Hydration of metal surfaces can be dynamically heterogeneous and hydrophobic

Abstract

We have applied molecular dynamics and methods of importance sampling to study structure and dynamics of liquid water in contact with metal surfaces. The specific surfaces considered resemble the 100 and 111 faces of platinum. Several results emerge that should apply generally, not just to platinum. These results are generic consequences of water molecules binding strongly to surfaces that are incommensurate with favorable hydrogen-bonding patterns. We show that adlayers of water under these conditions have frustrated structures that interact unfavorably with adjacent liquid water. We elucidate dynamical processes of water in these cases that extend over a broad range of timescales, from less than picoseconds to more than nanoseconds. Associated spatial correlations extend over nanometers. We show that adlayer reorganization occurs intermittently, and each reorganization event correlates motions of several molecules. We show that soft liquid interfaces form adjacent to the adlayer, as is generally characteristic of liquid water adjacent to a hydrophobic surface. The infrequent adlayer reorganization produces a hydrophobic heterogeneity that we characterize by studying the degrees by which different regions of the adlayers attract small hydrophobic particles. Consequences for electrochemistry are discussed in the context of hydronium ions being attracted from the liquid to the metal–adlayer surface.

Extended metal interfaces play a fundamental role in aqueous electrochemistry, a field of principal importance in the advancement of renewable, clean energy sources (1, 2). In many processes that occur at metal interfaces, such as electrolysis, corrosion, and electrocatalysis, water is ubiquitous, often acting as both solvent and reactant (3). Although many studies exist that detail the behavior of water across small length scales and timescales (4–7) and at low temperatures (8–10), at present there is little understanding of the large length scale correlations and emergent behavior of water on metal surfaces, even though such effects are likely to influence function in important ways (11–14). Here, we address this gap in knowledge with a theoretical model of the interactions between water and a metal surface. Specifically we illustrate how a metal surface can impose geometrical constraints within the adlayer of water, leading to a composite metal–water interface that is hydrophobic on large length scales. We further show how defects within the hydrogen-bonding patterns of the adlayer create transient regions of hydrophobic behavior that exist on small length scales and over long timescales. These results offer a microscopic explanation and generalization of previous experimental observations that have inferred hydrophobicity of a platinum surface at low temperatures (15–17).

To study the aqueous metal interface we use a molecular model (6, 18) that neglects explicit electronic degrees of freedom beyond accounting for electronic polarization of the metal. Despite its relative simplicity, the model is in reasonably good agreement with experimental values for the potential of zero charge and capacitance values of the aqueous platinum interface (11). (This particular property—the potential of zero charge—is discussed further in Methods.) The model is not designed to reproduce many intricate details manifested at low temperature and near vacuum conditions (8). Rather, it is designed to capture generic behavior of liquid water at standard conditions in contact with a metal surface. The behaviors we find in this way are expected to be general, and as we illustrate below, our principal results are qualitatively insensitive to many details of the underlying surfaces.

Accurate knowledge of the single-molecule binding energy of water to a platinum surface is currently unknown; however, quantum chemical calculations (19) and experimental thermal desorption measurements (10) yield a range spanning 0.3–0.6 eV. These energies are larger than typical hydrogen bond energies, which are ≲0.25 eV (10). The model used here (6) has been parameterized to recover this relatively strong attraction with binding energies of 0.46 eV and 0.37 eV for the 100 and 111 surfaces, respectively. The single-molecule geometries predicted by the model are in reasonable agreement with quantum chemical calculations (19), including predicting the relative stability of top site binding over bridge site binding by 0.2 eV (20).

These features of single-molecule geometries and binding energies depend weakly on the structure of the exposed metal. In contrast, the behavior of a full monolayer of water is sensitive to the underlying metal surface structure. This sensitivity at high coverage is the result of competition between water–metal and water–water interactions, is mediated by geometry, and for the platinum 111 surface results in the ground state (8). The model we use reproduces crucial features of the structure: the preference for water to bond predominately in the plane of the monolayer and the preference of nonbonded hydrogens to point toward the metal rather than away. These features, we shall see, are responsible for the hydrophobicity and heterogeneity of the hydrated metal surface. The model also reproduces the preference in the structure for local hexagonal rings of waters on top sites of the metal. On the other hand, the model is not sufficiently comprehensive to capture the formation of five- and seven-membered rings that also appear in the structure. Those details are interesting and possibly important in other contexts, but they are specific to Pt, and they do not change the generic features relevant to this work that the metal surface dictates a structure of the water monolayer that is both frustrated and incapable of favorable bonding to the adjacent liquid.

