current value of 0.4 mg Pt/cm2 to the automotive target of 0.05 mg Pt/cm2.
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12. 12
  Sheng, W.; Gasteiger, H. A.; Shao-Horn, Y. Hydrogen Oxidation and Evolution Reaction Kinetics on Platinum: Acid vs Alkaline Electrolytes. J. Electrochem. Soc. 2010, 157, B1529– B1536, DOI: 10.1149/1.3483106
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  12
  Hydrogen oxidation and evolution reaction kinetics on platinum: Acid vs alkaline electrolytes
  Sheng, Wenchao; Gasteiger, Hubert A.; Shao-Horn, Yang
  Journal of the Electrochemical Society (2010), 157 (11), B1529-B1536CODEN: JESOAN; ISSN:0013-4651. (Electrochemical Society)
  The kinetics of the hydrogen oxidn. reaction (HOR) and hydrogen evolution reaction (HER) on polycryst. Pt [Pt(pc)] and high surface area carbon-supported Pt nanoparticles (Pt/C) were studied in 0.1 M KOH using rotating disk electrode (RDE) measurements. After corrections of noncompensated soln. resistance from ac impedance spectroscopy and of hydrogen mass transport in the HOR branch, the kinetic current densities were fitted to the Butler-Volmer equation using a transfer coeff. of α=0.5, from which HOR/HER exchange current densities on Pt(pc) and Pt/C were obtained, and the HOR/HER mechanisms in alk. soln. were discussed. Unlike the HOR/HER rates on Pt electrodes in alk. soln., the HOR/HER rates on a Pt electrode in 0.1 M HClO4 were limited entirely by hydrogen diffusion, which renders the quantification of the HOR/HER kinetics impossible by conventional RDE measurements. The simulation of the hydrogen anode performance based on the specific exchange current densities of the HOR/HER at 80°C illustrates that in addn. to the oxygen redn. reaction cell voltage loss on the cathode, the slow HOR kinetics are projected to cause significant anode potential losses in alk. fuel cells for low Pt loadings (>130 mV at 0.05 mgPt/cmanode2 and 1.5 A/cmanode2), contrary to what is reported for proton exchange membrane fuel cells.
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13. 13
  Durst, J.; Siebel, A.; Simon, C.; Hasché, F.; Herranz, J.; Gasteiger, H. A. New insights into the electrochemical hydrogen oxidation and evolution reaction mechanism. Energy Environ. Sci. 2014, 7, 2255– 2260, DOI: 10.1039/C4EE00440J
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  13
  New insights into the electrochemical hydrogen oxidation and evolution reaction mechanism
  Durst, J.; Siebel, A.; Simon, C.; Hasche, F.; Herranz, J.; Gasteiger, H. A.
  Energy & Environmental Science (2014), 7 (7), 2255-2260CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
  The effect of pH on the hydrogen oxidn. and evolution reaction (HOR/HER) rates is addressed for the first time for the three most active monometallic surfaces: Pt, Ir, and Pd carbon-supported catalysts. Kinetic data were obtained for a proton exchange membrane fuel cell (PEMFC; pH ≈ 0) using the H2-pump mode and with a rotating disk electrode (RDE) in 0.1 M NaOH. Our findings point toward: (i) a similar ≈100-fold activity decrease on all these surfaces when going from low to high pH; (ii) a reaction rate controlled by the Volmer step on Pt/C; and (iii) the H-binding energy being the unique and sole descriptor for the HOR/HER in alk. electrolytes. Based on a detailed discussion of our data, we propose a new mechanism for the HOR/HER on Pt-metals in alk. electrolytes.
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14. 14
  Zheng, J.; Sheng, W.; Zhuang, Z.; Xu, B.; Yan, Y. Universal Dependence of Hydrogen Oxidation and Evolution Reaction Activity of Platinum-group Metals on pH and Hydrogen Binding Energy. Sci. Adv. 2016, 2, e1501602 DOI: 10.1126/sciadv.1501602
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  14
  Universal dependence of hydrogen oxidation and evolution reaction activity of platinum-group metals on pH and hydrogen binding energy
  Zheng, Jie; Sheng, Wenchao; Zhuang, Zhongbin; Xu, Bingjun; Yan, Yushan
  Science Advances (2016), 2 (3), e1501602/1-e1501602/9CODEN: SACDAF; ISSN:2375-2548. (American Association for the Advancement of Science)
  Understanding how pH affects the activity of hydrogen oxidn. reaction (HOR) and hydrogen evolution reaction (HER) is key to developing active, stable, and affordable HOR/HER catalysts for hydroxide exchange membrane fuel cells and electrolyzers. A common linear correlation between hydrogen binding energy (HBE) and pH is obsd. for four supported platinum-group metal catalysts (Pt/C, Ir/C, Pd/C, and Rh/C) over a broad pH range (0 to 13), suggesting that the pH dependence of HBE is metal-independent. A universal correlation between exchange c.d. and HBE is also obsd. on the four metals, indicating that they may share the same elementary steps and rate-detg. steps and that the HBE is the dominant descriptor for HOR/HER activities. The onset potential of CO stripping on the four metals decreases with pH, indicating a stronger OH adsorption, which provides evidence against the promoting effect of adsorbed OH on HOR/HER.
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15. 15
  Pentland, N.; Bockris, J. O. M.; Sheldon, E. Hydrogen Evolution Reaction on Copper, Gold, Molybdenum, Palladium, Rhodium, and Iron. J. Electrochem. Soc. 1957, 104, 182, DOI: 10.1149/1.2428530
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  15
  Hydrogen-evolution reaction on copper, gold, molybdenum, palladium, rhodium, and iron. Mechanism and measurement technique under high-purity conditions
  Pentland, N.; Bockris, J. O'M.; Sheldon, E.
  Journal of the Electrochemical Society (1957), 104 (), 182-94CODEN: JESOAN; ISSN:0013-4651.
  Various aspects of technique in measurements of electrode kinetics under conditions where competing reactions due to the presence of trace impurities in the soln. are important are examd. The kinetics of the H-evolution reaction in acid and alkaline solns. on several transition metals has been examd. with special reference to the low c.-d. region. Inferences concerning the rate-detg. step in the reaction 2H+ + 2e0- → H2 are drawn. In general, there is a tendency for the metals examd. in acid soln. to have a rate-controlling electrochem. desorption reaction and for those in alk. soln. to have a rate-detg. discharge step.
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16. 16
