Said Hamad

Juan Ramon Sanchez

Angel Barranco

Jose Antonio Mejias

Agustin R González-Elipe

Said; Hamad

Valencia Sanchez

Juan Ramon

Agustin ; González-Elipe

Juan Ramon Sanchez-Valencia

Agustin R Gonzalez-Elipe

Molecular dynamics simulation of the effect of pH on the adsorption of rhodamine laser dyes on TiO2 hydroxylated surfaces

Keywords: Rhodamine, adsorption, TiO2, anatase, simulation Rhodamine, adsorption, TiO 2, anatase, (101) surface, Molecular Dynamics, PZC

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Introduction

Rhodamines are biocompatible, photostable and luminescent dye molecules, widely used for a large variety of applications including laser, probe molecule of surface states, solar cells, or surface coatings [START_REF] Sasai | Luminescence Properties of Rhodamine 6G Intercalated in Surfactant/Clay Hybrid Thin Solid Films[END_REF][START_REF] Marlow | Doped Mesoporous Silica Fibers: A New Laser Material[END_REF][START_REF] Tleugabulova | Fluorescence Anisotropy in Studies of Solute Interactions with Covalently Modified Colloidal Silica Nanoparticles[END_REF][START_REF] Bahadur | Efficient photon-to-electron conversion with rhodamine 6G-sensitized nanocrystalline n-ZnO thin film electrodes in acetonitrile solution[END_REF] . For the majority of these uses, the dye molecule has to be incorporated into a solid, a feature that has fostered both the development of new synthesis and processing methods of the final materials and the study of their optical and fluorescent behaviours. Thus, for example, it has been shown that rhodamine-G molecules can be easily incorporated within the interlayer space of silicates and other layered materials [START_REF] Ohishi | An ethoxy-silano rhodamine B derivative and its application to surface coatings on display devices[END_REF][START_REF] Martínez Martínez | Characterization of Supported Solid Thin Films of Laponite Clay. Intercalation of Rhodamine 6G Laser Dye[END_REF][START_REF] Gemeay | Adsorption Characteristics and the Kinetics of the Cation Exchange of Rhodamine-6G with Na + -Montmorillonite[END_REF][START_REF] Bujdák | Spectral Properties, Formation of Dye Molecular Aggregates, and Reactions in Rhodamine 6G/Layered Silicate Dispersions[END_REF][START_REF] Bujdák | Molecular Orientation of Rhodamine Dyes on Surfaces of Layered Silicates[END_REF] . The incorporation of these molecules into sol-gel silica, mesoporous TiO 2 thin films or into polymeric matrices has been also intended for the fabrication of optical components and devices [START_REF] Martínez | Application of Fluorescence with Polarized Light to Evaluate the Orientation of Dyes Adsorbed in Layered Materials[END_REF][START_REF] Del Monte | Rhodamine fluorescent dimers adsorbed on the porous surface of silica gels[END_REF][START_REF] Barranco | Fluorescent Plasma Nanocomposite Thin Films Containing Nonaggregated Rhodamine 6G Laser Dye Molecules[END_REF][START_REF] Vogel | Mesostructured Dye-Doped Titanium Dioxide for Micro-Optoelectronic Applications[END_REF] .

Recently, we have shown that R6G and R800 dye molecules can be incorporated within transparent and porous films of TiO 2 or Ta 2 O 5 prepared by glancing angle evaporation just by immersing the films into an aqueous solution of the two dye molecules in cationic form [START_REF] Sánchez-Valencia | Preillumination of TiO2 and Ta2O5 Photoactive Thin Films As a Tool to Tailor the Synthesis of Composite Materials[END_REF] . The incorporation of the dye molecules into the film was driven by the pH of their solution and, in the case of the R6G, explained by using the classical concepts of the point of zero charge (PZC) developed in the 1960's to account for the adsorption of ions on the surface of colloidal oxides [START_REF] Kosmulski | Chemical Properties of Material Surfaces[END_REF] .

The results represents a clear evidence for the importance of the interaction of the hydroxilated porous oxide surfaces with the cationic dye molecules during the absorption processes. In particular, we found that the R6G only starts to become incorporated within the pores of the films when the pH of the solution was approaching or was higher than the PZC of TiO 2 (i.e., around 5.5 (refs. 14 and 15). The simplicity of the experimental method used for the preparation of these composite thin films has motivated the present theoretical work, where we account for the different effect of the pH and on the adsorption of R6G and R800 on the surface of TiO 2 . For this purpose we present here a theoretical study by using Molecular Dynamics techniques to obtain information about the adsorption of these two dye molecules. The results obtained can be of relevance for the study of other types of composite materials consisting of dye molecules adsorbed on the surface of TiO 2 . A classical example in this respect is that of the Grätzel solar cells [START_REF] O'regan | [END_REF]17 . In this context, previous theoretical studies in the literature have dealt with the adsorption of Ru(II)polypyridyl dyes on the surface of an ideal TiO 2 surface [START_REF] De Angelis | Time-Dependent Density Functional Theory Investigations on the Excited States of Ru(II)-Dye-Sensitized TiO 2 Nanoparticles: The Role of Sensitizer Protonation[END_REF] . However, to our knowledge, no theoretical studies have been carried out to investigate the interaction of these or similar dye molecules with a hydroxylated surface of this oxide, taking into account the effect of pH on their adsorption. For the present study, we have used four different types of surfaces, on which to model the adsorption of the rhodamine molecules. The chosen models of surfaces provide a description of the adsorption on non-hydroxylated surfaces, as well as on surfaces under basic, neutral and acidic conditions.

