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Influence of surface polarity on water dynamics at the water/rutile TiO2(110) interface
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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 244102 (8pp)
doi:10.1088/0953-8984/26/24/244102
Influence of surface polarity on water dynamics at the water/rutile TiO2(110) interface Tatsuhiko Ohto1,3,4 , Ankur Mishra1,4 , Seiji Yoshimune1 , Hisao Nakamura2 , Mischa Bonn1 and Yuki Nagata1 1
Max-Planck Institute for Polymer Research, Ackermannweg 10, D-55128, Mainz, Germany Nanosystem Research Institute (NRI), RICS, National Institute of Advanced Industrial Science and Technology (AIST), Central 2, Umezono 1-1-1, Tsukuba, Ibaraki 305-8568, Japan 2
E-mail: [email protected] and [email protected] Received 30 September 2013, revised 8 November 2013 Accepted for publication 20 November 2013 Published 27 May 2014
Abstract
We report molecular dynamics (MD) simulations of the water/clean rutile TiO2 (110) interface using polarizable and non-surface polarity force field models. The effect of surface polarity on the water dynamics near the TiO2 (110) surface is addressed, specifically by calculating the water hydrogen bond and reorientational dynamics. The hydrogen bond lifetime of interfacial water molecules is several times longer than that of bulk water due to the strong water–TiO2 interactions. A comparison of the dynamics simulated with the polarizable and non-surface polarity models shows that, while the hydrogen bond lifetime between the interfacial water and TiO2 surface is insensitive to the surface polarity, the reorientational dynamics around this hydrogen bond axis is significantly influenced by the surface polarity; the surface polarity of the TiO2 increases the water–TiO2 interactions, stabilizing the local structure of the interfacial water molecules and restricting their rotational motion. This reorientation occurs predominantly by rotation around the O–H group hydrogen bonded to the TiO2 surface. Furthermore, we correlate the dynamics of the induced charge on the TiO2 surface with the interfacial water dynamics. Our results show that the timescale of correlations of the atom charges induced by the local electric field in bulk water is influenced by the rotational motion, hydrogen bond rearrangement and translational motion, while the induced charge dynamics of the TiO2 surface is governed primarily by the rotational dynamics of the interfacial water molecules. This study demonstrates that the solid surface polarity has a significant impact on the dynamics of water molecules near TiO2 surfaces. Keywords: titanium dioxide, liquid/solid interface, interfacial water dynamics, charge response kernel, surface polarity (Some figures may appear in colour only in the online journal)
1. Introduction
homogeneous catalysis that products can be separated and extracted easily from the surface and reactants. Among surfaces relevant for heterogeneous catalysis, the water/rutile and anatase TiO2 interfaces have drawn considerable attention owing to their photocatalytic activity: an electron–hole pair can be generated in TiO2 near the surface by ultraviolet irradiation, which can subsequently be used to split a water
In heterogeneous catalysis, the chemical conversion takes place on a catalyst surface, which has the advantage over 3 Present address: Graduate School of Engineering Science, Osaka
University, Japan. 4 TO and AM have contributed equally to this work. 0953-8984/14/244102+08$33.00
1
c 2014 IOP Publishing Ltd
Printed in the UK
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To highlight the effect of the TiO2 surface polarity on the interfacial water dynamics, we compare the results from the polarizable force field model with those obtained using a non-surface polarity force field model. In the polarizable force field model, the CRK technique has been employed for describing both the molecular polarizability of the water molecules and the solid surface polarity of the TiO2 [26]. In the non-surface polarity model all the CRK parameters for the TiO2 surface are set to zero. By using the MD trajectories obtained from the simulations with these force field models, we calculate the hydrogen bond dynamics, water molecular reorientation dynamics, and the dynamics of charge fluctuations at the water/TiO2 interface and discuss the effect of the surface polarity on the water dynamics. This paper is organized as follows. Section 2 describes the MD simulation protocols, where the polarizable and nonsurface polarity force field models are introduced. In section 3 we report the hydrogen bond dynamics and anisotropy decays of the water molecules as well as the induced charge correlation functions of the TiO2 surface, which reveal the effect of the surface polarity on the water molecules. The concluding remarks are given in section 4.
molecule into hydrogen and oxygen [1]. This photocatalytic reaction also modifies the surface properties so that water droplets spread over the TiO2 surface with nearly zero contact angle, which is termed as superhydrophilicity [2]. These innate properties of the water/TiO2 interface have been utilized in a wide range of industrial applications; for example, hydrogen production [1, 3–5], self-cleaning coatings [6, 7], and antibacterial coatings [8, 9]. Since the intermolecular interactions between the interfacial water molecules and the TiO2 surface are responsible for the emergence of these special properties, obtaining molecular level insight into the structure and dynamics of the water molecules near the TiO2 surfaces is essential to understand these interactions and clarify the water (photo-)reactivity at the water/TiO2 interface. Since all-atom molecular dynamics (MD) simulation can visualize the microscopic structure and ultrafast dynamics of a system, it is an indispensable tool to study the intermolecular interactions between liquids and solid surfaces [10–13]. Kubicki and coworkers developed a non-polarizable force field model to reproduce the ab initio optimized geometry of a water molecule adsorbed on the rutile TiO2 surface [14, 15] and analyzed the interfacial water structures and dynamics near the TiO2 surface with this force field model [15, 16]. The results show good agreement with experimental data such as x-ray [17, 18] and second harmonic generation [19], whereas the structures of the interfacial water predicted by the force field model are different from those predicted by firstprinciples MD simulations [20–22]. A distinct limitation of the force field model is that charges are fixed and independent of the local electric field (hence the name non-polarizable force field model) [14, 15]. Accordingly, the discrepancy between the results of the force field model and the first-principles MD simulation likely originates from the polarizability of the water molecules and the TiO2 surface, not included in the former. However, an attempt to include the polarization effect explicitly in force field models of the water/TiO2 interface has not been made. Very recently, we have developed a novel methodology to generate a polarizable force field for the liquid/solid interface by using the charge response kernel (CRK) model [23–25] and applied this methodology to the water/clean rutile TiO2 (110) interface [26]. The polarizable force field model can reproduce the stable structures predicted by the ab initio MD simulation [21], indicating that the surface polarity of TiO2 critically affects the time-averaged conformations of the interfacial water [26]. Here, the next fundamental question is addressed: what is the influence of the TiO2 surface polarity on the interfacial water dynamics? The effect of the molecular polarization on the water dynamics at the aqueous interface has been examined previously at the water/vapor interface [27]. This study showed that the hydrogen bond correlation function, which reflects hydrogen bond lifetimes, decays faster at the interface than in the bulk with polarizable force field models, while this tendency is opposite when non-polarizable force field models are employed, indicating that the polarization effect plays a critical role when modeling the ultrafast dynamics of the aqueous interface [27]. In this study we examine the water dynamics at the water/clean rutile TiO2 (110) interface with the polarizable force field model.
