Proton Migration on Hydrated Surface of Cubic ZrO2: Ab initio

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Proton Migration on Hydrated Surface of Cubic ZrO: Ab initio Molecular Dynamics Simulation 2

Ryuhei Sato, Shohei Ohkuma, Yasushi Shibuta, Fuyuki Shimojo, and Shu Yamaguchi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b09026 • Publication Date (Web): 01 Dec 2015 Downloaded from http://pubs.acs.org on December 5, 2015

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The Journal of Physical Chemistry

Proton Migration on Hydrated Surface of Cubic ZrO2: Ab initio Molecular Dynamics Simulation Ryuhei Sato1*, Shohei Ohkuma1, Yasushi Shibuta1, Fuyuki Shimojo2, and Shu Yamaguchi1 1

Department of Materials Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku,

Tokyo 113-8656, Japan 2

Department of Physics, Kumamoto University, 2-39-1 Kurokami, Chuo-ku, Kumamoto 860-

8555, Japan E-mail address of Corresponding Author: yamaguchi@ material.t.u-tokyo.ac.jp

ABSTRACT. The proton migration on a cubic ZrO2 (110) surface is investigated by ab initio molecular dynamics simulation. H2O molecules form a hydrated multilayer on a ZrO2 surface consisting of terminating H2O adsorbates and hierarchically hydrogen-bonded H2O layers. A portion of H2O molecules chemisorbed on zirconium atoms (Zr-OH2) dissociates into H+ and OH−, forming polydentate and monodentate hydroxyls (>OH+ and Zr-OH−). The coexistence of acid and base sites (Zr-OH2 and Zr-OH−) in the equilibrium state is confirmed by analyses of both forward and reverse reactions of H2O dissociation on the ZrO2 surface. Proton hopping from Zr-OH2 to Zr-OH− occurs by both a direct proton transfer and a chain protonation reaction via surrounding H2O molecules. During these processes, Zr-OH2 donates an extra proton to ZrOH− directly or via H2O molecules in the multilayers, indicating that the coexistence of Zr-OH2

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and Zr-OH− is a necessary condition for the proton conduction on the oxide surface with various basicities.

KEYWORDS. Ab initio molecular dynamics simulation; zirconia; water adsorption; proton conduction; surface protonics

Surface protonics, defined as active proton functionalities on an oxide surface, is now attracting considerable attention not only from the viewpoint of basic science but also for applications such as solid state electrolytes in energy conversion devices operating in the temperature range between 200 and 500 °C. To achieve the required performances, proton conductivity along grain boundaries and on the hydrated surface of oxide nanoparticles such as yttria-stabilized zirconia (YSZ)1-5 and Sm-doped CeO2 (SDC)3,6 has been studied in recent years. For example, Miyoshi et al.1,2 proposed that the hydrated layers on YSZ nanoparticles show high proton conductivity via a proton hopping mechanism at intermediate temperatures between 60 and 500 °C. In addition proton conduction via a vehicle mechanism7 of the hydronium ion (H3O+) is observed at temperatures below 60 °C with anti-Arrhenius temperature dependence. On the other hand, most of the pH values at the point of zero charge (PZC) condition of ZrO2 measured by titration, electrokinetic measurement and so forth were found to be between 6 and 88,9, which seems too high to favor deprotonation. Therefore, it is surprising to observe proton hopping conduction on such a neutral to basic surface of hydrated ZrO2. On the basis of a model deduced from electrical conductivity data on an acidic surface of hydrated SiO2, Raz et al.5 proposed a proton hopping mechanism on the surface of a pressed compact micrometer-size YSZ


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powder. However, the proposed mechanism of proton delocalization expressed by the following dissociative chemisorption and subsequent disproportionation reactions,

M > O + H2O(g) → 2 M-OH, and M 2 M-OH → M-OH2+ + M-O−,

(1)

(2)

seems unlikely owing to the strong acidity and basicity of M-OH2+ and M-O−, respectively, in comparison with M-OH. On the other hand, the formation of Mg-OH2 is also reported for a basic hydrated surface of MgO10 by a theoretical approach using ab initio molecular dynamics, but no discussion on the proton migration has been provided so far. Our strong curiosity lies in the emergence of protonic conductivity, which is governed by proton delocalization and subsequent hopping on the hydrated surface, on almost every oxide with a wide spectrum of surface acidity, whereas no principle for a better understanding of the surface protonics has been available to date. In parallel with various experimental attempts1-6, computational approaches such as ab initio simulation have also contributed to the understanding of the nature of proton activity on the ZrO2 surface. For example, the adsorption of a few H2O molecules or one H2O monolayer on various ZrO2 surfaces such as tetragonal ZrO2 (101)11,12, (110) surfaces11, and so forth13,14 has been investigated by a static ab initio simulation, in which only dissociative adsorption is observed on a polar surface such as (110)11, whereas molecular and dissociative adsorption occurs on a nonpolar surface such as (101)11,12,14. Chemisorbed H2O molecules on a nonpolar surface, which form acidic Zr-OH2, are capable of being proton donors for proton conduction. However, thermodynamic calculation using the Gibbs energy for adsorption estimated in Refs. 11, 12, and 14 suggests Zr-OH2 desorption below room temperature. The Gibbs energy for


