Electric-Field Effects on Adsorbed-Water Structural and Dynamical

Aug 25, 2016 - (14) Tilocca and Selloni(15) have performed Car–Parrinello MD (CPMD) simulations of pristine and defective anatase (101) surfaces wit...
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Electric-Field Effects on Adsorbed-Water Structural and Dynamical Properties at Rutile- and Anatase-TiO2 Surfaces Zdenek Futera* and Niall J. English* School of Chemical and Bioprocess Engineering, University College Dublin, Belfield, Dublin 4, Ireland S Supporting Information *

ABSTRACT: We have investigated the effects of external static electric fields applied to a wide variety of TiO2/water interfaces using nonequilibrium molecular-dynamics techniques. The externally applied electric fields were found to be relatively weak vis-à-vis intrinsic electric fields computed in the interfacial regions, the magnitude of which varied from 1.8 V/Å toward bulklike water up to 4.5 V/Å at the interface. The molecular arrangement of the first hydration layer is determined fully by the surface structure of TiO2, where water is coordinated to unsaturated titanium atoms and/or interacting with exposed surface oxygen atoms. Moreover, the water dipoles tend to align with the strong intrinsic field. As a result, diffusion of water in this region was found to be by 1 order of magnitude lower than that of bulk water; application of an external electric field did not lead to a considerable change. In contrast to unperturbed diffusivity, a rather strong response of hydrogen-bond lifetime to the applied field was observed. The interfacial water is heavily confined, although the extent to which shows marked variation with specific surfaces; indeed, this environmental interplay has considerable effect on corresponding IR spectra in the interfacial-water region, and is affected by applied static fields.

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INTRODUCTION Titanium dioxide (TiO2, known popularly as titania) is widely investigated for many important technological applications, such as hydrogen production, and the degradation of environmentally harmful organic compounds.1−4 Three polymorphs of TiO2 can be found in nature: rutile, anatase, and brookite. Although rutile is the most thermodynamically stable phase in bulk, anatase is often found in nanomaterials.5,6 From a technological perspective, rutile (110) and anatase (101) surface facets are the most important.7,8 However, in spite of titania’s great potential importance at titania−water interfaces for catalysis,9 understanding of their behavior, particularly the rich tapestry of interfacial-water physicochemical properties and subtleties, is still rather limited. From inelastic neutron scattering experiments, it is known that the interfacial water is confined, the absorbed water molecules on TiO2 surfaces being less mobile, with their dynamical and vibrational features exhibiting behavior more redolent of ice than liquid water.10,11 Many theoretical studies have been performed on TiO2 surfaces in vacuo, and, later, also on their water interfaces using first-principles approaches based on density functional theory (DFT) in most cases.12 Aschauer et al. have assessed the influence of defects on anatase (101) surfaces, focusing on water adsorption energies at defective sites, confirming there is greater propensity for water dissociation,13 while Cheng et al. have considered hydroxide ions at these surfaces.14 Tilocca and Selloni15 have performed Car−Parrinello MD (CPMD) simulations of pristine and defective anatase (101) surfaces with one, two, and three layers of water adsorbed thereon, © XXXX American Chemical Society

reporting that defect structures alter the structure of the adsorbed water layers and enhance surface reactivity. Sun et al. have studied interactions of water with these anatase surfaces covered by fluorine, and concluded that the presence of fluorine tends to reduce water dissociation.16 Aschauer and Selloni have examined rutile (011) surfaces, and found via CPMD that the interaction with fuller coverage of water leads to a different surface reconstruction than under vacuum or low-coverage conditions.17 For rutile (110) surfaces, Lee et al. have examined the diffusion of CO2 and also the formation of water chains thereon.18,19 The computed activation energy barriers for various different directions of CO2 diffusion along the surface were reconciled with scanning tunneling microscopy (STM) insights,18 while further STM measurements and DFT calculations have elucidated structure and hydrogen-bonding arrangements as water coverage (from monomer to chain) and temperature increase.19 There has been some extensive debate in the recent literature on the extent of chemical adsorption of water on rutile (110) surfaces, if any;20−22 this is naturally dependent on temperature and coverage. Molecular dynamics (MD) has been useful to some extent in characterizing the dynamical and vibrational behavior of adsorbed water molecules on rutile (110) and anatase (101) surfaces.23,24 Indeed, ab initio MD (AIMD), especially, has offered key insights into the librational motion of higherReceived: February 25, 2016 Revised: August 9, 2016

