Hydrated Proton Structure and Diffusion at Platinum Surfaces - The

Mar 30, 2015 - Water-mediated hydrated proton solvation and diffusion at two types of platinum–water interfaces—namely, the Pt(111) and the Pt(100...
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Hydrated Proton Structure and Diffusion at Platinum Surfaces Zhen Cao,† Revati Kumar,‡ Yuxing Peng,† and Gregory A. Voth*,† †

Department of Chemistry, James Franck Institute, Computation Institute, The University of Chicago, 5735 South Ellis Avenue, Chicago, Illinois 60637, United States ‡ Department of Chemistry, Louisiana State University, 736 Choppin Hall, Baton Rouge, Louisiana 70803, United States S Supporting Information *

ABSTRACT: Water-mediated hydrated proton solvation and diffusion at two types of platinum−water interfacesnamely, the Pt(111) and the Pt(100) surfacesis investigated using reactive molecular dynamics simulations. The adsorbed water molecules on these platinum surfaces create different hydrogen-bonding networks, resulting in different proton solvation and transport behavior. Free energy calculations show that the excess proton can be stably adsorbed on the Pt(111) surface, while on the Pt(100) surface it prefers to stay at the interface between the hydrophobic layer of adsorbed water and the bulk. The hydrated excess proton can be viewed as a charge defect in the adsorbed water layer, where it diffuses with a low rate due to the slow reorientational dynamics of the adsorbed water molecules. However, the proton can sample a larger surface area by hopping between the adsorbed layer and the bulk at the Pt(111) surface.

I. INTRODUCTION Water-mediated excess proton solvation and diffusion on a metal surface is a critical step for a broad range of important applications, such as heterogeneously catalyzed oxidation/ reduction of organic compounds1,2 and hydrogen evolution and storage.3,4 Hence, this process has drawn interest from a variety of disciplines, with numerous investigations into its detailed mechanism. Studies of proton transport (PT) in aqueous solution show the complexity of this process,5−8 in part due to the so-called “Grotthuss shuttling” wherein the excess proton can hop between molecules giving rise to anomalously high diffusion constants.9 Understanding the mechanism of proton transfer, therefore, requires knowledge of both the hydrated excess proton solvation and the reorientational motion of the surrounding water molecules.10−12 However, in situ tracing of proton transport at interfaces can be extremely hard, despite significant developments in, e.g., scanning tunneling microscopy (STM)13 and atomic force microscopy (AFM)14 instruments. STM has revealed much concerning the static structures of single layers of absorbed water molecules on different types of metal surfaces. The oxygen atoms of these adsorbed water molecules form symmetric patterns,15−19 indicating that their interactions with the metal surface can constrain the water molecules to form ordered structures. Because the hydrogen atoms generate relatively weak signals in STM observations, density functional theory (DFT) calculations of optimized small water clusters on oxide and other surfaces as well as ab initio simulations of different water−metal interfaces have been employed to investigate the water structure at these interfaces.20−23 The ab initio simulations indicate that there are distinct water layers near the metal surface, including an adsorbed layer in which the water © 2015 American Chemical Society

molecules reside near metal top sites. The DFT cluster studies have revealed that hydrogen-bonded cyclic tetramers and hexamers of water molecules are fundamental components of the adsorbed water structure on surfaces. These fundamental components have been included in the development of an empirical force field that incorporates manybody interactions,24 and simulations show that this force field can reproduce a number of order parameters of water clusters on a variety of metal surfaces.24,25 Recently, this force field was used to perform large-scale molecular dynamics (MD) simulations of adsorbed water molecules on the Pt(111) and Pt(100) surfaces.26,27 In both cases, the adsorbed water molecules form an extensive, flat layer on the platinum surface, consistent with the latest STM observations and contrary to lower energy electron diffraction (LEED) results.19 Moreover, the hydrogen bonding of the adsorbed water molecules is almost saturated (i.e., most water molecules form four hydrogen bonds) due to an extensive hydrogen bonding network between water molecules in the layer. However, the structure of the water layer differs between the two platinum surfaces. In both cases, the bulk water experiences hydrophobic interactions with the adsorbed layer, but the hydrophobic interaction is much stronger for the Pt(100) surface.26 Meanwhile, the adsorbed water molecules are entropically driven to form different domains on the platinum surface, giving rise to heterogeneity on larger time and length scale than can be observed using DFT calculations.27 Special Issue: Steven J. Sibener Festschrift Received: December 27, 2014 Revised: March 25, 2015 Published: March 30, 2015 14675

