Kinetics of the Hydrogen Oxidation/Evolution Reaction on Polycrystalline Platinum in Alkaline Electrolyte Reaction Order with Respect to Hydrogen Pressure

The hydrogen oxidation and evolution reactions (HOR, HER) are of key importance to the development of novel alkaline membrane fuelcellsandelectrolyzers,whichfeatureapotentialcostadvantageovertheiracid-operatingcounterparts.However,theirmechanism remainspoorlyunderstoodevenonthemostcatalytically-activeplatinumsurfaces,forwhichsuchafundamentalparameterasthereactions’orderwithrespecttothehydrogenconcentrationisstillunknown.Withthismotivation,wehaveperformedrotatingdisc electrodemeasurementsonpolycrystallinePtin0.1MNaOHwithdifferenthydrogenpartialpressures(between10and100kPaH 2 ), from which we have derived a reaction order of 1/2. The latter value has important implications in the procedure to follow in order to derive kinetic currents free of diffusion contributions. More precisely, the HOR currents must be corrected for the diffusion overpotential and converted into a mass-transport free kinetic current using a modiﬁed version of the Koutecky-Levich equation that takes into consideration this non-unit reaction order, while the HER side only needs to be ohmically compensated due to the impossibility to supersaturate the electrolye with H 2 . Most importantly, our results point at a mechanism consisting of a dissociative adsorption (Tafel) reaction combined with a one-electron transfer (Volmer) rate-determining step, in terms consistent with the well-established view of the hydrogen-bonding strength as the main HOR/HER activity descriptor. © The

The electrochemical oxidation and evolution of molecular hydrogen are the key reactions at play in the anodes and cathodes of fuel cells and electrolyzers, respectively, which are likely energy conversion and storage devices for renewable energy concepts based on the use of H 2 as energy carrier. Beyond this practical interest, the hydrogen oxidation and evolution reactions (HOR and HER, respectively) have also played a pivotal role in the historical development of fundamental electrocatalysis theories. Indeed, the exponential relation between current and overpotential that describes the kinetics of many electrochemical reactions, viz., the Butler-Volmer equation, was originally validated for the HER, 1 which also became the first electrochemical process for which the rate-determining role of the bond strength of adsorbed intermediates (following Sabatier's principle) was verified. 2 Thus, the HOR/HER has become one of the most extensively studied electrochemical reactions, particularly at low pH values and on the catalytically most active platinum-based materials relevant to proton exchange membrane fuel cells (PEMFCs) and electrolyzers. In acid electrolytes, the HOR/HER kinetics on platinum electrodes are extremely fast, so that experimental methods which afford very high mass-transport rates are required in order to unambiguously differentiate kinetic-and diffusion-overpotentials (e.g., hydrogen pump experiments in PEMFC 3 or the recently developed floating porous gas diffusion electrode method 4 ). Using the hydrogen-pump approach, the very high exchange current densities (i 0 ) of ≈200 mA · cm Pt −2 obtained at 313 K 5 (or ≈600 mA · cm Pt −2 at 353 K) 3 are consistent with the fact that ultra-low Pt loadings of ≤0.05 mg Pt · cm −2 can be used at the anode of PEMFCs, 3,6 while much higher Pt loadings are required for the cathode electrode due to the much more sluggish oxygen reduction reaction (ORR). [6][7][8] On the contrary, the HOR/HER on Pt in alkaline electrolyte is two orders of magnitude slower than in acid, 5 therefore allowing for the quantification of the reaction kinetic parameters using rotating disc electrode (RDE) voltammetry 9 despite its much lower masstransport rates. Thus, in alkaline electrolytes the RDE method can be used to study the HOR/HER on platinum single crystals, providing crucial information concerning the structure-sensitivity of these reactions. 10 This was done by Schmidt and coworkers, 11 whose results suggest a strong structure sensitivity for the HOR/HER on Pt(hkl) in alkaline electrolyte, as inferred from the i 0 values of ≈0.6 and ≈0.07 mA · cm Pt −2 (at 293 K) for Pt(110) and Pt(111) single crystals, respectively. On the other hand, Sheng and collaborators 9 have recently estimated essentially identical HOR/HER exchange current densities of ≈0.7 mA · cm Pt −2 (at 293 K) for polycrystalline Pt and carbon-supported Pt nanoparticles of ≈2 nm diameter, which would suggest the absence of structure sensitivity for the HOR/HER, contrary to the well-known structure sensitivity of the ORR on Pt 6,12,13 and to the results of the HOR/HER studies on Pt single crystals 11,14,15 discussed above. One may speculate that this discrepancy might arise from the contamination of the Pt(hkl) surfaces with electrolyte impurities resulting from the leaching of glass components in the electrochemical cell upon contact with the alkaline solution, 16,17 which was successfully suppressed in Ref. 9 by minimizing the measurement delay.
Beyond these fundamental considerations, the two order of magnitude lower i 0 values in alkaline vs. acid electrolytes would imply the need for alkaline fuel cell anodes and electrolyzer cathodes with Pt loadings well above those required for their acid-operating counterparts. This larger noble metal requirement would attenuate the expected cost advantage of these alkaline electrochemical devices, which is based on the possibility to catalyze the oxygen reduction [18][19][20] and evolution 21,22 reactions using inexpensive non-noble metal catalysts. The resulting need for better-performing HOR/HER catalysts in alkaline medium would certainly benefit from a better understanding of the reaction mechanism, which remains elusive to this date in spite of the great body of work devoted to this topic. As suggested in Ref. 9, RDE measurements with different hydrogen partial pressures would allow to quantify the reaction order (m) with respect to H 2 concentration, which should provide further insight into the reaction mechanism and which is also critical for the quantification of kinetically controlled currents from RDE measurements. 23,24 In this respect, previous HOR/HER studies on Pt in alkaline electrolyte 5,9,11,14,25 assumed an m value of 1 that, to the best of our knowledge, has never been verified using this approach.