  Ives, D. J. G. Some Abnormal Hydrogen Electrode Reactions. Can. J. Chem. 1959, 37, 213– 221, DOI: 10.1139/v59-028
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  16
  Some abnormal hydrogen electrode reactions
  Ives, D. J. G.
  Canadian Journal of Chemistry (1959), 37 (), 213-21CODEN: CJCHAG; ISSN:0008-4042.
  cf. C.A. 51, 1498a; 52, 6976c. The reasonably normal behavior of the H overvoltage with H or N as the sweeping gas on a Au electrode in pre.ovrddot.electrolyzed 0.1N HCl was changed on prolonged annealing of the Au electrode at temps. below 800°. On restoration of the annealed Au electrode to the soln. it showed a rest potential of 400 mv., insensitivity to the substitution of N for H, enhanced cathodic overpotentials increasing with time, and curved Tafel plots of varying but excessively high gradients. Thermally deactivated Au was not capable of atomizing mol. H or catalyzing the recombination of H atoms and formed a "nonequil. H electrode." The dependence of open-circuit potential and prolonged growth of overpotential on cathodization time independent of c.d. above a min. value suggests that H atoms penetrate the Au lattice. Pt electrodes poisoned with Hg showed a similar behavior on cathodic polarization with rest potentials increasing from 350 to 625 mv. with increasing degrees of poisoning. The presence of a cathodic product with reducing properties was demonstrated by the imprint of W blue by bringing the Pt cathode in contact with a WO3 target. It is suggested that the results justify consideration of the desorption of the H2+ ion as a transition step in the H evolution reaction mechanism.
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17. 17
  Brug, G. J.; Sluyters-Rehbach, M.; Sluyters, J. H.; Hemelin, A. The Kinetics of the Reduction of Protons at Polycrystalline and Monocrystalline Gold Electrodes. J. Electroanal. Chem. Interfacial Electrochem. 1984, 181, 245– 266, DOI: 10.1016/0368-1874(84)83633-3
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  17
  The kinetics of the reduction of protons at polycrystalline and monocrystalline gold electrodes
  Brug, G. J.; Sluyters-Rehbach, M.; Sluyters, J. H.; Hamelin, A.
  Journal of Electroanalytical Chemistry and Interfacial Electrochemistry (1984), 181 (1-2), 245-66CODEN: JEIEBC; ISSN:0022-0728.
  The redn. of H+ from 1M HClO4 and 1M NaClO4 solns. at polycryst. and single-crystal faces of very pure Au electrodes was studied by detg. the forward rate const. (k1) as a function of potential and of H+ concn. The techniques applied are d.c. and impedance measurements both with a step-wise variation of d.c. potential (duration 4 s), and d.c. measurements with a continuous potential variation. The consistency of the results was extensively tested and was very satisfactory. Plots of ln kf vs. potential are curved and exhibit limiting slopes corresponding to values for the operational transfer coeffs. of α = 1 at pos. and α = 0.5 at neg. potentials. This behavior is discussed in terms of mech. models described in the literature, and also an alternative mechanism is tentatively proposed. An increase in the rate consts. is obsd. when the purity of the Au is less. The slight differences in the rate consts. obsd. at single-crystal faces of the same purity but with different crystallog. orientation are discussed.
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18. 18
  Conway, B. E.; Bai, L. State of Adsorption and Coverage by Overpotential-Deposited H in the H₂ Evolution Reaction at Au and Pt. Electrochim. Acta 1986, 31, 1013– 1024, DOI: 10.1016/0013-4686(86)80017-2
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  18
  State of adsorption and coverage by overpotential-deposited hydrogen in the molecular hydrogen evolution reaction at gold and platinum
  Conway, B. E.; Bai, L.
  Electrochimica Acta (1986), 31 (8), 1013-24CODEN: ELCAAV; ISSN:0013-4686.
  By means of potential decay measurements using a digital data acquisition and computer processing system, accurate values of overvoltage decay rates, dη/dt, may be obtained from which the pseudocapacitance and coverage behavior of overvoltage-deposited (OPD) H species in the cathodic H evolution reaction (HER)at Au electrodes may be quant. derived as a function of η. The behavior of the HER at Au is of interest in that an unusual Tafel slope value of 2.3 RT/F is exhibited in acid soln. while the value of alk. solns. is the more familiar value of ∼2.32 RT/F. Anal. of the overvoltage relaxation behavior on open-circuit, following interruption of cathodic polarization currents, gives an almost const. and small interfacial capacitance corresponding to a double-layer capacitance. Steady-state OPD H coverage (θ) is hence quite small (θH < 0.3%). The Tafel slope value of 2.3 RT/F requires, however, a potential-dependent H coverage detd. by an H electrosorption step almost at equil. but with θH small. The rate-detg. step is suggested to be surface diffusion to preferred desorption sites. Comparative results are presented for the HER at activated Pt where, contrary to the behavior of Au, a large pseudocapacitance for OPD H is derived that may be assocd. with some surface hydride formation, the possibility ofreadsorption of H from a boundary layer supersatd. with H having been minimized by electrode rotation at a sufficiently high rate of 3600 rpm.
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19. 19
  Khanova, L. A.; Krishtalik, L. I. Kinetics of the hydrogen evolution reaction on gold electrode. A new case of the barrierless discharge. J. Electroanal. Chem. 2011, 660, 224– 229, DOI: 10.1016/j.jelechem.2011.01.016
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  19
  Kinetics of the hydrogen evolution reaction on gold electrode. A new case of the barrierless discharge
  Khanova, Larisa A.; Krishtalik, Lev I.
  Journal of Electroanalytical Chemistry (2011), 660 (2), 224-229CODEN: JECHES; ISSN:1873-2569. (Elsevier B.V.)
  Kinetics of hydrogen evolution reaction on the electrodeposited gold electrode is studied. In semi-logarithmic coordinates, polarization curves consist of two linear segments with Tafel slopes 0.06 V at lower overpotentials and 0.12 V at the higher ones. The kinetics in the higher-slope region depends on the soln. pH and the ψ 1-potential (effects of the ionic strength and of the presence of the surface-active tetrabutylammonium cation) as it is predicted by the theory of the ordinary slow discharge. In the lower-slope region, overpotential does not depend on pH and ψ 1-potential; this is in full accordance with the theory of the barrierless discharge. We nevertheless analyze also several alternatives to the theory of barrierless discharge for the explanation of the low-slope region, but we show that they are not consistent with the exptl. data.