A

DOI: 10.1021/acs.jpcc.6b01907 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C frequency modes of adsorbed water in very interesting recent studies.24,25 In particular, the rutile (110)−water interface has been studied in much detail via MD.26−32 Zhang et al. have investigated ion adsorption,26 while Predota et al. have probed the electric double layer structure,27−29,33 and have studied the nature of the water layer structure,27 ionic adsorption,28 viscosity and diffusivity of the water layers,29 and dielectric properties of the interfaces.33 In particular, diffusivity was seen to increase toward bulklike values further away from the surface,29 which is in accordance with accurate scattering experimental measurements of Mamontov et al.34,35 Machesky et al. have studied surface protonation effects.30 We have studied recently the structure of water at interfaces with anatase and rutile facets by classical MD simulations.36,37 Later, we explored dynamical properties of these interfaces, namely the lifetime of the interfacial hydrogen bonding and the vibrational densities of states (VDOS);38−40 we also investigated this via ab initio MD.41 Although the DFT-based studies previously mentioned12−22,26,41 have undoubtedly large consequences on understanding of titanium dioxide reactivity and electronic structure, they often suffer from imperfect DFT functionals and the limited size of the studied systems. In particular, the application of external electric fields in DFT simulations of metal oxide/water interfaces has been, by and large, neglected in the past following formulation of the Berry phase approach to polarization in solids.42 For the investigation of structural and dynamical properties of interfacial water, such as selfdiffusivity or vibrational spectra, in either the absence or presence of externally applied electric fields, long simulation times and good statistics are necessary, using well-tested empirical potentials, to glean a rigorous insight thereto.43 In the present work, we focus on the effect of static electric fields on the structure and dynamics of interfacial water layer at a wide variety of titania surfaces. In the first part of the article, we focus on the structure of the first hydration layer at various TiO2 surfaces, and especially on the investigation of intrinsic electricfield strength and variations thereof in this interfacial region. We show that this intrinsic field is a dominant and crucially important factor, affecting not only the interfacial-layer structure, but also diffusion and vibration of water thereat; we discuss this hitherto-unappreciated insight in the second part of this study.

Table 1. Side Lengths of the Orthorhombic Simulation Supercells a, b, and c, Thickness of the TiO2 Slab ΔZTiO2 Measured from Bottommost to Topmost Atom (ZTi), and Width of the Water Interface Layer ZWat Measured from ZTi [Å]a surface

a

b

c

ΔZTiO2

ZWat

anatase (001) anatase (101) rutile (001) rutile (100) rutile (101) rutile (110)

26.495 26.495 32.088 32.088 32.088 23.624

30.280 40.956 36.672 23.624 21.812 45.381

94.508 69.873 63.273 98.219 106.379 69.450

17.4 12.9 10.3 17.8 18.9 12.3

5.7 5.7 4.9 4.9 5.2 5.8

a

Each supercell contains 224 TiO2 units and 2000 water molecules. Lower surface of the TiO2 slab is located at the bottom of the cell (z = 0).

noted that the used model cannot describe hydrogen transfer from one molecule to another and the simulations do not involve any dissociation processes. In this work, we are focusing on the changes of water orientation and their response to external electric fields, rather than (electro)chemical changes at the interfaces. Positions of atoms in TiO2 slab were kept fixed in all performed calculations. Referring to Figure 1, anatase (101), the most photoactive polymorph of titania, exhibits a terracelike structure formed by 5-coordinated titanium atoms (Ti5c) and 2-coordinated oxygens (O2c). These two atom types are present also on the flat surface of anatase (001); however, this surface is unstable, inclining to undergo reconstruction and thus experimentally less significant. On the contrary, rutile (110) is the most thermodynamically stable surface of titania formed by 5-coordinated and 6coordinated titanium atoms (Ti5c and T6c, respectively) which are interconnected by 3-coordinated oxygen (O3c).2,3 Bridging, 2-coordinated oxygen atoms (Ob) are exposed above the surface to the interfacial region and they are, together with unsaturated Ti5c, natural reactive sites at the surface. The rutile (100) surface is similar the rutile (110); however, the Ti5c− O b −Ti 5c bridging plane is inclined here rather than perpendicular to the surface, and forms the “ridging” structure typical for this surface. This tilted pattern can be found also on the rutile (101) surface, where “chains” of 2-coordinated oxygens O2c are attached to rows of surface Ti5c atoms. Finally, 4-coordinate atoms of titanium (Ti4c) characterize rutile (001) surfaces, which are connected to O2c and arranged to form a corrugated, ridgelike structure. Large coordination unsaturation of this surface makes it the least stable one, and inclined to spontaneous reconstruction.2,3 Classical MD simulations were performed in the microcanonical (NVE) ensemble, using DL_POLY 4.07,48 after careful equilibration of the system in the canonical (NVT) ensemble to reach the desired temperature of the system. The velocity Verlet scheme49 was used to integrate equations of motion with a time step of 0.5 fs, while the temperature 300 K was maintained by a Nosé−Hoover chain thermostat.50,51 The production trajectories were 500 ps long, which was found sufficient for investigation of discussed properties. No temperature or pressure drifts were observed in the simulations. Longrange electrostatic interactions were evaluated under periodic boundary conditions (PBC) by the smooth particle-mesh Ewald (SPME) summation,52 with a precision of 10−8. A cutoff of 10 Å was applied to short-range van der Waals interactions. Static external electric fields of 0.05, 0.10, 0.15, 0.20, and 0.25

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COMPUTATIONAL DETAILS Models of TiO2 anatase (001) and (101) and rutile (001), (100), (101), and (110) surfaces were prepared by cutting bulk anatase (I41/amd space group, tetragonal lattice, a = 3.785 Å, c = 9.514 Å) and rutile (P42/mnm space group, tetragonal lattice, a = 4.593 Å, c = 2.959 Å).44 Supercells of each model, containing 224 TiO2 units, were expanded in the z-direction perpendicular to the surface to accommodate 2000 water molecules, such that the bulk density thereof was 1 g/cm3. The resulting cell dimensions are summarized in Table 1, and snapshots of equilibrated interfacial structures are shown in Figure 1. Owing to its relatively good performance for titania,36−40 the systems were described by Matsui and Akaogi’s45 empirical potential for TiO2 with parameters reported by Bandura et al.46 and Predota et al.27 The flexible SPC model was used for water,47 wherein the Hw−Ow−Hw valence angle is described by harmonic potential, while a Morse stretching potential is applied for Hw−Ow bonds. Although the Morse potential allows changes of the bond lengths, it must be B

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Figure 1. Snapshots of TiO2/water interfacial structures: (a) anatase (001), (b) anatase (101), (c) rutile (001), (d) rutile (100), (e) rutile (101), and (f) rutile (110). Titanium atoms are shown in brown, with oxygen atoms in red. Only the first hydration layer is shown.

