Water diffusion on TiO 2 anatase surface

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1 Water diffusion on TiO 2 anatase surface L. Agosta, F. Gala, and G. Zollo Citation: AIP Conference Proceedings 1667, (2015); doi: / View online: View Table of Contents: Published by the American Institute of Physics Articles you may be interested in A DFT study of water adsorption on rutile TiO 2 (110) surface: The effects of surface steps The Journal of Chemical Physics 145, (2016); / Ab-initio study of hydrogen doping and oxygen vacancy at anatase TiO 2 surface AIP Advances 4, (2014); / Electrical and optical properties of TiO 2 anatase thin films Journal of Applied Physics 75, 2042 (1994); / CO 2 adsorption on TiO 2 (101) anatase: A dispersion-corrected density functional theory study The Journal of Chemical Physics 135, (2011); / Perspective: A controversial benchmark system for water-oxide interfaces: H 2 O/TiO 2 (110) The Journal of Chemical Physics 147, (2017); / Reaction pathway and free energy barrier for defect-induced water dissociation on the (101) surface of - anatase The Journal of Chemical Physics 119, 7445 (2003); /

2 Water Diffusion on TiO 2 Anatase Surface L. Agosta, F. Gala and G. Zollo Department of Materials and Environmental Chemistry, Stockholm University, 2014 Arrhenius Laboratory, Svante Arrhenius väg 16C, Stockholm Sweden Dipartimento di Scienze di Base e Applicate per l Ingegneria (Sezione di Fisica), Sapienza, Università di Roma, Via A. Scarpa 14-16, Rome Italy Abstract. Compatibility between biological molecules and inorganic materials, such as crystalline metal oxides, is strongly dependent on the selectivity properties and the adhesion processes at the interface between the two systems. Among the many different aspects that affect the adsorption processes of peptides or proteins onto inorganic surfaces, such as the charge state of the amino acids, the peptide 3D structure, the surface roughness, the presence of vacancies or defects on and below the surface, a key role is certainly played by the water solvent whose molecules mediate the interaction. Then the surface hydration pattern may strongly affect the adsorption behavior of biological molecules. For the particular case of (101) anatase TiO 2 surface that has a fundamental importance in the interaction of biocompatible nano-devices with biological environment, it was shown, both theoretically and experimentally, that various hydration patterns are close in energy and that the water molecules are mobile at as low temperature values as 190 K. Then it is important to understand the dynamical behavior of first hydration layer of the (101) anatase surface. As a first approach to this problem, density functional calculations are used to investigate water diffusion on the (101) anatase TiO 2 surface by sampling the potential energy surface of water molecules of the first hydration layer thus calculating the water molecule migration energy along some relevant diffusion paths on the (101) surface. The measured activation energy of water migration seems in contrast with the observed surface mobility of the water molecules that, as a consequence could be explained invoking a strong role of the entropic term in the context of the transition state theory. Keywords: titania, anatase, water, adsorption, diffusion, NEB, energy barrier PACS: A es, Db INTRODUCTION Titanium dioxide (TiO 2 ) is an adaptable material that has been widely applied in many technological fields including medicine and pharmacology [1], photo-catalysis and solar-hydrogen production [2], and surface recognition of organic materials [3]. In nature, TiO 2 crystallizes in three different structures: rutile, anatase and brookite, all formed by TiO 6 octahedra connected by shared edges and/or corners; however, at the nanoscale, anatase is the most stable polymorph that is also the most efficient (and widely used) in catalysis and (photo)electrochemistry. Its structure exhibits a saw-tooth-like morphology with five-fold coordinate Ti (Ti 5c ) and two-fold coordinated surface O (O 2c ) atoms arranged in rows along the [010] direction [9]. As most of these applications involve aqueous environment, the interaction between water and TiO 2 (101) anatase surface has attracted strong interest and has been extensively studied in the last years [5, 6, 7, 8, 9]; however such studies have focused their attention mainly on the adsorption properties of water on the titania surface, while little is known on the kinetic properties of the adsorbed water on that surface. Furthermore it has been shown that water molecules mediate the adsorption processes of biological molecules on TiO 2 (101) anatase surface [3, 