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adsorption is estimated from the total energy change for H2O adsorption using DFT calculation and its entropy change by classical statistical mechanics. In contrast, the first dehydration temperature, are commonly observed at approximately 100 ◦C1,2,5,15 in thermal desorption spectroscopy (TDS) and thermogravimetric and differential thermal analysis (TG-DTA), suggesting the presence of “free water” on the surface. The discrepancy of the dehydration temperature between experimental and theoretical approach is caused owing to the disregard of the hydrogen-bonded H2O molecules1,2,5,15, which strongly interact to stabilize the H2O adsorbates. This is a possible reason for the underestimation of the Gibbs energy values. In addition, it is proposed that the protonic conduction on oxide nanoparticles usually occurs in the H2O multilayer1,2,6 and such protonic conductivity strongly depends on temperature, owing to the variation of hydrated layer thickness with both temperature and the chemical potential of H2O. Therefore, it is essential to focus on the H2O multilayer at a finite temperature to understand the mechanism of protonic conductivity. Under such circumstances, we have closely investigated the chemical reaction and ion migration on oxide (SrTiO3 and SrCeO3)16 and metal (Al and Ni) surfaces17-19 by ab initio molecular dynamics (AIMD) simulation, which treats chemical reactions with not only the accuracy of static ab initio calculations but also the dynamics of atoms during the reaction. In this study, by AIMD simulation, we investigate the hydration reaction and the proton hopping process on the cubic ZrO2 (110) surface at a finite temperature and discuss the proton hopping mechanism on the hydrated surface.

Simulation methodology AIMD simulation is employed to study the hydration reaction and proton hopping process on the cubic ZrO2 (110) surface. Here, a cubic ZrO2 (110) surface is employed because


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of its in-plane electroneutrality, which is suitable for examining the partition ratio of H2O adsorbates and proton conductivity on the surface in the equilibrium state at PZC. The simulation methodology follows the approach of our previous studies16-20. The electronic states are calculated using the projector augmented wave (PAW) method21,22, which is an all-electron electronic structure calculation method within the frozen-core approximation. Projector functions are generated for the 4s, 4p, and 5s states of zirconium atoms, the 2s and 2p states of oxygen atoms, and the 1s state of hydrogen atoms. The Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA)23 is used as determining the exchange-correlation energy in the framework of density functional theory (DFT). The plane-wave cut-off energies are 30 and 300 Ry for the electronic pseudowave functions and the pseudocharge density, respectively. The gamma point is used for Brillouin zone sampling. The energy functional is minimized iteratively using a preconditioned conjugate gradient method20,24. Regarding dynamics calculations, the equation of motion is integrated numerically using an explicit reversible integrator25 with a time step of 0.242 fs (i.e., 10 a.u.). The Nose-Hoover thermostat26 is used for temperature control. An original code developed by one of the authors (F.S.) is used for all calculations in this study. As the initial configuration of AIMD simulation shown in Fig. 1(a), six layers of cubic ZrO2 (110) planes (consisting of 18 atoms (6 zirconium and 12 oxygen atoms) per layer) are placed parallel to the x-y plane at the bottom of a rectangular cell of 10.8 × 10.2 × 25.9 Å, and 27 H2O molecules are allocated regularly in the upper space of the cell. Both the zirconium atoms and oxygen atoms at the bottom layer are fixed during the calculation. According to previous studies11,12, a six-layer slab is sufficient for representing H2O adsorption on a ZrO2 surface. A potential wall represented by the repulsive term of the Lennard-Jones potential (12th power) is employed at the top of the cell to keep the H2O molecules in the calculation cell and to prevent


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the H2O molecules from adsorbing on the bottom of the slab. A periodic boundary is employed for the other side boundaries. In this study, AIMD simulation is carried out for 3267 fs (13,500 steps) at 500 K, at which proton hopping is suggested to contribute mainly to the total electrical conductivity according to the conductivity measurement of compacted YSZ nanoparticles2. To quantify the change in the bonding properties of atoms associated with dissociation and hydration reactions, a bond-overlap population (OVP) analysis27 is performed by expanding the electronic wave functions in an atomic-orbital basis set. That is, the OVP for each atomic pair is obtained on the basis of the formulation generalized to the PAW method28, which gives a semiquantitative estimate of the bonding strength between atoms.

Figure 1. (a) Initial configuration of the calculation cell: Six layers of the cubic ZrO2 (110) plane (consisting of 18 atoms (6 zirconium and 12 oxygen atoms) per layer) are placed parallel to the x-y plane at the bottom of a rectangle cell of 10.8 × 10.2 × 25.9 Å and 27 H2O molecules are allocated regularly in the upper space. (b) Snapshot of the atomic configuration of the cubic ZrO2 (110) surface and H2O molecules after the 13,500 step simulation (3,267 fs). The silver, red, and yellow spheres represent zirconium, oxygen, and hydrogen atoms, respectively, in this and subsequent figures.