V/Å intensities were applied in the z-directionperpendicular to the TiO2 surfaces. The field intensities (corresponding to 500 V applied to coplanar electrodes spaced by 1 μm in the case of 0.05 V/Å) were chosen in order to explore the linearresponse regime43 where only reorientation of water molecules can be expected, and the forces experienced by the atoms due to the external field are no more than a few percent of those experienced in the condensed phase under zero-applied-field conditions. We have also investigated effects of a weaker field of 0.01 V/Å; however, those are hardly detectable, as already pointed out by Parez et al.33 Water Ow−Hw bond lengths, Hw−Ow−Hw valence angles, and individual-water dipoles were calculated for each structure sample, collected to normalized histograms P(x), and their mean values were obtained by integration as ⟨x⟩ = ∫ xP(x) dx. Similarly, histograms of bond lengths, angles, and average numbers of hydrogen bonds were collected. The hydrogen bonds were selected by geometry criteria for donor (D), acceptor (A), and hydrogen (H) arrangement: the maximum allowed distance between donor and acceptor was 3.5 Å and the A−D−H angle was required to be less than 35°. For characterizing the dynamics of hydrogen bonds, we used the Luzar−Chandler model53 to calculate the average hydrogenbond lifetime. Water density profiles were calculated from the sampled trajectories and normalized to the bulk density of water (i.e., 1 g/cm3). The self-diffusion constant of water was obtained as the limit of mean-square displacement using the Einstein relation: D=

⟨(r(t0 + t ) − r(t0))⟩ 1 lim t →∞ 6 t

D=

1 3

∫0

∞

⟨v(t0) ·v(t0 + t )⟩ dt

(2)

The autocorrelation function was computed on the basis of Wiener−Khintchine relations54,55 employing fast Fourier transform (FFT) algorithm with efficient O(n log n) scaling: ⟨f (t0) f (t0 + t )⟩ =

1 2π

∫ | ∫ f (t′)e−iωt′ dt′|2 eiωt dω

(3)

Finally, the IR spectrum was computed as a power spectrum of the system-collective-dipole autocorrelation function I(ω) ∝ ω 2

∫ ⟨M(t0) M(t0 + t )⟩e−iωt dt

(4)

where M(t) can be written as sum of individual water dipoles M(t) = ∑i μ(t).

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RESULTS AND DISCUSSION First, we calculated density profiles of water; this demonstrates clearly the layered structure of the aqueous part of the interface. The density profiles shown in Figure 2 were obtained as the distribution of water oxygen (Ow) atoms in a direction perpendicular to the TiO2 surface, collected in bins of 0.1 Å widths. The reference point of the distribution was chosen as the position of the topmost Ti atom layer on the corresponding surfacenote that further details on the positioning of the TiO2 systems are provided in Table 1. Examining the anatase surfaces, a relatively wide hydration monolayer is formed 2.45 Å above the (001) interface, while the layered structure of the (101) interface indicates the presence of three types of water− TiO2 interactions in the first hydration shell. These are the water molecules adsorbed by Ow to Ti5c (first peak at 2.01 Å), water molecules hydrogen bonded by Hw to two neighboring O2c’s (2.58 Å), or water molecules hydrogen bonded by Hw to just one O2c (3.17 Å) as can be seen also in Figure 1. The hydrogen bonding is weaker than the adsorption to Ti5c, and

(1)

For comparison, the diffusion constant was also evaluated by the Green−Kubo relation as the integral of the velocity autocorrelation function C(t) = ⟨v(t0)·v(t0 + t)⟩ accumulated from 32-ps-long trajectories which were propagated with a 0.2 fs time step and sampled each 4 fs: C

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emerges from the surface tilted pattern. On the (001) interface, all water molecules are coordinated by Ow to Ti4c, with two unsaturated coordination sites. The second peak at 4.43 Å represents here the true second hydration layer of water molecules, which do not interact directly with the TiO2 surface. Finally, the most stable and abundant rutile (110) displays an interfacial structure rather similar to those of the (001), (100), and (101) facets. The first peak indicates the position of water molecules coordinated by Ow to the surface Ti5c atoms, while the second peak at 3.67 Å originates from water molecules Hbonded to Ob rows by their Hw. These two types of interfacial water interact together by hydrogen bonding, as can be seen also in Figure 1. The structure rearrangement of hydrogenbonded water layers as a result of applied external electric field, similar to that observed on anatase (101), can be seen on rutile (101) and (100) and partially on rutile (110). Next, we investigated how the average structure of a single water molecule changes in the interfacial region compared to bulk water. The width of the interface region in each model was set according to the water-density profile as indicated in Figure 2 and in Figure S1 in the Supporting Information. The numerical values of the TiO2 slab width and the interface water layer thickness are listed in Table 1. We calculated the distributions of Ow−Hw bond lengths and the Hw−Ow−Hw valence angle, which can be found in the Supporting Information, and their mean values at zero-field conditions are collected in Table 2. Except for anatase (001), where the

Figure 2. Density profile of water Ow atoms in the interfacial region. Zero-field profiles (solid red) as well as profiles affected by the static electric fields (0.10 V/Å in dashed green and 0.25 V/Å in dashed− dotted blue) applied in the surface-perpendicular direction are shown for comparison. Interfaces with surface normal parallel to the applied field are shown on the left-hand sides; those with surface normal antiparallel are on the right-hand sides. The vertical dashed green lines mark the boundary of the interface region.