4]; the adhesion properties of biological molecules, as the bonding selectivity of a specific amino acids onto the (101) anatase surface or the possibility for these amino acids to migrate on the surface, is strongly affected by the water molecules adsorbed on the first layers of the (101) anatase surface. The study of the mobility properties of water molecules adsorbed on the TiO 2 (101) anatase surface is fundamental importance in order to better understand the adhesion processes involved in complex biological systems. In this contest, we mainly refer to recent systematic studies of the water adsorption patterns on TiO 2 (101) anatase surface that was extensively investigated through ab-initio calculations [9]. The calculated adsorption and total energies of the possible stable and meta-stable hydration patterns indicate the existence of several hydration patterns with rather small energy difference ( E 1 mev) among them and with respect to the ground state pattern as compared to the adsorption energy of a single water molecule ( E ads 730 mev). This result suggests that several, nearly energetically equivalent, hydration patterns can form onto the (101) anatase surface. Moreover it has been shown [8] that the water adsorption onto the anatase surface is thermodynamically stable in vacuum up to 190 K, even if on a TiO 2 (101) surface with NANOFORUM 2014 AIP Conf. Proc. 1667, ; doi: / AIP Publishing LLC /$

3 subsurface defects and stable water adsorption has been observed up to 400 K [9]. From the same studies, however, it has been evidenced, by recording consecutive STM images of a TiO 2 (101) surface covered by water molecules with a density of 0.11 ML, that the hydration pattern of the first layer changes dynamically due to water migration even at as low temperature as 190 K. On the other hand, up to the authors knowledge there are no theoretical studies concerning the kinetic and the dynamical properties of the adsorbed water onto the TiO 2 anatase (101) surface that could explain the observed water mobility at low temperature. Both experimental and theoretical results emphasize the importance of understanding the kinetic and thermodynamic processes that could explain the observed diffusive behavior of water molecules on TiO 2 (101) surface. Therefore in order to give a reliable picture of these processes, we have focussed on the migration of adsorbed water molecules onto the (101) anatase surface and in this article we report on the calculation of the energy diffusion barriers of the possible water molecules migration paths on the (101) anatase surface with the aim to build a reliable representative model for the diffusion process of the adsorbed water molecules on TiO 2 (101) surface. On this basis a possible interpretation of more complicated systems involving the adsorption of biological molecule in water environment is expected. THEORETICAL METHOD Water diffusion on TiO 2 anatase surface has been studied through ab-initio atomistic modelling based on the Density Functional Theory (DFT) [10, 11]; in the recent literature, in fact, such scheme has been used extensively to model the water adsorption on various TiO 2 surfaces both of the rutile and the anatase phases [6, 8, 12, 13, 16], showing a good agreement with the experimental values obtained for water adsorption on (101) TiO 2 surface. Such experimental studies of water on anatase have confirmed the validity and the reliability of DFT atomistic modeling; the ab-initio calculations predict that the water molecule is bonded to a Ti 5c atom and forms weak hydrogen bonds with the neighbouring O 2c atoms. The DFT scheme here employed adopts a generalized gradient approximation (GGA) of the electron exchange and correlation energy using Perdew-Burke-Ernzerhof formula (PBE) [17]. Due to computational reasons, ultrasoft pseudopotentials (US-PP) have been employed that, according also to other authors [12], have been demonstrated to be suitable for this system. The lattice parameters a, b, c, d obtained for the anatase bulk phase using the US-PPs are closer to the experimental data than the ones obtained using norm-conserving Troullier-Martins [18] pseudopotentials. FIGURE 1. (Color Online) Top view of a single water molecule adsorbed on (101) anatase surface. US-PPs have allowed the usage of an energy cut-off of 60 Ry for the wave functions and 400 Ry for the electron density in the context of a plane wave expansion basis set. The (101) anatase TiO 2 surface has been modeled using a slab geometry laying in the xy plane composed by two surface unit cells along the y and the z directions and one along x. The slab contains 48 atoms and the supercell includes two vacuum regions nearly of 16.2 Å thick. The artificial electric field across the slab induced by the PBCs has been corrected following Ref. [19] and a (3x3x1) Mokhorst- Pack k-point grid [20] for the Brillouin zone sampling has been employed. In order to study the possible diffusion paths on the (101) anatase surface, the Nugded Elastic Band (NEB) [21] method is used