Using this model we can access length scales and timescales far beyond those currently available to ab initio calculations. We find that water adlayers on metal surfaces are hydrophobic, and the degree of hydrophobicity depends on the amount of passivation of the hydrogen bond network within the adsorbed water layer. Strong, favorable interactions pin the oxygens of water to the top sites of the crystal lattice, creating a spatially ordered arrangement of molecules. This paper considers two surfaces of a planar metal surface, whose geometry and lattice spacing most closely correspond to the 100 and 111 platinum surfaces. In both cases, the imposed water structures allow for facile hydrogen bonding within the adlayer and subsequently only a few, fleeting, hydrogen bonds are donated from the adlayer to the surrounding bulk. Although the adsorbed oxygens at both surfaces still afford hydrogen bond acceptor sites, the asymmetry associated with lacking donor sites results in an interface that is liquid–vapor-like in the sense that large density fluctuations occur through the collective formation and deformation of an interface (21).

Even though the underlying metal lattices we study are ordered, over large length scales the planar geometry of the surface is incommensurate with water’s preferred tetrahedral structure. A consequence of this frustration is the presence of an equilibrium number of defects in the hydrogen bond network within the adlayer. These defects facilitate reorganization within the surface and the resulting dynamics are heterogeneous and relax on timescales larger than nanoseconds. The characteristic time for this surface relaxation, τ_s ≲ 1 ns, is much larger than that for typical equilibrium density fluctuations in the bulk liquid, τ_b ∼ 5 ps. Therefore, although the presence of the surface introduces a static inhomogeneity, the water bound to this surface introduces a dynamic inhomogeneity. The resultant separation of timescales between bulk and surface reorganization is illustrated in Fig. 1. Fig. 1, Upper shows snapshots during slow reorganization of the surface water dipoles, whereas Fig. 1, Lower illustrates faster interfacial fluctuations.

Fig. 1.

Illustration of the separation of timescales between reorganizing surface configurations, which occurs on average every τ_s, and reorganizing the bulk density, which occurs on average every τ_b. Small tick marks are separated by 20 ps, which is on the order of although larger than timescales for typical density fluctuations. Large tick marks are separated by 100 ps, which is on the order of the typical relaxation times for relevant interfacial fluctuations.

These two features of the metal interface, the static heterogeneity of the extended interface and the slow dynamics of water at its surface, cause a decoupling of ensemble and dynamic averaging on timescales t < τ_s. The decoupling implies that for a given configuration of the adlayer, liquid water swiftly equilibrates, and for t ≫ τ_b the properties of the subsequent hydration layers are in dynamic equilibrium. Over intermediate timescales, however, temporal heterogeneity of the hydrogen bond network couples to the dynamically heterogeneous properties of the interface.

The next section illustrates the dependence of the adlayer structure with the exposed metal surface geometry and shows how the passivation of the hydrogen bond network on the surface creates a liquid–vapor-like interface that attracts hydrophobic particles. The subsequent section shows how frustration of the water structure on the surface, coupled with a separation of relaxation times between the surface and bulk, creates temporal regions of spatially heterogeneous hydrophobicity that decays over nanoseconds. We then discuss how the effects we have detailed can influence electrochemical properties. The techniques we apply to simulate this system are outlined in Methods and in our earlier paper (11).