Table 2. Average Values of Ow−Hw Bond Length d [Å], Hw− Ow−Hw Valence Angle φ [deg], and Dipole Moment [D] of Water Molecule in Interfacial Region of TiO2 Surfaces at Zero-Field Conditionsa

therefore the water distribution contribution to the latter two peaks is clearly affected by the applied static electric field up to a magnitude of 0.25 V/Å. The hydrogen-bonded molecules have their dipole moment oriented toward the surfacethat is, in the antiparallel surface direction. Therefore, the applied external field weakens the hydrogen-bond interaction on the parallel surface, and the water molecules are pushed further from the interface to 3.17 Å distance and the 2.58 Å peak disappears at an applied field of a magnitude of 0.15 V/Å and higher. Naturally, the opposite effect can be seen on the antiparallel interface where the hydrogen-bonded water molecule is pushed closer to the TiO2 surface by the external field. No such substantial interface-layer rearrangement can be seen on the less structured anatase (001) surface, although the slight response to stronger static electric fields is detectable there. In contrast to anatase (101), all studied rutile interfaces exhibit only a single water-density peak associated with the first hydration layer. These can be ordered from nearest to furthest as (100) ≤ (001) < (101) < (110) corresponding to positions at 1.53, 1.55, 1.79, and 2.12 Å, respectively, from the topmost surface Ti atom. The first peak of the rutile (100) density profile stems from practically immobilized water molecules, confined in the surface ridges by Ow coordination to Ti5c and simultaneous hydrogen bonding by Hw to the nearest row of Ob. The second pair of peaks at 3.52 and 4.18 Å corresponds to the hydration shell of Ob atoms, which is exposed above the surface ridges, and is thus more flexible. Therefore, only this part of interfacial water is, to some extent, affected by an applied external electric field. However, the less-structured water layers at the rutile (001) interface are similar to those observed on the same facet of anatase, while rutile (101) resembles the interfacial structure of the rutile (100), which

a

surface

d [Å]

φ [deg]

μ [D]

anatase (001) anatase (101) rutile (001) rutile (100) rutile (101) rutile (110) bulk water

1.020 1.027 1.031 1.023 1.022 1.024 1.018

105.33 103.59 102.91 104.54 105.07 104.54 105.39

2.45 2.52 2.54 2.48 2.47 2.49 2.44

For comparison, bulk water values are also included.

changes are negligible, the average water bond length increases in the interfacial region by 0.4−1.3% from its bulk value of 1.018 Å while the valence angle is reduced by 0.4−2.4% from 105.39°. Since we used a nonpolarizable water model with constant atomic charges, the structural changes of interfacial water molecules directly affect their dipole moments. These are increased from the bulk 2.44 D by 1.6−4.4% in the interface at zero-field conditions, as can be seen in the last column of Table 2, as well as in distributions shown in the Supporting Information. Looking at the water molecule dipole change as a response to applied external field, we can divide the TiO2 facets into two groups. The first, represented by anatase (101) and rutiles (100) and (101), reflect the external field by structural changes in the interface region that we discussed above, and the molecular dipole is not considerably changed there. On the other hand, anatase (001) and rutiles (001) and (110) compensate the external field by the visible change of the molecular dipole, as shown in Figure S8. The greatest dipole change exhibits the rutile (001) facet where little change in water density on the interface was observed (see Figure 2). D

DOI: 10.1021/acs.jpcc.6b01907 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C Although the position of the first hydration shell is kept by strong Ow coordination to Ti4c, the water molecules relax their position on the surface by reorientation of their hydrogen atoms to/out of the TiO2 surface on the antiparallel/parallel interfaces, respectively. These changes are noticeable in Figure S2 in the Supporting Information. Larger changes could be expected in hydrogen bonding between oxygen atoms exposed on the TiO2 surface and hydrogen atoms of the first hydration shell water molecules. The donor−acceptor distances of hydrogen bonds found on the interface are by 0.20−0.25 Å shorter than those in bulk water at zero-field conditions, which indicates that the interfacial H-bonds are relatively strong. Changes in these distances are minor when the system is exposed to a weak static electric field (≈0.05 V/Å); however, stronger fields lead to visible perturbations except for rutile (100) where no changes were observed (see Figure S10 in the Supporting Information). Examining hydrogen bond A−D−H angles, these are by 4° larger on (001) facets of both anatase and rutile than in bulk water, while they are by 1−4° smaller on all other studied surfaces. Nevertheless, the angles visibly respond to an external electric field only in the anatase (001) and rutile (101) cases, where they get larger on parallel surfaces and smaller on the antiparallel ones (see Figure S12). Finally, we checked the average number of hydrogen bonds per water molecule. As can be seen in Figure S14, the number of bonds is increasing with larger external fields on the antiparallel interfaces where the water dipoles are naturally aligned with the field. The opposite effect can be clearly seen on the parallel interfaces. Since the structural changes discussed above are detectable only when a relatively strong external field of 0.10 V/Å magnitude and higher is applied on the system, it is probable that there is a rather strong intrinsic electric field in the interface region keeping the structure of the first hydration layer. To confirm this hypothesis, we calculated the intrinsicfield profile across the simulation cell along its z-direction, perpendicular to the surface. Since the electrostatic force acting on atom i is proportional to the atomic charge qi and the intrinsic electric field, F⃗i(r)⃗ = qiE⃗ (r)⃗ , we can obtain the electric field profile the in z-direction as Ez(z) =