DOI: 10.1021/jp5129244 J. Phys. Chem. C 2015, 119, 14675−14682

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The remainder of this paper is structured as follows: In section II, the MS-EVB methodology will be briefly reviewed along with the polarizable electrode model, and an enhanced sampling methodnamely, Hamiltonian Replica Exchange Umbrella Sampling (HREUS)will be utilized as a means for efficiently obtaining the potential of mean force (PMF) as a function of the distance between the hydrated excess proton “center of excess charge” (CEC, as defined later) and the platinum surface. The system setup will also be presented in this section. In section III, the free energy curves of the CEC near the two types of Pt surfaces will be presented and compared, and the mechanism of proton diffusion will then be described. Finally, section IV will summarize the results.

When considering proton transport at these platinum−water interfaces, one might imagine that the large-scale hydrogenbonded network will provide a good pathway for proton diffusion. However, simulations indicate that these surface water molecules reorient very slowly, which can inhibit proton diffusion.27 Proton transfer in water requires reorientation of nearby waters to stabilize the transferred excess charge.7,9,10 Therefore, water-mediated proton transport at Pt surfaces might be slowed for the same reason as in ice;28,29 even though the perfect hydrogen bonding pathways are present, the slow reorientational motions of water might limit the proton hopping and diffusion rate. (We note, however, that this behavior is inconsistent with the recent observation of enhanced proton diffusion on the wet iron oxide surface.30) In addition experimental observations on platinum electrodes suggest that the mechanism of electrochemical hydrogen evolution at these electrodes from an acidic electrolyte depends on the crystallographic face of the platinum electrode exposed to the electrolyte.31 Recent laser-induced temperature jump experiments have shown that the rate constant of the charge transfer process of hydrogen adsorption on the electrode surface from an acidic proton in solution is an order of magnitude higher for the Pt(111) surface compared to the (100) surface.32 In an interesting computational study, Wilhelm et al. also developed a reactive model to simulate hydrogen adsorption from an acidic solution onto a Pt(111) electrode surface.33,34 However, their simulations did not explicitly include the effect of electrode polarizationan integral component of the physics of electrode−electrolyte interactions. The effect of an applied voltage was indirectly simulated by smearing the electrode surface with varying amounts of negative charge densities. Their focus was on the hydrogen adsorption at the Pt(111) surface rather than proton transport in the aqueous layers near the electrode surface, and their studies revealed that a protonated complex passed through a weakly adsorbed state, which is not present at higher electron densities, before discharge. The focus of this paper is to develop an understanding of the hydrated proton solvation and transport process in the aqueous layers near two different platinum electrode surfaces, namely, Pt(111) and Pt(100), in order to gain molecular-level insight into the factors that may influence electrochemistry in aqueous acidic media. In this study, multistate empirical valence bond (MS-EVB) simulations35 are performed to investigate the structural and dynamical properties of water-mediated proton solvation and transport at these platinum surfaces. A key ingredient is the use of a polarizable electrode model, developed previously by Peterson et al. and used to study other electrode−electrolyte systems, which includes the effect of electrode polarization by the electrolyte. 36−38 The simulations carried out in this work do not allow for the charge-transfer reactions between the electrode and electrolytean important step that results in the reduction of the (“hydronium”) hydrated proton structure that ultimately leads to hydrogen gas evolution at the platinum electrode. Hence the results presented in this work, including the free energy profiles, cannot be directly compared to experimental observations. Nonetheless these studies are useful in that they allow one to investigate the influence of the electrode−electrolyte interface for specific platinum interfaces, which in turn should influence the reduction of the hydrated proton at the electrode surface.

