Predicting Reaction Mechanisms and Potentials in Acid and Base from

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Predicting Reaction Mechanisms and Potentials in Acid and Base from Self-Consistent Quantum Theory: H(ads) and OH(ads) Deposition on the Pt(111) Electrode Meng Zhao, and Alfred B Anderson J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.5b02826 • Publication Date (Web): 02 Feb 2016 Downloaded from http://pubs.acs.org on February 4, 2016

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The Journal of Physical Chemistry Letters

Predicting Reaction Mechanisms and Potentials in Acid and Base from Self-Consistent Quantum Theory: H(ads) and OH(ads) Deposition on the Pt(111) Electrode by Meng Zhaoa and Alfred B. Andersonb Chemistry Department Case Western Reserve University 10900 Euclid Avenue Cleveland, Ohio 44106 USA

a

email: [email protected]

b

Corresponding author

Email: [email protected] Telephone: 216 3685 044

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Abstract It has been shown recently that when reactants and products are well-modelled within a comprehensive self-consistent theory for the electrochemical interface, accurate predictions are possible for reversible potentials, Urev, in acid electrolyte for reactions such as reduction of H+(aq) to form under potential deposited H(ads) and oxidation of an OH bond of H2O(ads) to deposit OH(ads). Predictions are based on calculated Gibbs energies for the reactant and product being equal at the reversible potential, which is the potential at the crossing point for reaction and product Gibbs energies, plotted as functions of electrode potential. In this Letter it is demonstrated that the same capability holds for these reactions in basic electrolyte. This demonstration opens up the opportunity for predictions of reversible potentials and mechanisms for other electrocatalytic reactions in base.

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In this Letter we demonstrate that the reversible potentials for oxidizing H2O(l) to form OH(ads) can be calculated to good accuracy for both acidic and basic electrolytes by using a selfconsistent density functional theory for the electrochemical interface. This is done by calculating the Gibbs energies of reactants and products as functions of electrode potential and identifying the reversible potential with the equilibrium potential, which is the potential where the Gibbs energies are the same. Additionally, we address the increase in width of the double layer potential range in base and relate it to calculated onset potentials for under-potential-deposited (UPD) H(ads) formation and for OH(ads) formation in acid and base. Most theoretical work to date has addressed reactions in acid electrolyte, primarily because of the experimental focus on hydrogen/oxygen fuel cells operating with proton conducting polymer electrolyte membranes. Oxygen is reduced at the cathode in acid by H+(aq) + e-, the H+(aq) having migrated through the electrolyte from the anode where hydrogen is oxidized. There have been relatively few quantum chemistry-based theory studies of electrochemical reactions in basic electrolyte. Oxygen is reduced at the cathode in base by H2O(l) + e-, and the OH-(aq) thus formed migrates through the electrolyte to the anode to join with the H+(aq). Anion conducting polymer electrolytes that might provide useful rates of hydroxyl conduction are under investigation.1 With development of successful electrolytes there will be increased interest in characterizing and understanding O2 reduction at the fuel cell cathode and hydrogen and, particularly alcohol, oxidation at the fuel cell anode in base. Theory can play a key role in establishing the mechanisms, as it has done for acid.2-9 Structures and Gibbs energies of the reactants and products for reactions in acid electrolyte have been calculated theoretically at several levels of approximation.2-9 Reference 9 contains an overview of theoretical approaches and applications for acid fuel cell reactions. 3 ACS Paragon Plus Environment


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Predictions of reversible potentials for O2 reduction reactions in base were first made using calculated reaction energies for hydrated reactants and products in outer-sphere reactions.10 Later, approximate potential-dependent electron transfer activation energies and reversible potentials were predicted using a local reaction center model for adsorbed intermediates. The theory employed calculated electron affinities or ionization potentials, and total energies of the reaction centers.11,12 There has also been development of a method to relate the structure of the electrochemical interface to pH.13 It has long been known from cyclic voltammograms for Pt(111) electrodes in 0.1 M perchloric acid that a under potential deposited (UPD) H(ads) phase forms at potentials between the H2 evolution onset and about 0.4 V on the reversible hydrogen electrode (RHE) scale.14 With increasing potential, a surface double-layer phase forms up to about 0.56 V, with the surface being bare of chemisorbed molecules and no current flowing aside from double-layer charging.14,15,17 At higher potentials, OH(ads) is deposited to 0.8 V followed by a second double-layer-like phase to about 1.0 V.14,15,17 Beginning at 1.0 V, an approximately 0.1 V wide peak in current attributed to formation of O(ads) and additional OH(ads) is seen.14-17 The voltammograms reported on the RHE scale for Pt(111) in 0.1 M OH-(aq) are similar to those in 0.1 M perchloric acid, but the double layer potential range is, in our estimation from voltammograms in refs 15 and 17, about 0.10 V wider in base, with the onset potential for UPD H(ads) formation shifted negative about 0.05 V and that for OH(ads) formation shifted positive about 0.05 V. The relationship between pH and the hydrogen evolution potential rests on the reaction at equilibrium