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20. 20
  Kahyarian, A.; Brown, B.; Nesić, S. Mechanism of the Hydrogen Evolution Reaction in Mildly Acidic Environments on Gold. J. Electrochem. Soc. 2017, 164, H365– H374, DOI: 10.1149/2.1061706jes
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  20
  Mechanism of the Hydrogen Evolution Reaction in Mildly Acidic Environments on Gold
  Kahyarian, Aria; Brown, Bruce; Nesic, Srdjan
  Journal of the Electrochemical Society (2017), 164 (6), H365-H374CODEN: JESOAN; ISSN:0013-4651. (Electrochemical Society)
  Despite numerous studies studying the kinetics of the H evolution reaction (HER) on a Au surface in acidic solns., the underlying mechanism of this reaction have remained controversial to date. The existing mechanisms are reevaluated and are inadequate in explaining the steady state polarization behavior of the H evolution reaction in an extended cathodic potentials and mildly acidic pH range. A mechanism including a surface diffusion step of Hads alongside the Volmer, Heyrovsky, and Tafel elementary steps, best describes the exptl. data obtained in acidic perchlorate solns. up to pH 5, while the rate detg. step changes both with pH and electrode potential. This overall HER mechanism was further verified using a comprehensive math. model based on the proposed elementary steps, where a satisfactory agreement with exptl. results was obtained.
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21. 21
  Obata, K.; Stegenburga, L.; Takanabe, K. Maximizing Hydrogen Evolution Performance on Pt in Buffered Solutions: Mass Transfer Constrains of H₂ and Buffer Ions. J. Phys. Chem. C 2019, 123, 21554– 21563, DOI: 10.1021/acs.jpcc.9b05245
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  21
  Maximizing Hydrogen Evolution Performance on Pt in Buffered Solutions: Mass Transfer Constrains of H2 and Buffer Ions
  Obata, Keisuke; Stegenburga, Liga; Takanabe, Kazuhiro
  Journal of Physical Chemistry C (2019), 123 (35), 21554-21563CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
  Although the electrochem. H evolution reaction (HER) on a Pt electrode is among the most studied electrocatalytic reactions, its reaction mechanism and exchange c.d. are still under debate. Particularly on the Pt catalyst, its facile reaction kinetics and lack of effective methods to compensate mass transport make it difficult to isolate kinetic and diffusion contributions. This study focuses on the quant. description of mass transfer constraints arising from both H2 and phosphate buffer ions using a Pt electrocatalyst in near-neutral pH regions, which are overlooked in the literature despite the relevance to various (photo-) electrochem. reactions for H2O splitting and CO2 redn. The established HER model that uses H+ as a reactant quant. breaks down the obsd. overpotentials with diffusion contributions of both H and buffer species while the intrinsic kinetics on Pt exhibits negligible contribution. The significance of electrolyte engineering, i.e., the optimization of the electrolyte identity and molality, is confirmed to det. the overall HER performance. To maximize the HER performance on Pt at ambient temp., the phosphate-buffer electrolyte should be adjusted to a pH close to pKa of the buffer that effectively minimizes the pH gradient and to the adequate molality of the buffer (typically ∼0.5 M phosphates) that H2 diffusion is maximized, which is related with H2 soly. and soln. viscosity. At pH far from pKa, concn. overpotential of buffer ion dominates the overall performance, which requires highly dense buffer (>1.5 M phosphates) to minimize the pH gradient.
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22. 22
  Hessami, S.; Tobias, C. W. In-Situ Measurement of Interfacial pH Using a Rotating Ring-Disk Electrode. AIChE J. 1993, 39, 149– 162, DOI: 10.1002/aic.690390115
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  In-situ measurement of interfacial pH using a rotating ring-disk electrode
  Hessami, Sholeh; Tobias, Charles W.
  AIChE Journal (1993), 39 (1), 149-62CODEN: AICEAC; ISSN:0001-1541.
  A nonintrusive technique for the in-situ measurement of interfacial pH and current efficiency was developed. A ring electrode, operated potentiometrically at open-circuit, is used to measure the pH change at a rotating disk electrode. The technique takes advantage of the well-characterized hydrodynamics at the rotating disk electrode and has the added advantage that the pH probe, the ring electrode, is not interfering with the flow field and the current distribution on the disk. To det. the pH at the disk electrode by measuring the potential of the ring, the radial transport of hydronium ions across the insulating gap and on the ring is analyzed taking into account the effect of homogeneous dissocn. reactions of H2O and metal-hydroxide ion complexes. Shifts in the ring potential caused by H supersatn. and ohmic drop are also evaluated. A platinized ring electrode in a H-satd. electrolyte provides a stable and reproducible H+-sensor with a Nernstian response to the changes in the bulk pH. Performance of the ring is evaluated by generating H2 at the disk electrode from a dil. acid soln., in the absence of other electrochem. reactions. The technique is then applied to det. the interfacial pH of Ni, Fe, and Ni-Fe alloy electrodeposition with concurrent H2 evolution. This method was also used to measure the current efficiency of Ni electrodeposition in a fast, nonintrusive, and in-situ manner.
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23. 23
  Katsounaros, I.; Meier, J. C.; Klemm, S. O.; Topalov, A. A.; Biedermann, U. P.; Auinger, M.; Mayrhofer, K. J. J. The Effective Surface pH during Reactions at the Solid-Liquid interface. Electrochem. Commun. 2011, 13, 634– 637, DOI: 10.1016/j.elecom.2011.03.032
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  23
  The effective surface pH during reactions at the solid-liquid interface