4 FIGURE 2. Two components make up the nudged elastic band force F NEB i : the spring force F S i, along the tangent direction τ i, and the perpendicular force due to the potential F i. The unprojected force due to the potential F i is also shown for completeness. Image taken from [21] The NEB method is aimed to find the minimum energy path (MEP) between two known stable or meta-stable configurations; it is indeed a chain-of-states method in which a string of geometric configurations (the images) is used to describe a reaction pathway. In the context of transition state theory, the first and the last images are two meta-stable states (i.e. local minima on the potential energy surface) that are separated by a potential energy saddle point that must be exceeded by the diffusing molecule; the saddle point is particularly important for characterizing the transition state, being the exponential term in the Arrhenius law determined by the energy difference between the saddle point configuration and the initial one. Each point of the MEP, constructed using the NEB, is obtained by minimizing the total energy in the sub-space that is orthogonal to the local direction of the diffusion path; it can be shown that the MEP found in this way contains at least one first-order saddle point and that the string of configurations describe the reaction process. Typically a NEB calculation is started from an initial guess pathway connecting the initial and the final states, then the images are relaxed until the MEP is reached, through a force projection scheme (see Fig. 2) where real forces act perpendicularly to the fixed path, while spring forces act along it. If τ i is the unit vector in the direction linking image i with i+1, the NEB force on image i can be written as the sum of two orthogonal components: where F i F NEB i = F i + F S i (1) is the component of the force due to the potential perpendicular to the path, and F S i is the spring force parallel to the path, F i = V (R i ) + ( V (R i ) τ i )τ i (2) F S i = k( R i+1 R i R i R i 1 )τ i (3) where R i is the position of the ith image, V is the total potential, and k is the spring constant; error bars in the construction of the MEPs have been evaluated as the absolute values of the forces on each image that are orthogonal to the chosen path. All the first-principles calculations, including NEB calculations, have been performed using the QUANTUM- ESPRESSO package[22]

5 Result and Discussion When a single water molecule adsorbs on the (101) TiO2 surface (as shown in Fig. 1) three bonds are formed: two hydrogen bonds (H-bonds) between the water H atoms and two surface two-fold coordinated oxygens O2c (dh O2c = 2.35 Å), and a dative covalent bond [9] between the water oxygen atom and a surface Ti5c atom (dowater Ti5c = 2.32 Å). The adsorption energy per water molecule is defined as: [ET ES neh2 O ] (4) n where ET and ES are the energy of the hydrated slab and the dry slab respectively, EH2 O is the energy of the isolated water molecule while n is the number of water molecules adsorbed, resulting for the configuration showed in Fig. 1 in Eads = ev. NEB calculations have been performed along those diffusion paths connecting Ti5c equivalent surface atoms, i.e. the adsorption sites where a water molecule can be adsorbed; following this criterion, two migration paths have been chosen along the [010] and [212 ] directions parallel to the surface, that basically connect two adjacent adsorption sites where the water can stay in its ground state configuration. Along the path, six equally spaced images have been considered; in Figs. 3 and 4 the energy barrier curves (obtained with a polynomial fit) and the water configurations are reported for respectively the [010] and the [212 ] diffusion paths. Eads = FIGURE 3. (Color Online) Water diffusion barrier along the [010] direction as a function of the distance between the O atom of the water molecule and the initial Ti5c adsorption site. The energy barriers measured for saddle points obtained along the [010] and the [212 ] migration paths are respec[010] [212 ] tively Esaddle ' 0.58 ev and Esaddle ' 0.52 ev that are rather similar if one considers the error bars inherent into the method used. In both cases the atoms belonging to the (101) anatase TiO2 slab (especially the topmost ones) slightly move