Computational details

The first step in any Molecular Dynamics (MD) simulation is the compilation of an adequate set of interatomic potentials to model the system. Our experimental observations require the use of computational features which are somehow more complicated than those of usual MD simulations, since we need to model the influence of hydroxylation and pH. TiO 2 surfaces are usually modelled as clean, non-hydrated, non-hydroxilated surfaces, although there are some exceptions in literature [START_REF] Predota | Electric Double Layer at the Rutile (110) Surface. 1. Structure of Surfaces and Interfacial Water from Molecular Dynamics by Use of ab Initio Potentials[END_REF][START_REF] Fortunelli | Simulations of Lipid Adsorption on TiO 2 Surfaces in Solution[END_REF][START_REF] Köppen | Adsorption Configurations and Energies of Amino Acids on Anatase and Rutile Surfaces[END_REF][START_REF] Tilocca | Methanol Adsorption and Reactivity on Clean and Hydroxylated Anatase(101) Surfaces[END_REF][START_REF] Tilocca | O 2 Interaction and Reactivity on a Model Hydroxylated Rutile(110) Surface[END_REF] . The initial set of parameters used to model the TiO 2 (101) anatase surface were taken from the modification that Predota et al. [START_REF] Predota | Electric Double Layer at the Rutile (110) Surface. 1. Structure of Surfaces and Interfacial Water from Molecular Dynamics by Use of ab Initio Potentials[END_REF][START_REF] Bandura | Derivation of Force Field Parameters for TiO 2 -H 2 O Systems from ab Initio Calculations[END_REF] made of the Matsui and Akaogi potentials [START_REF] Matsui | Molecular dynamics simulation of the structural and physical properties of the four polymorphs of TiO2[END_REF] to study (110) rutile hydroxylated surfaces. The parameters presented by Predota et al. [START_REF] Predota | Electric Double Layer at the Rutile (110) Surface. 1. Structure of Surfaces and Interfacial Water from Molecular Dynamics by Use of ab Initio Potentials[END_REF][START_REF] Bandura | Derivation of Force Field Parameters for TiO 2 -H 2 O Systems from ab Initio Calculations[END_REF] were not optimised to model the hydroxylated (101) anatase surface, and when they were used to minimise the surface, we observed the rupture of O-H bonds upon minimisation.

Deleted: 2. Experimental details and materials ¶ Composite R6G/TiO2 and R800/TiO2 thin films were prepared by using porous TiO2 thin films as host materials. For this purpose, transparent and amorphous TiO2 were prepared by Glacing Angle Physical Vapor Deposition (GAPVD) at room temperature on quartz and silicon substrates. Evaporation was carried out in an electron bombardment evaporator by using TiO2 pellets as target material. Stoichiometric thin films of TiO2 were obtained by performing the evaporation in 10 -4 torrs of O2. The evaporation was carried out by placing the substrates at a glancing angle of 70º with respect to the evaporator source. This geometry produces films with a tilted columnar microstructure with a high porosity [START_REF] Tomás | Influence of rhodamine 6G doping on the optical properties of TiO 2 sol-gel films[END_REF][START_REF] Sasai | Aggregated Structures of Rhodamine 6G Intercalated in a Fluor-Taeniolite Thin Film[END_REF][START_REF] Bujdák | Molecular Aggregation of Rhodamine Dyes in Dispersions of Layered Silicates: Influence of Dye Molecular Structure and Silicate Properties[END_REF] . The films with a thickness around 400 nm were prepared by this method. In the present case the porosity of the films was estimated to be 35% of the total volume of the films, with a 70% of pores consisting of mesopores. A full account of the characteristics of these films can be found in a previous publication [START_REF] Sánchez-Valencia | Preillumination of TiO2 and Ta2O5 Photoactive Thin Films As a Tool to Tailor the Synthesis of Composite Materials[END_REF] . ¶ The microstructure of the TiO2 thin films deposited on a silicon wafer was examined by Field Emission Scanning Electron Microscopy (FESEM) in a Hitachi S5200 microscope. Cross sectional views were obtained by cleaving the silicon substrates. ¶ UV-visible absorption spectra in transmission mode were recorded with a Perkin-Elmer Lambda 12 spectrometer for the thin films deposited on quartz plates. Although the absorbance is the typical magnitude used for presenting UV-vis absorption spectra of dyes in liquid solutions, we present here some spectra as the percentage of transmitted light. We have made this choice because this is the usual way of presenting these data when using optical thin films [START_REF] Robbie | Sculptured thin films and glancing angle deposition: Growth mechanics and applications[END_REF] . ¶ A chloride salt of R6G and R800 dye molecules was used for the experiments. The salts were supplied by ALDRICH and used without further purification. In solution, the cationic R6G or R800 bear a positive charge, a feature that is essential for the incorporation of the dye into the TiO2 thin films. ¶ A 10 -4 M solutions of the dyes in water at controlled values of pH were used for the infiltration experiments. The pH of the solution was controlled between 1.9 and 6.6 by adding giving amounts of HCl or NaOH. The TiO2 films were immersed in one of these solutions and maintained there for 10 min. The samples were then removed from the solution and washed with water at the same pH than that of the dye solutions. In general, the intensity of the colour of the films changed with the pH of the solution, a feature that suggests the dependence between this parameter and the ability to incorporate the dye molecules into the films. ¶ Figure 1 shows a series of UV-vis transmission spectra recorded for TiO2 ... Therefore, some changes were introduced into the interatomic potentials to allow us to study of the hydroxylated (101) anatase surface. In order to have a reference to test the results of the changes of the interatomic potentials parameters, we carried out the optimisation of a hydroxylated (101) anatase surface with the Density Functional Theory (DFT), using the plane-wave-pseudopotential approach within the projector augmented wave method (PAW) 30 , together with the Generalized Gradient Approximation (GGA) exchange correlation functional proposed by Perdew et al. 31 , as implemented in the Vienna Ab-initio Simulation Package (VASP) 4.6 code [32][33][34] . A plane-wave cutoff energy of 400 eV was used. The Ti (3s, 3p, 3d, 4s), O (2s, 2p) and H (1s) electrons were treated as valence states, while the remaining electrons were kept frozen as core states. The Brillouin-zone integrations were performed using Monkhorst-Pack grids 35 . The slab approximation was used to model the surface, with a TiO 2 slab thickness of 20Å, and a vacuum slab of 10Å. The cell dimensions are 5.44Å×3.78Å×30.0Å. The calculations were carried out by using a (7x7x1) mesh, with which convergence in energy was achieved.