2. MD simulation protocols 2.1. Polarizable model with CRK
We have recently reported a methodology to generate a polarizable force field model for liquid/solid interfaces in which the solid surface polarity is taken into account [26]. In this methodology, the polarizability of the solid surface is added to the non-polarizable force field model within the CRK scheme. Here, we briefly review this polarizable force field model. The Hamiltonian for the water/clean rutile TiO2 (110) interface can be decomposed into H = K + Uwater–water + UTiO2 –TiO2 + Uwater–TiO2 + Uwater,intra ,
(1)
where K represents the kinetic energy, UA−B is the intermolecular interaction potential between the atoms in A and B, and Uwater,intra denotes the intramolecular potential of water. The intermolecular interaction potentials, Uwater–water , UTiO2 −TiO2 , and Uwater−TiO2 , consist of the van der Waals interactions represented by the Lennard-Jones/Buckingham potentials and electrostatic potentials. The Buckingham potential parameters of the Ti–O bonds and those of Uwater−TiO2 are given by [14]. The Lennard-Jones potential parameters between Ow and Ob (see figure 1) can be found in [26]. The Lennard-Jones potentials of Uwater–water and Uwater,intra are described in [28]. The electrostatic potential of Uwater–water is given in the CRK scheme as Uwater−water,ele =
X qi q j i< j
rij
f Thole (rij ) +
1X Vi K ij V j , (2) 2 ij
where K ij is the CRK connecting sites i and j, and Vi is the electrostatic potential acting on site i [23, 24]. To avoid the 2
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T Ohto et al
the same as in the non-polarizable force field model [14]. The electrostatic potential of Uwater−TiO2 is given by Uwater−TiO2 ,ele =
X
qi q eff j
X
i∈water j∈atom site in TiO2
X
+
X
i∈water j∈WI in TiO2
+
1 2
X
rij
f Thole (rij )
qi q j f Thole (rij ) rij
Vi K ij V j ,
(7)
i, j
where on the Wannier ion (WI) sites, the charges are induced in the TiO2 by the electrostatic field of water [36]. The first term in equation (7) represents the water–TiO2 electrostatic interaction without the polarizable effect of the solid surface, while the second and third terms account for the polarization corrections and represent the electrostatic interaction between the charges of the water molecules and the charges at the WI sites of the TiO2 induced by the electric field of the water. These force field parameters can be found in [26]. Figure 1. (a) Axial distribution of the oxygen atoms of the water molecules normal to the water/TiO2 interface. (b) Schematic representations of stable water structures in the first and second layers near the TiO2 surface projected onto the cross-section normal to the (001) direction.
2.2. Non-surface polarity model
In the non-surface polarity force field model, the polarization correction terms were removed from equation (7) and thus the water–TiO2 electrostatic potential was given by
divergence of induced charges, Thole’s damping function was introduced: 1 for x ≥ 1 (3) f Thole (rij ) = 4 x − 2x 3 + 2x for x < 1,
Uwater−TiO2 ,ele =
(5) (0)
rij
,
f Thole (rij ). (8)
We conducted MD simulations at the water/TiO2 interface using both the polarizable and non-surface polarity force field models. Our system consisted of 510 water molecules and seven rutile TiO2 (110) layers consisting of 3 × 6 unit cells. The simulation cell size was 20.07 Å × 18.44 Å × 120 Å [37]. Periodic boundary conditions were used for the x and y axes, while a reflective wall condition was employed for the z axis. The electrostatic potential was calculated by using the isotropic periodic sum (IPS) method with a cutoff of 45 Å [38–40]. In the IPS method, long-range interactions are represented by interactions with isotropic periodic images of a defined local region [38, 41, 42], which eliminates the artifacts produced due to the periodic boundary conditions in the Ewald sum method [43, 44]. This method is computationally cheaper but similarly accurate when compared with the Ewald sum method [38, 39]. We implemented the reference system propagator algorithm (RESPA) for integrating the equations of motion [45], where the forces associated with the intramolecular potential of water were calculated every 0.125 fs and the
where the zeroth order charge at site i, qi , represents the gas-phase charge. For the electrostatic potential of UTiO2 –TiO2 , a non-polarizable force field model with fixed charges was employed
i> j
rij
2.3. MD simulation
j
X qieff q eff j
qi q eff j
This potential indicates that the surface charges of the TiO2 are not induced by the electric field of the water molecules. We use the same polarizable force field model for Uwater–water and UTiO2 –TiO2 . Note that although the second and third terms of equation (7) are missing in equation (8), the total charge of (0) the system is zero because qi = 0 at the WI sites.
j
UTiO2 –TiO2 ,ele =
X
i∈water j∈ atom site in TiO2
where x = rij /A(αi α j )1/6 and αi is the polarizability volume of the site i [29]. Although A = 2.8 [25] has been used for calculating the static structure of water [26], it makes the bulk water dynamics diffusive. We adjusted the parameter A to reproduce the anisotropy decay of the water experimentally measured [30–35] and obtained A = 2.65 for the water–water interaction and A = 2.8 for the water–TiO2 interactions. Charges are calculated by the self-consistent field equations [23, 24]: X (0) qi = qi + K ij V j , (4) X qj Vi = f Thole (rij ), rij
X
(6)
where q eff represents the effective site charge at the atom site in the TiO2 to which the polarization effect arising from the bulk TiO2 is renormalized [14]. Note that the UTiO2 –TiO2 ,ele is 3
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other forces were calculated every 1.0 fs. We generated twelve independent initial configurations of the water/TiO2 interface and ran the MD simulations by rescaling the atomic velocities so that the system temperature reached 300 K. We equilibrated the systems by performing 50 ps MD runs in the NVE ensemble and sequentially performed a 100 ps MD run for each sample to obtain the MD trajectories, which were used for computing the hydrogen bond dynamics, anisotropy decays, and induced charge correlation functions. 3. Results 3.1. Structure of interfacial water near the TiO2 surface Figure 2. Schematic representation of the water/TiO2 interface. Hw (Ow ) denotes the hydrogen (oxygen) atom of the water molecule, Tiv and Tivi denote the five-fold and six-fold coordinated Ti atoms on the surface, Ob represents the two-fold coordinated oxygen atom next to the Ti surface layer, and Os represents the oxygen atom on the Ti surface layer. Ws is the WI site and is defined as the center of mass of three titanium and two Os atoms indicated by the black arrows, while Wb is the WI site located at the Ob atom
To check the water structure near the TiO2 surface, the axial distribution of the water oxygen atoms (Ow ) was calculated, which is plotted in figure 1. The point of origin was set at the average position of the surface Ti atoms. Figure 1(a) shows that the axial distribution has several sharp peaks near the TiO2 surface, whereas the water density reaches a constant value (1.0 g cm−3 ) at a distance of 12 Å away from the Ti surface. Moving from the bulk water region to the interface, the anisotropic structure of water due to the TiO2 surface emerges at a distance of ∼10 Å from the surface. The water structures contributing to the peaks at 2.2 Å and 3.0–4.0 Å in the axial distribution have been studied previously [26], and are schematically depicted in figure 1(b). Note that the peak at 3.8 Å is enhanced and the peak at 3.4 Å is not as prominent as reported in [26]. Since A = 2.8 for the water–water interaction is used instead of A = 2.65 because of the diffusive bulk water dynamics with A = 2.8, the short-range electrostatic interactions are slightly enhanced and thus the peak at 3.8 Å becomes sharper than predicted by the previous study [26]. In this study we defined the water molecules located in the 0 Å < z < 3 Å and 3 Å < z < 4.6 Å ranges as the first and second layer water, respectively. Furthermore, the water molecules in the z > 12 Å are defined as bulk water. These definitions will be used below for simulating the anisotropy decays of water.
site indicated by the red arrow.
The simulated c(t) are displayed in figure 3. The hydrogen bond breaking dynamics is substantially slowed down for the water molecules near the TiO2 surface compared to bulk water. This can be attributed to the stronger water–TiO2 interactions than the water–water interactions. This tendency is consistent with the previous report that water molecules near the TiO2 surface are less diffusive than bulk water [15]. We subsequently explored the effect of the TiO2 surface polarity on the Ob · · · Hw hydrogen bond breaking dynamics by comparing c(t) for the polarizable and non-surface polarity force field models. Figure 3 shows that the decay of c(t) is slightly faster for the polarizable model than the non-surface polarity model for short times (t < 8 ps), whereas the surface polarity slows down the hydrogen bond breaking on longer timescales (t > 8 ps). This indicates that for t < 8 ps the fluctuation of the induced charges triggers fluctuations of the Ob · · · Hw hydrogen bond, while the induced dipole at the TiO2 surface strengthens the Ob · · · Hw hydrogen bond interactions, giving rise to slower hydrogen bond breaking on long timescales. However, the effect of the surface polarity of the TiO2 on the hydrogen bond dynamics of water is very limited.