  Katsounaros, Ioannis; Meier, Josef C.; Klemm, Sebastian O.; Topalov, Angel A.; Biedermann, P. Ulrich; Auinger, Michael; Mayrhofer, Karl J. J.
  Electrochemistry Communications (2011), 13 (6), 634-637CODEN: ECCMF9; ISSN:1388-2481. (Elsevier B.V.)
  In this work the activity of protons directly at the solid-liq. interface during a heterogeneous reaction is demonstrated without introducing any pH measurement device, in non-buffered and buffered solns. Due to a simple approach we can exptl. demonstrate the relation between reaction rate and surface pH directly from the cyclic voltammograms. Clearly, the pH at a solid-liq. interface can be quite different from the bulk in unbuffered or insufficiently buffered solns. even at moderate reaction rates, in particular in the pH range of 4 to 10. However, at the given mass-transport conditions, well controlled by a rotating disk electrode, a buffer concn. of 10- 2 M is already sufficient to pin the surface pH to the bulk value at reaction rates of up to 1 mA cm- 2.
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24. 24
  Auinger, M.; Katsounaros, J. C.; Meier, I.; Klemm, S. O.; Biedermann, P. U.; Topalov, A. A.; Rohwerder, M.; Mayrhofer, K. J. J. Near-surface ion distribution and buffer effects during electrochemical reactions. Phys. Chem. Chem. Phys. 2011, 13, 16384– 16394, DOI: 10.1039/c1cp21717h
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  24
  Near-surface ion distribution and buffer effects during electrochemical reactions
  Auinger, Michael; Katsounaros, Ioannis; Meier, Josef C.; Klemm, Sebastian O.; Biedermann, P. Ulrich; Topalov, Angel A.; Rohwerder, Michael; Mayrhofer, Karl J. J.
  Physical Chemistry Chemical Physics (2011), 13 (36), 16384-16394CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
  The near-surface ion distribution at the solid-liq. interface during the Hydrogen Oxidn. Reaction (HOR)/Hydrogen Evolution Reaction (HER) on a rotating platinum disk electrode is demonstrated in this work. The relation between reaction rate, mass transport and the resulting surface pH-value is used to theor. predict cyclic voltammetry behavior using only thermodn. and diffusion data obtained from the literature, which were confirmed by exptl. measurements. The effect of buffer addn. on the current signal, the surface pH and the ion distribution is quant. described by anal. solns. and the fragility of the surface pH during reactions that form or consume H+ in near-neutral unbuffered solns. or poorly buffered media is highlighted. While the ideal conditions utilized in this fundamental study cannot be directly applied to real scenarios, they do provide a basic understanding of the surface pH concept for more complex heterogeneous reactions.
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25. 25
  Shinagawa, T.; García-Esparza, A. T.; Takanabe, K. Insight on Tafel Slopes from a Microkinetic Analysis of Aqueous Electrocatalysis for Energy Conversion. Sci. Rep. 2015, 5, 13801 DOI: 10.1038/srep13801
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  Insight on Tafel slopes from a microkinetic analysis of aqueous electrocatalysis for energy conversion
  Shinagawa Tatsuya; Garcia-Esparza Angel T; Takanabe Kazuhiro
  Scientific reports (2015), 5 (), 13801 ISSN:.
  Microkinetic analyses of aqueous electrochemistry involving gaseous H2 or O2, i.e., hydrogen evolution reaction (HER), hydrogen oxidation reaction (HOR), oxygen reduction reaction (ORR) and oxygen evolution reaction (OER), are revisited. The Tafel slopes used to evaluate the rate determining steps generally assume extreme coverage of the adsorbed species (θ≈0 or ≈1), although, in practice, the slopes are coverage-dependent. We conducted detailed kinetic analyses describing the coverage-dependent Tafel slopes for the aforementioned reactions. Our careful analyses provide a general benchmark for experimentally observed Tafel slopes that can be assigned to specific rate determining steps. The Tafel analysis is a powerful tool for discussing the rate determining steps involved in electrocatalysis, but our study also demonstrated that overly simplified assumptions led to an inaccurate description of the surface electrocatalysis. Additionally, in many studies, Tafel analyses have been performed in conjunction with the Butler-Volmer equation, where its applicability regarding only electron transfer kinetics is often overlooked. Based on the derived kinetic description of the HER/HOR as an example, the limitation of Butler-Volmer expression in electrocatalysis is also discussed in this report.
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26. 26
  Strmcnik, D.; Uchimura, M.; Wang, C.; Subbaraman, R.; Danilovic, N.; van der Vliet, D.; Paulikas, A. P.; Stamenkovic, V. R.; Markovic, N. M. Improving the Hydrogen Oxidation Reaction Rate by Promotion of Hydroxyl Adsorption. Nat. Chem. 2013, 5, 300– 306, DOI: 10.1038/nchem.1574
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  Improving the hydrogen oxidation reaction rate by promotion of hydroxyl adsorption
  Strmcnik, Dusan; Uchimura, Masanobu; Wang, Chao; Subbaraman, Ram; Danilovic, Nemanja; van der Vliet, Dennis; Paulikas, Arvydas P.; Stamenkovic, Vojislav R.; Markovic, Nenad M.
  Nature Chemistry (2013), 5 (4), 300-306CODEN: NCAHBB; ISSN:1755-4330. (Nature Publishing Group)
  The development of hydrogen-based energy sources as viable alternatives to fossil-fuel technologies has revolutionized clean energy prodn. using fuel cells. However, to date, the slow rate of the hydrogen oxidn. reaction in alk. environments has hindered advances in alk. fuel cell systems. Here, we address this by studying the trends in the activity of the hydrogen oxidn. reaction in alk. environments. We demonstrate that it can be enhanced more than fivefold compared to state-of-the-art platinum catalysts. The max. activity is found for materials (Ir and Pt0.1Ru0.9) with an optimal balance between the active sites that are required for the adsorption/dissocn. of H2 and for the adsorption of hydroxyl species (OHad). We propose that the more oxophilic sites on Ir (defects) and PtRu material (Ru atoms) electrodes facilitate the adsorption of OHad species. Those then react with the hydrogen intermediates (Had) that are adsorbed on more noble surface sites.
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27. 27