In order to get a good agreement with the geometries obtained with the DFT calculations, we made some modifications in the interatomic potentials. Since one of the requirements was the modelling of the O-H bonds at the surface (such as bonds 2-3 and 4-5 in Figure 1), we introduced a harmonic force between the O and H atoms of the surface hydroxyl groups of the form E = 1/2·k 1 ·(r-r o ) [START_REF] Marlow | Doped Mesoporous Silica Fibers: A New Laser Material[END_REF] . The values of the parameters were: k 1 =500.4 kcal mol -1 /Å 2 and r o =0.95Å. Another important parameter in the description of the surface is the harmonic force that predicts a correct value of the Ti-O-H angles such as the angles 1-2-3 and 1-4-5 in Figure 1. This force is of the form [START_REF] Marlow | Doped Mesoporous Silica Fibers: A New Laser Material[END_REF] , where θ is the angle between the three atoms, θ o is the equilibrium value of this angle, around which θ oscillates and k 2 is the constant of the harmonic force that induces these oscillations. For O-H groups connected to terminal Ti atoms we did not change the parameters, but for O-H groups where the O involved is a bridging O (such as atom 4 in Figure 1), the new anatase surface obtained with this new set of interatomic potentials is in reasonable good agreement with that obtained with DFT calculations, as shown in Table 2. The larger disagreement, as expected, is found for the distance between atoms 5 and 11, since they interact by a weak hydrogen bond, a situation which is difficult to model accurately using interatomic potentials.

E = 1/2·k 2 ·(θ-θ o )
To model the rhodamine molecules we have employed the DREIDING force field [START_REF] Mayo | DREIDING: a generic force field for molecular simulations[END_REF] , which was developed to predict structures and dynamics of organic, biological and main-group inorganic molecules. The van der Waals parameters of the DREIDING force field are taken from the Williams potentials [START_REF] Williams | Nonbonded Potentials for Azahydrocarbons: the Importance of the Coulombic Interaction[END_REF][START_REF] Williams | Fluorine Nonbonded Potential Parameters Derived from Crystalline Perfluorocarbons[END_REF] , including some modifications. The electrostatic charges were calculated with ab initio calculations, by fitting the electrostatic potential at points selected according to the Merz-Singh-Kollman scheme 39,40 , as implemented in the program Gaussian03 41 . The Becke three parameter hybrid functional 42 (B3LYP) was used to fit the atomic charges, together with a 6-31+G* basis set. SI_Table 1 and SI_Table 2 show the atomic charges as well as the force type assignments. This level of theory has been previously used to study other dyes [START_REF] Capková | Effect of surface and interlayer structure on the fluorescence of rhodamine Bmontmorillonite: modeling and experiment[END_REF] . The DREIDING force field predicts an equilibrium angle of ~40º between the xanthene and phenyl moieties that form the rhodamine 6G molecule, whereas ab initio calculations predict that the planes of the two moieties lie perpendicular to each other. In order to predict correctly this angle of 90º, we included an additional torsional term in the force field. In DREIDING, the torsion interaction for two bonds (those between atoms IJ and KL) connected via a common bond JK takes the form,