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H+(aq,a =1) + e-(-4.454 eV) ⇌ ½ H2(g,1bar)

(1)

The electron energy in this equilibrium, -4.454 eV, was calculated variationally using the selfconsistent quantum code defined in Refs (6) and (7). The H+(aq) was modeled by a hydronium ion, H3O+, with three water molecules coordinated to it. The resulting H9O4+ was immersed in dielectric continuum with a distribution of 1 M cations and anions surrounding it and their distribution was optimized by means of modified Poisson-Boltzmann theory. The Gibbs energies for the H9O4+ and H2 were determined from calculated partition functions in standard thermodynamic formulas. From calculated reactant and product Gibbs energies for eq (1), the thermodynamic workfunction of the standard hydrogen electrode (SHE) is 4.454 eV. In strong acid, H+(aq) is reduced to H2(g) as in eq (1), but what about weak acid? We know that at 298.15 K Kw = [H+(aq)OH-(aq)] is 1.01x10-14. So weak acid corresponds to strong base and the absence of H+(aq). Yet the rate for H2(g) generation in strong base is rapid on Pt(111).15,17 This means when the electrolyte is strongly basic it is reasonable to assume that H2O(l) is being reduced instead of H+(aq): H2O(l) + e- ⇌ ½ H2(g) + OH-(aq)

(2)

For this reaction, when using a model with 3 H2O coordinated to OH-, we calculate ∆G0 = 3.609 eV. Subtracting eq (1) from eq (2), the difference, 0.845 eV, is close to 0.828 eV calculated using the Nernst equation for the potential difference between pH = 0 and pH = 14, and it gives Kw = 0.521x10-14 at 298.15 K. At pH = 7 the H+(aq) concentration is about 10-7 M and the reduction will mostly go by eq (2) because of the high concentration of H2O(l). At some pH value between 7 and 0, reactions in eq (1) and eq (2) will participate equally and at pH = 0 the



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reaction in eq (1) is expected to strongly dominate. A comparison of predicted results for reactions on electrode surfaces in strong acid and strong base is given below. The reactions in bulk water are, at pH = 0, H2O(l) ⇌ OH(aq) + H+(aq) + e-

(3)

for which ∆G0 = 6.890 eV is calculated; and at pH = 14, OH-(aq) ⇌ OH(aq) + e-

(4)

for which ∆G0 = 6.045 eV is calculated. These Gibbs energies yield respective reversible potentials, 2.436 V and 1.591 V for eqs (3) and (4), and the difference in the Gibbs energies is 0.845 eV, the auto ionization energy of H2O(l). The cyclic voltammogram for UPD H(ads) formation on Pt(111) in acid was calculated previously.18 It was found that reversible potentials for a series of UPD H(ads) coverages extrapolated to about 0.25 V when coverage approached zero, but the measured current density for UPD H(ads) formation goes to zero around 0.4 V. The calculated onset potential for deposition was extended by about 0.1 V to about 0.35 V by taking the configurational entropy at low coverage into account.18 It was not possible to define an exact potential at which the reduction current density becomes zero because the Langmurian contribution depends logarithmically on coverage, but the fit of theoretical and measured voltammograms was graphically close. Water molecules were not included in the interface calculations because they did not form significant hydrogen bonds to adsorbed H atoms; the effect of water was handled statistically by dielectric continuum in the calculations and the interfacial electrolyte distribution