In the following we will thus determine the value of m for the HOR/HER on polycrystalline platinum (Pt PC ) in 0.1 M NaOH by varying the H 2 concentrations in RDE experiments. Our results F1449 unambiguously point at a reaction order of 1/2 that needs to be accounted for in the determination of kinetically controlled HOR currents from RDE data. Furthermore, we will show that the Nernstian diffusion overpotential must be considered in the quantification of kinetically-controlled HOR currents, a fact that until now has been systematically overlooked in the literature. In the case of the HER, though, our data suggest that the electrolyte cannot be supersaturated with H 2 , so that the H 2 concentration at the electrode/electrolyte interface stays constant during the HER; this in turn means that kinetically-controlled HER currents are obtained without further diffusion/transport corrections other than the conventional correction by the un-compensated ohmic resistance between the reference and the working electrode. Finally, the reaction order of 1/2 with respect to H 2 concentration points at an HOR/HER mechanism consisting of a fast, dissociative H 2 adsorption (Tafel) reaction combined with a rate-determining electron transfer step (Volmer reaction).  (50,30,20 or 10% H 2 ) purchased from Westfalen AG (Münster, Germany). The carbon monoxide used in the CO-stripping measurements (4.7-grade) was also purchased from the same provider in the form of an aluminum cylinder equipped with a brass pressure reducer.
Working electrode (WE) preparation.-The measurements were performed using a rotating ring-disc electrode (RRDE) with a PTFE body and a 5 mm diameter Pt PC disc (99.99+% purity, Pine Research Instrumentation, Durham, NC) embedded at its center. Prior to the assembly of the electrode, the disc was hand-polished with 0.05 μm alumina suspension (Buehler, Dusseldorf, Germany) and ultrasonically cleaned in ultrapure water. Following the disc insertion, the assembled RRDE was subjected to a systematic cleaning procedure by immersing it in 5 M KOH (99.99% purity; Semiconductor Grade, Sigma Aldrich), ultrapure water, 2 M HClO 4 and ultrapure water again in 20 minute intervals.
Electrochemical setup and measurement procedure.-All experiments were performed in a single-compartment PTFE cell allowing for measurements without any contact between the electrolyte and glass surfaces, in order to avoid impurities produced by the leaching of glass in contact with alkaline solutions and their detrimental effect on the HOR kinetics on Pt PC which was demonstrated in Refs. 16 and 17. The PTFE cell was embedded in a stainless steel jacket connected to a calibrated thermostat (Julabo Labortechnik GmbH, Seelbach, Germany) at 293 K, and it was closed with a four-necked glass cover. The latter held a Pt wire counter electrode (99.99+% purity, Advent, Oxford, England) embedded in a PTFE stopper, a glass bubbler that allowed for gas blanketing above the surface of the electrolyte or direct bubbling through a fluorinated ethylene propylene (FEP) tube, and the reference electrode (RE) of choice. For the great majority of the measurements, the latter consisted of a palladium hydride RE prepared from a Pd wire (99.99+% purity, Advent) loaded with hydrogen by holding a constant current of -5 mA versus a Pt counter electrode for 10 min in H 2 -saturated 0.1 M NaOH. In the case of the experiments involving CO, though, the RE was a Ag/AgCl electrode consisting of a glass tube ended in a porous glass frit (Vycor 7930, Advanced Glass & Ceramics, Holden, MA) and filled with water saturated in AgCl (99.999% purity, Sigma Aldrich) and KCl (99.999% purity, Sigma Aldrich); its opposite end was covered with a plastic stopper with a silver wire embedded in it (Ametek GmbH, Meerbusch, Germany) and immersed in this electrolyte. This reference electrode was kept in a separated glass holder filled with the electrolyte of choice and connected to the main electrolyte compartment through a Luggin capillary consisting of a FEP tube closed with a 50 μm thick Nafion membrane (Ion Power, New Castle, DE). However, all potentials in this work are quoted against the reversible hydrogen electrode (RHE), which is referenced to the voltage at zero current in the recorded HOR/HER polarization curves.
The measurements started with the assembly of the cell filled with 100 mL of electrolyte and, when needed, its saturation with H 2 as to proceed with the H-loading of the Pd wire reference electrode described above. Subsequently, the electrolyte was replaced with another 100 mL of fresh solution and saturated with Ar for 15 min. The Pt PC RRDE working electrode was mounted onto a polyether ether ketone (PEEK) rotator shaft (Pine Research Instrumentation), immersed in the cell and electrochemically cleaned by recording cyclic voltammograms (CVs) between ≈0.05 and ≈1.2 V RHE at 200 mV · s −1 until a steady state CV was obtained. Subsequent CVs were then recorded up to 1.0 V RHE at a scan rate of 50 mV · s −1 , in all cases controlling the potential with a SP-200 potentiostat (BioLogic, Grenoble, France) and (as in the case of the polarization curves discussed below) while blanketing the electrolyte with the gas of choice, as to avoid the interference of gas bubbles during the course of the measurement.
The CO-stripping experiments used to estimate the Pt PC electrode's roughness factor were performed bubbling carbon monoxide in the electrolyte for 5 min while holding the working electrode at 0.05 V RHE . This was followed by the saturation of the solution with Ar for 35 min while keeping the working electrode at this potential, which was then swept positively up to 1.0 V RHE at 20 mV · s −1 , followed by the recording of another three CVs between 1.0 and 0.05 V RHE at the same scan rate.