[ ] { } ) ( cos 1 2 1 0 JK JK JK IJKL n V E ϕ ϕ - - = ,
where φ is the dihedral angle (angle between the IJK and JKL planes), n JK is the periodicity (an integer), V JK is the barrier for rotation (always positive), and 0 JK ϕ is the equilibrium angle. We did . This torsional force is only included to model the interaction between atoms C9 and C14 in Figure 2a. We checked the validity of this term by comparing the variation of the energy with respect to the rotation angle, this latter obtained with the interatomic potentials discussed and two ab initio methods: B3LYP/6-31+G* and MP2/6-31++G**. The results are shown in Figure 3. In the most critical region, between 90º and 110º, the three methods predict essentially the same dependency with respect to the rotation. For angles higher than 110º the less accurate methods (interatomic potentials and B3LYP/6-31+G*) predict a different change in energy than MP2/6-31++G**, although at 120º the energy difference is still less than 3 kcal/mol. We can therefore consider that the DREIDING force field, with this additional term, predicts correctly the behaviour of rhodamine 6G. In the case of rhodamine 800 there is no need to include any additional terms, since the DREIDING force field describes it correctly. The van der Waals interaction between the rhodamine molecules and the surface are taken from the DREIDING force field. The existence of parameters to describe the interaction between the molecules and the TiO 2 surface (which is not the case for other force fields such as AMBER or CHARMM) is the main reason why the DREIDING force field is used.

All interatomic potentials based energy minimisations and Molecular Dynamics simulations have been performed with the GULP code [START_REF] Gale | GULP: A computer program for the symmetry-adapted simulation of solids[END_REF] , at the high performance computing facilities of CSIC in Madrid. The timestep for the integration of the equations of motion is 1fs.

The systems are modelled in the canonical (NVT) ensemble, employing the Hoover thermostat, with a friction constant for the temperature bath of 0.1, to maintain the temperature around 298 ºC. The systems are equilibrated for 50 ps, followed by 100 ps of production. Since the number of degrees of freedom associated with the motion of the rhodamine molecules is relatively small, there is no need to perform very long simulations to sample the most relevant region of the phase space.

The ab initio calculations (using Gaussian03 and VASP) have been carried out in the Finis Terrae supercomputer, in Santiago de Compostela, Spain.

Materials, Theoretical Results and Discussion

Experimental details and materials.

Composite R6G/TiO 2 and R800/TiO 2 thin films were prepared by using porous TiO 2 thin films as host materials. For this purpose, transparent and amorphous TiO 2 were prepared by Glacing Angle Physical Vapor Deposition (GAPVD) at room temperature on quartz and silicon substrates. Evaporation was carried out in an electron bombardment evaporator by using TiO 2 pellets as target material. Stoichiometric thin films of TiO 2 were obtained by performing the evaporation in 10 -4 torrs of O 2 . The evaporation was carried out by placing the substrates at a glancing angle of 70º with respect to the evaporator source. This geometry produces films with a tilted columnar microstructure and a high porosity [START_REF] Tomás | Influence of rhodamine 6G doping on the optical properties of TiO 2 sol-gel films[END_REF][START_REF] Sasai | Aggregated Structures of Rhodamine 6G Intercalated in a Fluor-Taeniolite Thin Film[END_REF][START_REF] Bujdák | Molecular Aggregation of Rhodamine Dyes in Dispersions of Layered Silicates: Influence of Dye Molecular Structure and Silicate Properties[END_REF] . Thin films with a thickness around 400 nm were prepared by this method. In the present case the porosity of the films was estimated to be 35% of the total volume of the films, with a 70% of pores consisting of mesopores. A full account of the characteristics of these films can be found in a previous publication [START_REF] Sánchez-Valencia | Preillumination of TiO2 and Ta2O5 Photoactive Thin Films As a Tool to Tailor the Synthesis of Composite Materials[END_REF] . UV-visible absorption spectra in transmission mode were recorded with a Perkin-Elmer Lambda 12 spectrometer for the thin films deposited on quartz plates. Although the absorbance is the typical magnitude used for presenting UV-vis absorption spectra of dyes in liquid solutions, we present here some spectra as the percentage of transmitted light. We have made this choice because this is the usual way of presenting these data when using optical thin films [START_REF] Robbie | Sculptured thin films and glancing angle deposition: Growth mechanics and applications[END_REF] .

A chloride salt of R6G and R800 dye molecules was used for the experiments. The salts were supplied by ALDRICH and used without further purification. In solution, the cationic R6G or R800 bear a positive charge, a feature that is essential for the incorporation of the dye into the TiO 2 thin films.