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was calculated with the modified Poisson-Boltzmann theory. The same is done for the present UPD H(ads) calculations in base. We recalculated reversible potentials for forming UPD H(ads) for changing from zero to 1/12 ML coverage at 1-fold sites. Different theoretical and experimental methods give varying site preferences, as reviewed briefly in ref. 18. The reaction in acid is H+(aq) + Pt(111) + e- → H(ads)

(5)

H2O(aq) + Pt(111) + e- → H(ads) + OH-(aq)

(6)

and, in base,

The difference in Gibbs energies for these two reduction reactions is -0.845 eV. The Gibbs energies of the left and right hand sides of these equations were calculated for different surface charges, q, using a 3-layer Pt slab model of the (111) surface. Added surface charges determine the electrode potential, and in two-dimensional density functional band theory the electrode potential, U(q), is given on the SHE scale as U(q) = [-4.454 eV - Ef(q)] V/eV

(7)

where Ef is the calculated Fermi energy. The calculated Gibbs energies for reactant and product were plotted as functions of U. The reversible potential, Urev, for the electron transfer reaction is the crossing point of the curves.6-9 Calculated reversible potentials are -0.673 V(SHE) in base and 0.222 V (SHE) in acid (Figure 1). The difference, 0.895 V, is 0.050 V greater than the 0.845 V(SHE) reference value calculated above. Converting to the RHE scale and adding the extrapolation and Langmuir energy contributions gives 0.30 V (RHE) for the UPD H(ads) formation onset in base, which is 0.05 V 7 ACS Paragon Plus Environment


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Figure 1. Gibbs energy curves for 1/12 ML H(ads) in pH = 0 (red) and pH = 14 (blue) electrolytes on the (111) surface of a 3-Pt atom layer slab and energy curve for the bare slab. Predicted reversible potentials are at the intersections. The blue and red curves are separated by 0.845 eV. See text for further details.

less than for acid. The same result was recently calculated using a dipole model involving the platinum surface and UPD H overlayers.19 Our self-consistent calculations thus provide strong confirmation for the accuracy of the ad-hoc dipole model in ref. 19, as do the experimental measurements. It is noted that when performing the shifts from calculated SHE potentials to RHE potentials, the difference in an RHE potential for a change of 1 pH unit is small and therefor taken as negligible in our work. Voltammograms for 0.1 M perchloric acid and 0.1 M sodium hydroxide show the onset for OH(ads) deposition to be about 0.56 V RHE in acid and about 0.62 V RHE in base.17 These differ by 0.06 V because the Gibbs energies of the interfacial systems depend on the positions of the Fermi level. The reversible potentials for OH(ads) formation were calculated for the acid reaction, 8 ACS Paragon Plus Environment

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H2O(ads) ⇌ OH(ads) + H+(aq) + e-

(8)

H2O(ads) + OH-(aq) ⇌ OH(ads) + H2O(l) + e-

(9)

and for the base reaction,

The difference in Gibbs energies for these reactions is 0.845 eV. We calculated the Gibbs energies of two-dimensional slab models of the Pt(111) electrode with adsorbed reactants and products, with OH at 1-fold sites, according to the reactions in eqs (8) and (9). The dielectric continuum model and modified Poisson-Boltzmann theory were included in the calculations and charges were added to the translational cells to move Ef. All the calculations used 2/3 ML saturation coverage for combined H2O(ads) and OH(ads). The modified Poisson-Boltzmann and dielectric continuum calculations treated the electrolyte above the saturated surface in the fully self-consistent calculations. It has been found in previous theoretical work that water bonds weakly to or not at all to clean Pt(111), depending on its coverage.7 In consequence, several nearly degenerate structures are calculated for the 2/3 ML hexagonal array of water on the surface. The variations are likely caused by the dielectric continuum representation of the bulk water contacting the adsorbed layer. Hydrogen bonding between H2O molecules and adsorbed OH, on the other hand, causes unique stable structures in adsorbates. Of the three 2/3 ML H2O(ads) structures, the one that gives reversible potentials closest to measurement is also the most stable. On the RHE scale the result for forming 1/6 ML OH(ads) acid is 0.643 V, 0.08 V higher than the approximate experimental value of 0.56 V for the onset. The result for base is 0.748 V, 0.13 V higher than the approximate experimental value of 0.62 V. See Figure 2. While both predictions are high, the base result is 0.10 V higher than for acid and the experimental difference is about 0.06 V. 9 ACS Paragon Plus Environment


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Figure 2. As in Figure 1 but for 2/3 ML H2O(ads) oxidation to 1/6 ML OH(ads) + 1/2 ML H2O(ads).