The HOR/HER activity measurements were preceded by the bubbling of the electrolyte with the gas mixture of choice for 15 minutes, during which the RRDE was rotated at 900 rpm while the working electrode was swept between −0.1 and 1.0 V RHE at 20 mV · s −1 . Subsequently, steady-state HOR/HER polarization curves were systematically acquired by scanning the potential between −0.1 and 1.0 V RHE at 20 mV · s -1 and a given rotation speed in the saturated solution. Moreover, all polarization curves reported hereafter correspond to negativegoing scans since, in agreement with our previous observations, 25 these were systematically slightly more active than the positive-going ones. While the reason for this dependency of the activity on the scanning direction is beyond the scope of this work, it may result from the trace contamination with transition metals of the NaOH which could possibly lower the HOR/HER activity of Pt. 26 Indeed, these metallic impurities would get adsorbed on the Pt surface at low potentials and get stripped from it at higher potentials, implying that at the beginning of each negative-going scan the Pt surface would be cleaner (and more HOR/HER-active) than in the subsequent, positive-going one.
Finally, the ohmic drop between the working and the reference electrode was quantified by potentio electrochemical impedance spectroscopy (PEIS), applying a 5 mV voltage perturbation (1 MHz to 1 Hz) at 0.5 V RHE . The cell resistance estimated from the linearly extrapolated intercept with the real axis in the resulting Nyquist plot was systematically between 40 and 45 and was used to determine the ohmic drop-corrected potential (E iR-free ).

Results and Discussion
Quantifying the roughness factor of polycrystalline platinum in acid and alkaline electrolyte.-The rigorous assessment of a material's catalytic activity for a given (electro)chemical reaction requires the quantification of the active surface area/number of sites in order to determine the intrinsic activity descriptors, respectively referred to as specific activity (current normalized to the active surface area) or turnover frequency (TOF, i.e., number of reaction turnovers per active surface site and second). For catalysts based on metal nanoparticles (either without support or dispersed on high-surface area supports),  Fig. 1) and to the oxidation of CO potentiostatically-adsorbed at 0.05 V RHE ('CO-stripping', see Fig. 2) in acid and alkaline electrolyte. The corresponding roughness factor (RF) values are calculated assuming Pt surface-normalized charges of 210 μC · cm Pt −2 for H upd and 420 μC · cm Pt −2 for CO-stripping. their active surface area (in units of m 2 metal ) is often referenced to the metal weight, yielding the so-called dispersion (typically in units of m 2 metal · g −1 metal ). On the other hand, for solid metal discs like the one used herein, the active surface area is generally referenced to the disc's geometrical area, yielding the so-called roughness factor (RF, in units of cm 2 Pt · cm −2 disc ). Cyclic voltammetry is routinely applied to quantify the RF of Ptbased catalysts because, unlike for other noble metals like Ru 27 or Ir, 28 the cyclic voltammograms (CVs) recorded on platinum feature a well-defined separation between the potentials corresponding to the formation and reduction of Pt-(hydr)oxides and those related to the underpotential deposition of hydrogen (H upd ). This voltammetric behavior is illustrated in Figure 1, which displays the CVs recorded at 50 mV · s −1 between 1.0 and ≈0.05 V RHE on the same polycrystalline platinum (Pt PC ) electrode immersed in Ar-saturated 0.1 M HClO 4 or 0.1 M NaOH (Figs. 1a vs. 1b, respectively). The voltammogram in acid agrees with previous reports, 6 and features a rectanglelike, pseudocapacitive charge extending from ≈0.05 V RHE and up to ≈0.45 V RHE that can be related to the adsorption and desorption of H upd on (111) and (100) crystallographic domains, along with a superimposed, well-defined peak at ≈0.12 V RHE corresponding to H upd on (110) planes. 13 This last peak is subsequently positioned at ≈0.26 V RHE upon transfer of the electrode to the alkaline electrolyte, 13 in good agreement with the positive peak shift of ≈10 mV per pH unit on the RHE scale observed on polycrystalline platinum 29 and stepped Pt single crystals. 30 Moreover, the CVs in Figures 1a and 1b also depict the integrated areas used to quantify the H upd charges, and the resulting RF values of 1.6-1.8 cm 2 Pt · cm −2 disc are summarized in Table I. More precisely, this conversion was performed using the customary charge 31 of 210 μC · cm Pt −2 and a lower integration limit of ≈0.05 V RHE ; we note by passing that while this last value is lower than the H 2 -evolution onset suggested in other studies, 32,33 it appears appropriate when considering that the H upd process is known to extend below this HER onset potential. 34,35 Alternatively, the RF value can also be derived from the charge required to oxidize a monolayer of adsorbed carbon monoxide (CO ad ), using the so-called CO-stripping method illustrated in Figure 2. The results collected in acid (Fig. 2a) using a CO-dosing potential of 0.05 V RHE feature one well-defined oxidation peak at ≈0.75 V RHE , the onset of which coincides with that of the surface (hydr)oxide formation discernable in the CV subsequently recorded in the CO-free electrolyte (cf. Equation 1). This behavior is generally rationalized by the involvement of this adsorbed hydroxide (OH ad ) in the CO oxidation reaction formulated in Equation 2: 36 Interestingly, the CO-stripping profile in Figure 2a is in good agreement with the one reported in Ref. 37 for a Pt PC electrode voltammetrically-cleaned and tested in 0.5 M HClO 4 , but differs slightly from those observed for flame-annealed 38 or sputteredcleaned 27 Pt PC in H 2 SO 4 media, whereby a pre-wave some tens of millivolts negative of the main oxidation feature was observed. While these differences in the CO-stripping profiles are beyond the scope of this study, they are likely related to the different electrode preparation procedures and/or to the nature of the acids used in each study [i.e, the weakly-adsorbing ClO 4 − used herein and in Ref. 37, vs. the strongly adsorbed (bi)sulfate in Refs. 27 and 38].