Results and Discussion Hydrated Multilayers on Cubic ZrO2 (110) Surface


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Figure 1(b) shows a snapshot of the atomic configuration of the cubic ZrO2 (110) surface and H2O molecules after the 13,500 step simulation. All the H2O molecules that accumulated on the surface to form a hydrated multilayer have been uniformly dispersed in the upper space in the initial configuration, as shown in Fig. 1(a). This accumulation of H2O molecules on the surface suggests that the water vapor pressure is sufficiently lower than 1 bar, which agrees with the experimental observation by Miyoshi et al. (from 0.017 to 0.032 atm of water vapor pressure at 25 to 600 °C)1,2. Figure 1(b) also shows that the hydrated multilayer consists of H2O adsorbates on the surface (layer (i) in Fig. 1(b)) and H2O molecules hydrogen-bonded to the adsorbates (layer (ii) in Fig. 1(b)). This hierarchical multilayer structure shows good agreement with the conclusion deduced from the peak assignment of thermal dehydration behavior on the oxide surface in previous studies,2,5,15. Figure 1(b) also shows that the hydrogen atom is adsorbed on the surface oxygen atom, which implies that H2O dissociation occurs on the surface.

Adsorption and Dissociation of H2O on Cubic ZrO2 (110) Surface Figure 2 shows snapshots of the atomic configuration and OVPs during the chemisorption and dissociation reactions of a H2O molecule on a surface zirconium atom (ZrOH2). Note that the other H2O and fragment molecules are not shown in the snapshots for clarity in this and subsequent figures. In the atomic configuration at 760 fs, one Zr-OH2 is formed on a surface zirconium atom (labeled Zr1) with the oxygen atom (labeled O1) facing Zr1. Then, an oxygen atom in an adjacent H2O molecule (labeled O2) forms a hydrogen bond with the hydrogen atom in Zr-OH2 (labeled H1), forming H3O+. At the same time, the hydrogen atom in the adjacent H2O molecule (labeled H2) forms a hydrogen bond with an oxygen atom on the ZrO2 surface (labeled O3). Finally, the O-H bonds between atoms O1 and H1 and between atoms O2 and H2 are broken. The OVPs for the O1-H1 and O2-H2 bonds decrease abruptly and those


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for the O2-H1 and O3-H2 bonds suddenly increase at approximately 780 fs, which means that proton migration from Zr-OH2 to the adjacent H2O molecule and that from the adjacent H2O molecule to the oxygen atom occur almost at the same time. Finally, monodentate and polydentate OH groups (Zr-OH− and >OH+) are formed on the ZrO2 surface, as shown in the snapshot of 823 fs. In this way, several Zr-OH2 groups dissociate into Zr-OH− and >OH+ pairs, with the help of hydrogen-bonded H2O molecules, whereas one Zr-OH2 dissociates directly without the assistance of hydrogen-bonded H2O molecules and the rest of Zr-OH2 stably exists on the surface.

Figure 2. (a) Snapshots of the atomic configuration and (b) time series of bond-overlap populations during the dissociation of a H2O molecule via an adjacent H2O molecule at approximately 800 fs. The other H2O and fragment molecules are not shown in the snapshots for clarity.

Partition Ratio of Adsorbates in Equilibrium State The cubic ZrO2 (110) surface is terminated by Zr-OH2, Zr-OH−, and >OH+ and the partition ratio of these adsorbates is governed by the equilibrium of H2O dissociation reaction on the surface. In this section, the partition ratio in the equilibrium state is estimated by analyzing both forward and reverse reactions of H2O dissociation by AIMD simulation.


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Figure 3(a) shows the time series of the numbers of adsorbates on the cubic ZrO2 (110) surface. The distance between atoms is employed to deduce the bond formation because the chemical bond is mainly formed before it reaches the bond length in the equilibrium state. We note that the distance employed to deduce the bond formation is determined as the upper end of the peak for the radial distribution function (RDF) between corresponding atoms (see S1 in Supporting Information). In Fig. 3(a), both Zr-OH2 and Zr-OH− are defined as being formed on a surface zirconium atom when the distance between the zirconium and the oxygen atoms in a H2O molecule or an OH group is smaller than 2.5 Å. Moreover, it is defined that a proton is adsorbed on a surface oxygen atom and forms >OH+ when the distance between the proton and the surface oxygen atom is less than 1.2 Å. The O-H bonds in Zr-OH2 and Zr-OH− are also defined as being formed when the distance is less than 1.2 Å. After 500 fs, two to four Zr-OH2 groups are formed on the zirconium atoms. Subsequently, two pairs of Zr-OH− and >OH+ are observed at approximately 700 fs by the dissociation of Zr-OH2 groups. All six zirconium atoms on the surface are terminated by four Zr-OH2 and two Zr-OH− groups by approximately 1,500 fs. Then, two of the Zr-OH2 groups dissociate into Zr-OH− and >OH+ pairs after 1,500 fs. Consequently, the surface is stabilized by two Zr-OH2 groups and four pairs of Zr-OH− and >OH+ until the end of the calculation of approximately 3,300 fs, as shown in Fig. 3(b), which is considered to be in the equilibrium state of the surface.


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Figure 3. (a) Time series of the total numbers of Zr-OH2 (green area), Zr -OH− (blue area), and >OH+ (red area) in AIMD simulation of the forward reaction of H2O dissociation. (b) Snapshot of the atomic configuration of H2O adsorbates on the cubic ZrO2 (110) surface after a 13,500 step simulation. The other H2O and fragment molecules are not shown in the snapshots for clarity.