  Grozovski, V.; Vesztergom, S.; Láng, G. G.; Broekmann, P. Electrochemical Hydrogen Evolution: H⁺ or H₂O Reduction? A Rotating Disk Electrode Study. J. Electrochem. Soc. 2017, 164, E3171– E3178, DOI: 10.1149/2.0191711jes
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  27
  Electrochemical Hydrogen Evolution: H+ or H2O Reduction? A Rotating Disk Electrode Study
  Grozovski, Vitali; Vesztergom, Soma; Lang, Gyozo G.; Broekmann, Peter
  Journal of the Electrochemical Society (2017), 164 (11), E3171-E3178CODEN: JESOAN; ISSN:0013-4651. (Electrochemical Society)
  The authors study the effect of H+ and OH- diffusion on the H evolution reaction in unbuffered aq. electrolyte solns. of mildly acidic pH values. The cathodic polarization curves measured on a Ni rotating disk electrode in these solns. can be modeled by assuming two irreversible reactions, the redn. of H+ and of H2O mols., both following Erdey-Gra´a´u´z-Volmer-Butler kinetics. The redn. of H+ yields a transport-limited and thus, rotation rate-dependent current at not very neg. potentials. At more cathodic potentials the polarization curves are dominated by the redn. of H2O and no mass transfer limitation seems to apply for this reaction. Although prima facie the two processes may seem to proceed independently, by the means of finite-element digital simulations a strong coupling (due to the recombination of H+ and OH- to H2O mols.) exists between them. The authors also develop an anal. model that can well describe polarization curves at various values of pH and rotation rates. The key indication of both models is that hydroxide ions can have an infinite diffusion rate in the proximity of the electrode surface, a feature that can be explained by assuming a directed Grotthuss-like shuttling mechanism of transport.
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28. 28
  Vesztergom, S. Encyclopedia of Interfacial Chemistry: Surface Science and Electrochemistry;Wandelt, K., Ed.; Elsevier: Amsterdam, 2018; pp 421– 444.
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29. 29
  Nagel, K.; Wendler, F. Die Wasserstoffelektrode als zweifache Elektrode. Z. Elektrochem. 1956, 60, 1064– 1072, DOI: 10.1002/bbpc.19560600924
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  The hydrogen electrode as a two-fold electrode
  Nagel, K.; Wendler, F.
  Zeitschrift fuer Elektrochemie und Angewandte Physikalische Chemie (1956), 60 (), 1064-72CODEN: ZEAPAA; ISSN:0372-8323.
  The H electrode is considered as an example of double-equil. electrodes, involving the reactions H+ + e- → 1/2H2 (α) and H2O + e- → 1/2H2 + OH- (β) together with the equil. H+ + OH- .dblharw. H2O. Thermodynamic properties and kinetics of this system of reactions are derived. The relations between the stationary electrode reaction currents iα and iβ, the total current i, the polarization Δg of the electrode, and the overvoltages Δgα and Δgβ of the electrode reactions are discussed. Stationary current vs. polarization curves are derived for the special case of pure concn. overvoltage and are compared with exptl. curves. The theoretical development also permits insight into more complex electrode processes.
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30. 30
  Kanzaki, Y.; Tokuda, K.; Bruckenstein, S. Dissociation Rates of Weak Acids Using Sinusoidal Hydrodynamic Modulated Rotating Disk Electrode Employing Koutecky-Levich Equation. J. Electrochem. Soc. 2014, 161, H770– H779, DOI: 10.1149/2.0221412jes
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  Dissociation rates of weak acids using sinusoidal hydrodynamic modulated rotating disk electrode employing koutecky-levich equation
  Kanzaki, Yasushi; Tokuda, Koichi; Bruckenstein, Stanley
  Journal of the Electrochemical Society (2014), 161 (12), H770-H779, 10 pp.CODEN: JESOAN; ISSN:0013-4651. (Electrochemical Society)
  The hydrogen evolution reaction of HCOOH, CH3COOH, and C2H5COOH solns. consists of two different redn. processes depending on the evaluated potential region; (1) independent redn. of RCOOH and (2) simultaneous redn. of RCOOH and H2O. The redn. of each carboxylic acid generates an apparent convective diffusion-controlled limiting current. The first achievement of the present study is that by using a rotating disk electrode (RDE) and a sinusoidal hydrodynamic modulated-rotating disk electrode (SHM), it was elucidated that the additive property of the redn. currents of RCOOH and H2O was not effective, and the convective-diffusion current was successfully distinguished from the total current. The second achievement is the successful anal. of the rotation-speed dependency of the limiting current in RDE and SHM using a modified theory of the Koutecky-Levich equation. The slopes of the plots for each carboxylic acid increased in the following sequence: RDE, SHM (p = 0.05), and SHM (p = 0.24), which is consistent with the theory. The dissocn. rates of the carboxylic acids and the reverse recombination rate were calcd.
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31. 31
  Wiberg, G. K. H.; Arenz, M. On the Influence of Hydronium and Hydroxide Ion Diffusion on the Hydrogen and Oxygen Evolution Reactions in Aqueous Media. Electrochim. Acta 2015, 159, 66– 70, DOI: 10.1016/j.electacta.2015.01.098
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  31
  On the influence of hydronium and hydroxide ion diffusion on the hydrogen and oxygen evolution reactions in aqueous media
  Wiberg, Gustav Karl Henrik; Arenz, Matthias
  Electrochimica Acta (2015), 159 (), 66-70CODEN: ELCAAV; ISSN:0013-4686. (Elsevier Ltd.)
  We present a study concerning the influence of the diffusion of H+ and OH- ions on the hydrogen and oxygen evolution reactions (HER and OER) in aq. electrolyte solns. Using a rotating disk electrode (RDE), it is shown that at certain conditions the obsd. current, i.e., the reaction rate, does not depend on the kinetics but on diffusion properties; In fact we demonstrate how studying these reactions in 0.1 M non-buffered aq. electrolytes with pH-values ranging between pH 1 to pH 13, the diffusion coeffs. of H+ and OH- ions can be detd. Within the exptl. error limits, we found no pH dependency on the diffusion coeffs. for any of the investigated ions.
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32. 32
  Carneiro-Neto, E. B.; Lopes, M. C.; Pereira, E. C. Simulation of Interfacial pH Changes during Hydrogen Evolution Reaction. J. Electroanal. Chem. 2016, 765, 92– 99, DOI: 10.1016/j.jelechem.2015.09.029