A 10 -4 M solutions of the dyes in water at controlled values of pH were used for the infiltration experiments. The pH of the solution was controlled between 1.9 and 6.6 by adding given amounts of HCl or NaOH. The TiO 2 films were immersed in one of these solutions and maintained there for 10 min. The samples were then removed from the solution and washed with water at the same pH than that of the dye solutions. In general, the intensity of the colour of the films changed with the pH of the solution, a feature that suggests the dependence between this parameter and the ability to incorporate the dye molecules into the films.

shows a series of UV-vis transmission spectra recorded for TiO 2 thin films containing different concentrations of R6G and R800, as indicated in Table 1. The spectra are characterized by the presence of a series of bands typical of the R6G dye molecules (i.e., bands centred at ~520 nm) and R800 (i.e., bands centred at ~650 nm) [START_REF] Sánchez-Valencia | Preillumination of TiO2 and Ta2O5 Photoactive Thin Films As a Tool to Tailor the Synthesis of Composite Materials[END_REF] superimposed on the typical oscillations due to For the purposes of the present work, the most important result is the dependence of the intensity of the features attributed to the two dye molecules and the pH of the solution used for the preparation of the films. Thus, it is observed that the intensity of the R6G features are strongly dependent on the pH, increasing with this parameter. By contrast, R800 is little or no sensitive to this parameter and the intensity of its spectral features remains almost invariable for all the pHs. This different behaviour suggests that these two molecular cations interact differently with the surface of TiO 2 and that, particularly for the R800, the state of charge on the TiO 2 does not affect significantly the adsorption of this molecule. to each Ti atom, as shown in Figure 1. The charge of the O atoms in the hydroxyl groups is -0.848e and the charge of the H atoms is 0.424e. To model surface 2, we take into account that at low pHs there will be a large number of H atoms available to interact with the surface. The following or a similar process will happen readily: 1) Surf-TiOH + H + Surf-Ti + + H 2 O, i.e. a proton from the acidic solution will interact with a hydroxyl group at the surface and form a water molecule, which will then move into the solution. Once the surface is dried, this water molecule is removed from the surface and our model of a TiO 2 surface in acidic conditions will have a positive charge of +1e left in the surface. Since the charge of the hydroxyl group removed from the surface is only -0.424e, there will be an additional +0.576e to be distributed among the atoms of the surface. This charge was distributed among the surface atoms as shown is Table 3. Surface 3 is created taking into account a different process occurring in the basic solution.

Since under these conditions there is a large amount of OH -groups, the following process will take place:

2) Surf-Ti-OH + OH -Surf-O -+ H 2 O.
Thus, the result of the interaction between the hydroxylated surface and the OH -species from the solution is the removal of one proton from the surface to form a water molecule. This water molecule will be removed into the basic solution, leaving a bridging O at the surface and a charge of -1e, distributed among the atoms as shown in Table 3. Processes 1) and 2) are similar to the common mechanisms considered within the PZC theory of oxides [START_REF] Kosmulski | Chemical Properties of Material Surfaces[END_REF] . The UV-vis spectra shown in a suggest that the maximum adsorption of rhodamine 6G molecules will occur under basic conditions. This experimental behaviour is not unexpected, since these dye molecules are positively charged, and there will be an electrostatic attraction between this charge and the negative charge present on the surface due to the basic solution. As the pH decreases, the amount of negative charges on the surface decreases, and therefore the adsorption decreases. When the pH is below the PZC, the surface is positively charged, a situation that must produce an electrostatic repulsion between the positive charge of the rhodamine molecule and the positive charges on the surface induced by the proton adsorbed from the acidic solutions. This general trend is also observed in the simulations. Figure 5 In Figure 6 the values of the (x,y) coordinates of some relevant atoms of the molecule are plotted. The shape of the cell (from a top view) is also shown. In Figure 6a we can see the (x,y) values of the atom H7 of the rhodamine 6G when adsorbed on the bare, non-hydroxylated surface.

Adsorption of rhodamine 6G.

The adsorption energy, in that case -51.0 kcal/mol, is higher than that of the other three cases in which the surface is hydroxylated. But there are no experimental results to be compared with these data, since bare TiO 2 surfaces are quickly hydrated and hydroxylated. The set of points are scattered over a wide range of values, indicating that the attraction between the molecule and the surface is evenly distributed over the surface, i.e. it is very easy for the molecule to hop around the surface. Under basic conditions we observe the opposite effect: there is a strong attraction towards the negatively charged surface defect, a feature which creates a preference for the molecule to stay around it. In Figure 6b we see the (x,y) values of the atoms O1 and H7, as well as the position of the O atom that has lost its H due to the basic solution. The positions of the O1 and H7 atoms are localised in small areas, indicating that the molecule does not diffuse easily once it is absorbed.

Under neutral conditions (Figure 6c) the mobility of the molecule is higher, and E ad is lower, -28.6 kcal/mol, a result that agrees with the experimental observations. Under acidic conditions the mobility is still higher, as suggested by the scattered set of points corresponding to the movement of the H7 atom (Figure 6d). The molecule moves around the Ti atom which has lost its hydroxyl group, and is part of the positively charged defect. During the simulation, the phenyl moiety of the rhodamine 6G molecule is often inserted within the region previously occupied by the hydroxyl group. E ad is now -7.1 kcal/mol, a value which is much smaller than in the case of adsorption 14 under neutral conditions. The most relevant geometric parameters that describe the adsorption of the rhodamine 6G molecules are the angles α and β. α is defined as the angle between the axis a of the molecules (which is shown in Figure 2), and the z axis of the unit cell. Analogously, β is the angle between the molecular axis b and the z axis. A value of 90º in both angles would correspond to an adsorption geometry in which the molecule lies parallel to the surface. The convention we have used to calculate the angles means that an angle lower than 90º implies that the corresponding molecular axis (a or b) points upwards, and viceversa. Figure 7 shows the values of the angles α and β during the simulations, for the two rhodamine molecules at the four conditions of pH studied.