To confirm whether the configuration shown in Fig. 3(b) is in the equilibrium state, the AIMD simulation for the reverse reaction of H2O dissociation is performed. In this 13,500 step AIMD simulation, the upper side of a cubic ZrO2 (110) slab is terminated by six pairs of Zr-OH− and >OH+, as shown in Fig. 4(b), and 21 H2O molecules are allocated regularly in the upper space of the cell (Fig. 4(a)) as an initial configuration. The other calculation conditions are the same as those of the previous forward simulation, as briefly summarized in the Simulation Methodology section. In this simulation, the reverse reaction of H2O dissociation is actually observed at approximately 1000 fs, as shown in Fig. 5. Opposite to the forward reaction shown in Fig. 2, >OH+ protonates at 1058 fs to an adjacent H2O molecule forming a H3O+ ion, which immediately donates a proton to Zr-OH− and forms Zr-OH2.


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Figure 4. (a) Initial configuration of calculation cell for analyzing the reverse reaction of H2O dissociation on the surface: Six layers of the cubic ZrO2 (110) plane (consisting of 18 atoms (6 zirconium and 12 oxygen atoms) per layer) are placed parallel to the x-y plane at the bottom of a rectangle cell of 10.8 × 10.2 × 25.9 Å, whose upper layer is terminated by six pairs of Zr-OH− and >OH+ and 21 H2O molecules are allocated regularly in the upper space. (b) Snapshot of the initial configuration; six pairs of Zr-OH− and >OH+ on the cubic ZrO2 (110) surface for the reverse reaction of H2O dissociation. The other H2O and fragment molecules are not shown in the snapshots for clarity.

Figure 5. Snapshots of atomic configuration during the reverse reaction of H2O dissociation with interaction with a surrounding H2O molecule at about 1000 fs. The other hydrogen-bonded H2O molecules are not shown in the snapshots for clarity and these snapshots are taken from the AIMD simulation to analyze the reverse reaction of H2O dissociation on the surface.

Figure 6(a) shows the time series of the numbers of adsorbates on the surface in the AIMD simulation of the reverse reaction of H2O dissociation, in which the same distance to distinguish the adsorbates as that employed in Fig. 3(a) is applied. After 1000 fs, two Zr-OH2 groups are formed on the surface from Zr-OH− and >OH+ pairs. However, one of these two ZrOH2 groups dissociates into a pair of Zr-OH− and >OH+ at approximately 1700 fs. Consequently,


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at the end of the calculation of approximately 3300 fs, one Zr-OH2 and five Zr-OH− groups are observed on the surface, as shown in Fig. 6(b). Because the AIMD simulations of both forward and reverse reactions of H2O dissociation lead to the mixed structure of Zr-OH2, Zr-OH−, and >OH+ groups, the authors conclude that comparable numbers of Zr-OH2, Zr-OH−, and >OH+ are present on the cubic ZrO2 (110) surface in the equilibrium state and the partition ratio of Zr-OH2 to Zr-OH− can be roughly estimated to be between 1:5 and 2:4. The presence of mixed adsorbates of Zr-OH2, Zr-OH−, and >OH+ agrees well with the H2O adsorption species on other nonpolar ZrO2 surfaces calculated by static ab initio simulation11-14, although the ratio is slightly different from the ratio of 1:1 for the (101) surface in Refs. 11 and 12, possibly owing to the contribution of the thermal fluctuation (entropy effect) and solvation effect by the H2O multilayer.

Figure 6. (a) Time series of the total numbers of Zr-OH2 (green area), Zr-OH− (blue area), and >OH+ (red area) in AIMD simulation of the reverse reaction of H2O dissociation. (b) Snapshot of the atomic configuration of H2O adsorbates on the cubic ZrO2 (110) surface after a 13,500 step simulation for the reverse reaction of H2O dissociation. The other H2O and fragment molecules are not shown in the snapshots for clarity.

From the time-averaged values of [Zr-OH2] and [Zr-OH-] using the last 4000 steps of the AIMD simulation data, the equilibrium values of the partition ratio, γ = [Zr-OH2]/[Zr-OH-] (see S2 in Supplemental Information), are calculated as 0.54±0.08 for the forward reaction and


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0.22±0.05 for the reverse reaction. In this article, the site fraction, shown with brackets, such as [Zr-OH−], is employed to express the concentration of the surface adsorbates. This slight difference might be caused by the small size of the supercell used in this study, but we believe that the equilibrium value lies between these two values.

Proton Hopping on Cubic ZrO2 (110) Surface Figure 7 summarizes the two types of proton hopping processes observed in the present simulations; the proton hopping by a chain reaction of protonation via hydrogen-bonded H2O molecules and the direct proton transfer between Zr-OH2 and Zr-OH- adsorbates, as schematically shown in Fig. 7(c). Figure 7(a) shows snapshots of the atomic configuration of the former case: The Zr-OH2 on the Zr2 site (Zr2-OH2) observed at 2,776 fs donates one proton to an adjacent H2O molecule, forming H3O+ by the following reaction, Zr-OH2 + H2O → Zr-OH− + H3O+.

(2)

Then, a successive fast proton transfer to an adjacent H2O molecule expressed by the following reaction takes place, H3O+ + H2O → H2O + H3O+,

(3)

and finally, H3O+ approaches the Zr-OH− on the Zr3 site (Zr3-OH−) to transfer proton by the following reaction at 2,901 fs, H3O+ + Zr-OH− → H2O + Zr-OH2.