3.2. Hydrogen bond dynamics
The hydrogen bond breaking dynamics can be characterized by the time correlation function c(t) =
hh(0)h(t)i , hhi
(9)
3.3. Anisotropy decay
where h(t) equals 1 when a hydrogen bond is present at time t, and 0 otherwise [46]. h· · · i denotes the thermal average. We defined that a hydrogen bond formed when the intermolecular O · · · H distance was less than the cutoff length of 2.41 Å [47]. Note that although several different definitions have been proposed for judging the hydrogen bond formation, the resulting c(t)s simulated with these different definitions are very similar [47]. We calculated c(t) for the Ob · · · Hw hydrogen bonds contributed by the second layer water and Ow · · · Hw hydrogen bonds in the bulk, where Ob stands for the two-fold coordinated oxygen atom near the Ti surface, and Hw is the hydrogen atom of a water molecule (see figure 2).
The orientational dynamics of liquids can be characterized by the anisotropy decay, and has been addressed experimentally using polarization dependent pump–probe spectroscopy [48–50]. This anisotropy decay can be calculated by [48] r ν (t) = 52 hP2 (Eν (t) · νE (0))i,
(10)
where P2 is the second Legendre polynomial and νE (t) is the unit vector of the targeted normal mode at time t. We calculated the anisotropy decays for the O–H bond (r OH (t)), the H–O–H angle bisector (r b (t)) and the normal to the plane formed by 4
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Table 1. Time constants for the anisotropy decays of the water molecules in units of picoseconds.
r OH (t) r b (t) r n (t)
First layer First layer (polarizable) (non-surface polarity)
Second layer (polarizable)
Second layer (non-surface polarity)
Bulk
6.1 14.8 6.2
8.5 7.5 7.0
6.9 5.6 5.0
2.2 2.2 1.8
5.0 8.3 4.8
allowing the angle bisector to rotate around the Ow –Hw · · · Ob axis. The observation that the dynamics is different along different molecular axes is strongly reminiscent of dynamics previously reported in ionic aqueous solutions. Tielrooij et al found that ions of different charge affect the orientations of the water molecules near the ions along different molecular axes: cations slow the orientation of the H–O–H bisector, while anions mainly slow down the reorientation dynamics of the O–H group pointing toward the anion [51, 52]. Revisiting the water/TiO2 interface, the atomic charges of the Tiv and Ob atoms assigned in the force field model are ∼2e and ∼−1e, respectively [14]. The simulated r OH (t) and r b (t) show that water molecules in the first layer interacting with the positive Tiv atom exhibit slower anisotropy decay of the H–O–H angle bisector, whereas the O–H bond orientation of the second layer water molecules bound to the negative Ob is less mobile, with the H–O–H angle bisector relatively free to rotate around that O–H bond. This picture is fully consistent with the pump–probe reorientational study in bulk ionic aqueous solutions [51, 52]. The anisotropy decay of the normal to the plane with atoms of a water molecule, r n (t), which is shown in the bottom panel of figure 4, shows faster decay in the first layer than the second layer. This indicates that in the first layer the out-of-plane motion of the water molecules faces less hindrance than in the second layer. The anisotropy decays, r OH (t), r b (t), and r n (t), of the interfacial water molecules clearly illustrate that the interfacial water dynamics is heterogeneous and dependent on the different moieties of the TiO2 adjacent to the water molecules. We now focus on the effect of the TiO2 surface polarity on the anisotropy decays of water. Figure 4 shows that the anisotropy decays of r OH (t), r b (t), and r n (t) are significantly faster with the non-surface polarity model than with the polarizable model, implying that the surface polarity of the TiO2 slows down the anisotropy decays of the interfacial water molecules. The larger impact of the surface polarity on the anisotropy decay than on the hydrogen bond dynamics indicates that the surface polarity stabilizes the local structure of the water molecules near the TiO2 interface [21, 26], leading to the slowing down of the anisotropy decay.
Figure 3. Hydrogen bond correlation function c(t) for the Ob · · · Hw in the second layer water and the Ow · · · Hw in the bulk water
simulated by the polarizable force field model. c(t) for the Ob · · · Hw simulated by using the non-surface polarity force field model is also plotted.
the atoms of a water molecule (r n (t)), which are shown in figure 4. By fitting an exponential function to r OH (t), r b (t), and r n (t) in the range of 1 ps < t < 3 ps for the interfacial water and bulk water, we obtained the time constants for the anisotropy decays, which are summarized in table 1. The time constant of r OH (t) obtained for bulk water is comparable with experimental values [30–35] and is similar to the value predicted by the SPC/E water model [50, 53]. We first focus on the anisotropy decay of the O–H bond. The top panel of figure 4 shows that r OH (t) is faster in the first water layer than in the second layer. This can be attributed to the different water–TiO2 interactions. Since the Ow atom in the first layer water is tightly bonded to the five-fold coordinated Ti (Tiv ) atom on the Ti surface and the Hw atoms interact with other water molecules, the O–H bond orientations are easily modulated by the fluctuations of surrounding water molecules. Meanwhile, the Hw atom of the second layer water is strongly hydrogen bonded to the Ob atom, leading to less modulation of the O–H bond orientations. The middle panel of figure 4 shows that the anisotropy decay of the H–O–H angle bisector, r b (t), is slower in the first layer than in the second layer, while the opposite trend is observed for r OH (t). This can be accounted for as follows. The angle bisector of the water molecules in the first layer is nearly parallel to the Ow · · · Tiv axis, restricting the rotational motion of the H–O–H angle bisector. On the other hand, the Hw atom of the second layer water is hydrogen bonded with the Ob atom,
3.4. Induced charge correlation
In our CRK polarizable force field modeling, the surface charge of the TiO2 is induced by the water molecules. To connect the interfacial water dynamics with the induced charge 5
J. Phys.: Condens. Matter 26 (2014) 244102
T Ohto et al
Figure 4. Anisotropy decays of r OH (t) for the O–H bond (top), r b (t) for the angle bisector (middle), and r n (t) for the surface normal to the
plane formed by a water molecule (bottom) simulated with the polarizable and non-surface polarity force field models.
dynamics on the TiO2 surface, we calculated the correlation function for the atom charge induced by the local electric field P h i 1qi (t)1qi (0)i p(t) = , (11) P h i 1qi2 (0)i
This indicates that the induced atom charge dynamics of the TiO2 surface is governed by the rotational motion of water molecules.
for the WI site charges (Ws and Wb , see figure 2), where 1qi (t) = qi (t) − hqi (t)i. In addition we calculated p(t) for the Ow site charges in the bulk region as a reference. These correlation functions are plotted in figure 5. By fitting an exponential curve to p(t) in the 1 ps < t < 3 ps regions for the Ws , Wb , and Ow sites, we obtained time constants of 8.8 ps, 10.1 ps, and 1.1 ps for the Ws , Wb , and Ow site charges, respectively. The shorter lifetime of p(t) in bulk water than that at the interface is consistent with the hydrogen bond dynamics and anisotropy decays. However, the relation between p(t) and r (t) is different in the bulk and interfacial water; the lifetime of p(t) for the Ow site is almost half of those of r OH (t) and r b (t) in the bulk water, whereas the time constants of p(t) for the Ws and Wb sites are slightly larger than those of r OH (t) and r n (t) for the interfacial water. The much shorter correlation time of p(t) than the anisotropy decays in the bulk water indicates that the decay of the induced atom charge correlation of the bulk water molecules is influenced by not only the reorientational motion but also the translational motion. In contrast, the correlation functions of the induced atom charge of the Wb and Ws sites show similar decay times to the rotational dynamics of the interfacial water molecules.
We performed MD simulations with the CRK based polarizable force field model and studied the ultrafast water dynamics near the TiO2 surface by calculating the hydrogen bond breaking dynamics and anisotropy decays of water at the water/TiO2 interface. The dynamics dramatically slows down at the water/TiO2 interface compared to bulk water because of the strong water–TiO2 interactions. The ultrafast dynamics is, however, not homogeneous in the interfacial water region: the O–H bond anisotropy decays faster in the first layer water than in the second layer water, while the H–O–H angle bisector shows the opposite tendency. This can be attributed to the first and second layer water molecules interacting with the different moieties of the TiO2 surface, specifically moieties of different charge. The Ow atom in the first layer water interacts with the positive Ti atom of the TiO2 surface, which immobilizes the water along its H–O–H angle bisector, and this gives rise to the slow r b (t). For the second layer, one of the Hw atoms interacts with the O atom of the TiO2 surface. This immobilizes the O–H group, but allows the rotational motion around that O–H bond, so that the bisector can reorient relatively freely. We then investigated the effect of the surface polarity on these dynamics by performing MD simulations with the
4. Concluding remarks
6
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Figure 5. Normalized induced charge correlation functions p(t) for the Ws and Wb site charges on the TiO2 surface, and the Ow site charge
in the bulk region.