1 N

∑ i ∈ [z]

Figure 3. z-component of intrinsic electric field in the interfacial region. Zero-external-field profiles (solid red) as well as profiles affected by the static electric fields (0.10 V/Å in dashed green and 0.25 V/Å in dashed−dotted blue) applied in the surface-perpendicular direction are shown for comparison. Interfaces with surface normal parallel to the applied field are shown on the left-hand sides; those with surface normal antiparallel are on the right-hand sides. The vertical dashed green lines mark the boundary of the interface region.

depending whether all water atoms or just water oxygens are used for the field evaluations since the distributions of those atoms are different. For comparison, we decomposed the field profile of bulk water at zero-field conditions (shown in Figure S15) to its atomic contributions. Naturally, the oxygen-based field profile differs from the hydrogen-based one in the interface region where the atoms are well-organized and located in distinguishable layers (compare the upper and lower panels of Figure S15). Therefore, we prefer to involve the field contributions probed by all the charged atoms in the system to sample properly the most interesting field variations near the surface. It is readily apparent from Figure 3 that the effect of an applied external field up to 0.25 V/Å in the z-direction results in still a relatively small perturbation of the intrinsic interfacial field. Significant changes are visible practically only on anatase (101), where the layer of hydrogen-bonded water molecules is reorganized as we discussed above. Therefore, the intrinsic field, originating from the rich and complex physicochemical makeup of the surface structure, has its primary effect on the interfacial water structure (which interacts directly with the external field’s torque by its dipole moment43,56−58). For comparison, the profile of the collective interfacial-water dipole (in terms of its z-component, perpendicular to the surface) is shown in Figure 4. It is evident that the collective dipole, in most cases, responds to the strong intrinsic field by alignment due to reorientation of the water molecules in the interfacial region. Noticeable disagreement can be seen only for the anatase (101) interface, where, interestingly, all three types of water molecules in the first hydration layer discussed above have their dipole moments practically opposed to the direction of the interfacial intrinsic field. This layout is partially compensated by the water reorientation on the antiparallel

Fi , z(z) qi

(5)

where all atoms from each water molecule whose center-ofmass z-component lies in the interval [z − Δz/2, z + Δz/2] are included in the summation and N is the number of such atoms. In this way, we exploit all charged particles in the system to probe the local intrinsic field as is typical in classical electrostatics. The electrostatic force was calculated by Ewald summation52 as implemented in DL_POLY48we modified the code to print out the electrostatic force vector for each atom (i.e., without intramolecular bonding and Coulomb terms and without all van der Waals contributions). The resulting intrinsic-field profiles, which show the mean field acting on all atoms in the given z-slice of the system, are plotted in Figure 3. Indeed, it can be seen that there is considerable variation of the intrinsic field magnitude on each interface spanning from 3.0 V/ Å on anatases to 5.0 V/Å near the rutile (110) surface. The interfacial regions on all surfaces have widths of approximately 5−6 Å. Beyond that distance from the surface, the field’s zcomponent is averaged to zero, as one would expect at the bulk-water region. Note that the field profiles may differ E

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Figure 4. z-component of collective water dipole in the interfacial region. Zero-external-field profiles (solid red) as well as profiles affected by the static electric fields (0.10 V/Å in dashed green and 0.25 V/Å in dashed−dotted blue) applied in the surface-perpendicular direction are shown for comparison. Interfaces with surface normal parallel to the applied field are shown on the left-hand sides; those with surface normal antiparallel are on the right-hand sides. The vertical dashed green lines mark the boundary of the interface region.

Figure 5. Orientation of molecular-water dipole moment with respect to z-direction perpendicular to the surface. Zero-external-field profiles (solid red) as well as profiles affected by the static electric fields (0.10 V/Å in dashed green and 0.25 V/Å in dashed−dotted blue) applied in the surface-perpendicular direction are shown for comparison. Interfaces with surface normal parallel to the applied field are shown on the left-hand side; those with surface normal antiparallel are on the right-hand side of each panel.

interface when the static electric field is applied on the system. The arrangement of the water is driven by electrostatic interaction between individual water molecules and charged surface atoms, responsible for water coordination to Ti5c and hydrogen bonding to O2c/Ob atoms. Thus, the resultant orientation adopted by water molecules is a result of a delicate force balance between strong charge−charge interactions and weaker field−dipole interactions. Decomposition of the overall electrostatics on the interface into these contributions, although they are not themselves measurable, is helpful for better understanding what type of forces act on the water molecules. The orientation of the dipole moment with respect to the zdirection axis of the supercell is shown in Figure 5, where normalized histograms of the angle cosines have been collected. The cosine range spans from −1 (antiparallel arrangement), through 0 (perpendicular arrangement), to 1 (parallel arrangement). It is clear that application of the external field in the zdirection increases the population of parallel-oriented dipoles on all studied TiO2 surfaces. Examining the orientation of interfacial water molecules in the first hydration shell, two peaks characteristic of the anatase (101) interface are clearly evident, featuring significant parallel and antiparallel ordering of water molecules coordinated to Ti5c and hydrogen-bonded to O2c, respectively. Similar histogram patterns are found also for rutile (110); however, hydrogen-bonded water molecules tend to lower their energy by distortion from the antiparallel directionas a consequence, the peak at −1 is absent. As we already observed from consideration of density profiles, the external electric field affects somewhat slightly only moredistant interfacial water molecules, the positions of which are not confined by interaction with the surface of TiO2. This can be seen rather clearly in the broad peak between −0.6 and −0.2 for the anatase (101) parallel-interface case, corresponding to