II. METHODOLOGY AND SIMULATION SETUP 2.1. Multistate Empirical Valence Bond (MS-EVB) Method. The diffusion of an excess proton in bulk solution is characterized by delocalized Eigen (H9O4+) and Zundel (H5O2+) complexes, together with their fluctuating solvation shells.5−8 The “special pair dance” mechanism39 as well as the long-range contribution from the reorientation of water molecules several solvation shells away10 can be described well by the MS-EVB framework developed in the Voth group.6,35,40 In MS-EVB, the system is described as a linear combination of states, each of which corresponds to a different bonding topology. The diagonal Hamiltonian elements Hii are the energies of the ith state described by a classical nonreactive force field, while the off-diagonal terms, Vij, which represent the coupling between the states, are calculated by incorporating several fitted parameters. The ground state is the lowest-energy eigenvector of the Hamiltonian, determined by diagonalization of the MS-EVB matrix at every time step. By construction, this is an eigenvalue problem, and hence one can obtain the force on each atom by invoking the Hellman−Feynman theorem. Within the MS-EVB framework, the excess proton charge defect is inherently delocalized, as each diagonal element of the Hamiltonian may identify a different water molecule as the excess charge carrier. It is thus convenient to describe excess proton solvation and transport in terms of the motion of a charge defect in the solution, whose position can be traced as rCEC = ∑ic2i riCOC (the hydrated excess proton CEC), where c2i and riCOC are the probability amplitude squared and the center of charge (COC), respectively, of the ith MS-EVB state (bonding topology). For this study, the newly developed MSEVB3.2 parameters are employed (see Supporting Information). Unlike previous generations of the MS-EVB model, the MS-EVB3.2 parameters employ condensed-phase ab initio MD simulations of the excess proton in bulk water to add to the empirical parameters from the MP2 studies of protonated gasphase water clusters. 2.2. Polarizable Electrode Model. As discussed in the Introduction, the metal surfaces can constrain the nearby solvent to form a highly ordered structure. Therefore, a reasonably accurate description of the interactions between the metal and solvent is essential. This involves two components, namely, the van der Waals interaction and the polarization of the electrode by the electrolyte. The former is addressed using the description of Siepmann and Sprik24 with the water− platinum parameters from their work and the hydrated proton−platinum parameters from previous work by Cao et al.37 The latter term is described using a polarizable electrode model, developed in previous work and briefly described here.36 This model is based on an image charge formalism. Any charge 14676

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of charge −1e and with a Lennard-Jones (LJ) function (ε = 0.1500 kcal/mol and σ = 4.045 Å) for the van der Waals term.47 The platinum−chloride van der Waals interaction is obtained using the Lorentz−Berthelot combination rule, with the following parameters for platinum: ε = 0.2013 kcal/mol and σ = 2.41 Å.36 Two commonly used surfaces, the Pt(100) surface and the Pt(111) surface, were chosen for this study, and an empirical force field developed previously was used to treat the interactions between platinum atoms and the water/hydronium particles.37 The HREUS method was used to calculate the PMF as a function of the distance between the CEC and the platinum surfaces under applied potentials of 0 and 1 V, with simulations for each window accumulated for 2 ns. For the analysis of the proton diffusion near the Pt surfaces, a number of initial configurations were chosen to perform simulations in the constant NVT ensemble using the Nose−Hoover thermostat at a temperature of 300 K with a 100 fs temperature damping parameter for a total simulation time of 1 ns using a 1 fs time step.49 Wall potentials of the form U = k0[(z/z0)12 − (z/ z0)6] for z ≥ z0, where z0 is the chosen distance and z is the instantaneous distance in the z-direction (namely, the axis perpendicular to the electrode surface), between the CEC and the platinum surface were employed with a value of 10 kcal/ mol for k0. This was done to confine the hydrated excess proton CEC within either the adsorbed water layer or within two water layers from the Pt surface.

qi between two electrodes will induce primary image charges − qi on the other side of the electrode, which will in turn generate an infinite series of higher-order image charges across each electrode surface. The effect of an applied voltage, V, is incorporated using a capacitor model. Therefore, the total charge smeared on the positive (PE) and negative (NE) electrode is given by qPE =