References
polarizable and non-surface polarity force field models. In the non-surface polarity model, the polarization in the TiO2 is switched off, while the molecular polarization of the water molecules is included. The surface polarity dramatically slows down the reorientational motion of the interfacial water molecules rotating around the water–TiO2 hydrogen bond axis, while the impact of the surface polarity on the water–TiO2 hydrogen bond dynamics is very limited. The surface charge in the TiO2 induced by the interfacial water molecules makes the water–TiO2 interactions stronger, instantaneously stabilizing the local structure of water. These results demonstrate that the surface polarity of the TiO2 critically affects the ultrafast dynamics of the interfacial water molecules at the water/TiO2 interface, and has to be taken into account for an accurate description of those dynamics. Since the surface charge was induced by the interfacial water molecules, we examined whether their dynamics were correlated with the dynamics of the induced atom charges on the TiO2 surface. In bulk water, the decay of the correlation function of the induced atom charge is much faster than the reorientational motion, indicating that the induced atom charge dynamics of the bulk water molecules is governed by not only the anisotropy decay but also the translational motion. In contrast, the induced atom charge correlations for the WI sites of the TiO2 surface exhibit similar lifetimes to the anisotropy decays for the O–H bond and the normal to the plane formed by atoms of a water molecule, for the first layer and second layer water next to the Ws and Wb sites, respectively. This suggests that the atom charge dynamics of the TiO2 surface induced by the interfacial water molecules is governed by their rotational motion due to limited translational motion. Our MD simulation reveals that the induced atom charge is strongly linked with the water dynamics, making the interfacial water dynamics slower.
[1] Fujishima A and Honda K 1972 Nature 238 37 [2] Hashimoto K, Irie H and Fujishima A 2005 Japan. J. Appl. Phys. 44 8269 [3] Ni M, Leung M K, Leung D Y and Sumathy K 2007 Renew. Sust. Energ. Rev. 11 401 [4] Yu J, Qi L and Jaroniec M 2010 J. Phys. Chem. C 114 13118 [5] deKrafft K E, Wang C and Lin W 2012 Adv. Mater. 24 2014 [6] Diebold U 2003 Surf. Sci. Rep. 48 53 [7] Nakata K, Sakai M, Ochiai T, Murakami T, Takagi K and Fujishima A 2011 Langmuir 27 3275 [8] Yu J C, Ho W, Lin J, Yip H and Wong P K 2003 Environ. Sci. Technol. 37 2296 [9] Armelao L, Barreca D, Bottaro G, Gasparotto A, Maccato C, ˇ Maragno C, Tondello E, Stangar U L, Bergant M and Mahne D 2007 Nanotechnology 18 375709 [10] Carrasco J, Hodgson A and Michaelides A 2012 Nature Mater. 11 667 [11] Li X Z, Probert M I, Alavi A and Michaelides A 2010 Phys. Rev. Lett. 104 066102 [12] Feng J, Slocik J M, Sarikaya M, Naik R R, Farmer B L and Heinz H 2012 Small 8 1049 [13] Gaigeot M P, Sprik M and Sulpizi M 2012 J. Phys.: Condens. Matter 24 124106 [14] Bandura A V and Kubicki J D 2003 J. Phys. Chem. B 107 11072 [15] Pˇredota M, Bandura A V, Cummings P T, Kubicki J D, Wesolowski D J, Chialvo A A and Machesky M L 2004 J. Phys. Chem. B 108 12049 [16] Bandura A V, Kubicki J D and Sofo J O 2008 J. Phys. Chem. B 112 11616 [17] Zhang Z et al 2004 Langmuir 20 4954 [18] Zhang Z, Fenter P, Sturchio N C, Bedzyk M J, Machesky M L and Wesolowski D J 2007 Surf. Sci. 601 1129 [19] Fitts J P, Machesky M L, Wesolowski D J, Shang X, Kubicki J D, Flynn G W, Heinz T F and Eisenthal K B 2005 Chem. Phys. Lett. 411 399 [20] Wesolowski D J et al 2012 Phys. Rev. B 85 167401 [21] Liu L, Zhang C, Thornton G and Michaelides A 2010 Phys. Rev. B 82 161415 [22] Liu L, Zhang C, Thornton G and Michaelides A 2012 Phys. Rev. B 85 167402 [23] Morita A and Kato S 1997 J. Am. Chem. Soc. 119 4021 [24] Morita A and Kato S 1998 J. Chem. Phys. 108 6809 [25] Iuchi S, Morita A and Kato S 2002 J. Phys. Chem. B 106 3466
Acknowledgments
We appreciate Dr T Hasegawa and C S Hsieh for fruitful discussions. HN was supported by Scientific Research on Innovative Areas, a MEXT Grant-in-Aid Project ‘Materials Design through Computics’ (no. 25104724). TO acknowledges the support from the Japan Society for the Promotion of Science. 7
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[41] Wu X and Brooks B R 2008 J. Chem. Phys. 129 154115 [42] Wu X and Brooks B R 2009 J. Chem. Phys. 131 024107 [43] H¨unenberger P H and McCammon J A 1999 J. Chem. Phys. 110 1856 [44] H¨unenberger P H and McCammon J A 1999 Biophys. Chem. 78 69 [45] Tuckerman M, Berne B J and Martyna G J 1992 J. Chem. Phys. 97 1990 [46] Luzar A and Chandler D 1996 Nature 379 55 [47] Kumar R, Schmidt J R and Skinner J L 2007 J. Phys. Chem. 126 204107 [48] Bakker H J and Skinner J L 2009 Chem. Rev. 110 1498 [49] Hsieh C S, Campen R K, Verde A C V, Bolhuis P, Nienhuys H K and Bonn M 2011 Phys. Rev. Lett. 107 116102 [50] Lin Y S, Pieniazek P A, Yang M and Skinner J L 2010 J. Chem. Phys. 132 174505 [51] Tielrooij K J, Garcia-Araez N, Bonn M and Bakker H J 2010 Science 328 1006 [52] Tielrooij K J, Van Der Post S T, Hunger J, Bonn M and Bakker H J 2011 J. Phys. Chem. B 115 12638 [53] Wu Y, Tepper H L and Voth G A 2006 J. Chem. Phys. 124 024503
[26] Nakamura H, Ohto T and Nagata Y 2013 J. Chem. Theory Comput. 9 1193 [27] Liu P, Harder E and Berne B J 2005 J. Phys. Chem. B 109 2949 [28] Nagata Y and Mukamel S 2010 J. Am. Chem. Soc. 132 6434 [29] Thole B T 1981 Chem. Phys. 59 341 [30] van der Maarel J R C, Lankhorst D, de Bleijser J and Leyte J C 1985 Chem. Phys. Lett. 122 541 [31] Struis R P W J, de Bleijser J and Leyte J C 1987 J. Phys. Chem. C 91 1639 [32] Bieze T W N, van der Maarel J R C and Leyte J C 1993 Chem. Phys. Lett. 216 56 [33] Ludwig R 1995 Chem. Phys. 195 329 [34] Moilanen D E, Fenn E E, Lin Y S, Skinner J L, Bagchi B and Fayer M D 2008 Proc. Natl Acad. Sci. 105 5295 [35] Piatkowski L, Eisenthal K B and Bakker H J 2009 Phys. Chem. Chem. Phys. 11 9033 [36] Stengel M 2011 Phys. Rev. B 84 205432 [37] Koitaya T, Nakamura H and Yamashita K 2009 J. Phys. Chem. C 113 7236 [38] Wu X and Brooks B R 2005 J. Chem. Phys. 122 044107 [39] Takahashi K Z, Narumi T and Yasuoka K 2011 J. Chem. Phys. 134 174112 [40] Fukuda I and Nakamura H 2012 Biophys. Rev. 4 161
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Influence of surface polarity on water dynamics at the water/rutile TiO2(110) interface
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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 244102 (8pp)
doi:10.1088/0953-8984/26/24/244102
Influence of surface polarity on water dynamics at the water/rutile TiO2(110) interface Tatsuhiko Ohto1,3,4 , Ankur Mishra1,4 , Seiji Yoshimune1 , Hisao Nakamura2 , Mischa Bonn1 and Yuki Nagata1 1
Max-Planck Institute for Polymer Research, Ackermannweg 10, D-55128, Mainz, Germany Nanosystem Research Institute (NRI), RICS, National Institute of Advanced Industrial Science and Technology (AIST), Central 2, Umezono 1-1-1, Tsukuba, Ibaraki 305-8568, Japan 2
E-mail: [email protected] and [email protected] Received 30 September 2013, revised 8 November 2013 Accepted for publication 20 November 2013 Published 27 May 2014
Abstract