(4)

A similar chain reaction of protonation via H2O molecules is known one of the representative mechanisms of proton conduction in aqueous solutions, called the Grotthuss mechanism29. An identical proton migration by the Grotthuss mechanism is also reported in the AIMD simulation of hydrated Boehmite (AlOOH)30.


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Figure 7. Snapshots of the atomic configuration during the proton hopping between Zr-OH2 and Zr-OH− (a) by a chain reaction of protonation via hydrogen-bonded H2O molecules (i.e., the Grotthuss mechanism) and (b) by direct proton transfer between the adsorbates. The other H2O and fragment molecules are not shown in the snapshots for clarity. (c) Schematic illustration of proton hopping processes on the cubic ZrO2 (110) surface observed in the AIMD simulation.

Figure 7(b) shows the snapshots of the atomic configurations during the direct proton transfer between Zr-OH2 and adjacent Zr-OH−. The proton hopping from Zr3-OH2 to Zr2-OH− is initiated at 2,904 fs, without the assistance of adjacent H2O molecules. This series of proton exchange is identical to the one between M-OH2 and M-OH− sites observed on a basic MgO (100) and ZnO (10-10) surface by the AIMD simulation10,31. In these two processes of the proton hopping above, Zr-OH2 (as Brønsted acid site) donates a proton to Zr-OH- that works as a proton acceptor or “proton hole” as Brønsted base site to attract protons by the following reaction, Zrm-OH2 + Zrn-OH− → Zrm-OH− + Zrn-OH2,

(5)

where m and n stand for the m-th and the n-th Zr on-top site, respectively.


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These protonation and deprotonation reactions either via direct hopping or via the Grotthuss mechanism explain the proton hopping conduction on the oxide surface with such a wide range of basicities. Note that, although >OH+ can work as a proton donor as well because of its acidic nature, >OH+ never works directly as a proton donor throughout the 13,500 step AIMD simulation, probably owing to steric hindrance as well as the slightly weaker acidity of >OH+ than Zr-OH2.

Thermodynamic Stability of Adsorbates and Surface Basicity The thermodynamic treatment of the surface acid and base reaction has been well established by employing the 1-pK and 2-pK model, as summarized in Ref. 9. Since the present ZrO2 surface is different from that proposed by Raz et al.5, who tried to discuss the surface proton conduction mechanism on the basis of a model with a 2-pK on a single adsorption site, we employed here a 1-pK model with two different adsorption sites (Zr on-top and >O site). The thermodynamic properties of the surface hydration, using the two-site model similar to that in Ref 32, are developed on the basis of the observation of the AIMD simulation in the following discussion. Please refer to Appendix for the generalized discussion on the thermodynamics for the two-site model in detail. In the case of the cubic ZrO2 (110) plane, the adsorption site ratio of the >O site to the Zr on-top site, z = (# of total >O site)/(# of total Zr on-top site), is z = 2. The partition between molecular and dissociative adsorptions on the surface is governed by the following equilibrium protonation and deprotonation pair reactions between Zr-OH2 and the surface oxygen atoms (>O), Zr-OH2 + >O → Zr-OH− + >OH+.

(6)


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In addition, the electrical neutrality condition ([Zr-OH−] = 2[>OH+]) has to be satisfied. The pH of the surface under the PZC condition (pHPZC) is expressed as follows under the saturated condition (see eq. (a6”)),  1 + 8∆ − 1  , pH PZC = pKa1 − log  4  

(7)

in which ∆ is expressed by the acidity constants for >OH+ and Zr-OH2, pKa0 and pKa1, pKa − pKa respectively, as ∆ = 10∆pKa = 10 1 0 = Ka 0 Ka1 . Ka0 and Ka1 are the equilibrium constants for

the deprotonation reactions for >OH+ and Zr-OH2, respectively, and therefore, the equilibrium constant for eq. (6) is expressed as K0 = 1/∆. The partition ratio (γPZC) at pHPZC is expressed as follows.

γ PZC =

[ Zr - OH 2 ]PZC 1 + 8∆ − 1 = [ Zr - OH ]PZC 4

(8)

The γPZC is independent of pHPZC, but dependent solely on ∆: The large [Zr-OH2] value is possible even on the basic surface with higher pHPZC values, if ∆ is large.

The large ∆

corresponds to a small difference in pKas, as shown in Appendix.

o ) at The standard Gibbs energy for the H2O dissociation reaction shown in eq. (6) ( ∆ r G(6) 500K is estimated to be between -0.052 and 0.005 eV by determining the possible K0 ranges from 0.89 to 3.36 using eq. (8) with the equilibrium partition analyses of the forward and reverse reaction of H2O dissociation described above. As the zeroth approximation, we assume here

o = -0.02 eV from a simple numerical average, and then the standard entropy of the reaction ∆ r G(6) o ) is estimated as follows. The standard internal energy change for the reaction (eq. (6)) ( ∆ r S (6) o ) at 0K is estimated from the total energy difference between one Zr-OH and a pair of ( ∆ rU (6) 2