Static Heterogeneity of the Extended Metal Interface

Equilibrium adlayer structures can exhibit incomplete surface coverage, the extent of which depends on surface geometry and reflects a competition between adsorption and hydrogen-bonding energetics (20). The interplay between water–metal and water–water interaction energetics is reflected in the structural motifs present on the different crystal faces. Fig. 2 A and C shows characteristic snapshots of the adlayer of water for both surfaces obtained from our simulations, as well as their subsequent effect on wetting (Fig. 2 B and D). (A liquid phase lies above the pictured metal surfaces and adlayers in Fig. 2 A and C, but the liquid molecules are not rendered.) For the 100 surface, metal atoms are locally fourfold coordinated and are commensurate with a 2D projection of local hydrogen-bonding patterns. As a result, the structure of water on the surface is highly ordered with water dipoles oriented parallel to the surface and approximately all top sites are occupied. At any particular instant, however, line defects exist on the surface, separating planes of dipole aligned molecules by 90° turns in their orientations. For the 111 surface, metal atoms are locally sixfold coordinated and although they also have lattice spacings that are commensurate with a hydrogen bond, the sixfold coordination frustrates preferred bonding patterns. As a result this surface has regions of local hexagonal order, rings of water surrounding a vacancy, that are seen in the monolayer structures of water absorbed on the 111 surface of many face-centered cubic (FCC) metals (22). Because such a hexagonal arrangement cannot tile space, this surface also has a fluctuating concentration of interstitials that occupy the empty top sites with water dipoles that point away from the surface on average. This disorder results in an average coverage of about 85% of all top sites. For both surfaces the lattices are entirely regular, and therefore the heterogeneity in the hydrogen-bonding network is dynamic. However, the imposed order within the adlayer dictates that relaxation occurs over long timescales. Similar hydrogen-bonding defects have been observed experimentally under ultrahigh vacuum conditions at low temperatures on Pd(111) (23) and in water-hydroxyl films on Cu(110) (24).

Fig. 2.

Sections of the 100 and 111 adlayers, each measuring 3 nm², and their effect on macroscopic solvation. (A) The 100 surface is locally four coordinated and commensurate with favorable hydrogen-bonding patterns. Large ordered domains are separated by line defects. (B) The highly ordered domains donate few hydrogen bonds to the subsequent water layers, discouraging those layers from wetting the composite metal–water surface. (C) The 111 surface is locally six coordinated and frustrates hydrogen bonding. Although water is still ordered, vacancies and interstitial defects are common. (D) Hydrogen bond donor sites are more common than on the 100 surface, and subsequently the contact angle is smaller.

The presence of extended interfaces in solution, such as the solvated metal surface, is expected to influence the properties of subsequent solvent layers over distances corresponding to the bulk correlation length. For a liquid near coexistence with its vapor, such as water at ambient conditions, extended inhomogeneities can give rise to a dewetting transition (21), whose interfaces subsequently have larger correlation lengths. Fig. 3A graphs the mean density of water molecules as functions of the distance away from the metal surface. Although the structure on the adlayer depends intimately on the metal geometry, the surrounding water is fairly insensitive to the exposed crystal face. We find for both surface geometries that the density profile for water away from the interface exhibits a sharp peak at the metal surface, indicative of the adlayer, followed by a region of a density depletion ∼3 Å thick. Density oscillations decay over 1 nm away from the surface. The asymmetry between hydrogen bond donors and acceptors at the interface results in an unbalanced attraction; however, the effective interaction with the surface is not so weak so as to allow the formation of capillary waves that would destroy the density oscillations seen away from the metal.

Fig. 3.

Structure and solvation of the composite water–metal interface. (A) The density profile of water molecules away from both surfaces, divided by the bulk water density, ρ_w = 0.033A⁻³. The density is characterized by a strongly bound adsorbed layer and solvent layering that extends roughly 10 Å into the bulk. Immediately adjacent to the adsorbed layer is a region of density depletion. (B) The excess solvation free energy for a 3 Å in radius ideal hydrophobe as a function of distance away from the 111 and 100 surfaces. The dashed lines in A and B define z* as the distance of closest approach of the 3-Å sphere to the adlayer. (C) For the 100 surface, shown, or a 111 surface, a typical configuration of water molecules and its instantaneous liquid interface (blue). (D) Probability distribution for finding N particles in a cuboid probe volume, v = 20 × 20 × 3ų, whose outer edge is located at z*, with a mean occupancy . , and 40 for the 100 surface, the 111 surface, and bulk, respectively.