We report molecular dynamics (MD) simulations of the water/clean rutile TiO2 (110) interface using polarizable and non-surface polarity force field models. The effect of surface polarity on the water dynamics near the TiO2 (110) surface is addressed, specifically by calculating the water hydrogen bond and reorientational dynamics. The hydrogen bond lifetime of interfacial water molecules is several times longer than that of bulk water due to the strong water–TiO2 interactions. A comparison of the dynamics simulated with the polarizable and non-surface polarity models shows that, while the hydrogen bond lifetime between the interfacial water and TiO2 surface is insensitive to the surface polarity, the reorientational dynamics around this hydrogen bond axis is significantly influenced by the surface polarity; the surface polarity of the TiO2 increases the water–TiO2 interactions, stabilizing the local structure of the interfacial water molecules and restricting their rotational motion. This reorientation occurs predominantly by rotation around the O–H group hydrogen bonded to the TiO2 surface. Furthermore, we correlate the dynamics of the induced charge on the TiO2 surface with the interfacial water dynamics. Our results show that the timescale of correlations of the atom charges induced by the local electric field in bulk water is influenced by the rotational motion, hydrogen bond rearrangement and translational motion, while the induced charge dynamics of the TiO2 surface is governed primarily by the rotational dynamics of the interfacial water molecules. This study demonstrates that the solid surface polarity has a significant impact on the dynamics of water molecules near TiO2 surfaces. Keywords: titanium dioxide, liquid/solid interface, interfacial water dynamics, charge response kernel, surface polarity (Some figures may appear in colour only in the online journal)
1. Introduction
homogeneous catalysis that products can be separated and extracted easily from the surface and reactants. Among surfaces relevant for heterogeneous catalysis, the water/rutile and anatase TiO2 interfaces have drawn considerable attention owing to their photocatalytic activity: an electron–hole pair can be generated in TiO2 near the surface by ultraviolet irradiation, which can subsequently be used to split a water
In heterogeneous catalysis, the chemical conversion takes place on a catalyst surface, which has the advantage over 3 Present address: Graduate School of Engineering Science, Osaka
University, Japan. 4 TO and AM have contributed equally to this work. 0953-8984/14/244102+08$33.00
1
c 2014 IOP Publishing Ltd
Printed in the UK
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To highlight the effect of the TiO2 surface polarity on the interfacial water dynamics, we compare the results from the polarizable force field model with those obtained using a non-surface polarity force field model. In the polarizable force field model, the CRK technique has been employed for describing both the molecular polarizability of the water molecules and the solid surface polarity of the TiO2 [26]. In the non-surface polarity model all the CRK parameters for the TiO2 surface are set to zero. By using the MD trajectories obtained from the simulations with these force field models, we calculate the hydrogen bond dynamics, water molecular reorientation dynamics, and the dynamics of charge fluctuations at the water/TiO2 interface and discuss the effect of the surface polarity on the water dynamics. This paper is organized as follows. Section 2 describes the MD simulation protocols, where the polarizable and nonsurface polarity force field models are introduced. In section 3 we report the hydrogen bond dynamics and anisotropy decays of the water molecules as well as the induced charge correlation functions of the TiO2 surface, which reveal the effect of the surface polarity on the water molecules. The concluding remarks are given in section 4.
molecule into hydrogen and oxygen [1]. This photocatalytic reaction also modifies the surface properties so that water droplets spread over the TiO2 surface with nearly zero contact angle, which is termed as superhydrophilicity [2]. These innate properties of the water/TiO2 interface have been utilized in a wide range of industrial applications; for example, hydrogen production [1, 3–5], self-cleaning coatings [6, 7], and antibacterial coatings [8, 9]. Since the intermolecular interactions between the interfacial water molecules and the TiO2 surface are responsible for the emergence of these special properties, obtaining molecular level insight into the structure and dynamics of the water molecules near the TiO2 surfaces is essential to understand these interactions and clarify the water (photo-)reactivity at the water/TiO2 interface. Since all-atom molecular dynamics (MD) simulation can visualize the microscopic structure and ultrafast dynamics of a system, it is an indispensable tool to study the intermolecular interactions between liquids and solid surfaces [10–13]. Kubicki and coworkers developed a non-polarizable force field model to reproduce the ab initio optimized geometry of a water molecule adsorbed on the rutile TiO2 surface [14, 15] and analyzed the interfacial water structures and dynamics near the TiO2 surface with this force field model [15, 16]. The results show good agreement with experimental data such as x-ray [17, 18] and second harmonic generation [19], whereas the structures of the interfacial water predicted by the force field model are different from those predicted by firstprinciples MD simulations [20–22]. A distinct limitation of the force field model is that charges are fixed and independent of the local electric field (hence the name non-polarizable force field model) [14, 15]. Accordingly, the discrepancy between the results of the force field model and the first-principles MD simulation likely originates from the polarizability of the water molecules and the TiO2 surface, not included in the former. However, an attempt to include the polarization effect explicitly in force field models of the water/TiO2 interface has not been made. Very recently, we have developed a novel methodology to generate a polarizable force field for the liquid/solid interface by using the charge response kernel (CRK) model [23–25] and applied this methodology to the water/clean rutile TiO2 (110) interface [26]. The polarizable force field model can reproduce the stable structures predicted by the ab initio MD simulation [21], indicating that the surface polarity of TiO2 critically affects the time-averaged conformations of the interfacial water [26]. Here, the next fundamental question is addressed: what is the influence of the TiO2 surface polarity on the interfacial water dynamics? The effect of the molecular polarization on the water dynamics at the aqueous interface has been examined previously at the water/vapor interface [27]. This study showed that the hydrogen bond correlation function, which reflects hydrogen bond lifetimes, decays faster at the interface than in the bulk with polarizable force field models, while this tendency is opposite when non-polarizable force field models are employed, indicating that the polarization effect plays a critical role when modeling the ultrafast dynamics of the aqueous interface [27]. In this study we examine the water dynamics at the water/clean rutile TiO2 (110) interface with the polarizable force field model.