water interacting by one hydrogen bond with surface O2c atoms; comparison with the third peak of the corresponding density profile in Figure 2 confirms this. A similar response is detectable also on other surfaces as the stronger field is applied across the supercell. To glean a better sense of how strong an electric field the interfacial water molecules really “perceive”, we projected the intrinsic field along the direction of each water molecule’s dipole and collected this projection into histograms, shown in Figure 6. Note that only the field probed by oxygen atom was projected here. In the bulk region, this is practically identical to the Hw-probed field since the intrinsic field is varying smoothly there and can be regarded as locally homogeneous (see Figure S16 in the Supporting Information); however, larger differences could be expected in the interface region where the field

Figure 6. Probability distribution of intrinsic electric field projected onto the water-dipole direction in the bulk (solid blue) and in the interfacial region (dotted red) at zero-external-field conditions. F

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The Journal of Physical Chemistry C

hydration layer, where the water molecules are already confined by interaction with the TiO2 surface and the applied fields represent just a small contribution to the intrinsic field in the interfacial region. For comparison, we have also integrated the velocity autocorrelation function to calculate the diffusion constant by the Green−Kubo approach (see eq 2). The coefficients obtained by this method are consistent with those obtained by mean-square-displacement fitting. Although the interface-water diffusivity does not seem to be affected by the external static electric field, we observed relatively large changes of average hydrogen-bond lifetimes in this region. The lifetimes were obtained by using the Luzar− Chandler model of H-bond kinetics,53 which takes into account not only hydrogen-bond making/breaking, but also diffusivity. The calculated lifetimes as a function of external electric field are plotted in Figure 8. Although the hydrogen bonds in bulk

exhibits more rapid variations. As can be seen from the position of the blue Gaussian-curve peak in Figure 6, the bulk-water value of the intrinsic field, which can be regarded as a reference value for the water model used, is 1.8 V/Å. This value is consistent with 2 V/Å recently found for bulk water in DFT calculations.59 Interestingly, the distributions of field projections of interfacial water are split into two or three peaks, except for the (001) anatase where only a single peak was found. This indicates that the fraction of the hydration layer (50−58%) experiences the same, or slightly higher, intrinsic electric field as for bulk water (1.9−2.1 V/Å) at zero-applied-field conditions. However, the rest of the water molecules in the interfacial layer are exposed to a considerably stronger field (3−5 V/Å). Application of the external electric field on the system affects the intrinsic field perception mainly on rutile (100) and (110) surfaces where the response is larger than the magnitude of the applied field, as can be seen in Figure S17 in the Supporting Information. Finally, we have explored dynamical properties of the interfacial water. We computed the diffusion constant of water from the time limit of its mean-square displacement (cf. eq 1). For the bulk region of our models, we obtained a value of 2.8 × 10−9 m2/s at zero-field conditions, which is fairly close to the experimental value of 2.3 × 10−9 m2/s,60,61 and it is consistent with our previous work.38 The self-diffusivity of water in the interfacial region was calculated from the displacement of the first hydration shell defined on the basis of the density profile discussed above. As can be seen in Figure 7, the diffusion constants of the interface water are by 1 order

Figure 8. Average hydrogen-bond lifetime in bulk (solid green), in the interface with surface normal parallel with the applied external field (dashed−dotted blue) and in the antiparallel interface (dotted red) as functions of the external electric field magnitude. The lifetime was obtained from the Luzar−Chandler model of hydrogen-bond kinetics.

water remain on average for 3 ps, the lifetime of the interface hydrogen bonds is around 6−8 ps at zero-field conditions, except for rutile (100) comparable to the bulk water and rutile (001), which exhibits considerably shorter-time hydrogen bonds. The response to the external field is practically unique for each type of TiO2 surface, depending on the surface structure and direction of the applied field. On anatase (001), where a small number of the hydrogen bonds were found, the lifetime is decreasing as the external field gets larger. The opposite behavior can be seen on rutile (101), while only minor changes were observed on rutile (001). On rutile (100) and (110) surfaces with ridges and exposed bridging oxygen atoms, the hydrogen-bond lifetime increases with the external field on parallel interfaces while it slightly decreases on the antiparallel ones. Finally, a rather complicated nonlinear response was found on anatase (101), where the hydrogen-bond lifetime first decreases and then increases with the applied field. These results suggest that the hydrogen-bond kinetics on the interface

Figure 7. Value of water self-diffusion coefficient in bulk (solid green), in the interface with surface normal parallel with the applied external field (dashed−dotted blue), and in the antiparallel interface (dotted red) as functions of the external electric field magnitude are shown.

of magnitude lower than in the bulk. This is not surprising since the first hydration layer is confined by interaction with the TiO2 surfacethat is, by coordination to unsaturated surface Ti4c/ Ti5c atoms and hydrogen bonding to surface oxygen O2c/Ob atoms.10,11,38 From Figure 7, it is also obvious that there is no considerable effect of the external static electric field on the water diffusion. This is rather expected behavior of the first G