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  Simulation of interfacial pH changes during hydrogen evolution reaction
  Carneiro-Neto, Evaldo B.; Lopes, Mauro C.; Pereira, Ernesto C.
  Journal of Electroanalytical Chemistry (2016), 765 (), 92-99CODEN: JECHES; ISSN:1873-2569. (Elsevier B.V.)
  This work investigates the possibility of interfacial pH changes during a hydrogen evolution reaction using a finite elements simulation approach. This reaction is a common side step obsd. in many electrochem. systems, such as electrodeposition or corrosion. To develop a general approach, different mechanisms, i.e., Volmer/Tafel and Volmer/Heyrovsky´, were investigated. It is obsd. that for V-H mechanism the interfacial pH change increases 4.2 pH units for those cases where the bulk pH is 5.0. Therefore, in this case, the instant pH at the interface become alk., although the bulk is still acidic, which could justify parallel reactions such as metal hydroxide formation in metal electrodeposition. Besides, the interfacial pH changes and the corresponding pH profiles were calcd. under several exptl. conditions including the compn. of the metallic electrode, the bulk soln. pH and the total buffer concn. ([HA] + [A-]).
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33. 33
  Vanýsek, P. CRC Handbook of Chemistry and Physics, 93rd ed.; Haynes, W. M., Ed.; Chemical Rubber Company: Boca Raton FL, 2012.
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34. 34
  Guidelli, R.; Compton, R. G.; Feliu, J. M.; Gileadi, E.; Lipkowski, J.; Schmickler, W.; Trasatti, S. Defining the Transfer Coefficient in Electrochemistry: An Assessment (IUPAC Technical Report). Pure Appl. Chem. 2014, 86, 245– 258, DOI: 10.1515/pac-2014-5026
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  Defining the transfer coefficient in electrochemistry: An assessment (IUPAC Technical Report)
  Guidelli, Rolando; Compton, Richard G.; Feliu, Juan M.; Gileadi, Eliezer; Lipkowski, Jacek; Schmickler, Wolfgang; Trasatti, Sergio
  Pure and Applied Chemistry (2014), 86 (2), 245-258CODEN: PACHAS; ISSN:0033-4545. (Walter de Gruyter, Inc.)
  The transfer coeff. α is a quantity that is commonly employed in the kinetic study of electrode processes. In the 3rd edition of the IUPAC Green Book, the cathodic transfer coeff. αc is defined as -(RT/nF)(dlnkc/dE), where kc is the electroredn. rate const., E is the applied potential, and R, T, and F have their usual significance. This definition is equiv. to the other, -(RT/nF)(dln|jc|/dE), where jc is the cathodic c.d. cor. for any changes in the reactant concn. at the electrode surface with respect to its bulk value. The anodic transfer coeff. αa is defined similarly, by simply replacing jc with the anodic c.d. ja and the minus sign with the plus sign. This definition applies only to an electrode reaction that consists of a single elementary step involving the simultaneous uptake of n electrons from the electrode in the case of αc, or their release to the electrode in the case of αa. However, an elementary step involving the simultaneous release or uptake of more than one electron is regarded as highly improbable in view of the abs. rate theory of electron transfer of Marcus; the hardly satisfiable requirements for the occurrence of such an event were examd. Also, the majority of electrode reactions do not consist of a single elementary step; rather, they are multistep, multi-electron processes. The uncrit. application of the above definitions of αc and αa led researchers to provide unwarranted mechanistic interpretations of electrode reactions. In fact, the only directly measurable exptl. quantity is dln|j|/dE, which can be made dimensionless upon multiplication by RT/F, yielding (RT/F)(dln|j|/dE). One common source of misinterpretation consists in setting this exptl. quantity equal to αn, according to the above definition of the transfer coeff., and in trying to est. n from αn, upon ascribing an arbitrary value to α, often close to 0.5. The resulting n value is then identified with the no. of electrons involved in a hypothetical rate-detg. step or with that involved in the overall electrode reaction. A few examples of these unwarranted mechanistic interpretations are reported. In view of the above considerations, it is proposed to define the cathodic and anodic transfer coeffs. by the quantities αc= -(RT/F)(dln|jc|/dE) and αa= (RT/F)(dlnja/dE), which are independent of any mechanistic consideration.
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35. 35
  Bard, A. J.; Faulkner, L. R. Electrochemical Methods. Fundamentals and Applications; John Wiley & Sons: New York, 2001.
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36. 36
  Bronstein, I. N.; Semendjajew, K. A.; Musiol, G.; Muehlig, H. Taschenbuch der Mathematik; Verlag Harri Deutsch: Frankfurt am Main, 2008.
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  Haghighat, S.; Dawlaty, J. M. pH Dependence of the Electron-Transfer Coefficient: Comparing a Model to Experiment for Hydrogen Evolution Reaction. J. Phys. Chem. C 2016, 120, 28489– 28496, DOI: 10.1021/acs.jpcc.6b10602
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  pH Dependence of the Electron-Transfer Coefficient: Comparing a Model to Experiment for Hydrogen Evolution Reaction
  Haghighat, Shima; Dawlaty, Jahan M.
  Journal of Physical Chemistry C (2016), 120 (50), 28489-28496CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
  The empirical electron-transfer coeff. α is a valuable electrochem. observable that bridges the thermodn. and kinetics of redox reactions. For reactions that involve protons, the value of α is expected to be pH-dependent. However, even for the simplest redox processes, the nature of this dependency remains unclear. Toward clarifying this problem, the authors follow two goals. First, the authors calc. the electron-transfer coeff. α and its pH dependence based on a model 2-dimensional potential energy surface that was studied by Koper and Schmickler for proton redn. According to the model, α is pH-independent for high-pH values and pH-dependent for low-pH values, with α increasing as the pH is lowered. Second, the authors report the authors' exptl. measured α for H evolution on several electrode materials over a wide pH range. Several features of the data show similarities to the predictions of the model. The data show different behavior in two distinct pH regions. In the acidic region, a linearly increasing α with decreasing pH and in the basic side a pH-independent α are obsd. for several electrodes. However, certain predictions of the model, in particular the transition pH between the two regions, do not seem consistent with the data, which the authors propose likely arises due to mass-transfer limitations of the rate. The authors hope that this work will help better understand the pH dependence of interfacial electron-proton transfer reactions and, in particular, inspire further work to isolate mass-transfer limitations from interfacial chem. effects in measuring and interpreting the electron-transfer coeff.