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Zr-OH− and >OH+ on a bare surface: The total energy for the former estimated as -1.06 and the

o = -0.56 eV. The standard latter as -1.62 eV by ab initio calculation at 0K leads to ∆ rU (6) o ) is estimated as ∆ H o = -0.56 eV by enthalpy for the H2O dissociation reaction (eq. (6)) ( ∆ r H (6) r (6) assuming the PV term as being negligibly small. With an approximation of no temperature

o , ∆ S o at T = 500K is evaluated as 104 J/K (1.08 meV/K) from the dependence for ∆ r H (6) r (6) o = ∆ H o − T ∆ S o . Of course, the influence of the hydration multilayers on the relation ∆ r G(6) r (6) r (6)

o itself is in a reasonable range compared first chemisorbed layer seems significant, but the ∆ r S (6) o and ∆ H o values reported by Chen and Sprik32. Our with the value estimated from the ∆ r G(6) r (6) method of determining the equilibrium constant is, while so simple, advantageous for evaluating the partition ratio of surface adsorbates with a low calculation cost and moderate accuracy in comparison with the highly sophisticated method reported by Sprik and co-workers32-34, which includes large computational errors to the extent of 2 pKa units.

Proton Conductivity and Surface Basicity Here, let us discuss the relationship between basicity and proton conductivity on the surface on the basis of the thermodynamic partition of adsorbates that we simulated. The present simulation results indicate that the proton transfer from Zr-OH2 to Zr-OH− is active either by a direct jump or by a series of transfer via surrounding H2O molecules according to the Grotthuss mechanism, whereas no proton transfer was observed between >OH+ to Zr-OH−. The hopping probability of the direct jump (p0) is proportional to the concentration product of proton-donor sites and protonacceptor sites adjacent to the proton donor site as


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p0 ∝ Z 0 ⋅ [ Zr - OH 2 ]PZC ⋅ [ Zr - OH - ] PZC = Z 0 ⋅ Λ PZC ,

(9)

where Z0 is the coordination number of the nearest neighbor site of the Zr on-top site. In the case of the Grotthuss mechanism with j consecutive jumps on H2O molecules, p j ∝ Z j ⋅ [ Zr - OH 2 ]PZC ⋅ [ Zr - OH - ] PZC = Z j ⋅ Λ PZC .

(9’)

Therefore, the total proton conductivity (σH+) by these various proton jumps can be expressed as ∞

σ H = σ 0 ⋅ e ⋅ ∑ µ Hj ⋅ t j ⋅ Z j ⋅ Λ PZC = σ 0′ ⋅ Λ PZC , +

(9”

+

i =0

+

where e, µ Hj , and tj are the elementary charge of electrons, the proton mobility for each process, and the probability for the selection of each process, respectively, and σ0 and σ’0 are proportionality constants. γPZC in case of z = 2 is expressed as follows (See Appendix for derivation). Λ PZC =

4( 1 + 8 ⋅ ∆ − 1) ( 1 + 8 ⋅ ∆ + 3) 2

(10)

Therefore, the proton conductivity is solely dependent on ∆ and independent of pHPZC itself. Note that this is the reason why a similar proton conductivity is observed on the surface of solid acid surfaces such as α-SiO2,35,36 as well as neutral and weak-to-strong basic surfaces of Al2O35, CeO23,6, and ZrO21-5. A key issue is the presence of two different acid and base sites like Zr-OH2 and Zr-OH−, which work as a proton donor and an acceptor, respectively, with or without the help of the Grotthuss mechanism via surrounding H2O molecules.

Therefore, the authors

conclude that the proton hopping on the hydrated oxide surface is a general and common feature of the oxide surface with two pKas for different acidity adsorption sites.


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Conclusions By performing an AIMD simulation, the hydration reaction and proton hopping on a cubic ZrO2 (110) surface have been investigated. The H2O molecules form a hydrated multilayer on the ZrO2 surface, which consists of terminating surface adsorbates of Zr-OH2, Zr-OH−, and >OH+ and the hierarchically hydrogen-bonded H2O layers. Some of the Zr-OH2 groups dissociate into >OH+ and Zr-OH− pairs with the assistance of hydrogen-bonded H2O molecules, whereas the rest of Zr-OH2 coexist stably on the surface. By analyzing both the forward and reverse reactions of H2O dissociation, it is successfully estimated that, in the equilibrium state, both acid and base sites like Zr-OH2 and Zr-OH− stably exist on the cubic ZrO2 (110) surface. Under such a hydrated surface condition, two types of proton hopping are confirmed; the proton hopping between Zr-OH2 and Zr-OH− by the Grotthuss mechanism, which is a chain reaction of protonation via surrounding H2O molecules, and the direct proton transfer between the adsorbates. Although further study, particularly at temperatures below 60 °C, is necessary to illustrate the whole proton conduction mechanism on the hydrated surface, the authors conclude that a possible mechanism of the proton migrations on the hydrated surface of YSZ nanoparticles is the protonation and deprotonation reactions between Brønsted acid and base sites, whose ratio is independent of pHPZC but governed by the difference in the acidity constants of acid and base sites.

This unique, common, but general feature of surface protonics signifies a possible

occurrence of similar proton hopping processes on various oxide surfaces with various acidities, which agrees with experimental observations.