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The Journal of Physical Chemistry C is affected even by subtle changes in first-hydration-shell structure. From the autocorrelation function of the interfacial-water collective dipole, we calculated IR spectra by their Fourier transform (cf. eq 4). The bulk-water spectrum reproduces the librational, bending, as well as stretching band in reasonable agreement with experiment (for comparison see Figure S18 in the Supporting Information). Spectra of the interface water on the most important surfaces, anatase (101) and rutile (110), are shown in Figures 9 and 10, providing a better insight into

in lateral (x and y) directions, as can be seen from the component decomposition of the spectra. These directions are not equivalent, because of the ridgelike structure of the anatase (101) surface and surface Ob chains on rutile (110), respectively, which are both oriented along the x-direction. The perpendicular, z-component of the spectra is suppressed considerably in this energy region between 50 and 150 meV, suggesting only minimal movement in this direction. While the bending modes are dominated by their z-components on both interfaces, the stretching bands show a rather distinctive pattern. On anatase (101), one can see different stretching modes in lateral directions, while the z-component contribution does not have significant peak structure in the whole range between 350 and 450 meV. This contrasts to the rutile (110) spectrum, where the perpendicular contribution exhibits twopeak character while the lateral vibrations contribute to the same peak. The first monolayer of water molecules that are coordinated to Ti5c by an oxygen atom contribute exclusively to the higher-energy peak located around 425 meV. This band therefore corresponds to hydrogen bonds between the first and second monolayers. The second monolayer is coordinated by hydrogen atoms to surface Ob, and it contributes to the both stretching peaks in the spectrum. Although only minor changes of spectra were observed upon application of a weak 0.05 V/Å field, the effect is more visible as the field intensity increases. As water molecules get closer to the antiparallel surface, the x- and y-components of the spectrum begin to dominate the spectrum shape. This can be clearly seen in librational and stretching bands in Figures 9 and 10, where effects of the 0.25 V/Å field are shown. Interestingly, enhancement of the x-component in the librational band of rutile (110) on the parallel interface was observed, which obviously stems from surface bridging oxygen chains. The IR spectra of other studied TiO2 interfaces where similar changes were observed can be found in the Supporting Information. For comparison, we have also checked the effect of the weak, surface-plane-oriented 0.05 V/Å fields on anatase (101) and rutile (110) surfaces; however, only minor changes of the IR spectra were observed (see Figures S23 and S24).

Figure 9. IR spectra of interfacial water on anatase (101) surfaces. Effects of the external static electric fields in the z-direction perpendicular to the TiO2 surface, parallel and antiparallel to the surface normal, are compared with the zero-field conditions. The spectra are decomposed to the simulation-cell coordinate system.

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CONCLUSIONS In nonequilibrium MD, we have applied static electric fields of 0.05, 0.10, 0.15, 0.20, and 0.25 V/Å magnitudes to TiO2 anatase (001) and (101) and rutile (001), (100), (101), and (110) interfaces with water. We found out that the external electric field of magnitudes achievable in experimental measurements (≈0.05 V/Å) represents only a small perturbation of the relatively large intrinsic field detected in the interfacial region, within 5−6 Å of the TiO2 surface. Therefore, all static properties, such as the structure of the first hydration layer and orientation of water dipoles, are dominated by the intrinsic field. The average field acting on the water molecule dipole in the bulk state has a magnitude of approximately 1.8 V/Å. However, it can reach remarkably high values, such as 4.5 V/Å in the interfacial region of the TiO2 surfaces. In an analogous manner to structural properties, the dynamical behavior of interfacial water near TiO2 surfaces is also only slightly affected by applied external static electric fields, in the current magnitude range considered. The selfdiffusion constant calculated in this interfacial region was found to be 1 order of magnitude lower than its bulk-water value. The interfacial water is confined by coordination to unsaturated surface Ti atoms and hydrogen bonding to oxygen atoms. This

Figure 10. IR spectra of interfacial water on rutile (110) surfaces. Effects of the external static electric fields in the z-direction perpendicular to the TiO2 surface, parallel and antiparallel to the surface normal, are compared with the zero-field conditions. The spectra are decomposed to the simulation-cell coordinate system.

confinement in movement of the first hydration layer. Obviously, the interaction of water with the TiO2 surface has the most significant effect on low-energy, librational bands. The band is split into two peaks corresponding to water vibrations H

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The Journal of Physical Chemistry C