The width of the part of the voltammograms associated with OH(ads) formation and reduction to H2O(ads) is a little over 0.2 V: as the potential increases, the OH(ads) coverage increases.14-17 Beginning with a saturated surface with 1/6 ML OH(ads) and 1/2 ML H2O(ads), the predicted reversible potential for forming 1/3 ML OH(ads) in acid is higher, as expected, but by only 0.02 V. In base the potential decreases by 0.08V. The small fluctuation stems from using idealized models for interface compositions. Oxidation of the saturated surface with 1/3 ML OH(ads) and 1/3 ML H2O(ads) to form 1/2 ML OH(ads) and 1/6 ML H2O(ads) is calculated to have much higher reversible potentials, 1.254 V in acid and 0.859 V in base. Oxidation of the saturated surface with 1/3 ML OH(ads) and 1/3 ML H2O(ads) to form 1/6 ML O(ads), 1/6 ML OH(ads) and1/3 ML H2O(ads) has previously been calculated in acid to have 1.12 V reversible potential.8 These findings agree qualitatively with experimental studies which have found that when OH(ads) coverage reaches a little over 1/3 ML, O(ads) begins to form and both are seen on the surface at about 1/2 ML total coverage at 1.2 V.14,16


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We have shown that, by means of the electrochemical interface theory of refs (6) and (7), reactions in strongly basic electrolytes can be studied to good accuracy just as they have been in strongly acidic electrolytes. In this theory the reactants are selected to be compatible with the acid or base chemistry and the Fermi level is then automatically determined by self-consistency during the calculations. The ease and accuracy of the approach opens the prospect for significant advancement in understanding electrochemical reactions in base as well as acid. Saturation coverage, meaning 2/3 ML of H2O(ads) and OH(ads) combined, which should closely represent the actual interfacial condition at standard conditions, yielded useful results. In general, the theory can yield reversible potentials in close agreement with experiment whether the reactants and products are in bulk solution or adsorbed on the electrode. For intermediate pH values there are insufficient ionic charge carriers in the electrolyte to allow generation of significant power for portable power fuel cell applications. However the pH range around 7 is where charge transfer takes place in physiological systems. To accurately calculate reversible potentials in such systems, which are in the realm of biofuel cells,20-22 with the theory will require knowledge of the structures of the active sites.23 Acknowledgement Meng Zhao thanks the Chemistry Department at Case Western Reserve University for financial support.



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References (1) Merle, G.; Wessling, M.; Nijmeijer, K. Anion Exchange Membranes for Alkaline Fuel Cells: A Review. J. Membr. Sci. 2011, 377, 1–35. (2) Anderson, A. B.; Albu, T. V. Ab Initio Determination of Reversible Potentials and Activation Energies for Outer-Sphere Oxygen Reduction to Water and the Reverse Oxidation Reaction. J. Am. Chem. Soc. 1999, 121, 11855-11863. (3) Anderson, A. B.; Albu, T. V. Catalytic Effect of Platinum on Oxygen Reduction: An Ab Initio Model Including Electrode Potential Dependence. J. Electrochem. Soc. 2000, 147, 4229-4238. (4) Norskov. J. K.; Rossmeisl, J.; Logadottir, A.; Lindqvist, L.; Kitchin, J. R.; Bligaard, T.; Jonsson, H. Origin of the Overpotential for Oxygen Reduction at a Fuel-Cell Cathode. J. Phys. Chem. B 2004, 108, 17886-17892. (5) Rossmeisl, J.; Norskov, J. K.; Taylor, C. D.; Janik, M. J.; Neurock, M. Calculated Phase Diagrams for the Electrochemical Oxidation and Reduction of Water over Pt(111). J. Phys. Chem. B 2006, 110, 21833-21839. (6) Jinnouchi, R.; Anderson, A. B. Aqueous and Surface Redox Potentials from Self-Consistently Determined Gibbs Energies. J. Phys. Chem. C 2008, 112, 8747-8750. (7) Jinnouchi, R.; Anderson, A. B. Electronic Structure Calculations of Liquid-Solid Interfaces: Combination of Density Functional Theory and Modified Poisson-Boltzmann Theory. Phys. Rev. B 2008, 77, 245417-1-18. (8) Tian, F.; Anderson, A. B. Effective Reversible Potential, Energy Loss, and Overpotential on Platinum Fuel Cell Cathodes. J. Phys. Chem. C 2011, 115, 4076-4088. (9) Anderson, A. B. Insights into Electrocatalysis. Phys. Chem. Chem. Phys. 2012, 14, 13301338.


