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J. Phys. Chem. C 2010, 114, 14946–14952
Solvation and Zero-Point-Energy Effects on OH(ads) Reduction on Pt(111) Electrodes Alfred B. Anderson,*,† Jamal Uddin,† and Ryoske Jinnouchi‡ Chemistry Department, Case Western ReserVe UniVersity, 10900 Euclid AVenue, CleVeland Ohio 44106-7078, and Toyota Central R&D Laboratories, Inc., Nagakute, Aichi 480-1192, Japan ReceiVed: May 7, 2010; ReVised Manuscript ReceiVed: July 12, 2010
The linear Gibbs energy relationship (LGER) is a theoretical model in which one adds to the known bulk solution-phase reversible potential for a reaction involving electron transfer the internal energy change, divided by nF, when the reactants and products are adsorbed, where n is the number of electrons transferred and F is the Faraday constant. This yields predictions of the reversible potentials for the same reactions but with the reactants and products in adsorbed states on the electrode surface. The LGER theory has been used in previous studies where De bond strengths, measured from the bottom of the Born-Oppenheimer potential at equilibrium, were used rather than the Do values, which include zero-point vibrational energies. Here, it is shown that, when zero-point energies are included, the result is to increase the reversible potential for OH(ads) reduction to H2O(ads) on Pt(111) electrodes, an important fuel-cell cathode reaction, by 0.05 V. The effects of solvation are also shown to be small, leading to decrease in the LGER prediction by 0.09 V. These results were calculated by using a self-consistent theory incorporating two-dimensional slab-band density functional calculations with the solvation handled by a modified Poisson-Boltzmann theory and a dielectric-continuum model. The net result is to decrease the LGER prediction of 0.86 V for the reaction with hydrogen bonding of the reactant and product to adsorbed water to 0.82 V, which is a close match with the experimental value of about 0.77 V. These findings explain the usefulness of the LGER theory for rapid screening of fuel-cell electrocatalysts. Introduction Experimental determinations of reversible potentials for forming reaction intermediates on surfaces of electrodes are not often reported. Some may be short-lived and difficult to detect. The last reduction intermediate during the four-electron reduction of O2 to water on platinum electrodes is OH(ads), which is also the first product of H2O(ads) oxidation. According to cyclic voltammetry measurements, for this reaction, the onset potential on platinum (111) immersed in 0.1 M pH ) 1 perchloric acid is about 0.55 V on the reversible-hydrogen-electrode (RHE) scale. When the potential is increased, the coverage of OH(ads) increases to about 0.1 monolayer (ML) at 0.69 V, 0.25 ML at 0.77 V, and 1/3 ML at 0.80 V.1 These OH(ads) coveragedependent findings were matched closely by ex-situ X-ray photoelectron spectroscopic (xps) measurements of platinum (111) electrode surfaces that were removed from 1.0 M aqueous HF electrolyte while under potential control.2 This work also showed that the onset potential for OH(ads) oxidation to O(ads) in 0.1 M acid is about 0.80 V (RHE) on Pt(111). The O(ads) and OH(ads) reduction potentials have also been obtained by using a unified self-consistent theory for the electrochemical interface.3 For low OH(ads) coverage on the water-saturated surface, the reversible potential for OH(ads) reduction was calculated to be about 0.63 V, and for O(ads) reduction to OH(ads) in the presence of coadsorbed OH and H2O, a value around 0.8 V was calculated. From the two experimental determinations, the coverage of OH(ads) on a Pt(111) in 0.10 M acid as a function of potential behaves as shown in Figure * Corresponding author. Phone: 216-368-5044. Fax: 216-368-3006. E-mail:
[email protected]. † Case Western Reserve University. ‡ Toyota Central R&D Laboratories, Inc.
Figure 1. Measured coverage vs potential, V (RHE) behavior based on refs 1 and 2 for the OH(ads) coverage as a function of H2O(ads) oxidation/OH(ads) reduction reversible potentials on Pt(111) electrodes in 0.10 M acid.
1. Over a narrow 0.10 V range, the OH(ads) coverage varies from about 0.10 ML to its maximum coverage of about 1/3 ML. Fuel cells operate with maximum power output when the cathode potential is near that for the low OH(ads) coverage limit where O(ads) is unlikely to be present. Low coverage may be needed for the initial stages of the reaction to commence, namely, the adsorption of O2 and its reduction to OOH followed by dissociation to O(ads) and OH(ads). During steady-state operation, the OH(ads) coverage will remain at a constant value that depends on the applied overpotential, which under standard conditions equals the electrode potential on the standardhydrogen-electrode (SHE) scale minus 1.229 V. Coverage will increase if the electrode potential is increased, and this will slow the first step and decrease the power that is produced. However, the first step, forming OOH(ads), is activated and may make a parallel contribution to reducing the overall rate of the fourelectron reduction as the potential is increased.4 The activation
10.1021/jp1041734 2010 American Chemical Society Published on Web 08/18/2010
Solvation and ZPE Effects on OH(ads) Reduction
J. Phys. Chem. C, Vol. 114, No. 35, 2010 14947