(9) Lun Pang, C.; Lindsay, R.; Thornton, G. Chemical Reactions on Rutile TiO2(110). Chem. Soc. Rev. 2008, 37, 2328−2353. (10) Levchenko, A. A.; Kolesnikov, A. I.; Ross, N. L.; Woodfield, B. F.; Li, G.; Navrotsky, A.; Boerio-Goates, J. Dynamics of Water Confined on a TiO2 (Anatase) Surface. J. Phys. Chem. A 2007, 111 (49), 12584−12588. (11) Spencer, E. R.; Levchenko, A. A.; Ross, N. L.; Kolesnikov, A. I.; Boerio-Goates, J.; Woodfield, B. F.; Navrotsky, A.; Li, G. Inelastic Neutron Scattering Study of Confined Surface Water on Rutile Nanoparticles. J. Phys. Chem. A 2009, 113 (12), 2796−2800. (12) De Angelis, F.; Di Valentin, C.; Fantacci, S.; Vittadini, A.; Selloni, A. Theoretical Studies on Anatase and Less Common TiO2 Phases: Bulk, Surfaces, and Nanomaterials. Chem. Rev. 2014, 114, 9708−9753. (13) Aschauer, U.; He, Y.; Cheng, H.; Li, S.-C.; Diebold, U.; Selloni, A. Influence of Subsurface Defects on the Surface Reactivity of TiO2: Water on Anatase (101). J. Phys. Chem. C 2010, 114, 1278−1284. (14) Cheng, H.; Selloni, A. Hydroxide Ions at the Water/Anatase TiO2(101) Interface: Structure and Electronic States from First Principles Molecular Dynamics. Langmuir 2010, 26 (13), 11518− 11525. (15) Tilocca, A.; Selloni, A. DFT-GGA and DFT+U Simulations of Thin Water Layers on Reduced TiO2 Anatase. J. Phys. Chem. C 2012, 116, 9114−9121. (16) Sun, C.; Selloni, A.; Du, A.; Smith, S. C. Interaction of Water with the Fluorine-Covered Anatase TiO2 (001) Surface. J. Phys. Chem. C 2011, 115, 17092−17096. (17) Aschauer, U.; Selloni, A. Structure of the Rutile TiO2 (011) Surface in an Aqueous Environment. Phys. Rev. Lett. 2011, 106, 166102. (18) Lee, J.; Sorescu, D. C.; Deng, X. Y.; Jordan, K. D. Diffusion of CO2 on the Rutile TiO2 (110) Surface. J. Phys. Chem. Lett. 2011, 2, 3114−3117. (19) Lee, J.; Sorescu, D. C.; Deng, X. Y.; Jordan, K. D. Water Chain Formation on TiO2 (110). J. Phys. Chem. Lett. 2013, 4, 53−57. (20) Liu, C. Z.; Thornton, G.; Michaelides, A.; Zhang, C. Structure and Dynamics of Liquid Water on Rutile TiO2 (110). Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 161415. (21) Wesolowski, D. J.; Sofo, J. O.; Bandura, A. V.; Zhang, Z.; Mamontov, E.; Predota, M.; Kumar, N.; Kubicki, J. D.; Kent, P. R. C.; Vlcek, L.; et al. Comment on “Structure and Dynamics of Liquid Water on Rutile TiO2(110)”. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 85, 167401. (22) Liu, M. L.; Zhang, C.; Thornton, G.; Michaelides, A. Reply to “Comment on ‘Structure and Dynamics of Liquid Water on Rutile TiO2(110)’”. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 85, 167402. (23) Mattioli, G.; Filippone, F.; Caminiti, R.; Bonapasta, A. A. Short Hydrogen Bonds at the Water/TiO2 (Anatase) Interface. J. Phys. Chem. C 2008, 112, 13579−13586. (24) Kumar, N.; Neogi, S.; Kent, P. R. C.; Bandura, A. V.; Kubicki, J. D.; Wesolowski, D. J.; Cole, D.; Sofo, J. O. Hydrogen Bonds and Vibrations of Water on (110) Rutile. J. Phys. Chem. C 2009, 113, 13732−13740. (25) Russo, D.; Teixeira, J.; Kneller, L.; Copley, J. R. D.; Ollivier, J.; Perticaroli, S.; Pellegrini, E.; Gonzalez, M. A. Vibrational Density of States of Hydration Water at Biomolecular Sites: Hydrophobicity Promotes Low Density Amorphous Ice Behavior. J. Am. Chem. Soc. 2011, 133, 4882−4888. (26) Zhang, Z.; Fenter, P.; Cheng, L.; Sturchio, N. C.; Bedzyk, M. J.; Predota, M.; Bandura, A.; Kubicki, J. D.; Lvov, S. N.; Cummings, P. T.; et al. Ion Adsorption at the Rutile-Water Interface: Linking Molecular and Macroscopic Properties. Langmuir 2004, 20, 4954−4969. (27) Predota, M.; Bandura, A. V.; Cummings, P. T.; Kubicki, J. D.; Wesolowski, D. J.; Chialvo, A. A.; Machesky, M. L. Electric Double Layer at the Rutile (110) Surface. 1. Structure of Surfaces and Interfacial Water from Molecular Dynamics by Use of ab Initio Potentials. J. Phys. Chem. B 2004, 108, 12049−12060.

restraint on motion can be clearly seen in calculated IR spectra where the librational and stretching bands are considerably affected. Interestingly, a rather large and unique response to applied electric field was found in the lifetime of interfacial hydrogen bonding. Although the external static electric fields induce considerable changes only when strong intensities of 0.10 V/Å magnitude and higher are applied, we expect that the water motion might be affected further by time-varying fields, which we are planning to investigate in a forthcoming study. A detailed understanding of these fundamental properties is crucial for more efficient and better-controlled electrochemical applications62 of titanium dioxide.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b01907. Whole supercells with indicated interface and bulk-water regions; snapshots of zero-field and field-perturbed interface structures; calculated distributions of water Ow−Hw bond lengths, water Hw−Ow−Hw valence angles, and water dipole moments and their mean values as a function of external field intensity; distributions and mean values of lengths, angles, and average number of hydrogen bonds; decomposition of intrinsic field profile and distribution; IR spectra of bulk water and IR spectra of TiO2 interfaces not shown in the main text (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Tel.: +353-1-7161646. Fax: +353-1-7161177. *E-mail: [email protected]. Fax: +353-1-7161177. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Science Foundation Ireland for funding under Grant SFI 15/ERC-I3142. REFERENCES

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