On the other hand, pre-waves at even lower potentials did appear in CO-stripping measurements in 0.1 M NaOH (Fig. 2b), agreeing again with previous observations in alkaline media for the same polycrystalline substrate 37 and Pt single crystals. 39,40 Considering the role of OH ad in the CO oxidation reaction (cf. Eq. 2), these pre-waves have been regarded as indicative of the early adsorption of hydroxyl anions on the Pt surface in alkaline electrolyte. 36,40 In particular, the peak at ≈0.45 V RHE in Fig. 2b would point at the onset of OH adsorption at potentials within the H upd region, which complicates the quantification of the CO-stripping charge due to the absence of a baseline free of pseudocapacitive contributions. In Figure 2b, this problem was circumvented by using the positive-going scan of the steady-state CV recorded in 0.1 M HClO 4 as the baseline, yielding an RF value of 1.3 cm 2 Pt · cm −2 disc in excellent agreement with the one derived in acid (see Table I). This consistency in the RF values estimated in both electrolytes extends to the roughness factors derived from the H upd charges in acid and alkaline, and gives proof of the excellent reproducibility of both techniques. On the other hand, the ≈15-25% lower RF estimated by CO-stripping vs. H upd doubtlessly results from the different degrees of coverage of each probing molecule (CO vs. H upd ), which in terms depends on such parameters as the Pt PC -surface crystallographic composition, the CO adsorption potential, and the lower integration boundary for the quantification of the H upd charge (note that in acid electrolytes the most negative inflection point in the negative-going scan is frequently used to determine the lower integration limit, 3,32,33 which in our case would result in a ≈10% lower H upd charge and RF value). Owing to the uncertainty in the lower integration value for the H upd charge, we have chosen to use the RF value of 1.3 cm 2 Pt · cm −2 disc estimated from CO-stripping in the Pt surface normalization of all the currents presented hereafter.
HOR/HER polarization curves at various H 2 partial pressures and preliminary estimate of the reaction order.-Following the quantification of the RF value, the 0.1 M NaOH electrolyte was saturated with the H 2 /Ar mixture of choice; the subsequently recorded HOR/HER polarization curves (at 1600 rpm, 20 mV · s −1 and 293 K) are plotted against the ohmic drop-corrected potential (E iR-free ) in Figure 3. The latter Figure also displays the hydrogen oxidation current (at 100 kPa H 2 ) expected for infinitely fast kinetics as described by the (Color online) Ohmically corrected polarization curves (negativegoing scans at 1600 rpm and 20 mV · s −1 ) recorded on a Pt PC -disc in 0.1 M NaOH at 293 K and with various hydrogen partial pressures. The dashed gray line shows the H 2 oxidation diffusion overpotential estimated for a H 2 partial pressure of 100 kPa and an electrode rotation speed of 1600 rpm (for which the corresponding diffusion-limited current is ≈2.5 mA · cm −2 disc ). The inset shows a Levich-Koutecky plot that displays the linear relation between the H 2 partial pressure (and concentration) and the current measured at 0.4 V RHE and, with its zero-intercept, confirms that the current measured at this potential is diffusion-limited.
Nernstian diffusion overpotential (η diff,HOR ) expression: [3] where R corresponds to the gas constant (8.314 J · mol −1 · K −1 ), T is the temperature (in Kelvin), n HOR/HER represents the number of electrons involved in the reaction (i.e., n = 2 for the oxidation/evolution of one H 2 molecule), F is the Faraday constant (96,485 A · s · mol −1 ), and i HOR and i lim,HOR are the measured and (H 2 transport) diffusion-limited currents, respectively. Since the concentration of H + (the reactant in the HER) is ≈100-fold higher than the H 2 concentration (the reactant in the HOR), no diffusion-limited currents can be observed for the HER within the measured current range. For the HOR, however, i lim,HOR is directly proportional to the concentration of hydrogen in the bulk of the electrolyte (C bulk ), as formulated in the Levich equation: where D is the H 2 diffusion coefficient, ν is the electrolyte's kinematic viscosity, and ω stands for the electrode rotation speed (in rad/s). Moreover, assuming Henry's Law, the value of C bulk should be directly proportional to the partial pressure of hydrogen (p H2 ) above the electrolyte. This is confirmed by the inset in Figure 3, which displays the linear relationship between the values of i at 0.4 V RHE and the corresponding H 2 partial pressures, and proves that the currents measured at this potential were solely diffusion-limited. Moreover, the diffusion-limited current density of ≈2.5 mA · cm −2 disc in the measurement with 100 kPa H 2 (at 1600 rpm and 293 K) agrees well with previous reports under equivalent conditions, 9,25,26 and is also consistent with the values for the kinematic viscosity of 0.1 M NaOH (1.023 · 10 −2 cm 2 · s −1 at 293 K), 41 the diffusion coefficient of H 2 in ≈0.1 M KOH (≈3.4 · 10 −5 cm 2 · s −1 at 298 K), 42 and the H 2 solubility in 0.1 M KOH (≈0.7 mM at 303 K). 43 Unlike these diffusion-controlled currents at 0.4 V RHE , those closer to the reversible potential are limited by the HOR/HER kinetics, which are often considered to follow a simple Butler-Volmer equation: 44,45 where η is the overpotential, i 0 is the exchange current density (in units of A · cm Pt −2 ), RF is the roughness factor, and α a and α c are the anodic and cathodic transfer coefficients, respectively. Additionally, for small η values, i.e., near 0 V RHE , Equation 5 can be linearized into the form: and the measured currents can be regarded as being kineticallycontrolled (i.e., i ≈ i kin , see discussion below). Following this approach, Figure 4a displays the currents within ±5 mV of the reversible potential along with their linear fits, from which we derived the i 0 · (α a + α c ) values summarized in Figure 4b. The latter appear plotted against the corresponding p H2 , keeping in mind again Henry's law and the proportionality between C bulk and i 0 formulated in Equation 7: 46 where i 0 * stands for the exchange current density at a reference H 2 concentration C bulk * (e.g., at p H2 * = 100 kPa H 2 ), and m represents the sought-after reaction order, for which the chart's slope yields a preliminary value of ≈0.6, well below the m = 1 assumed in previous RDE studies in alkaline medium. 