energy for OOH(ads) formation is 0.0 eV at the reductionprecursor potential, which was estimated from measured temperature dependencies of Tafel plots to be about 0.22 V (SHE).5,6 The activation enthalpy increases as the electrode potential increases from this value and has been, from Arrhenius plots, estimated to be about 0.3 eV at 0.80 V.6 Resonant electrontransfer calculations of the activation energies for electron and proton transfer using constrained variation theory and a localreaction-center (LRC) model for the reduction, a technique developed in this lab, yielded a reduction-precursor potential of about 0.4 V(SHE) for forming a planar surface-OO · · · H transition state, which is the assumed structure for the congested surface. The calculated activation energy increased to about 0.2 eV at 0.80 V.4 Given the uncertainties in measurement and modeling, this is a good agreement for these properties. The activation energy for reducing OH(ads) at the reversible potential has been calculated by using resonant electron-transfer LRC method to be about 0.2 eV.7 All these above-mentioned estimated activation energies are small and, although the surface models used omitted band widening, which affected the Ptadsorbate interactions to some extent, the low values suggest fast kinetics. In acid solution in the absence of O2, the coverage of OH(ads) formed from water oxidation increases rapidly from 1/10 to 1/3 ML as the potential is increased from 0.70 to 0.80 V. In 0.1 M acid at 0.80 V (RHE), O2 reduction is nearly snuffed out. This makes 0.75 V (RHE) and 1/4 ML characteristic parameters in 0.1 M acid, below which the four-electron oxygenreduction activity can be expected to be high as the electrode potential is decreased, and above which it can be expected to quickly become low as the potential is increased. A relationship has been found in this lab to be useful for predicting reduction potentials for reactions between species rev , in terms of the standard adsorbed on an electrode surface, Usurf reduction potentials in bulk solution, Uo, and the difference in energies of adsorption for the species on the electrode surface: rev Usurf ) Uo + [∆adsG(P) - ∆adsG(R)]/nF
(1)
rev Usurf ≈ Uo + [∆adsE(P) - ∆adsE(R)]/nF
(2)
Here, G is the Gibbs energy, E is the internal energy, n is the number of electrons transferred, and F is the Faraday constant. As an example of its use: according to eq 2, if the internal energy of adsorption of the product (P) exceeds that of o the reactant (R), Urev surf > U . Equation 2 comes from substituting the internal energies of adsorption for the Gibbs energies of adsorption. The relationship was first applied to reactions in acid:8 rev R(ads) + H+(aq) + e-(Usurf ) a P(ads)
(3)
By means of the Nernst equation, it has been applied equally well to reactions in base:9
Figure 2. Circles around H+, OH, and H2O represent solvation atmospheres in the aqueous environment, and when adsorbed, some of the solvation atmospheres for OH and H2O are displaced by bonds to the electrode surface.
by replacing part of the solvation atmospheres with bonds to the surface.10 This concept is illustrated in Figure 2. Adsorption bond strengths will generally be much larger than solvation energies; therefore, it has been assumed that the effects of loss of some solvation stabilizations upon adsorption will be negligible when using eqs 1 and 2 to predict reversible potentials. When assuming that the proton, in the form of an hydronium ion, which is the case in strong acid, or a water molecule, which is the case in base, does not adsorb on the surface so that its reference state is always aqueous, its solvation energy drops out. This is proved as follows. The standard hydrogen-electrode work function, φ, is used to generate the Gibbs energy equality for solution: o G(Raq) + G(H+ aq) - φ - eU ) G(Paq)
(5)
For reactions transferring a single electron, the Gibbs energy equality for the adsorbed species is rev G(Raq) + ∆adsG(R) + G(H+ aq) - φ - eUsurf ) G(Paq) + ∆adsG(P) (6)
rev R(ads) + H2O(1) + e-(Usurf ) a P(ads) + OH-(aq)
(4) The success of eq 2 depends on how well ∆Eads approximates ∆Gads. It has been suggested that, when the reactant and product are adsorbed on an electrode surface, their Gibbs energies can be viewed as being perturbed from the solution-phase values
From the difference of eqs 5 and 6, the following is found: rev Usurf ) Uo + [∆adsG(P) - ∆adsG(R)]/e
Substituting internal energies for Gibbs energies yields
(7)
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J. Phys. Chem. C, Vol. 114, No. 35, 2010 rev Usurf ≈ Uo + [∆adsE(P)-∆adsE(R)]/e
Anderson et al.
(8)
Equations 1 and 8 are the same and state what we refer to as the linear Gibbs energy relationship (LGER). There are other theoretical approaches that predict the reversible potential for the OH(ads) + H+(aq) + e- a H2O(ads) equilibrium. An approach recently developed in this lab calculates the whole Gibbs energy by using a two-dimensional band theory and changing potential by adding charge to the system while at the same time performing a self-consistent variational optimization of the electrochemical interface by using a modified Poisson-Boltzmann approach to distribute counterions in the electrolyte and a dielectric-continuum approach to solvation.11,12 The reversible potential then is the potential where the Gibbs energies of the reactant and product are equal. The code for these calculations is called Interface 1.0. For details, the reader is referred to the original communication11 and full paper.12 Reference 3 shows many such determinations for forming OH(ads) from H2O(ads) based on several surfacecoverage models including both of these molecules in reactant and product states. In that work, it was shown that the predicted reversible potential was affected by any change in the number of hydrogen bonds present in the product and reactant. Thus, in this paper, the hybrid model is used where only the water molecules from the first solvation shell that are rigidly bonded with the solute are included in the energy and wave-function determinations. The remaining solvent is treated with a statistical averaging by the dielectric-continuum procedure, accurately yielding solvation energies. This is the approach used in past studies with the Interface 1.0 code.11,12 It was found in ref 11 that one or more water molecules were required in first solvation shells for several ions treated, such as OH-, H3O+, and HO2-, with the chloride ion an exception. The chloride ion is the textbook success story for the Born approximation to treating solvation without the presence of explicit solvation shells. None of the uncharged molecules required explicit solvation shells. The hybrid model is presently more accurate than explicit solvation models which can lack statistical averaging and produce results that oscillate as a function of size. However, despite the variations in OH(ads) coverage and H2O(ads) coverage modeled in ref 11, the results were of insufficient resolution, which would have to be