from their equilibrium positions giving just a small contribution to the potential energy surface; hence the main contribution to the calculated energy barrier is certainly coming from the energy of the water molecule interacting with the surface atoms at different positions along the path. In particular, along the [010] diffusion path, the water molecule undergoes a simple horizontal rigid shift, with no significant rearrangement. The greatest contribution to the energy barrier is given by the breaking of the dative covalent bond between the H2 O oxygen and the Ti5c surface atom, while at least one hydrogen bond is active along the entire migration path. Thus the saddle point for the [010] diffusion path is the

6 FIGURE 4. (Color Online) Water diffusion barrier along the [212 ] directions a function of the distance between the O atom of the water molecule and the initial Ti5c adsorption site. configuration where the oxygen atom belonging to the water molecule is in the middle point between the two Ti5c atoms where the oxygen is bonded in the initial and final states of the diffusion path. The water molecule basically lies in the horizontal plane along the entire path. Along the [212 ] migration path, instead, a sort of "rolling stone" behavior of the water molecule arises; again the dative bond breaking contributes most to the energy barrier, but in this case we can notice that the two initial hydrogen bonds are maintained along the first half of the path, i.e. the molecule rotates about the axis that contains the two hydrogens bonded on the surface, while in the second half of the path the water molecule rotates about the axis containing the oxygen atom that stays bonded with the surface Ti5c atom. FIGURE 5. (Color Online) Water diffusion path together with the corresponding energy barrier along the [212 ] direction for the "rolling stone" case. The initial and final configurations represent an unstable adsorption site for a H2 O molecule with respect the adsorption on a Ti5c surface atom

7 The above described migration kinetic behavior and the corresponding energetics are better evidenced looking at Fig. 5; such NEB calculation, in fact, shows the diffusion path along the [21 2] direction that connects two meta-stable adsorption configurations with the H 2 O molecule that is bonded to the surface only through two hydrogen bonds between the water H atoms and two surface O 2c atoms. This meta-stable configuration represents a water adsorption configuration as well with an adsorption energy significantly higher (of about 0.22 ev) than the one of the ground state configuration; furthermore it has been shown that this adsorption configurations are likely to occur when a high coverage of water on the surface is achieved [8, 14]. During the first step of the migration (see the first half of the migration path), one water molecule migrates from the initial meta-stable adsorption site to the adjacent ground state one along the [21 2] direction; the migration basically occurs through a rotation of the molecule about the axis that contains the two hydrogen atoms. The molecule sticks onto the surface by means of two hydrogen bonds and the rotation ends in the ground state configuration, i.e. when the water oxygen is captured by the surface Ti atom and the dative bond is formed; the maximum drop of the total energy occurs in this step being E dative bond 0.52 ev (see Fig. 5a-c). As the migration proceeds, the hydrogen bonds break and the water molecule rotates about an horizontal axis containing the water oxygen (involved in the dative bond with the Ti 5c atom); the total energy increases from the ground state one by about E 2xH-bond 0.22 ev (see Fig. 5d-e). Then, as the migration proceeds, we observe the formation of two new hydrogen bonds and the breaking of the dative bond with an increase of the total energy by E 0.3 ev (see Fig. 5f-g). The above migration processes take place when the adsorbed water molecules are isolated, i.e. are surrounded by empty adsorption sites where they can freely migrate. However, if one considers the ground state pattern of the first hydration layer, this is not always the case. In the ground state hydration pattern, indeed, water molecules are adsorbed at neighboring adsorption sites [9] and also diffusion paths involving at least two water molecules (belonging to the first water layer) should be considered; this circumstance may represent, in principle, a serious obstacle that might contribute to inhibit the H 2 O molecule migration. In order to consider also this migration process, we have considered a water molecule moving from its minimum energy site to another site along a migration path where