9,11,14 Here we must note in passing that the HOR/HER polarization curves in Figs. 3 and 4a were not corrected for pseudocapacitive contributions that cannot be easily differentiated from the hydrogen evolution process initiating at potentials below ≈0.05 V RHE (see CVs in Figures 1a and 1b). 35 Considering that the capacitive currents at potentials > 0.1 V RHE on the CV in Figure 1b account to ≈35 μA · cm −2 disc , along with the 2.5-fold difference between the scan rate of 50 mV · s −1 used in the recording of that voltammogram and the 20 mV · s −1 implemented for the polarization curves in Figures 3 and 4a, this pseudocapacitive contribution would be in the order of ≈15 μA · cm disc −2 . This value is well within the order of the current measured at 5 mV RHE and 10 kPa H 2 in Fig. 4a, and would ultimately imply that the value of i 0 · (α a + α c ) estimated at this lower partial pressure is not reliable. Nevertheless, the currents at higher p H2 values are well above this pseudocapacitive threshold, and the corresponding values of i 0 · (α a + α c ) derived at higher partial pressures still point at a reaction order of ≈1/2 that, as will be shown in the following sections, has important implications not only in the elucidation of the HOR/HER mechanism, but also in the determination of kinetically-controlled HOR currents.
Validation of a procedure to estimate the HOR/HER kinetic currents.-In RDE voltammetry, the continuous rotation of the electrode at a given speed results in the buildup of a stagnant boundary layer of thickness δ BL , across which molecular transport toward the electrode surface occurs exclusively through diffusion. 47 For an electrochemical process involving the consumption of a reactant, like the HOR, the current (i HOR ) associated to the drop of reactant concentration over this boundary layer (schematized in Figure 5) can be described by: where C surf corresponds to the reactant concentration at the electrode/electrolyte interface. Moreover, at the diffusion-limited currents reached at high overpotentials (i lim,HOR ), all reactant molecules get consumed as soon as they reach the electrode surface (C surf = 0), and Equation 8 can be re-written into the form: i lim,HOR = n HOR/HER · F · D δ BL · C bulk [9] which can then be divided by Equation 8 and rearranged to yield: [10] Implicitly, this difference between surface-and bulkconcentrations across the boundary layer contributes to the measured potential (E meas ) in the form of the Nernstian diffusion overpotential: 48 η diff,HOR = − R · T n HOR/HER ·F ln C surf C bulk [11] which becomes equal to the form of the Nernstian diffusion overpotential given in Eq. 3 upon substitution of Eq. 10 in Eq. 11. However, to the best of our knowledge, this contribution of η diff,HOR has been systematically overlooked in previous studies dealing with the evaluation of the surface potential (E surf ) formulated in Equation 12: where R is the ohmic drop between the working and reference electrodes. On the other hand, the so-called kinetic current (i kin,HOR ) represents the value that one would measure in the absence of this concentration drop along the boundary layer (i.e., if C surf were to be equal to C bulk ); the magnitudes of i HOR and i kin,HOR are therefore set by these surface and bulk concentrations, according to the expression: 23 [13] which, for m = 1, would yield the so-called Koutecky-Levich equation that is customarily used to asses O 2 -reduction reaction kinetics. 6,24 While the H 2 concentration at the electrode/electrolyte interface during H 2 oxidation is clearly a function of the HOR current (as described in Eq. 10), it is unclear whether the H 2 concentration at the electrode/electrolyte interface can increase above its saturation value during the H 2 evolution reaction. Indeed, under the assumption that supersaturation of the electrolyte with hydrogen were to be possible (i.e., if the H 2 concentration could exceed the saturation concentration for the given hydrogen partial pressure), the H 2 -concentration profile schematized in Figure 5 would build up over the boundary layer, and an expression for the hydrogen evolution current (i HER ) equivalent to the one formulated in Equation 8 could be written: ) unless CC License in place (see abstract  Moreover, this expression could subsequently be divided by Eq. 9 and rearranged to yield: |i HER | i lim,HOR [15] which, in an analogy with the hydrogen oxidation reaction discussed above, would have implications in the derivation of HER diffusion overpotential (η diff,HER ) and -kinetic current (i kin,HER ) terms, formulated in Equations 16 and 17, respectively:  [17] In an attempt to determine whether H 2 supersaturation might occur, we proceeded to record new sets of HOR/HER polarization curves at 100 or 20 kPa H 2 partial pressure and different electrode rotation rates (between 3600 and 400 rpm). The results are featured in Figure 6, which includes a Levich-Koutecky plot relating the inverse of the currents measured at 0.4 V RHE with ω −1/2 ; as in Figure 3, both linear fits intercept at the origin of the axes and thus confirm again that these i 0.4V values are diffusion-limited.