∑ qizi/D + VAε0/D i

(2.1)

and qNE =

∑ qi(D − zi)/D − VAε0/D i

(2.2)

where qPE and qNE are the effective charges added to the positive and negative electrodes, respectively; ε0 is the vacuum permittivity; A is the area of the electrode surface; D is the distance between two electrode surfaces; and zi is the distance between the real charge and the left electrode surface. The first term in the two equations corresponds to the higher-order charges, and the second term comes from the applied voltage V. 2.3. Hamiltonian Replica Exchange Umbrella Sampling (HREUS) Method. To obtain the potential of mean force (PMF) along a reaction coordinate, the umbrella sampling method41,42 has been widely used and shown to be robust under the proper conditions. This method divides the reaction coordinates into a number of windows, and harmonic constraints are added to each window to ensure that the entire reaction path is sampled well. Nonetheless, this method is prone to “quasi-ergodicity” problems when a given window is insufficiently sampled due to coupling to slow motions in other degrees of freedom. To address these problems and to further improve sampling efficiency, other enhanced sampling methods can be combined with umbrella sampling. In this study, the Hamiltonian Replica Exchange Umbrella Sampling (HREUS) method,43 implemented as an add-on to the LAMMPS MD package44 using an in-house code,45 was employed. In HREUS, the conformational sampling of each window is enhanced by periodically attempting swaps between the configurations corresponding to neighboring windows. The energy difference between the pre- and postswap states is calculated as ΔE = H(x) + H′(x′) − H(x′) − H′(x), where x and x′ are the configurations corresponding to neighboring windows, and H and H′ correspond to different bias potentials. Swap acceptance is governed by the Metropolis criterion, Pexch = min{1, exp(−βΔE)}, where β = 1/kBT and kB is the Boltzmann constant. For this work in particular, the energy difference arises primarily from the harmonic bias potential added to different windows, such that ΔE can be approximated as ΔEbias = 2kΔξ0ijΔξij,45 where k is the spring constant of the harmonic bias potential; Δξ0ij is the distance between the centers of the two bias potentials; and Δξij is the distance between the instantaneous reaction coordinates of two configurations. 2.4. System Setup. A solution consisting of 2591 SPC/Fw water molecules,46 one excess proton, and one chloride47 was equilibrated in the constant NPT ensemble48 at a temperature of 300 K and a pressure of 1 atm using a Nose−Hoover thermostat and barostat with a 100 fs temperature damping parameter and 1000 fs pressure damping parameter. The simulation was carried out for 2 ns, with a time step of 1 fs, and the last 1 ns trajectory was recorded to obtain the equilibrated volume. Then, the aqueous solution was inserted between two electrodes. The chloride ion is treated as a monatomic particle

III. RESULTS AND DISCUSSION 3.1. PMFs as a Function of the Excess Proton Distance from the Surface. In Figure 1(a) and (b), the PMFs for the

Figure 1. Free energy (with error bars) as a function of the distance, in the z-direction (namely, the axis perpendicular to the electrode surface), of the hydrated excess proton center of excess charge (CEC) from the positive electrode at two different voltages (0 and 1 V) for: (a) Pt(111) surface and (b) Pt(100) surface. The inset in each graph is a snapshot of the local environment of the hydronium surrounded by the water molecules adsorbed on the corresponding Pt surface. The black dashed line shows the water density. 14677

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Consistent with previous studies, the simulations in this paper indicate that the adsorbed water layer on the Pt(100) surface is rather hydrophobic: almost all of the water molecules form four hydrogen bonds with other interfacial waters and cannot hydrogen bond to water molecules above them. This results in the second minimum, between the hydrophobic adsorbed layer and the bulk, in the PMF profile since hydronium prefers to reside near hydrophobic interfaces.51,52 The results presented above emphasize the large structural variations possible upon interaction with different types of platinum surfaces. The spontaneous evolution of hydrogen gas in electrochemical systems, such as platinum electrodes placed in an acidic solution, suggests that the real PMFs would also show a steep downward trend near the electrode surface that reflects the favorable free energy of charge transfer and the reduction reaction. While the free energy profiles obtained in this work are, therefore, not a description of the electrochemical reaction, due to the aforementioned features, they do reveal the underlying differences in the hydrated proton solvation near the Pt electrode surfaces that likely contribute to observed experimental behavior. Future work will incorporate these missing reactive elements, such as the explicit reduction of the hydrated proton at Pt electrode sites, in order to provide more realistic simulations of the complete electrochemical process. Such an extension of the present modeling is a nontrivial task. 3.2. Proton Diffusion near Platinum Surfaces. A unique strength of the MS-EVB simulations performed here is that they allow the dynamics of the excess proton CEC to be examined on relatively long time and length scales (compared to ab initio MD). Before examining the CEC dynamics, however, it is important to understand the dynamics of the solvation water, as proton diffusion is coupled to the water reorientation. Therefore, the reorientational dynamics of the water molecules are characterized using an instantaneous measure of the reorientational mobility q(a⃗,ui(t)), as developed by Willard et al.27