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Appendix: Generalized Treatment of Average Surface Basicity at Point of Zero Charge (PZC) and Partition of Dissociative and Molecular Adsorbates on the Surface of Various Zirconium-to-Oxygen Site Ratios

In this appendix, we describe a generalized expression for the partition ratio between dissociative and molecular adsorbates in the intrinsic equilibrium, where the in-plane electrical neutrality is maintained. This intrinsic equilibrium corresponds to the point of zero charge (PZC) condition and pH under the PZC condition (pHPZC) is defined by a combination of two independent elementally acid and base reactions, or in other words, protonation and deprotonation pair reactions. Since various facet planes have different acid and base sites with various total site ratios, a generalized expression is derived for further discussion. Here, we assume two base and acid sites of the polydentate >O and the Zr on-top site with its total site ratio of z. In the case of the ZrO2 (110) surface, z = 2, whereas z = 1 for (100) and (111) planes. As an initial step of the adsorption reaction, H2O(g) molecules chemisorb on the Zr on-top site to form Zr-OH2 by the following reaction, Zr-V + H2O(g) → Zr-OH2(ad), and

K ad =

[ Zr - OH 2 ] , [ Zr - V] ⋅ PH2O

(r0) (a0)

where Zr-V and Zr-OH2(ad) indicate an unoccupied Zr on-top site and a chemisorbed H2O molecule on the Zr on-top site, respectively, and Kad is the equilibrium constant for the reaction (r0). The brackets, such as [Zr-OH2], indicate the concentration of each site expressed by the site fraction. Some of Zr-OH2 then dissociate by the following proton transfer reaction between ZrOH2 and >O, Zr-OH2 + >O → Zr -OH− + >OH+, and

(r1)


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K0 =

Ka1 [Zr - OH- ][> OH+ ] = , Ka 0 [Zr - OH2 ][> O]

(a1)

in which K0, Ka0, and Ka1 are the equilibrium constants for the reactions (r1), (r2), and (r3), respectively. The reaction (r1) is the neutralization reaction between the acid site (Zr-OH2) and the base site (>O), and can be split into the following two deprotonation reactions for >OH+ and Zr-OH2 with Ka0 and Ka1 as the respective equilibrium constants. >OH+ → >O + H+

Ka 0 = 10 − pKa 0 =

[> O][H + ] [> OH + ]

Zr-OH2 → Zr-OH− + H+

Ka1 = 10− pKa 1 =

[ Zr - OH- ][H + ] [ Zr - OH2 ]

(r2) (a2)

(r3)

(a3)

pKa0 and pKa1 are the acidity constants for >OH+ and Zr-OH2. If a further deprotonation reaction for Zr-OH− proceeds, corresponding to the 2-pKa model on a single site, the following reaction has to be considered. Zr-OH− → Zr-O2- + H+

Ka 2 = 10− pKa 2 =

[ Zr - O 2- ][H + ] [ Zr - OH - ]

Meanwhile, owing to the strong basicity, Zr-O2- is almost completely protonated back to Zr-OH− and is not considered in the following discussion. Since no ions other than the derivatives of H2O are involved in the surface ionic equilibria, defined here as the intrinsic surface equilibrium, the surface neutrality has to be satisfied by the following equation.


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z ⋅ [> OH+ ] = [Zr - OH− ]

Page 22 of 32

(a4)

This condition corresponds to PZC, which is identical to the isoelectric point. Also assumed is the saturation of the Zr on-top site by both dissociative and molecular adsorbates, which leads to the equation below. [Zr-OH2] + [Zr-OH-] = 1

(a5)

Then, by elementary math, we can deduce the following relations for the concentrations of surface groups at the PZC condition by letting α =

1− z Ka 0 1 = = 10∆pKa ( = pKa 1 − pKa 0 ) . and ∆ = 2z Ka 1 K 0

  ∆ [H + ]PZC = Ka1  α 2 + + α  z  

[ Zr - OH − ]PZC =

(a6)

1 ∆ α 2 + + α +1 z

(a7)

α2 + [ Zr - OH 2 ]PZC = 1 − [ Zr - OH − ]PZC =

[> OH + ]PZC = [ Zr - OH − ]PZC z =

[ > O]PZC = 1 − [> OH + ]PZC

∆ +α z

∆ α 2 + +α +1 z

1   ∆ z α 2 + + α + 1 z  

  ∆ z  α 2 + + α + 1 − 1 z  =    ∆ z  α 2 + + α + 1 z  

(a8)

(a9)

(a10)

We finally obtain the following important equations from (a7) and (a8).


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γ PZC =

[Zr - OH2 ]PZC ∆ = α2 + +α − [Zr - OH ]PZC z

(a11)

α2 + Λ PZC = [ Zr - OH 2 ]PZC ⋅ [ Zr - OH − ]PZC =

∆ +α z

  ∆  α 2 + + α + 1   z  

2

(a12)

When z = 1, [H+]PZC and pHPZC are both transformed into very simple well-known equations as follows. 1

[H + ]PZC = ( Ka 0 ⋅ Ka1 )2 and pH PZC =

1 ( pKa 0 + pKa1 ) 2

(a6’)

Then, eqs. (a7), (a8), (a11), and (a12) can be simplified as follows.