Water–Metal Interface Is Hydrophobic

The unbalanced attraction immediately adjacent to the adlayer is enough to make solvation of ideal hydrophobes (hard spheres) favorable at the interface. Fig. 3C illustrates a representative configuration of water near the interface. In this snapshot, the instantaneous liquid interface constructed using the procedure in ref. 25 shows the characteristic large fluctuations expected for a hydrophobic interface that easily accommodates the solvation of small solutes. Fig. 3B plots the excess chemical potential for a hard sphere with a radius of 3 Å. We calculate this quantity by monitoring the number fluctuations within a probe volume. Specifically, we calculate the probability of observing N molecules in the probe volume, v,

where δ(N_v −N) is a Kronecker delta function and 〈…〉 denotes equilibrium average. This distribution is related to the excess solvation free energy for an ideal hydrophobe through the relation (26)

where Δμ_v is the reversible work to create a cavity of size and shape v and β is one over temperature times Boltzmann’s constant.

For the systems we consider here, the existence of the planar surface breaks translational invariance. To accommodate this aspect we denote, P_v(r)(N), where r is the position of the center of the probe volume. This distribution reduces to P_v(r)(N) → P_v(N) when r is far away from the surface. Correspondingly, we also define P_v(r)(0) = exp[−βΔμ_v(r)]. In other words, solvation free energy in an inhomogeneous system is generally spatially dependent.

Due to the separation of timescales between surface and bulk relaxation, our system is also dynamically heterogeneous. Therefore, on intermediate timescales, τ_b ≪ t τ_s, the solvation free energy carries a time dependence. This time dependence is denoted as

where x₀ denotes the initial surface configuration and t is the timescale over which the distribution is averaged. For t ≫ τ_s, Eq. 3 simplifies to, P_v(r)(N, t; x₀) → P_v(r)(N). For the case of n = 0, Eq. 3 yields a time-dependent generalization of the solvation free energy,

Finally, the difference between the value of the solvation free energy located at r, averaged over a time t, and its equilibrium bulk value is defined as

For t → ∞, δμ_v(r, t; x₀) → δμ_v(r) and for r far away from the surface δμ_v(r) → 0. At long times, and averaged over the plane of the surface, the solvation free energy has a minimum at the distance of closest approach to the composite water–metal surface, z*, indicated by a dashed line in Fig. 3 A and B. The negative solvation free energy implies that whereas the bare metal surface attracts water, the composite water–metal surface is hydrophobic and as such preferentially attracts oil. Although both metal geometries exhibit enhanced hydrophobic solubility, the 100 surface is more hydrophobic as measured by its excess solvation free energy at z*, βδμ_v(z*) ∼ −2.0, compared with the 111 surface, βδμ_v(z*) ∼ −0.7 for the 3-Å sphere. Modulating the strength of the water–metal binding energy up to 30% through changes in the model parameters effects changes in these mean chemical potential values by less than 10%.

Hydrophobicity Is a Manifestation of a Liquid–Vapor-Like Interface

Using the method of indirect umbrella sampling (INDUS) (27) we are able to compute stationary distribution functions, P_v(r)(N), for extremely rare fluctuations involved in solvating large probe volumes. By studying the tails of these distributions we can determine to what extent interface formation, as opposed to Gaussian density fluctuations, is important in solvation at the interface.

The specific dimensions of the probe volume we use are chosen to focus on the role of interfacial fluctuations. In particular, the probe volume is thin enough, 3 Å, to include molecules that can be part of a liquid interface while not also containing molecules that are part of the bulk; and it is wide enough, 20 × 20 Ų, to capture nanoscale fluctuations intrinsic to the soft liquid interface. Fig. 3C shows a configuration of water and the instantaneous liquid interface (25), highlighting how solvation at the surface occurs by deforming a soft interface. The signature of this behavior is demonstrated in Fig. 3D, where highly correlated behavior, interface formation in this case, is apparent by the appearance of an exponential tail in the probability distribution, P_v(r)(N), for small N for both surfaces relative to the bulk.