The average values for the whole simulations are shown in Figure 8. For rhodamine 6G the average value of the angle α is very close to 90º in all cases. The larger deviation is found for the adsorption under basic conditions. The value of 88º obtained suggests an adsorption almost parallel to the surface. The angle β is more affected by the presence of the phenyl group, which has the effect of decreasing the adsorption angle of the molecule. As a result, the average value of the angle β ranges from 80.7º, in the case of non-hydroxylated surface, to 84.0º for the adsorption under acidic conditions. This higher angle for acidic conditions is due to the mentioned ability of the molecule to introduce the phenyl moiety within the region previously occupied by the removed hydroxyl group, a feature which permits a more parallel adsorption.

Adsorption of rhodamine 800.

The experimental observations suggest that the adsorption of rhodamine 800 is less affected than the rhodamine 6G by changes in the pH of the surface, although the maximum adsorption also takes place under basic conditions and the minimum under acidic conditions. The values of the energies of adsorption calculated from the simulations for basic, neutral and acidic conditions are -51.6 kcal/mol, -33.2 kcal/mol and -29.4 kcal/mol respectively. The difference between the energies for neutral and acidic conditions is just 3.8 kcal/mol, almost five times smaller than the difference between the values for neutral and basic conditions, which is 18.4 kcal/mol. This effect is in agreement with the observation that a low pH only produces a small decrease in the intensity of the UV-vis adsorption bands (see b).The simulations provide some hints to understand the reasons for this behaviour. As it happens for rhodamine 6G, under basic conditions E ad is higher because the negative charge of the surface site defect modelling the basic conditions attracts the positive charge of the molecule. The N atom of the nitrile group of the rhodamine R800 molecule (N3 in Figure 2b) has a negative charge of -0.417e. Therefore, the negatively charged site at the surface interacts preferentially with the opposite side of the molecule, where most of the positive charge of the molecule is concentrated. It can be observed in Figure 6f that the N atom does not get close to the surface O atom. To represent the movement of the xanthene moiety we have chosen the atom O1. It has a small negative charge (-0.183e), and is surrounded by positive charges, so the position of the O1 atom is oscillating around the surface O atom. Regarding Looking to the angles accounting for this interaction, the average values of both angles α and β are within the range 90º-92º (see Figure 8), which means that the molecule is basically lying parallel to the surface.

In the surface that models neutral conditions the negatively charged site defect is not present, and the interaction between the rhodamine molecule and the surface is mainly due to their mutual van der Waals interactions. As a result, E ad decreases from -51.6 kcal/mol to -33.2 kcal/mol. The negatively charged N atom in the nitrile group is now mainly attracted to the positively charged H atoms of the hydroxyl groups, and falls in the potential well created by the H atoms belonging to three adjacent hydroxyl groups. This can be seen in Figure 6g, where we have plotted the coordinates of the atoms N3 and O1 of the rhodamine 800 molecules, as well as the coordinates of the O atoms of the hydroxyl groups, which are less mobile than the H atoms with which they are bonded. The distance from the superficial H atoms to the centre of the xanthene moiety, 2.82 Å, is roughly the same as in the case of adsorption under basic conditions, and the adsorption geometry in both cases is very similar. This similarity is also found for the values of the angles α and β, which lie within a range of 90º-92º (Figure 7g and Figure 8), thus indicating that the adsorption is parallel to the surface.

Experimentally, the relatively high adsorption of rhodamine 800 under acidic conditions (which is very similar to the level of adsorption in neutral conditions) is somewhat unexpected, because under these conditions, both the surface and the rhodamine 800 molecule are positively charged. Our simulations provide a basis to understand why a significant adsorption takes place.

The value of E ad predicted by our simulations is -29.4 kcal/mol, which is very close to the value obtained under neutral conditions, -33.2 kcal/mol. The reason why the electrostatic repulsion between the two charged systems does not produce a significant decrease in the value of E ad is due to the fact that the positive charge around the Ti atom at the surface does not interact directly with the positive charge of the rhodamine molecule. Instead, it is the negatively charged N atom of the nitrile group the one that is closer to it. Figure 6h shows that the positively charged region of the molecule (which surrounds the O1 atom) stays as far away as possible from the Ti atom, whereas the N3 atom is attracted by the positive charge of the Ti atom. There is a change in the angles of adsorption respect to the cases of basic and neutral conditions. The average value of the angle α, 90º, is similar to the previous cases, but the average value of the angle β has increased to 95º (Figure 7h and Figure 8). This is due to the mentioned attraction between the N3 atom and the surface Ti atom, which tends to keep them together. Indeed, this attraction induces a decrease of the distance between the molecule and surface (which changes from 2.8 Å to 2.7 Å). Since the rest