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38. 38
  Nørskov, J. K.; Bligaard, T.; Logadottir, A.; Kitchin, J. R.; Chen, J. G.; Pandelov, S.; Stimming, U. Trends in the Exchange Current for Hydrogen Evolution. J. Electrochem. Soc. 2005, 152, J23– J26, DOI: 10.1149/1.1856988
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  Trends in the exchange current for hydrogen evolution
  Norskov, J. K.; Bligaard, T.; Logadottir, A.; Kitchin, J. R.; Chen, J. G.; Pandelov, S.; Stimming, U.
  Journal of the Electrochemical Society (2005), 152 (3), J23-J26CODEN: JESOAN; ISSN:0013-4651. (Electrochemical Society)
  A d. functional theory database of hydrogen chemisorption energies on close packed surfaces of a no. of transition and noble metals is presented. The bond energies are used to understand the trends in the exchange current for hydrogen evolution. A volcano curve is obtained when measured exchange currents are plotted as a function of the calcd. hydrogen adsorption energies and a simple kinetic model is developed to understand the origin of the volcano. The volcano curve is also consistent with Pt being the most efficient electrocatalyst for hydrogen evolution.
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  Koutecky, J.; Levich, V. G. The use of a rotating disk electrode in the studies of electrochemical kinetics and electrolytic processes. Zh. Fiz. Khim. 1958, 32, 1565– 1575
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  The use of a rotating disk electrode in the study of electrochemical kinetics and electrolytic processes
  Koutecky, J.; Levich, V. G.
  Zhurnal Fizicheskoi Khimii (1958), 32 (), 1565-75CODEN: ZFKHA9; ISSN:0044-4537.
  cf. C.A. 49, 1447e. Rotating disk electrodes were preferable to Hg drop electrodes in the study of reactions on electrodes involving kinetic and catalytic processes. The reactions on disk electrodes proceeded as stationary processes which permitted the formulation of reactions, even if they were complicated. Moreover, the properties of the solns. and the angular rotation velocities could be varied within wide limits with disk electrodes, while only the pH and the compn. of the soln. can be varied with the Hg drop electrode. The limiting diffusion currents were calcd. for typical cases on the assumption that the diffusion coeffs. (D) of the reacting substances were equal, because they frequently are very close. When D1 ≠ D2, the calcns. are no more complex in principle but require longer computations.
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  Cheng, A. H.-D.; Cheng, D. T. Heritage and early history of the boundary element method. Eng. Anal. Boundary Elem. 2005, 29, 268– 302, DOI: 10.1016/j.enganabound.2004.12.001
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  Kucernak, A. R.; Zalitis, C. General Models for the Electrochemical Hydrogen Oxidation and Hydrogen Evolution Reactions: Theoretical Derivation and Experimental Results under Near Mass-Transport Free Conditions. J. Phys. Chem. C 2016, 120, 10721– 10745, DOI: 10.1021/acs.jpcc.6b00011
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  General Models for the Electrochemical Hydrogen Oxidation and Hydrogen Evolution Reactions: Theoretical Derivation and Experimental Results under Near Mass-Transport Free Conditions
  Kucernak, Anthony R.; Zalitis, Christopher
  Journal of Physical Chemistry C (2016), 120 (20), 10721-10745CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
  Full derivations of Heyrovsky-Volmer (HV), Tafel-Volmer (TV), Heyrovsky-Tafel (HT), and Heyrovsky-Tafel-Volmer (HTV) mechanisms under steady state conditions are provided utilizing a new theor. framework which allows better understanding of each of the mechanistic currents and part currents. Simple and easily implemented equations are presented, which provide both the hydrogen coverage and electrochem. current as a function of overpotential and relevant kinetic parameters. It is shown how these responses are governed by a set of dimensionless parameters assocd. with the ratio of electrokinetic parameters. For each of the different mechanisms, an "atlas" of Hads coverage with overpotential and corresponding c.d. is provided, allowing an understanding of all possible responses depending on the dimensionless parameters. Anal. of these mechanisms provides the limiting reaction orders of the exchange c.d. for protons and bimol. hydrogen for each of the different mechanisms, as well as the possible Tafel slopes as a function of the mol. symmetry factor, β. Only the HV mechanism is influenced by pH, whereas the TV, HT, and HTV mechanisms are not. The cases where the equations simplify to limiting forms are discussed. Anal. of the exchange c.d. from exptl. data is discussed, and it is shown that fitting the linear region around the equil. potential underestimates the true exchange c.d. for all of the mechanisms studied. Furthermore, ests. of exchange c.d. via back-extrapolation from large overpotentials are also shown to be highly inaccurate. Anal. of Tafel slopes is discussed along with the mechanistic information which can and cannot be detd. The new models are used to simultaneously fit 16 exptl. responses of Pt/C electrodes in acid toward the hydrogen evolution reaction (her)/hydrogen oxidn. reaction (hor) as a function of η, pH, p(H2), and temp., using a consistent set of electrokinetic parameters. Examples of implementation of the equations as both computable document format and Excel spreadsheets are provided.
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Full Model for the Two-Step Polarization Curves of Hydrogen Evolution, Measured on RDEs in Dilute Acid Solutions