The pictured distributions along with Eqs. 2 and 4 allow us to calculate the excess solvation free energy for this large probe volume. We find that this is negative at both surfaces; however, solvation for this large probe volume at the 100 surface is more favorable by 40 k_BT compared with the 111 surface. Although both surfaces afford hydrogen bond acceptor sites, only the 111 surface has a nonzero number of hydrogen bond donors. Using a standard criterion for defining a hydrogen bond (28), we calculate an average hydrogen bond donor density on the surface to be ∼1.0/nm² for the 111 surface and 0.0/nm² for the 100 surface. This means that in the large probe volume on the 111 surface, there are on average four hydrogen bonds donated to the bulk. These few hydrogen bonds produce the 40-k_BT change in solvation and it is expected that the addition of further hydrogen bond defects would make the surface hydrophilic.

This microscopic measure of solvation can be related to traditional macroscopic measures probed experimentally. As described above, large length-scale solvation at hydrophobic surfaces is dominated by deforming existing interfaces, so the excess chemical potential is expected to be well approximated by βδμ(z*) = −Aγ_LV(1 − cos θ), where A is the cross-sectional area of a large probe volume, γ_LV is the liquid–vapor surface tension, and θ is the water droplet contact angle on the surface. The more favorable solvation at the surface of the 100 surface is expected to result in a contact angle θ ∼ 90°, whereas the subtly favorable solvation at the 111 surface is expected to result in a contact angle of θ ∼ 40°. These are in qualitative agreement with the configurations shown in Fig. 2.

These results are in agreement with previous experiments on the platinum 111 surface that inferred hydrophobicity under low-temperature ultrahigh-vacuum conditions (15) and in mixed water–hydroxyl overlayers (17). As discussed, the model we use does not account for water dissociation at the surface or produce the correct ground state structure for platinum at low temperatures. However, it simply patterns fully hydrogen-bonded contact layers. For this reason these results are not expected to be unique to water on metals but rather a general result of surfaces that similarly constrain the number of donated hydrogen bonds. Instances of this behavior have already been observed in clays (29) and could potentially be observed in other oxides and even in biological settings (30).

Dynamic Heterogeneity of Slowly Relaxing Surface Water

The data presented in Fig. 3 graph equilibrium values of the excess solvation free energy averaged over the plane parallel to the surface, computed by averaging over long molecular dynamics trajectories, of roughly 10 ns. The presence of a region of strong water density depletion induced by the local structure of the water adlayer implies that only on timescales much longer than the correlation time for typical bulk density fluctuations, τ_b ∼ 5 ps (31), will solvation within this plane be homogeneous; i.e., βδμ(x, y) ∼ const. However, the ordering within this surface adlayer makes reorganization difficult, and as a result the timescale associated with decorrelating surface configurations, τ_s ∼ 1 − 10 ns, is long (Methods). For intermediate times, τ_b ≪ t < τ_s, this long time surface relaxation couples to the solvation in interesting ways. In particular, we find that for averages computed over this time, 1 ns < t < 10 ns, the solvation calculated within the surface is heterogeneous.