excess proton CEC position are displayed as a function of the distance from the Pt(111) and Pt(100) surfaces, respectively, along with water density profiles for both surfaces. The excess proton is attracted to the surface by both the polarization effect and dispersion interactions but is drawn to the bulk by its tendency to maintain complete solvation shells. This competition is not easily modeled using ab initio calculations due to the large system sizes and simulation times needed to accurately model these effects. It is also not obvious from experiments that are sensitive only to the interfacial water layer. However, this competition can be important for applications, especially in systems that have an interface between two bulk phases. The effects of this competition can be observed from the two free energy minima for the PMFs of the CEC near the Pt surfaces, which also coincide with peaks in the water density profiles. The first minimum as one moves away from the metal surface, which is pronounced only for Pt(111), corresponds to the excess proton adsorbed onto the Pt surface. Increasing the applied voltage can enhance the adsorption, deepening the well in the PMF. The inset in Figure 1(a) shows a representative configuration for hydronium on the Pt(111) surface. Consistent with previous simulations,26,27 the water molecules form a highly ordered structure, mainly consisting of cyclic hexamers, near the interface. These water clusters provide a complete first solvation shell for the adsorbed hydronium. Unlike the hydrated excess proton in bulk solution, however, the adsorbed hydronium is confined to a two-dimensional surface, and the solvating waters cannot form the complete series of solvation shells characteristic of the delocalized Eigen structure (H9O4+) in bulk water. Still, the influence of this long-range order on the free energy is relatively small compared to the strong interaction between the hydronium and the Pt atoms, stabilizing hydronium at the interface. The second minimum corresponds to hydronium positioned at the interface between the interfacial water layer, which is slightly hydrophobic,26,27 and bulk water. Previous simulations50−52 and experiments53−55 suggest that the hydronium is weakly attracted to interfaces between water and hydrophobic surfaces. As the interfacial layer is hydrophobic for the Pt(111) surface, a shallow minimum is consistent with those studies. For the Pt(100) surface, a very different scenario is expected considering that the interfacial water molecules tend to form tetramers, which are not favorable for solvating hydronium and also lead to a more hydrophobic interfacial layer. Consistent with this, the first minimum along the PMF curve is very shallow, and the second is deeper. The inset in Figure 1(b) displays a configuration corresponding to the first minimum: the hydronium is embedded onto the Pt surface, while all the water molecules form ordered cyclic tetramers. Almost every water molecule forms four hydrogen bonds with the neighboring absorbed water molecules, and the hydronium oxygen is a defect that breaks this network in the adsorbed layer. Meanwhile, two of the hydronium hydrogen atoms form hydrogen bonds with water molecules in the adsorbed water layer, while the third points upward toward another water oxygen from the second layer. This solvation structure is unfavorable, as the hydronium’s first solvation shell is twisted, and the interaction with water in the second layer is weak. Still, the strong polarization effect originating from the platinum atoms contributes favorably to the energy, leading to the shallow free energy minimum, albeit much higher in free energy than for Pt(111).

q(a ⃗ , ui(t )) =

∑ (1 − ui⃗ (t )⋅u ⃗(t + Δt )) i

1 ⎯a (t ))2 /2ξ 2)Θ(2ξ − |z (t ) − z*|) × exp(− (a ⃗ − → i i ξ 2π (3.1)

Here, u⃗i is the unit vector corresponding to the dipole moment of the ith water molecule, averaged over 2 ps to remove noise due to librational motions; Δt is chosen as 10 ps, consistent with work by Willard et al.; a⃗i(t) is the coordinate of the oxygen atom of the ith water molecule projected onto the platinum surface; ξ is a parameter which determines the resolution of the map (chosen to be 1.5 in this work); and Θ = 1 if the ith water molecule stays within the adsorbed layer within the testing time or 0 otherwise. In Figure 2(a), this order parameter has been used to characterize the adsorbed water layer for the Pt(111) surface under an applied voltage of 1 V. The order parameter has been integrated over the simulation time to yield a result as a function of a;⃗ the red regions represent areas of higher water mobility in which the adsorbed water layer reorients quickly and the blue regions of lower mobility. The result is consistent with the previous simulations26,27 in two regards. First, the adsorbed water molecules reorient very slowly. Second, the adsorbed water molecules form domains on the Pt(111) surface, and water molecules at domain boundaries reorient more quickly. 14678