Next, the currents recorded at various electrode rotation rates and 100 kPa H 2 (cf. Fig. 6a) were transformed into kinetically-controlled values taking into consideration the different correction terms discussed above. In this analysis, we only consider HER currents of |i HER | ≤ 4 mA · cm −2 disc , as to avoid the possible shielding of the electrode caused by the formation of H 2 bubbles at current densities in excess of this value. In a first step, the potentials for both HORand HER-branches were corrected for η diff using Equations 3 and 16, respectively, and i kin was also derived for both sets of currents using Eqs. 13 and 17 with an assumed m value of 1. As shown in Figure 7a, the correction of the polarization curves with this approach Figure 7. (Color online) Tafel plots illustrating the effect of various correction approaches upon transformation of the polarization curves (negative-going scans, 20 mV · s −1 ) recorded with various electrode rotation speeds in 0.1 M NaOH at 293 K and with 100 kPa H 2 into kinetically-controlled currents (i kin ). In (a), i kin is estimated for both the HOR-and HER-branches by assuming a reaction order (m) of 1 and taking the diffusion overpotential into consideration for both the oxidation-and evolution-branches. In (b), the HER currents are only iR corrected, and the HOR branches are corrected for the diffusion overpotential and transformed into i kin by assuming m = 1. In (c), the HER currents are only iR corrected, and the HOR branches are corrected for the diffusion overpotential and transformed into i kin by assuming m = 0.5. yielded different Tafel plots for all ω values, instead of superimposing curves independent of the rotation rate, as would be expected for a proper extraction of kinetically-controlled HOR/HER currents. In this respect, the matching HER currents in the polarization curves in Figure 6 (solely iR corrected) suggest that the hydrogen evolution branch may not be subjected to the diffusion limitations affecting the HOR, as it had already been assumed in previous works. 9,11,14 This possibility appears confirmed in Figure 7b, where the HER branches at all rotation rates do superimpose when not corrected for any of the effects associated to an increase of the H 2 concentration along the electrode's boundary layer (i.e., not applying the η diff,HER -and i kin,HER -corrections in Eqs. 16 and 17). As for the HOR currents, Figure 7c shows that the required superposition of the Tafel curves is only attained when considering η diff,HOR (cf. Eq. 3) and when a reaction order of m = 1/2 (suggested by our preliminary estimate above) is used to determine i kin,HOR via Equation 13. While this consistency check of the kinetically-controlled currents extracted from RDE data at different rotation rates is a useful method to determine whether  Figure 7c, the HER currents are only iR corrected, while the HOR currents are additionally corrected for the diffusion overpotential and transformed into i kin assuming m = 0.5. the correct transport corrections have been applied, we caution that a reliable determination of the reaction order with respect to p H2 can only be done through measurements at different H 2 partial pressures.
In summary, meaningful Tafel plots were obtained by correcting the HOR branch for the H 2 concentration drop between the electrode surface and the bulk of the electrolyte, namely by subtraction of the Nernstian diffusion overpotential (η diff,HOR ) from the iR corrected potential and by determining the kinetically-limited HOR currents using a reaction order of m = 1/2. On the other hand, only the customary iR correction must be used to obtain the kinetically-limited HER currents, suggesting that the evolution of hydrogen does not lead to any significant supersaturation of the electrolyte with H 2 . Finally, the validity of this combined approach was verified by extending it to the treatment of the polarization curves recorded at 20 kPa H 2 and various electrode rotation speeds (Fig. 6b), whereby the resulting Tafel plots featured in Figure 8 also showed excellent superposition, as is expected when transport resistances are properly accounted for.
Fitting of the Tafel plots to the Butler-Volmer equation.-Having defined a rigorous procedure for the derivation of kineticallycontrolled currents free of diffusion-related contributions, we proceeded to extend it to the treatment of the polarization curves recorded at other hydrogen partial pressures. The HOR-i kin values determined according to the above procedure and plotted in Figure 9 were derived from measured currents equal to or below 80% of the corresponding i lim . In the case of the HER branches, all the currents recorded down to a non iR-compensated potential of -0.1 V RHE (see Experimental Section) were considered, and appear plotted after the required iR correction in Figure 9. In the particular case of the polarization curves at 10 and 20 kPa H 2 , though, this approach yielded Tafel plots with HER branches significantly larger than the HOR ones, and that could not be successfully fitted to the Butler-Volmer equation following the approach presented below. It is for this reason that the Tafel plots at these lower hydrogen partial pressures (i.e., at 10 and 20 kPa H 2 ) and included in Fig. 9 only extend down to HER overpotential values equal to those applied in the corresponding HOR branches.
Keeping all these considerations in mind, the subsequent fitting of the HOR/HER kinetic data to the Butler-Volmer equation was done by fitting log i HOR/HER vs. η, which yields more precise fits near η = 0 compared to fitting Eq. 5 directly. Moreover, a first set of fits was performed on the basis of the logarithm of Eq. 5 with three independent fitting variables (namely, i 0 , α a and α c ), while in the second set of fits the sum of the transfer coefficients (α a + α c ) was set to a value of 1 (i.e., α c = 1 -α a ), as previously suggested in Ref. 9. The results obtained with both approaches were fully comparable in terms of the derived quantities and of the fitting errors and, since the addition of an extra degree of freedom (α c ) did not improve the quality of the fits, only the results obtained with two fitting parameters (i.e., i 0 and α a , whereby α c = 1 -α a ) are plotted in Figure 9 and are considered hereafter.