[ Zr - OH− ]PZC =

1

(a7’)

1 2

∆ +1 1

∆2

[ Zr - OH 2 ]PZC =

(a8’)

1

∆2 + 1

Finally, we obtain the following. 1

[ Zr - OH 2 ]PZC 1 1 γ PZC = = ∆2 , and log γ PZC = (pKa1 - pKa 0 ) = ∆pKa [ Zr - OH ]PZC 2 2

(a11’)

1

Λ PZC =

∆2  ∆2 + 1     1

(a12’)

2

As both γPZC and ΛPZC are independent of pHPZC, there exists certain concentration of acidic protons represented by [Zr-OH2] on a hydrated oxide surface regardless of pHPZC but dependent solely on ∆. This is an important conclusion to understand why proton conductivity is commonly observed on various oxide surfaces with a wide range of surface basicity.


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Page 24 of 32

In the case of z = 2, corresponding equations are obtained similarly to those for z = 1, but in slightly complicated forms. However, the same conclusion can be deduced: Although pHPZC is determined by both acidity constants, γPZC and ΛPZC are solely determined by ∆ as follows. [H + ]PZC =

Ka 1 4

( 1 + 8∆ − 1), and pH

PZC

 1 + 8∆ − 1   = pKa1 − log  4  

(a6’’)

[ Zr - OH − ]PZC =

4 1 + 8∆ + 3

(a7”)

[ Zr - OH 2 ]PZC =

1 + 8∆ − 1 1 + 8∆ + 3

(a8”)

γ PZC =

Λ PZC =

1 + 8∆ − 1 , and log γ PZC = pKa1 − pHPZC 4

(

)

4 1 + 8∆ − 1

( 1 + 8 ∆ + 3)

2

(a11”)

(a12”)

Discussions for z = 1 are available on the surface of tetragonal ZrO2 (101)11,12, MgO (100)10, ZnO (10-10)31, rutile TiO2 (110)32, and so forth and schematic illustrations for z = 1 are shown in Fig. A1 for (a) pHPZC = 7 with ∆pKa = −0.5, (b) pHPZC = 11 with ∆pKa = −0.5, and (c) pHPZC = 7 with ∆pKa = −2. As suggested by eqs. (a7’), (a8’), (a11’), and (a12’), we can immediately recognize the facts that Zr-OH2 is stably present regardless of pHPZC and that ΛPZC is solely dependent on ∆pKa and independent of pHPZC, from the comparison between Fig. A1(a) and (b) and between Fig. A1(a) and (c).


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Figure A1. Schematic illustrations of neutralization reaction between Zr-OH2, and >O for z = 1, showing [] (ordinate), the site fraction of each adsorption site as a function of pH (abscissa). Each line except for the dotted one shows the concentrations of Zr-OH−, >OH+, Zr-OH2, and >O. The dotted line represents the product of the concentrations of Zr-OH2 and Zr-OH−. The concentration of each group in the equilibrium state corresponds to the intersection points with pH = pHPZC. pHPZC and ∆pKa, assumed in each graph are; (a) pHPZC = 7, ∆pKa = −0.5, (b) pHPZC = 11, ∆pKa = −0.5, and (c) pHPZC = 7, ∆pKa = −2.

Figure A2 shows schematic illustrations of the neutralization reaction for z = 2. Note that the other conditions are the same as those in Fig. A1. From the comparison between Figs. A1 and A2, one may easily find that, in the case of z = 2 and pKa1 < pKa0, [Zr-OH2] and Λpzc decrease more rapidly than in the z=1 case, with the decrease in ∆pKa, and that pHpzc is mainly determined by pKa0. Therefore, the surface with z = 1 is favorable for proton conduction because it has comparable amounts of Zr-OH2 and Zr-OH− with a wider range of ∆pKa values.

Figure A2. Schematic illustrations of neutralization reaction between Zr-OH2 and >O for z = 2, showing [] (ordinate), the site fraction of each adsorption site as a function of pH (abscissa).


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Page 26 of 32

Each line except for the dotted one shows the concentrations of Zr-OH−, >OH+, Zr-OH2, and >O. The dotted line represents the product of the concentrations of Zr-OH2 and Zr-OH−. The concentration of each group in the equilibrium state corresponds to the intersection points with pH = pHPZC. pHPZC and ∆pKa, assumed in each graph are; (a) pHPZC = 7, ∆pKa = −0.5, (b) pHPZC = 11, ∆pKa = −0.5, and (c) pHPZC = 7, ∆pKa = −2.

ASSOCIATED CONTENT

Supporting Information Available: Radial distribution function (RDF) to determine the distance to deduce the numbers of Zr-OH2, Zr-OH− and >OH+ on the surface (Figure S1), time-average of the partition ratio, [Zr-OH2]/[ZrOH−], during AIMD simulation (Figure S2). This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION

Corresponding Author E-mail address of corresponding author (S. Y.): yamaguchi@ material.t.u-tokyo.ac.jp

Notes The authors declare no competing financial interests. ACKNOWLEDGMENTS Part of this research was supported by a Grant-in-Aid for Scientific Research (A) (#23246112) from the Japan Society for the Promotion of Science (JSPS). R.S. was supported by JSPS through the Program for Leading Graduate Schools (MERIT). REFERENCES


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Insert Table of Contents Graphic and Synopsis Here


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Proton Migration on Hydrated Surface of Cubic ZrO2: Ab initio

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