Concluding remarks

The simulations reported here offer a preliminary atomistic insight into the adsorption processes on TiO 2 of two industrially relevant dye molecules, namely rhodamine 6G and rhodamine 800. The task of simulating TiO 2 surfaces is very challenging. Theoretical studies of the adsorption of molecules are often carried out by employing bare TiO 2 surfaces. Our results show that there are large differences in adsorption energies and geometries when the state of the surface is changed. Thus, for the two studied molecules the adsorption energy on a hydroxylated surface is almost half of that calculated in the case of a bare surface. One of the greatest challenges regarding the simulation of TiO 2 surfaces is to model the effect of the different pHs. Using two models to simulate high and low pH conditions, we have calculated the adsorption energies of the two molecules under basic, neutral and acidic conditions. For rhodamine 6G the simulations predict a high energy of adsorption and therefore much adsorption under basic conditions, less adsorption under neutral conditions, and practically no adsorption under acidic conditions. For rhodamine 800 there is a high energy of adsorption under basic conditions, while the adsorption energies under neutral and acidic conditions are lower than the latter, but very similar to each other. These results are in qualitative agreement with the experimental observations, which provides additional confidence on the ability of the simulations to model realistic adsorption conditions. However, despite this success in achieving a qualitative agreement between experimental and theoretical results, there are still many factors involved in the adsorption of molecules on TiO 2 which we have not taken into account. For example, we have studied the final states, in which the rhodamine molecules are adsorbed onto the dry surface, but we have not modelled the transition from the wet to the dry TiO 2 surface. This is an interesting process, since there is a loss of water molecules, while the rhodamine molecules are kept attached to the surface.

Another relevant factor that influences the adsorption of rhodamine molecules is the presence of counterions [START_REF] Capková | Effect of surface and interlayer structure on the fluorescence of rhodamine Bmontmorillonite: modeling and experiment[END_REF][START_REF] Klika | The rhodamine B intercalation of montmorillonite[END_REF] . On the other hand, there is a rich variety of ways in which rhodamine molecules can interact, both in solution and on the surface, such as forming monomers, H-dimers, J-dimers, etc [START_REF] Martínez Martínez | Characterization of Supported Solid Thin Films of Laponite Clay. Intercalation of Rhodamine 6G Laser Dye[END_REF][START_REF] Gemeay | Adsorption Characteristics and the Kinetics of the Cation Exchange of Rhodamine-6G with Na + -Montmorillonite[END_REF][START_REF] Bujdák | Spectral Properties, Formation of Dye Molecular Aggregates, and Reactions in Rhodamine 6G/Layered Silicate Dispersions[END_REF][START_REF] Bujdák | Molecular Orientation of Rhodamine Dyes on Surfaces of Layered Silicates[END_REF][START_REF] Martínez | Application of Fluorescence with Polarized Light to Evaluate the Orientation of Dyes Adsorbed in Layered Materials[END_REF][START_REF] Del Monte | Rhodamine fluorescent dimers adsorbed on the porous surface of silica gels[END_REF] , which have a great influence on the photoluminescence properties [START_REF] Bujdák | Molecular Aggregation of Rhodamine Dyes in Dispersions of Layered Silicates: Influence of Dye Molecular Structure and Silicate Properties[END_REF][START_REF] López Arbeloa | Aggregation of Rhodamine 3B Adsorbed in Wyoming Montmorillonite Aqueous Suspensions[END_REF][START_REF] Martínez Martínez | Characterization of Rhodamine 6G Aggregates Intercalated in Solid Thin Films of Laponite Clay. 1. Absorption Spectroscopy[END_REF] . Thus another interesting problem is to asses how the dimerisation process affects the adsorption on the surfaces.

The ultimate goal of the inclusion of all these other effects would be to obtain a more accurate description of these systems, which could provide theoretical data to guide the experimental research. For these reasons an intense theoretical work is being carried out in our group along this line.

Acknowledgements

We dedicate this work to the memory of José Antonio Mejías, an excellent friend and good scientist, who put the first stones of this research line in our group. We will always remember him kindly. We thank the Ministry of Science and Education of Spain (project MAT 2007-65764/NAN2004-09317 and the CONSOLIDER INGENIO 2010-CSD2008-00023) and the Junta de Andalucía (projects TEP2275 and P07-FQM-03298) for financial support. Concentration of the adsorbed dyes in the porous TiO 2 thin films as a function of the pH. Charges of all the atoms involved in the defects appearing at high and low pH, as well as the charges of the atoms of the hydroxylated surface under neutral conditions. Change in energy as the angle between the xanthene and phenyl moieties is changed, calculated with two ab initio methods (B3LYP/6-31+G* and MP2/6-31++G**) and with the classical interatomic potentials used in this study. x (Å)

Dye concentration [ mol cm

Plot of the values of the (x,y) coordinates of some relevant atoms, taken every 0.1 ps during the whole simulations. a) R6G on non-hydroxylated surface, b) R6G under basic conditions, c) R6G under neutral conditions, d) R6G under acidic conditions, e) R800 on non-hydroxylated surface, f) R800 under basic conditions, g) R800 under neutral conditions, h) R800 under acidic conditions.