Prior to the discussion of the results derived from these fits, we revisit our initial estimate of the values of i 0 · (α a + α c ) vs. p H2 from the iR corrected micropolarization currents (presented in Fig. 4), but this time correcting for the transport related effects as described above. As expected, the i kin values shown in Fig. 10a are slightly higher than those shown in Fig. 4a, particularly for the low H 2 concentrations due to their correspondingly lower diffusion-limited currents. Considering the plots' linearity and the finding that the sum of the transfer coefficients is equal to 1 (discussed above), the slopes in the micropolarization region can now be used to directly estimate the corresponding i 0 values (see Eq. 6). These exchange currents are summarized in Figure 10b, showing the expected proportionality between log(i 0 ) and log(p H2 ) (s. Eq. 7); the extracted reaction order with respect to p H2 equates to m ≈0.54, i.e., now reasonably close to the value of m = 1/2 assumed in the derivation of the HOR kinetic currents and lower than the value of m ≈0.61 initially estimated in Figure 4b, where no transport corrections had been considered.
Following this consistency check, Figure 11a (red symbols/line) shows again the evolution of the exchange current density with the hydrogen partial pressure, now for i 0 values derived from a Butler-Volmer fit (with α a + α c = 1) of kinetically-controlled currents extracted from the RDE data by applying Eq. 13 with m = 1/2 for the HOR branch (data and fits shown in Figure 9). However, it is noteworthy that almost identical i 0 values are obtained if m = 1 is used in the derivation of the kinetically-controlled HOR data (black symbols/line in Figure 11a), as has been done so far in the literature. Thus, while the estimated i 0 values only depend very little on the value of m used to extract the kinetically-controlled HOR currents via Eq. 13, the resulting dependence of log(i 0 ) with log(p H2 ) demonstrates unambiguously the reaction order of m = 1/2 for the HOR/HER in alkaline electrolyte (if a reaction order of m = 1 were correct, the i 0 values would have to follow the gray line drawn in Figure 11a). Owing to the small sensitivity of the extracted i 0 values on the assumed reaction order with respect to p H2 , our values (based on m = 1/2) may be compared to those from previous studies on Pt PC and Pt/C 9 as well as on Pt(110) and Pt(111) 11 where m = 1 was assumed (see Table II). There is good agreement between the various i 0 values, except for the ≈10-fold lower value for Pt(111). The latter might be related to contamination resulting from the use of glass components leachable in the alkaline electrolyte, 16 which might also explain the ≈5-fold lower i 0 values reported in older studies on polycrystalline 49 or single crystal 14 platinum surfaces.
Interestingly, the minor effect of the assumed value of m on the exchange currents derived from the fitting of the Tafel plots to the Butler-Volmer equation or the micropolarization region (at least for the values of m = 1 or 1/2 considered herein) implies that the accuracy of this fitting cannot be used to extract any information about the reaction order with respect to H 2 partial pressure. Instead, experiments with different hydrogen partial pressures or a rigorous analysis of the effect of the electrode rotation speed on the Tafel plots (as presented in Figure 7) are required. Unfortunately, though, we are not aware of any previous studies that had implemented either of these procedures to derive this fundamental kinetic parameter.
Finally, Figure 11b displays the effect of p H2 on the anodic transfer coefficient values derived from the same fits (for m = 1/2 and α a + α c = 1), which change progressively from ≈0.4 to ≈0.5 when increasing the pressure from 10 to 100 kPa H 2 . As we have discussed above, the polarization curves and corresponding Tafel plots at lower hydrogen partial pressures are more affected by non-correctable capacitive effects that could explain this deviation of α a from the value of 0.5 observed as p H2 approaches 100 kPa.
In summary, the unambiguous determination of the value of m is only possible by performing experiments with varying hydrogen partial pressures; the derived reaction order can in turn be verified by recording polarization curves with different electrode rotation rates. On the other hand, the i 0 values extracted from Tafel plots of the resulting kinetic currents are very similar even if the wrong value of m is used, suggesting that the exchange current densities reported in previous studies that assumed an order of 1 remain correct. 5,9,25 Nevertheless, as we will discuss in the next and last section, the combination of a reaction order of 1/2 with respect to p H2 along with the confirmation that the sum of the transfer coefficients is 1 provides key information to unveil the HOR/HER mechanism on Pt PC in alkaline electrolyte. where Pt * represents an available platinum surface site. Moreover, only those mechanisms involving Heyrovsky or Volmer rate determining steps (RDS) yield kinetic expressions similar to the Butler-Volmer equation 44,45,50 formulated above and for which our diffusion corrected currents show an excellent fit (see Fig. 9). Therefore, three possible reaction pathways can be envisaged for the HOR/HER on Pt PC : (i) a Tafel step with a Volmer-RDS, (ii) a Heyrovsky step with a Volmer-RDS, or (iii) a Heyrovsky-RDS with a Volmer reaction. Sheng and coworkers 9 have hypothesized that this last reaction pathway may be preponderant, owing to the similarities between DFT-calculated 51 and measured 9,11 activation energies and transfer coefficients for a Heyrovsky-RDS. Nevertheless, the same authors regarded this comparison between values derived from measurements 11 at a pH of 13 or calculations 51 at a pH of 0 as highly tentative, since the latter DFT estimates cannot explain the ≈100-fold lower i 0 values in alkaline electrolyte compared to acid electrolyte. 9 Another constraint which might give insight into the reaction mechanism can be found through our finding that the best fit of the Butler-Volmer equation was obtained with the assumption that the sum of the transfer coefficients (α a + α c ) be equal to one. The values adopted by this sum must comply with the limitation of being equal to the quotient of the number of electrons involved in the overall reaction for the HOR/HER (n HOR/HER = 2) and the so-called stoichiometry number (ν), [52][53][54][55] which corresponds to the number of times that the RDS has to proceed in order for the complete reaction to take place once. In this respect, the combinations of Heyrovsky and Volmer steps (or the Tafel-RDS + Volmer mechanism discarded above) yield ν values of one that result in α a + α c = 2, for which the resulting Butler-Volmer equation does not fit our HOR/HER kinetically-controlled currents. Indeed, only the Tafel + Volmer-RDS combination yields the stoichiometry number of 2 that results in the condition of α a + α c = 1, with which we could fit our kinetic data, strongly suggesting that this reaction sequence determines the HOR/HER kinetics on Pt PC surfaces in alkaline electrolyte.