Fig. 4 depicts the spatially resolved solvation free energy, βδμ({x, y, z*}, t; x₀) at both surface geometries for a 3-Å sphere, as a function of position in the x, y plane and observation time, for a given surface configuration. This method of spatially resolving the local hydrophobicity is a time-dependent extension of previous work by others on protein surfaces, which have static heterogeneity (32). As shown in Fig. 4 the structure of the solvation on this surface reflects neither the underlying lattice symmetry nor the homogeneous symmetry of the above liquid, but rather the coupling between hydrogen-bonding defect structures of the bound water adlayer and the above solvent layers. We can quantify the surface heterogeneity by calculating a time-dependent variance C(t) = 〈[δμ({x, y, z*}, t; x₀) − δμ(z*)]²〉, where δμ(z*) is an average excess solvation free energy at z* and as before 〈…〉 denotes averages over realizations of initial surface conditions. We find for times satisfying t ≫ τ_b, the spatial average over the surface is equal to the long time average. Using this measure we find that for all times the solvation on the 111 is more heterogeneous than on the 100 surface, owing to the larger domain sizes seen on the ordered bound layer in the 100 surface. These domain sizes are on average ∼1 Ų for the 111 surface and 3 Ų for the 100 surface, as obtained by coarse graining Fig. 4 A and B over 1 k_BT. Fig. 5 A–C shows βδμ({x, y, z*}, t; x₀) as t is increased for the 111 surface. Generically, reorganization on the surface occurs as t is increased, and the amount of heterogeneity is reduced. Similar behavior is found for the 100 surface. To quantify the timescales for relaxing this heterogeneity we measure the decay of C(t)/C(0), where the argument of the denominator is taken at the smallest t where τ_b ≪ t ∼ 0.5 ns. Fig. 5D plots C(t)/C(0) for both surfaces and illustrates that the time to reach a uniform solvation potential at the surface is on the order of 10 ns. This time is on the order of many of the slow processes that occur on the metal surface such as the mean dipole correlation time 1–10 ns.

Fig. 4.

Heterogeneous solvation at the metal surface. (A and B) The excess free energy for a 3-Å ideal hydrophobe is heterogeneous at both 111 and 100 surfaces. Regions of favorable and unfavorable solvation have been determined by averaging over 1 ns from an initial surface configuration, x₀.

Fig. 5.

Evolution of the solvation free energy as the surface reorganizes from an initial configuration, x₀. (A–C) Maps of the excess free energy averaged over different observation times for a 1-nm² section of the 111 surface. Contour plots are reported using the same scale shown in the color bar (Left). (D) The time correlation function for solvation heterogeneities for each surface. Points a, b, and c coincide with times for A, B, and C.

Implications for Electrochemistry

In this paper, we have shown that a hydrophobic surface formed from a passivated adlayer of water is accompanied by the existence of a liquid–vapor-like interface separating the adlayer from the bulk liquid. Previous work has discussed how such a soft liquid interface can itself act catalytically, offering a dangling OH bond that can stabilize transition states or donate protons (33). Others have demonstrated that excess protons (34, 35), as well as some anions (36), preferentially adsorb to a liquid–vapor interface.

As one means of testing the assertion of a proton enhancement at the water–metal interface, we have calculated the density profile for a fixed point charge model of a hydronium (37) cation, using umbrella sampling. We chose this model as it has been shown previously that excess protons at the liquid–vapor interface preferentially adopt a hydronium geometry over other forms, such as the Zundel cation (34, 35). The local solvation structure of a hydronium in bulk is characterized by donation of a hydrogen bond by each of its three hydrogens, but also its inability to accept any hydrogen bonds at the oxygen position due to the localized positive charge on the molecule. It has been demonstrated previously that this structure is conserved at the liquid–vapor interface (34).

At the water–metal interface the adlayer is composed almost entirely of hydrogen bond acceptor sites and thus it is expected that the density of hydronium ions will be even further enhanced by their ability to donate hydrogen bonds into the adlayer. A characteristic snapshot of this type of configuration at the 111 surface is shown in Fig. 6, Inset. Fig. 6 confirms a large density enhancement of hydronium ions at the interface relative to the bulk. This density distribution is calculated from , where ρ_ref is the density of the hydronium in the bulk and F(z) is the potential of the mean force for moving the center of mass of the hydronium along the z direction. The enhancement found from this simplistic calculation is ρ(z*) ∼ 10ρ_bulk, much larger than the enhancement found at the liquid–vapor interface, which for this model we calculate to be 1.5ρ_bulk. We note that whereas important aspects of proton delocalization and polarizability are neglected in this calculation, each effect is expected to further enhance interfacial adsorption. Thus, whereas this calculation is overly simplistic, we nevertheless suspect this behavior to be conserved in more detailed models.

Fig. 6.

Structure and density enhancement of hydronium ions at the liquid–vapor and water–metal interface. Shown are density distributions for water (gray) and hydronium (blue), with a reference bulk density of the hydronium, ρ_ref = 0.1 g/cm³ chosen for scale. (Inset) Characteristic snapshot of H₃O⁺ at the 111 interface.