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(10) Narayanasamy, J.; Anderson, A. B. Calculating Reversible Potentials in Acid and Base from Model Reaction Energies. J. Phys. Chem. B 2003, 107, 6898-6901. (11) Cai, Y.; Anderson, A. B. Calculating Reversible Potentials for Pt-H and Pt-OH Bond Formation in Basic Solutions. J. Phys. Chem. B 2005, 109, 7557-7563. (12) Zhang, T.; Anderson, A. B. Oxygen Reduction on Platinum Electrodes in Base: Theoretical Study. Electrochim. Acta 2007, 53, 982-989. (13) Rossmeisl, J.; Chan, K.; Ahmed, P.; Tripkovic, V.; Bjorketun, M. E. pH in Atomic Scale Simulations of Electrochemical Interfaces. Phys. Chem. Chem. Phys. 2013, 15, 10321-10325. (14) Clavilier, J.; Armand, D.; Wu, B. L. Electrochemical Study of the Initial Surface Condition of Platinum Surfaces with (100) and (111) Orientations. J. Electroanal. Chem. 1982, 135, 159166. (15) Markovic, N. M.; Ross, P. N. Jr. Electroctalysis at Well-Defined Surfaces: Kinetics of Oxygen Reduction and Hydrogen Oxidation/Evolution on Pt(hkl) Electrodes. In Interfacial Electrochemistry:Theory, Experiment, and Application; Wieckowski, A., Ed.; Marcel Dekker, Inc.: New York, 1999; pp 821-841. (16) Wakisaka, M.; Suzuki, H.; Mitsui, S.; Uchida, H.; Watanabe, M. Identification and Quantification of Oxygen Species Adsorbed on Pt(111) Single-Crystal and Polycrystalline Electrodes by Photoelectron Spectroscopy. Langmuir 2009, 25, 1897-1900. (17) Gomez-Marin, A. M.; Rizo, R.; Feliu, J. M. Some Reflections on the Understanding of the Oxygen Reduction Reaction at Pt(111). Beilstein J. Nanotechnol. 2013, 4, 956-976. (18) Asiri, H. A.; Anderson, A. B. Using Gibbs Energies to Calculate the Pt(111) Hupd Cyclic Voltammogram. J. Phys. Chem. C 2013, 117, 17509-17513.



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(19) Bonnet, N.; Mazari, N. First-Principles Prediction of the Equilibrium Shape of Nanoparticles under Realistic Electrochemical Conditions. Phys. Rev. Lett. 2013, 110, 086104-14. (20) Mano, N.; Mao, F.; Heller, A. A Miniature Biofuel Cell Operating in a Physiological Buffer. J. Am. Chem. Soc. 2002, 124, 12962-12963. (21) Atanassov, P.; Apblett, C.; Banta, S,; Brozik, S.; Barton, S. C.; Cooney, M.; Liaw, B. Y.; Mukerjee, S.; Minteer, S. D.; Enzymatic Biofuel Cells. Electrochem. Soc. Interface 2007, 16, 2831. (22) Zebda, A.; Cosnier, S.; Alcaraz, J.-P.; Holzinger, M.; Le Goff, A.; Gondran, C.; Boucher, F.; Giroud, F.; Gorgy, K.; Lamraoui, H.; Cinquin, P. Single Glucose Biofuel Cells Implanted in Rats Power Electronic Devices. Sci. Rep. 2013, 3, 1516-1-5. (23) Vayner, E.; Schweiger, H.; Anderson, A. B. Four-electron Reduction of O2 over Multiple CuI Centers: Quantum Theory. J. Electroanal. Chem. 2007, 607, 90-100.


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