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Next, the diffusion of the excess proton CEC within this water layer was examined. Simulations with the excess proton near the platinum surface were carried out with an additional wall potential to confine the excess proton to a certain distance from the electrode. As noted earlier, the form of the wall potential used was U = k0[(z/z0)12 − (z/z0)6] for z ≥ z0, where z0 is the chosen distance and z the instantaneous distance, in the z-direction, between the hydrated proton CEC and the platinum surface. The wall potential U is set to 0 for z < z0 so that the wall potential will not disturb the excess proton diffusion near the Pt surface area. The instantaneous density field, R, of the CEC of the hydrated excess proton in the adsorbed water layer at time t, projected on the electrode surface, a⃗(t), is determined using the equation R (a ⃗ , t ) =

1 exp(− (a ⃗ − a ⃗(t ))2 /2ξ 2)Θ ξ 2π

(2ξ − |z(t ) − z*|2 )

(3.2)

which is analogous to the water mobility defined in eq 3.1, with z* being the averaged z coordinate of the adsorbed water layer. The time average value of R, as a function of the twodimensional electrode surface, from a representative simulation with the excess proton confined to the adsorbed water layer on the negative Pt(111) electrode, is shown in Figure 2(b). The color scale in these figures goes from white to red to blue, with the regions in white indicating that the hydrated proton CEC did not visit these regions during the simulation and blue indicating regions showing the maximum probability of the CEC. The CEC is seen to be mobile only within a small area. This is because proton transport requires collective motions of the solvating waters, which are only mobile along domain boundaries. In Figure 2(c), the density field, R, of the excess proton adsorbed on the Pt(111) surface is again plotted but from a simulation in which the wall potential is modified to allow the excess proton to visit the second water layer. From this figure it is clear that when the excess proton is allowed to visit the second layer adjacent to the adsorbed layer it becomes more mobile. By visiting the second water layer, the proton is able to sample disconnected boundary regions on the Pt surface.

Figure 2. (a) Average reorientational mobility, q, of an adsorbed water layer on the negative Pt(111) electrode surface (under an applied voltage of 1 V) as a function of projection on the xy plane of the electrode surface. Red indicates regions of higher mobility while blue regions of low mobility. (b) Average value of R, the hydrated excess proton center of excess charge (CEC) density projected on the electrode surface, for a representative trajectory obtained from a simulation with the excess proton confined to the adsorbed water layer on the negative Pt(111) surface. (c) Average value of R for the CEC when it is adsorbed on the electrode surface, from simulations where the excess proton is constrained to be within two waters layers of the negative Pt(111) electrode surface. In both (b) and (c) the scale goes from white to red to blue, with white indicating zero probability of the CEC and blue indicating a substantial probability of the CEC.

Figure 3. (a) Top view of proton hopping transport within the adsorbed water layer above the Pt(111) surface. (b) Side view of proton hopping transport from the adsorbed water layer to the second water layer above the Pt(111) surface. 14679