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Abstract

Introduction

Figure 1

Figure 2

Theory

Thermodynamic Considerations

Kinetic Considerations

Problem of Transport

Modeling the Polarization Curve of an RDE

Experimental

Figure 3

Results

Figure 4

Discussion

General Behavior of the Model; Polarization Curve Segments

Figure 5

Catalytic Current of H+ Reduction, jcat,H+

Figure 6

Limiting Current of H+ Reduction, jlim

Case of Mixed Charge-Transfer/Transport Control for H+ Reduction

Charge-Transfer-Controlled H2O Reduction

Mixed Charge-Transfer Control of H2O Reduction and Transport Control of H+ Reduction

Parameter Dependencies

Dependence on αc

Figure 7

Dependence on k

Kinetic Parameters from Plateau Lengths

Figure 8

pH Profiles

Figure 9

Figure 10

Concluding Remarks; Comparison to Other Works

Conclusions

Author Information

Acknowledgments

References

Cited By

Abstract

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References

STEP 1:

STEP 2:

Catalytic Current of H⁺ Reduction, j_cat,H⁺

Limiting Current of H⁺ Reduction, j_lim

Case of Mixed Charge-Transfer/Transport Control for H⁺ Reduction

Charge-Transfer-Controlled H₂O Reduction

Mixed Charge-Transfer Control of H₂O Reduction and Transport Control of H⁺ Reduction

Dependence on α_c