In the specific case of hydrogen evolution at a platinum electrode, it is generally assumed that the reaction proceeds through two steps: the Volmer step, where a proton is transferred from the bulk and discharged at the metal surface, followed by the Tafel step where two adsorbed protons combine to form hydrogen and desorb from the surface (38). The latter is considered to be the rate-determining step. The enhancement of the hydronium concentration at the interface is consistent with platinum’s ability to easily transfer and accumulate protons on and near the surface, whereas the long time relaxation on the surface detailed here undoubtably makes diffusion of adsorbents slow. Although these results are consistent with mechanistic assertions for hydrogen evolution, further work must be done to explore the full implications of the effects illustrated here on catalysis.

Methods

The system simulated consists of a slab of water in contact with a metal on one side and with a free interface on the other side with a vacuum layer of 40 Å. The metal surface consists of three layers of atoms, totaling nearly 500 particles, held fixed in an FCC lattice with spacing of 3.92 Å and with either the 100 or the 111 facet exposed to the solution. A slab of water nearly 40 Å thick was placed in contact with the metal, and the dynamics of the nearly 1,800 molecules were propagated using a Nose Hover integrator (39), with SHAKE imposing bond and angle constraints for the water as implemented in LAMMPS (40). All simulations were run at 298 K. Interactions between the water molecules were computed from the SPC/E potential (18). The water–metal potential is modeled following Siepmann and Sprik (6), where the platinum water interaction is a sum of two and three body terms, parameterized to get the correct value of the adsorption energy and ground-state geometry as determined by quantum chemical calculations. Additionally, to model the polarizable metal surface each atom carries a Gaussian charge of fixed width but variable amplitude, which is updated at each time step by minimizing the energy of the slab subject to a constraint of equal potential across the conductor. Periodic boundary conditions are used in the plane parallel to the surface. Ewald summations appropriate for mixed-point and Gaussian charge densities were used (41). A more thorough description of the model can be found elsewhere (6, 11). The calculations of the excess hydronium ion were accomplished using umbrella sampling along the z coordinate. For charge neutrality a small anion was placed in the water slab but kept at distances greater than 15 Å from the hydronium.

As discussed, relaxation of the water on the metal surface is slow. To quantify the timescales associated with surface reorganization we calculate a water’s dipole time correlation function given it starts and ends adsorbed to the surface, , where is the dipole vector for the i water molecule and h_i is an indicator function that is equal to 1 if the center of mass of the water molecule i is within 3 Å of a metal atom and is 0 otherwise. Correlation functions for both surfaces have stretched exponential forms and decay over timescales greater than 1 ns.

The long relaxation times in the system relative to the timescales accessible by our simulations make ensuring equilibration on the surface difficult. To check the sensitivity of our results to their initial conditions we have prepared an ensemble of 40 independent surfaces, for both the 100 and 111 crystal faces. Twenty surfaces were produced through quenching the system at a rate of 10 K/ns from a system equilibrated at T = 400 and 20 from a process of vapor deposition where water molecules are exposed to the surface at a rate of 2 molecules/1 ns nm². We have redone all of the calculations presented in the main text over this extended surface ensemble and found results that were indistinguishable from those presented above.

Using our atomistic model for the water–metal interface, we compute the potential of zero charge, U_pzc, relative to the hydrogen electrode to compare it to the known experimental value (42). Previous work has shown that the surface dipole induced by the adsorption of water on a platinum surface can be decomposed into two components: an indirect polarization of the metal surface and a direct contribution from the dipoles of the water. Whereas the latter effect is strongly dependent on surface coverage and instantaneous configuration of the adsorbed water, the former is relatively constant. Thus, although the classical model we use here is expected to underestimate the polarization contribution, we would expect a reasonable estimate for the direct water contribution. For the 111 surface, the contact potential across the water bilayer we measure is ψ_D = −0.7V. Using the polarization contribution found from quantum chemical calculations, ψ_P = 1.2V (43), we calculate the potential of zero charge to be U_pzc = 0.9V compared with the experimental value of U_pzc = 0.4V (43).