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The Journal of Physical Chemistry C A clear picture of the proton transport at the Pt(111) surface emerges from observing representative snapshots, which is consistent with the above analysis. Figure 3(a) shows a typical proton transport event within a single boundary region. Most commonly, the excess proton exists in an Eigen-like structure, with three water molecules forming a complete first solvation shell around the central hydronium. Proton transport proceeds through an Eigen−Zundel−Eigen mechanism7 analogous to the process in bulk water, despite the confinement to a twodimensional surface. Figure 3(b) depicts proton transport between water molecules in the first and second layer from the platinum surface. This process, which also qualitatively resembles the bulk mechanism, often occurs near a boundary area, where hydrogen bonds form between water molecules in different layers. Because the mechanism resembles the bulk case, the free energy barrier between the first and second minima of the PMF is relatively small, as shown in Figure 1(a). It is likely that this second process facilitates the faster proton diffusion rate observed in experiment30,32 rather than diffusion solely within the adsorbed layer. Proton diffusion proceeds rather differently on the Pt(100) surface. Similar to the Pt(111) surface, the reorientation of the adsorbed water molecules under an applied potential of 1 V is characterized using eq 3.1 and shown in Figure 4(a). Again, the reorientations of the adsorbed water molecules are rather slow. However, the structure of the adsorbed water molecules on these two types of platinum surfaces is clearly different. For Pt(100), boundary areas between different domains have a more narrow structure, consistent with previous MD simulations.26,27 The different water structure gives rise to different diffusion behavior for the excess proton CEC, as calculated using eq 3.2 and presented in Figure 4(b). With a wall potential that confines the proton within the adsorbed water layer, the proton is even less mobile than for Pt(111). Allowing the proton to diffuse into the second water layer essentially reduces the likelihood of it being adsorbed on the Pt surface to only a negligible degree. This is seen from Figure 4(c) in which the distance in the z direction (axis perpendicular to the electrode surface) between the center of excess charge and the platinum electrode is potted as a function of time. A molecular-level picture of the proton transport mechanism for Pt(100), consistent with the above results, is obtained on examining representative snapshots and is shown in Figure 5. When the excess proton is located in the adsorbed water layer, its solvation shell is not well-formed, and in fact, one of the hydronium hydrogen atoms must point directly away from the surface toward the bulk layer. This happens because all the nearby water molecules form four hydrogen bonds with their neighbors rather than orienting so as to stabilize the hydronium. Therefore, it is not favorable for the excess proton to stay within the adsorbed water layer, and only a small free energy minimum corresponding to this state is observed in the PMF. In contrast, the solvation structure is much more favorable in the second water layer. The corresponding free energy minimum is therefore deeper. Moreover, because the hydronium in the adsorbed water layer can easily form a hydrogen bond with a water molecule in the second layer, it is easy for the excess proton to escape from the adsorbed water layer, as depicted in Figure 5. Meanwhile, a high free energy barrier prevents the proton from returning to the adsorbed layer. These results indicate that the proton diffusion near electrode surfaces is clearly dependent on the structure of the surface.

Figure 4. (a) Average reorientational mobility, q, of the adsorbed water layer on the negative Pt(100) surface (under an applied voltage of 1 V) as a function of projection on the xy plane on the electrode surface. Red indicates regions of higher mobility and blue regions of low mobility. (b) Average value of R, the hydrated excess proton center of excess charge (CEC) density projected on the electrode surface, for a representative trajectory obtained from a simulation with the excess proton confined to the adsorbed layer of water on the negative Pt(100) surface. The scale goes from white to red to blue, with white indicating zero probability of the CEC and blue indicating a subsantial probability of the CEC. (c) The distance d (along the axis perpendicular to the electrode surface) between the negative Pt(100) electrode and the CEC as a function of time from a simulation where the proton is constrained to be within two waters layers of the negative Pt(100) electrode surface.

IV. CONCLUSIONS In this paper, the mechanism of water-mediated excess proton diffusion on two types of platinum surfaces was investigated through MS-EVB simulations. Confinement by these two types of platinum surfaces created rather different environments, leading to varying proton transport behavior. For the Pt(111) surface, it is easier for the hydronium to embed itself into the hydrogen-bonding network formed by the adsorbed water molecules since the water molecules can form a complete first solvation shell around the hydronium. On the other hand, near the Pt(100) surface, the hydronium prefers to stay at the interface between the hydrophobic adsorbed water layer and the bulk water above it. For both surfaces, proton diffusion within the adsorbed water layer is inhibited, while for the Pt(111) surface protons can jump back and forth between the interface and the adsorbed water layer. The latter mechanism allows the excess proton to diffuse at a higher rate. 14680

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Figure 5. Side view of proton hopping transport from the adsorbed water layer to the second water layer above the Pt(100) surface.

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ASSOCIATED CONTENT

S Supporting Information *

The Hamiltonian of the Multi-State Empirical Valence Bond (MS-EVB) Method and the parameters for the MS-EVB3.2 version of the parameters are included. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: (773) 702-9092. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported in part by the Office of Naval Research (ONR Grant N0014-12-1-1021) and the National Science Foundation (NSF grant CHE-1214087). This work was partially completed with resources provided by the University of Chicago Research Computing Center (RCC).

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REFERENCES

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