Regarding the observed reaction order of 1/2 with respect to p H2 for the HOR/HER, one might look at other examples of electrochemical processes which exhibit a half-order dependency with respect to one of the reactant's concentrations, like the oxidation of HO 2 − on Au 23,56 and of HCOOH on Pt. 57,58 Interestingly, both processes are believed to proceed through a fast adsorption step followed by an RDS involving the donation of an electron by an adsorbed intermediate, reminiscent of a Tafel + Volmer-RDS or a Heyrovsky + Volmer-RDS pathway. Moreover, in heterogeneous catalysis, 59 half-order reaction orders are often regarded as indicative of a fast dissociative adsorption/desorption step followed by a rate-determining surface reaction step. Assuming that the dissociative adsorption of H 2 to 2 · H ads (or its reverse) described by the Tafel equation were in quasi-equilibrium, the factional coverage of adsorbed hydrogen on the Pt surface (θ H ) could be related to the hydrogen partial pressure through a Langmuir adsorption isotherm: 60,61 [21] where the value of K is set by the quotient of the forward and backward reaction constants, and the θ H term could then be substituted into the kinetic expression for the Volmer-RDS. 61 However, according to Equation 21, θ H would only become directly proportional to (p H2 ) 1/2 if θ H were to tend to zero, i.e., if the surface concentration of adsorbed hydrogen, θ H , were very low. This is clearly not the case between the +0.1 and −0.1 V RHE considered in the fitting to the Butler-Volmer equation, and so this approach cannot explain the observed reaction order of 1/2 with respect to p H2 for the HOR/HER. Seeking to further explain the observed reaction order of 1/2 with respect to p H2 , we would like to propose a tentative hypothesis related to the binding energy of adsorbed H. In this respect, the determining role of the H adsorption strength on the HOR/HER kinetics over a wide range of transition metal surfaces is well established in acid electrolyte, 2,51 and has recently been shown to extend to alkaline reaction media. 62 In addition, based on a comparison of the charge transfer resistance for the H upd reaction (obtained by impedance spectroscopy) and the HOR/HER exchange current density (based on RDE data), we have recently suggested 5 that the H upd reaction may be identical with the Volmer step. Furthermore, we suggested that the form of this Volmer reaction does not change with the solution pH, i.e., that it follows Eq. 20, contrary to the prevalent opinion that in alkaline electrolytes it may change into the following reaction: 63 H ad − Pt + OH − ↔ Pt * + H 2 O + e − [22] Under these assumptions, the H-binding energy would play a major role in the overall HOR/HER kinetics and would correspond to the H upd -binding energy. For a one-electron reaction, this H-binding energy ( E H-binding ) should change with potential by: This would imply that the H-binding energy of H upd increases with increasing potential, equivalent to stating that underpotentially deposited hydrogen adsorbed at more positive potentials has a higher binding energy. On the other hand, the HOR/HER equilibrium potential increases with decreasing p H2 , as described by the Nernst equation ( V = -R · T/(2 · F) · ln[p H2(1) /p H2 (2) ], for a change from a p H2(1) condition to p H2(2) ) and illustrated in Figure 12. Combining Eq. 23 with this Nernst equation would imply that E H-binding at the reversible HOR/HER potential varies by -RT/2 · ln[p H2(1) /p H2 (2) ]. If now we assume that changes in the H-binding energy are correlated to changes in the exchange current density through an Arrhenius type relationship, 5 we obtain: i 0 ( p H2(1) ) i 0 ( p H2 (2) ) ∝ e − The dashed black and red lines mark the equilibrium potential for 100 and 10 kPa H 2 , respectively. Additionally, the CV recorded at 20 mV · s −1 in the same electrolyte saturated in argon (solid blue line) is plotted over the same abscissa.
) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see 207.241.231.81 Downloaded on 2018-07-18 to IP which would predict the observed reaction order of 1/2 with respect to p H2 confirmed by our RDE measurements, if grantedly on the basis of a rather tentative hypothesis.

Conclusions
In summary, our RDE measurements in 0.1 M NaOH with different hydrogen partial pressures show that, in this electrolyte, the kinetics of the HOR/HER on Pt PC follow a reaction order of 1/2 with respect to p H2 . We also showed that the quantification of kineticallycontrolled HOR currents from RDE data requires the correction for the Nernstian diffusion overpotential in addition to the correction for the concentration dependence of the HOR kinetics (1/2 with respect to p H2 , rather than 1 st order) and for the ohmic resistance. On the other hand, only the latter ohmic resistance correction is required for determining kinetically-controlled HER currents, since there is no evidence for supersaturation of the electrolyte with H 2 .
After the above transport/resistance correction of the RDE data, the HOR/HER kinetics can be described by a simple Butler-Volmer equation with α a + α c = 1, which implies a mechanism consisting of a fast Tafel reaction in combination with a rate-determining Volmer reaction. As we will further prove in a forecoming work, 64 the ratedetermining Volmer reaction seems to be identical with the underpotential deposition of hydrogen, discarding the hypothesized role of a different H ads species (often quoted as "overpotentially deposited hydrogen") in the HOR/HER. 35 Finally, a tentative hypothesis to rationalize the observed reaction order of 1/2 with respect to p H2 was proposed under the assumption that the binding energy of H ads governs the HOR/HER kinetics, emphasizing the importance of tuning the strength of the hydrogen adsorption in order to obtain increasingly active surfaces. 51,62