2. MD simulation protocols 2.1. Polarizable model with CRK
We have recently reported a methodology to generate a polarizable force field model for liquid/solid interfaces in which the solid surface polarity is taken into account [26]. In this methodology, the polarizability of the solid surface is added to the non-polarizable force field model within the CRK scheme. Here, we briefly review this polarizable force field model. The Hamiltonian for the water/clean rutile TiO2 (110) interface can be decomposed into H = K + Uwater–water + UTiO2 –TiO2 + Uwater–TiO2 + Uwater,intra ,
(1)
where K represents the kinetic energy, UA−B is the intermolecular interaction potential between the atoms in A and B, and Uwater,intra denotes the intramolecular potential of water. The intermolecular interaction potentials, Uwater–water , UTiO2 −TiO2 , and Uwater−TiO2 , consist of the van der Waals interactions represented by the Lennard-Jones/Buckingham potentials and electrostatic potentials. The Buckingham potential parameters of the Ti–O bonds and those of Uwater−TiO2 are given by [14]. The Lennard-Jones potential parameters between Ow and Ob (see figure 1) can be found in [26]. The Lennard-Jones potentials of Uwater–water and Uwater,intra are described in [28]. The electrostatic potential of Uwater–water is given in the CRK scheme as Uwater−water,ele =
X qi q j i< j
rij
f Thole (rij ) +
1X Vi K ij V j , (2) 2 ij
where K ij is the CRK connecting sites i and j, and Vi is the electrostatic potential acting on site i [23, 24]. To avoid the 2
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the same as in the non-polarizable force field model [14]. The electrostatic potential of Uwater−TiO2 is given by Uwater−TiO2 ,ele =
X
qi q eff j
X
i∈water j∈atom site in TiO2
X
+
X
i∈water j∈WI in TiO2
+
1 2
X
rij
f Thole (rij )
qi q j f Thole (rij ) rij
Vi K ij V j ,
(7)
i, j
where on the Wannier ion (WI) sites, the charges are induced in the TiO2 by the electrostatic field of water [36]. The first term in equation (7) represents the water–TiO2 electrostatic interaction without the polarizable effect of the solid surface, while the second and third terms account for the polarization corrections and represent the electrostatic interaction between the charges of the water molecules and the charges at the WI sites of the TiO2 induced by the electric field of the water. These force field parameters can be found in [26]. Figure 1. (a) Axial distribution of the oxygen atoms of the water molecules normal to the water/TiO2 interface. (b) Schematic representations of stable water structures in the first and second layers near the TiO2 surface projected onto the cross-section normal to the (001) direction.
2.2. Non-surface polarity model
In the non-surface polarity force field model, the polarization correction terms were removed from equation (7) and thus the water–TiO2 electrostatic potential was given by
divergence of induced charges, Thole’s damping function was introduced: 1 for x ≥ 1 (3) f Thole (rij ) = 4 x − 2x 3 + 2x for x < 1,
Uwater−TiO2 ,ele =
(5) (0)
rij
,
f Thole (rij ). (8)
We conducted MD simulations at the water/TiO2 interface using both the polarizable and non-surface polarity force field models. Our system consisted of 510 water molecules and seven rutile TiO2 (110) layers consisting of 3 × 6 unit cells. The simulation cell size was 20.07 Å × 18.44 Å × 120 Å [37]. Periodic boundary conditions were used for the x and y axes, while a reflective wall condition was employed for the z axis. The electrostatic potential was calculated by using the isotropic periodic sum (IPS) method with a cutoff of 45 Å [38–40]. In the IPS method, long-range interactions are represented by interactions with isotropic periodic images of a defined local region [38, 41, 42], which eliminates the artifacts produced due to the periodic boundary conditions in the Ewald sum method [43, 44]. This method is computationally cheaper but similarly accurate when compared with the Ewald sum method [38, 39]. We implemented the reference system propagator algorithm (RESPA) for integrating the equations of motion [45], where the forces associated with the intramolecular potential of water were calculated every 0.125 fs and the
where the zeroth order charge at site i, qi , represents the gas-phase charge. For the electrostatic potential of UTiO2 –TiO2 , a non-polarizable force field model with fixed charges was employed
i> j
rij
2.3. MD simulation
j
X qieff q eff j
qi q eff j
This potential indicates that the surface charges of the TiO2 are not induced by the electric field of the water molecules. We use the same polarizable force field model for Uwater–water and UTiO2 –TiO2 . Note that although the second and third terms of equation (7) are missing in equation (8), the total charge of (0) the system is zero because qi = 0 at the WI sites.
j
UTiO2 –TiO2 ,ele =
X
i∈water j∈ atom site in TiO2
where x = rij /A(αi α j )1/6 and αi is the polarizability volume of the site i [29]. Although A = 2.8 [25] has been used for calculating the static structure of water [26], it makes the bulk water dynamics diffusive. We adjusted the parameter A to reproduce the anisotropy decay of the water experimentally measured [30–35] and obtained A = 2.65 for the water–water interaction and A = 2.8 for the water–TiO2 interactions. Charges are calculated by the self-consistent field equations [23, 24]: X (0) qi = qi + K ij V j , (4) X qj Vi = f Thole (rij ), rij
X
(6)
where q eff represents the effective site charge at the atom site in the TiO2 to which the polarization effect arising from the bulk TiO2 is renormalized [14]. Note that the UTiO2 –TiO2 ,ele is 3
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other forces were calculated every 1.0 fs. We generated twelve independent initial configurations of the water/TiO2 interface and ran the MD simulations by rescaling the atomic velocities so that the system temperature reached 300 K. We equilibrated the systems by performing 50 ps MD runs in the NVE ensemble and sequentially performed a 100 ps MD run for each sample to obtain the MD trajectories, which were used for computing the hydrogen bond dynamics, anisotropy decays, and induced charge correlation functions. 3. Results 3.1. Structure of interfacial water near the TiO2 surface Figure 2. Schematic representation of the water/TiO2 interface. Hw (Ow ) denotes the hydrogen (oxygen) atom of the water molecule, Tiv and Tivi denote the five-fold and six-fold coordinated Ti atoms on the surface, Ob represents the two-fold coordinated oxygen atom next to the Ti surface layer, and Os represents the oxygen atom on the Ti surface layer. Ws is the WI site and is defined as the center of mass of three titanium and two Os atoms indicated by the black arrows, while Wb is the WI site located at the Ob atom
To check the water structure near the TiO2 surface, the axial distribution of the water oxygen atoms (Ow ) was calculated, which is plotted in figure 1. The point of origin was set at the average position of the surface Ti atoms. Figure 1(a) shows that the axial distribution has several sharp peaks near the TiO2 surface, whereas the water density reaches a constant value (1.0 g cm−3 ) at a distance of 12 Å away from the Ti surface. Moving from the bulk water region to the interface, the anisotropic structure of water due to the TiO2 surface emerges at a distance of ∼10 Å from the surface. The water structures contributing to the peaks at 2.2 Å and 3.0–4.0 Å in the axial distribution have been studied previously [26], and are schematically depicted in figure 1(b). Note that the peak at 3.8 Å is enhanced and the peak at 3.4 Å is not as prominent as reported in [26]. Since A = 2.8 for the water–water interaction is used instead of A = 2.65 because of the diffusive bulk water dynamics with A = 2.8, the short-range electrostatic interactions are slightly enhanced and thus the peak at 3.8 Å becomes sharper than predicted by the previous study [26]. In this study we defined the water molecules located in the 0 Å < z < 3 Å and 3 Å < z < 4.6 Å ranges as the first and second layer water, respectively. Furthermore, the water molecules in the z > 12 Å are defined as bulk water. These definitions will be used below for simulating the anisotropy decays of water.
site indicated by the red arrow.
The simulated c(t) are displayed in figure 3. The hydrogen bond breaking dynamics is substantially slowed down for the water molecules near the TiO2 surface compared to bulk water. This can be attributed to the stronger water–TiO2 interactions than the water–water interactions. This tendency is consistent with the previous report that water molecules near the TiO2 surface are less diffusive than bulk water [15]. We subsequently explored the effect of the TiO2 surface polarity on the Ob · · · Hw hydrogen bond breaking dynamics by comparing c(t) for the polarizable and non-surface polarity force field models. Figure 3 shows that the decay of c(t) is slightly faster for the polarizable model than the non-surface polarity model for short times (t < 8 ps), whereas the surface polarity slows down the hydrogen bond breaking on longer timescales (t > 8 ps). This indicates that for t < 8 ps the fluctuation of the induced charges triggers fluctuations of the Ob · · · Hw hydrogen bond, while the induced dipole at the TiO2 surface strengthens the Ob · · · Hw hydrogen bond interactions, giving rise to slower hydrogen bond breaking on long timescales. However, the effect of the surface polarity of the TiO2 on the hydrogen bond dynamics of water is very limited.
3.2. Hydrogen bond dynamics
The hydrogen bond breaking dynamics can be characterized by the time correlation function c(t) =
hh(0)h(t)i , hhi
(9)
3.3. Anisotropy decay
where h(t) equals 1 when a hydrogen bond is present at time t, and 0 otherwise [46]. h· · · i denotes the thermal average. We defined that a hydrogen bond formed when the intermolecular O · · · H distance was less than the cutoff length of 2.41 Å [47]. Note that although several different definitions have been proposed for judging the hydrogen bond formation, the resulting c(t)s simulated with these different definitions are very similar [47]. We calculated c(t) for the Ob · · · Hw hydrogen bonds contributed by the second layer water and Ow · · · Hw hydrogen bonds in the bulk, where Ob stands for the two-fold coordinated oxygen atom near the Ti surface, and Hw is the hydrogen atom of a water molecule (see figure 2).