another water molecule is encountered. In other words, what we are studying here is the process of overtaking a second adsorbed water molecule by a migrating water that moves along its diffusion path. Among all the possible hydration patterns of the (101) anatase surface involving at least two water molecules [9], we have chosen the one reported in Fig. 6 for computational reasons; indeed, this hydration pattern, that is just few mev more energetic than the ground state one, allows the usage of not so large supercells thus making affordable the NEB calculation. For this hydration pattern, the only possible migration path involving two water molecules is the one along the [21 2] direction; then the process here studied is the migration of one water molecule from A to B (that are energetically equivalent equilibrium sites) by overtaking a second water molecule that is adsorbed and located along the path ( see Fig. 7 for the corresponding energy barriers the diffusing H 2 O molecule experiences). Concerning such a migration process various events are observed: the migrating water molecule undergoes again a dative bond breaking (that mostly contributes to the energy barrier) and a continuous breaking and forming of hydrogen bonds; these processes causes very different possible migration configurations with the eventual presence of different local minima: indeed, the polynomial interpolation of the energy curve along the path is compatible with the presence of meta-stable states with local minima (on both sides of the saddle point). In order to confirm the presence of these local minima and to measure the energy of such meta-stable states, a further refinement of the image grid is needed and is under consideration. Anyway, it clearly emerges that the saddle point corresponds to a wide plateau along the reaction coordinate being basically obtained when the diffusing water molecule stays above the water molecule that is being overtaken during the migration process. In this case, the topmost water molecule is bonded to the one that stays below by an additional hydrogen bond, is a similar way that was evidenced for two layer hydration models in a previous article [3]. The measured energy barrier of this saddle point, E saddle 0.51 ev, is pretty close to the single water diffusion barriers discussed before, meaning that also this migration process may occur with the same activation energy as the previous ones that involved just one water molecule and empty adjacent sites on the (101) TiO 2 surface. This result means that, at this stage of knowledge, water migration in the first hydration layer seems rather independent on the coverage degree of the anatase (101) surface, the energy barriers being quite similar for both the cases of free migration through empty sites and migration through already occupied sites. Hence, on the basis of the above reported NEB calculations, it it possible to state that in all the cases examined, either the free migration processes along the [010] and the [21 2] migration paths or the migration process occurring

8 FIGURE 6. (Color Online) Top view of a configuration made of two water molecules on (101) anatase surface, together with the diffusion path (from A to B) connecting two equivalent Ti5c adsorption sites studied in the present work. FIGURE 7. (Color Online) Water migration barrier up a second adsorbed water molecule along the [212 ] direction versus d. through already occupied sites, the measured energy barrier is in the range 0.51eV Esaddle 0.58 ev that are quite similar values. We can thus assume that, within the error bar of the technique, that the migration activation energy of water in the first hydration layer of the TiO2 anatase (101) surface is, independently of the process studied, of this order of magnitude. Therefore, while at this stage it is not possible to state definitely which one is the diffusion path along with the water molecules travel most likely, a partial conclusion is that, independently of the diffusion path considered, the measured energy barriers are so large that they seem to inhibit the migration of the adsorbed water on the (101) anatase surface even at room temperature ( where KB2T is of the order of ev), that is clearly in contrast with the experimental evidences [8] and also dynamical calculations [14] referred in the introduction. However the above reported data are far to be conclusive because together with the energy barrier, the entropic term might play the determinant role to explain the observed mobility at as low temperature as 190 K. Indeed, according to the transition state theory, the migration/reaction rate, i.e. the hopping rate of the single water molecule transition across the saddle point, is: ν= s kb T Zvib Esaddle e kb T h Zvib (5) s are the partition functions of the initial and of the saddle state respectively, E where Zvib and Zvib saddle is the activation energy, namely the energy difference between the saddle-point and the configuration of minimum energy. Thus the Zs hopping rate depends also on the prefactor kbht Zvib that should be responsible of the observed water migration in the vib