The orientational dynamics of liquids can be characterized by the anisotropy decay, and has been addressed experimentally using polarization dependent pump–probe spectroscopy [48–50]. This anisotropy decay can be calculated by [48] r ν (t) = 52 hP2 (Eν (t) · νE (0))i,
(10)
where P2 is the second Legendre polynomial and νE (t) is the unit vector of the targeted normal mode at time t. We calculated the anisotropy decays for the O–H bond (r OH (t)), the H–O–H angle bisector (r b (t)) and the normal to the plane formed by 4
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Table 1. Time constants for the anisotropy decays of the water molecules in units of picoseconds.
r OH (t) r b (t) r n (t)
First layer First layer (polarizable) (non-surface polarity)
Second layer (polarizable)
Second layer (non-surface polarity)
Bulk
6.1 14.8 6.2
8.5 7.5 7.0
6.9 5.6 5.0
2.2 2.2 1.8
5.0 8.3 4.8
allowing the angle bisector to rotate around the Ow –Hw · · · Ob axis. The observation that the dynamics is different along different molecular axes is strongly reminiscent of dynamics previously reported in ionic aqueous solutions. Tielrooij et al found that ions of different charge affect the orientations of the water molecules near the ions along different molecular axes: cations slow the orientation of the H–O–H bisector, while anions mainly slow down the reorientation dynamics of the O–H group pointing toward the anion [51, 52]. Revisiting the water/TiO2 interface, the atomic charges of the Tiv and Ob atoms assigned in the force field model are ∼2e and ∼−1e, respectively [14]. The simulated r OH (t) and r b (t) show that water molecules in the first layer interacting with the positive Tiv atom exhibit slower anisotropy decay of the H–O–H angle bisector, whereas the O–H bond orientation of the second layer water molecules bound to the negative Ob is less mobile, with the H–O–H angle bisector relatively free to rotate around that O–H bond. This picture is fully consistent with the pump–probe reorientational study in bulk ionic aqueous solutions [51, 52]. The anisotropy decay of the normal to the plane with atoms of a water molecule, r n (t), which is shown in the bottom panel of figure 4, shows faster decay in the first layer than the second layer. This indicates that in the first layer the out-of-plane motion of the water molecules faces less hindrance than in the second layer. The anisotropy decays, r OH (t), r b (t), and r n (t), of the interfacial water molecules clearly illustrate that the interfacial water dynamics is heterogeneous and dependent on the different moieties of the TiO2 adjacent to the water molecules. We now focus on the effect of the TiO2 surface polarity on the anisotropy decays of water. Figure 4 shows that the anisotropy decays of r OH (t), r b (t), and r n (t) are significantly faster with the non-surface polarity model than with the polarizable model, implying that the surface polarity of the TiO2 slows down the anisotropy decays of the interfacial water molecules. The larger impact of the surface polarity on the anisotropy decay than on the hydrogen bond dynamics indicates that the surface polarity stabilizes the local structure of the water molecules near the TiO2 interface [21, 26], leading to the slowing down of the anisotropy decay.
Figure 3. Hydrogen bond correlation function c(t) for the Ob · · · Hw in the second layer water and the Ow · · · Hw in the bulk water
simulated by the polarizable force field model. c(t) for the Ob · · · Hw simulated by using the non-surface polarity force field model is also plotted.
the atoms of a water molecule (r n (t)), which are shown in figure 4. By fitting an exponential function to r OH (t), r b (t), and r n (t) in the range of 1 ps < t < 3 ps for the interfacial water and bulk water, we obtained the time constants for the anisotropy decays, which are summarized in table 1. The time constant of r OH (t) obtained for bulk water is comparable with experimental values [30–35] and is similar to the value predicted by the SPC/E water model [50, 53]. We first focus on the anisotropy decay of the O–H bond. The top panel of figure 4 shows that r OH (t) is faster in the first water layer than in the second layer. This can be attributed to the different water–TiO2 interactions. Since the Ow atom in the first layer water is tightly bonded to the five-fold coordinated Ti (Tiv ) atom on the Ti surface and the Hw atoms interact with other water molecules, the O–H bond orientations are easily modulated by the fluctuations of surrounding water molecules. Meanwhile, the Hw atom of the second layer water is strongly hydrogen bonded to the Ob atom, leading to less modulation of the O–H bond orientations. The middle panel of figure 4 shows that the anisotropy decay of the H–O–H angle bisector, r b (t), is slower in the first layer than in the second layer, while the opposite trend is observed for r OH (t). This can be accounted for as follows. The angle bisector of the water molecules in the first layer is nearly parallel to the Ow · · · Tiv axis, restricting the rotational motion of the H–O–H angle bisector. On the other hand, the Hw atom of the second layer water is hydrogen bonded with the Ob atom,
3.4. Induced charge correlation
In our CRK polarizable force field modeling, the surface charge of the TiO2 is induced by the water molecules. To connect the interfacial water dynamics with the induced charge 5
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T Ohto et al
Figure 4. Anisotropy decays of r OH (t) for the O–H bond (top), r b (t) for the angle bisector (middle), and r n (t) for the surface normal to the
plane formed by a water molecule (bottom) simulated with the polarizable and non-surface polarity force field models.
dynamics on the TiO2 surface, we calculated the correlation function for the atom charge induced by the local electric field P h i 1qi (t)1qi (0)i p(t) = , (11) P h i 1qi2 (0)i
This indicates that the induced atom charge dynamics of the TiO2 surface is governed by the rotational motion of water molecules.
for the WI site charges (Ws and Wb , see figure 2), where 1qi (t) = qi (t) − hqi (t)i. In addition we calculated p(t) for the Ow site charges in the bulk region as a reference. These correlation functions are plotted in figure 5. By fitting an exponential curve to p(t) in the 1 ps < t < 3 ps regions for the Ws , Wb , and Ow sites, we obtained time constants of 8.8 ps, 10.1 ps, and 1.1 ps for the Ws , Wb , and Ow site charges, respectively. The shorter lifetime of p(t) in bulk water than that at the interface is consistent with the hydrogen bond dynamics and anisotropy decays. However, the relation between p(t) and r (t) is different in the bulk and interfacial water; the lifetime of p(t) for the Ow site is almost half of those of r OH (t) and r b (t) in the bulk water, whereas the time constants of p(t) for the Ws and Wb sites are slightly larger than those of r OH (t) and r n (t) for the interfacial water. The much shorter correlation time of p(t) than the anisotropy decays in the bulk water indicates that the decay of the induced atom charge correlation of the bulk water molecules is influenced by not only the reorientational motion but also the translational motion. In contrast, the correlation functions of the induced atom charge of the Wb and Ws sites show similar decay times to the rotational dynamics of the interfacial water molecules.
We performed MD simulations with the CRK based polarizable force field model and studied the ultrafast water dynamics near the TiO2 surface by calculating the hydrogen bond breaking dynamics and anisotropy decays of water at the water/TiO2 interface. The dynamics dramatically slows down at the water/TiO2 interface compared to bulk water because of the strong water–TiO2 interactions. The ultrafast dynamics is, however, not homogeneous in the interfacial water region: the O–H bond anisotropy decays faster in the first layer water than in the second layer water, while the H–O–H angle bisector shows the opposite tendency. This can be attributed to the first and second layer water molecules interacting with the different moieties of the TiO2 surface, specifically moieties of different charge. The Ow atom in the first layer water interacts with the positive Ti atom of the TiO2 surface, which immobilizes the water along its H–O–H angle bisector, and this gives rise to the slow r b (t). For the second layer, one of the Hw atoms interacts with the O atom of the TiO2 surface. This immobilizes the O–H group, but allows the rotational motion around that O–H bond, so that the bisector can reorient relatively freely. We then investigated the effect of the surface polarity on these dynamics by performing MD simulations with the
4. Concluding remarks
6
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Figure 5. Normalized induced charge correlation functions p(t) for the Ws and Wb site charges on the TiO2 surface, and the Ow site charge
in the bulk region.
References
polarizable and non-surface polarity force field models. In the non-surface polarity model, the polarization in the TiO2 is switched off, while the molecular polarization of the water molecules is included. The surface polarity dramatically slows down the reorientational motion of the interfacial water molecules rotating around the water–TiO2 hydrogen bond axis, while the impact of the surface polarity on the water–TiO2 hydrogen bond dynamics is very limited. The surface charge in the TiO2 induced by the interfacial water molecules makes the water–TiO2 interactions stronger, instantaneously stabilizing the local structure of water. These results demonstrate that the surface polarity of the TiO2 critically affects the ultrafast dynamics of the interfacial water molecules at the water/TiO2 interface, and has to be taken into account for an accurate description of those dynamics. Since the surface charge was induced by the interfacial water molecules, we examined whether their dynamics were correlated with the dynamics of the induced atom charges on the TiO2 surface. In bulk water, the decay of the correlation function of the induced atom charge is much faster than the reorientational motion, indicating that the induced atom charge dynamics of the bulk water molecules is governed by not only the anisotropy decay but also the translational motion. In contrast, the induced atom charge correlations for the WI sites of the TiO2 surface exhibit similar lifetimes to the anisotropy decays for the O–H bond and the normal to the plane formed by atoms of a water molecule, for the first layer and second layer water next to the Ws and Wb sites, respectively. This suggests that the atom charge dynamics of the TiO2 surface induced by the interfacial water molecules is governed by their rotational motion due to limited translational motion. Our MD simulation reveals that the induced atom charge is strongly linked with the water dynamics, making the interfacial water dynamics slower.
[1] Fujishima A and Honda K 1972 Nature 238 37 [2] Hashimoto K, Irie H and Fujishima A 2005 Japan. J. Appl. Phys. 44 8269 [3] Ni M, Leung M K, Leung D Y and Sumathy K 2007 Renew. Sust. Energ. Rev. 11 401 [4] Yu J, Qi L and Jaroniec M 2010 J. Phys. Chem. C 114 13118 [5] deKrafft K E, Wang C and Lin W 2012 Adv. Mater. 24 2014 [6] Diebold U 2003 Surf. Sci. Rep. 48 53 [7] Nakata K, Sakai M, Ochiai T, Murakami T, Takagi K and Fujishima A 2011 Langmuir 27 3275 [8] Yu J C, Ho W, Lin J, Yip H and Wong P K 2003 Environ. Sci. Technol. 37 2296 [9] Armelao L, Barreca D, Bottaro G, Gasparotto A, Maccato C, ˇ Maragno C, Tondello E, Stangar U L, Bergant M and Mahne D 2007 Nanotechnology 18 375709 [10] Carrasco J, Hodgson A and Michaelides A 2012 Nature Mater. 11 667 [11] Li X Z, Probert M I, Alavi A and Michaelides A 2010 Phys. Rev. Lett. 104 066102 [12] Feng J, Slocik J M, Sarikaya M, Naik R R, Farmer B L and Heinz H 2012 Small 8 1049 [13] Gaigeot M P, Sprik M and Sulpizi M 2012 J. Phys.: Condens. Matter 24 124106 [14] Bandura A V and Kubicki J D 2003 J. Phys. Chem. B 107 11072 [15] Pˇredota M, Bandura A V, Cummings P T, Kubicki J D, Wesolowski D J, Chialvo A A and Machesky M L 2004 J. Phys. Chem. B 108 12049 [16] Bandura A V, Kubicki J D and Sofo J O 2008 J. Phys. Chem. B 112 11616 [17] Zhang Z et al 2004 Langmuir 20 4954 [18] Zhang Z, Fenter P, Sturchio N C, Bedzyk M J, Machesky M L and Wesolowski D J 2007 Surf. Sci. 601 1129 [19] Fitts J P, Machesky M L, Wesolowski D J, Shang X, Kubicki J D, Flynn G W, Heinz T F and Eisenthal K B 2005 Chem. Phys. Lett. 411 399 [20] Wesolowski D J et al 2012 Phys. Rev. B 85 167401 [21] Liu L, Zhang C, Thornton G and Michaelides A 2010 Phys. Rev. B 82 161415 [22] Liu L, Zhang C, Thornton G and Michaelides A 2012 Phys. Rev. B 85 167402 [23] Morita A and Kato S 1997 J. Am. Chem. Soc. 119 4021 [24] Morita A and Kato S 1998 J. Chem. Phys. 108 6809 [25] Iuchi S, Morita A and Kato S 2002 J. Phys. Chem. B 106 3466
Acknowledgments
We appreciate Dr T Hasegawa and C S Hsieh for fruitful discussions. HN was supported by Scientific Research on Innovative Areas, a MEXT Grant-in-Aid Project ‘Materials Design through Computics’ (no. 25104724). TO acknowledges the support from the Japan Society for the Promotion of Science. 7
J. Phys.: Condens. Matter 26 (2014) 244102
T Ohto et al
[41] Wu X and Brooks B R 2008 J. Chem. Phys. 129 154115 [42] Wu X and Brooks B R 2009 J. Chem. Phys. 131 024107 [43] H¨unenberger P H and McCammon J A 1999 J. Chem. Phys. 110 1856 [44] H¨unenberger P H and McCammon J A 1999 Biophys. Chem. 78 69 [45] Tuckerman M, Berne B J and Martyna G J 1992 J. Chem. Phys. 97 1990 [46] Luzar A and Chandler D 1996 Nature 379 55 [47] Kumar R, Schmidt J R and Skinner J L 2007 J. Phys. Chem. 126 204107 [48] Bakker H J and Skinner J L 2009 Chem. Rev. 110 1498 [49] Hsieh C S, Campen R K, Verde A C V, Bolhuis P, Nienhuys H K and Bonn M 2011 Phys. Rev. Lett. 107 116102 [50] Lin Y S, Pieniazek P A, Yang M and Skinner J L 2010 J. Chem. Phys. 132 174505 [51] Tielrooij K J, Garcia-Araez N, Bonn M and Bakker H J 2010 Science 328 1006 [52] Tielrooij K J, Van Der Post S T, Hunger J, Bonn M and Bakker H J 2011 J. Phys. Chem. B 115 12638 [53] Wu Y, Tepper H L and Voth G A 2006 J. Chem. Phys. 124 024503
[26] Nakamura H, Ohto T and Nagata Y 2013 J. Chem. Theory Comput. 9 1193 [27] Liu P, Harder E and Berne B J 2005 J. Phys. Chem. B 109 2949 [28] Nagata Y and Mukamel S 2010 J. Am. Chem. Soc. 132 6434 [29] Thole B T 1981 Chem. Phys. 59 341 [30] van der Maarel J R C, Lankhorst D, de Bleijser J and Leyte J C 1985 Chem. Phys. Lett. 122 541 [31] Struis R P W J, de Bleijser J and Leyte J C 1987 J. Phys. Chem. C 91 1639 [32] Bieze T W N, van der Maarel J R C and Leyte J C 1993 Chem. Phys. Lett. 216 56 [33] Ludwig R 1995 Chem. Phys. 195 329 [34] Moilanen D E, Fenn E E, Lin Y S, Skinner J L, Bagchi B and Fayer M D 2008 Proc. Natl Acad. Sci. 105 5295 [35] Piatkowski L, Eisenthal K B and Bakker H J 2009 Phys. Chem. Chem. Phys. 11 9033 [36] Stengel M 2011 Phys. Rev. B 84 205432 [37] Koitaya T, Nakamura H and Yamashita K 2009 J. Phys. Chem. C 113 7236 [38] Wu X and Brooks B R 2005 J. Chem. Phys. 122 044107 [39] Takahashi K Z, Narumi T and Yasuoka K 2011 J. Chem. Phys. 134 174112 [40] Fukuda I and Nakamura H 2012 Biophys. Rev. 4 161
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