9 first hydration layer. At the authors knowledge the pre-factor concerning the water migration onto the (101) anatase surface has not been calculated so far and is not known exactly so that typical values are currently used to interpret the experimental results. Therefore to fully explain the observed migration processes in the first hydration layer the entropic pre-factor should be calculated and standard DFT phonon spectra calculations are in course for this purpose. Conclusions In conclusion we have employed NEB calculations to sample the migration energy curve of water along the [010] and [012] diffusion paths on the (101) surface of the TiO 2 anatase surface. We have considered both free migration processes where water molecules move across free adsorption sites and migration processes involving two molecules as it occur in ground state configurations of the first layer hydration pattern. The migration processes have been studied in detail evidencing different kinetic behaviors of the water molecules as they move along the different diffusion paths where free or occupied adsorption sites are encountered. In particular, water migration along the [21 2] direction has evidenced a "rolling stone" kinetic behavior where the saddle point is related to the Ti-O bond breaking in the case of free diffusion, while the migration kinetic in the case of the two waters is rather complicated with the saddle point configuration that basically consists of a local two water layers model. Besides the large adsorption energy of water molecules onto the (101) surface (E ads 0.73 ev), also the migration processes studied evidence large values of the migration energy 0.51eV E saddle 0.58 ev so that both the adsorption and the migration energies seem so large to inhibit diffusion and desorption, in contrast with the experimental evidences [8]. These results, thus, indicate that the key factor that should be considered to explain the observed behavior is the entropic term [15], thus further investigations are currently in progress to calculate the entropic pre-factor that might account for the observed migration and desorption behavior of the first hydration layer. ACKNOWLEDGMENTS The computing resources and the related technical support used for this work have been provided by CRESCO/ENEAGRID High Performance Computing infrastructure and its staff (see for information) and by the CINECA under the HPC Grant Project HP10CPAIB5. CRESCO/ENEAGRID High Performance Computing infrastructure is funded by ENEA, the Italian National Agency for New Technologies,Energy and Sustainable Economic Development and by national and European research programs. We warmly acknwledge these institutions for contributing to the present work. REFERENCES 1. K. Shiba, Current opinion in biotechnology 21, 412 (2010). 2. D. A. T. Akira Fujishima, Xintong Zhang, Surf. Sci. Rep. 63, 515 (2008). 3. L. Agosta, G. Zollo, C.Aracangeli, F. Buonocore, F. Gala, and M. Celino, Phys. Chem, Chem. Phys. 17, 1556 (2015). 4. J. Schneider and L. C. Ciacchi, J. Am. Chem. Soc. 134, (2012). 5. Z. Zhao, Z. Li, and Z. Zou, Phys. Lett. A 375, 2939 (2011). 6. C. Sun, L.-M. Liu, A. Selloni, G. Q. M. Lu, and S. C. Smith, J. Mater. Chem. 20, (2010). 7. Andrea Vittadini, M.Casarin, and A. Selloni, Theor. Chem. Acc. 117, 663 (2007). 8. G. S. Herman, Z. Dohnhalek, N. Ruzycki, and U. Diebold, J. Phys. Chem. B 107, 2788 (2003). 9. Y. He, A. Tilocca, O. Dulub, A. Selloni, and U. Diebold, Nature Materials 8, 585 (2009). 10. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964). 11. W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). 12. M. Lazzeri, A. Vittadini, and A. Selloni, Phys. Rev. B 63, (2001). 13. A. Vittadini, A. Selloni, F. P. Rotzinger, and M. Grätzel, Phys. Rev. Lett. 81, 2954 (1998). 14. A. Tilocca, A. Selloni, Langmuir 20, (2004) 15. P. A. Redhead, Vacuum 12, 203 (1962). 16. A. V. Bandura and J. D. Kubicki, J. Phys. Chem. B 107, (2003). 17. J. Perdew, K. Burke, and M.Ernzerhof, Phys. Rev. Lett. 77(4), 3865 (1996). 18. N. Troullier and J. Martins, Phys. Rev. B 43(14), 1993 (1991). 19. L. Bengtsson, Phys. Rev. B 59, (1999). 20. H. Mokhorst and J. Pack, Phys. Rev. B 13(5), 5188 (1973)

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