Values of the angles α and β during the simulations for the different simulations. α (β) is defined as the angle between the axis a (b) of the molecules (which is shown in Figure 2), and the z axis of the unit cell. a) R6G on non-hydroxylated surface, b) R6G under basic conditions, c) R6G under neutral conditions, d) R6G under acidic conditions, e) R800 on non-hydroxylated surface, f) R800 under basic conditions, g) R800 under neutral conditions, h) R800 under acidic conditions. Average distance between the surfaces and the rhodamine molecules.

F

Experimental details and materials

Composite R6G/TiO 2 and R800/TiO 2 thin films were prepared by using porous TiO 2 thin films as host materials. For this purpose, transparent and amorphous TiO 2 were prepared by Glacing Angle Physical Vapor Deposition (GAPVD) at room temperature on quartz and silicon substrates. Evaporation was carried out in an electron bombardment evaporator by using TiO 2 pellets as target material. Stoichiometric thin films of TiO 2 were obtained by performing the evaporation in 10 -4 torrs of O 2 . The evaporation was carried out by placing the substrates at a glancing angle of 70º with respect to the evaporator source. This geometry produces films with a tilted columnar microstructure with a high porosity [START_REF] Tomás | Influence of rhodamine 6G doping on the optical properties of TiO 2 sol-gel films[END_REF][START_REF] Sasai | Aggregated Structures of Rhodamine 6G Intercalated in a Fluor-Taeniolite Thin Film[END_REF][START_REF] Bujdák | Molecular Aggregation of Rhodamine Dyes in Dispersions of Layered Silicates: Influence of Dye Molecular Structure and Silicate Properties[END_REF] . The films with a thickness around 400 nm were prepared by this method. In the present case the porosity of the films was estimated to be 35% of the total volume of the films, with a 70% of pores consisting of mesopores. A full account of the characteristics of these films can be found in a previous publication [START_REF] Sánchez-Valencia | Preillumination of TiO2 and Ta2O5 Photoactive Thin Films As a Tool to Tailor the Synthesis of Composite Materials[END_REF] .

The microstructure of the TiO 2 thin films deposited on a silicon wafer was examined by Field Emission Scanning Electron Microscopy (FESEM) in a Hitachi S5200 microscope. Cross sectional views were obtained by cleaving the silicon substrates.

UV-visible absorption spectra in transmission mode were recorded with a Perkin-Elmer Lambda 12 spectrometer for the thin films deposited on quartz plates. Although the absorbance is the typical magnitude used for presenting UV-vis absorption spectra of dyes in liquid solutions, we present here some spectra as the percentage of transmitted light. We have made this choice because this is the usual way of presenting these data when using optical thin films [START_REF] Robbie | Sculptured thin films and glancing angle deposition: Growth mechanics and applications[END_REF] . A chloride salt of R6G and R800 dye molecules was used for the experiments. The salts were supplied by ALDRICH and used without further purification. In solution, the cationic R6G or R800 bear a positive charge, a feature that is essential for the incorporation of the dye into the TiO 2 thin films.

A 10 -4 M solutions of the dyes in water at controlled values of pH were used for the infiltration experiments. The pH of the solution was controlled between 1.9 and 6.6

by adding giving amounts of HCl or NaOH. The TiO 2 films were immersed in one of these solutions and maintained there for 10 min. The samples were then removed from the solution and washed with water at the same pH than that of the dye solutions. In general, the intensity of the colour of the films changed with the pH of the solution, a feature that suggests the dependence between this parameter and the ability to incorporate the dye molecules into the films.

Figure 1 shows a series of UV-vis transmission spectra recorded for TiO 2 thin films containing different concentrations of R6G and R800, as indicated in Table 1. The spectra are characterized by the presence of a series of bands typical of the R6G dye molecules (i.e., bands centred at ~520 nm) and R800 (i.e., bands centred at ~650 nm) [START_REF] Sánchez-Valencia | Preillumination of TiO2 and Ta2O5 Photoactive Thin Films As a Tool to Tailor the Synthesis of Composite Materials[END_REF] superimposed on the typical oscillations due to interference phenomena between a substrate and a transparent layer of different refraction index [START_REF] Sánchez-Valencia | Preillumination of TiO2 and Ta2O5 Photoactive Thin Films As a Tool to Tailor the Synthesis of Composite Materials[END_REF] . For the purposes of the present work, the most important result is the dependence of the intensity of the features attributed to the two dye molecules and the pH of the solution used for the preparation of the films. Thus, it is observed that the intensity of the R6G features are strongly dependent on the pH, increasing with this parameter. By contrast, R800 is little or no sensitive to this parameter and the intensity of its spectral features remains almost constant for all the pHs. This different behaviour suggests that these two molecular cations interact differently with the surface of TiO 2 and that, particularly for the R800, the state of charge on the TiO 2 does not affect significantly the adsorption of this molecule. Atomic charges and DREIDING force field types of the atoms of rhodamine 800 shown in Figure 3b.

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  2 =14.136 kcal mol -1 rad -2 and θ o =120º. The geometry of the hydroxylated (101)

Formatted

  the TiO 2 thin films deposited on a silicon wafer was examined by Field Emission Scanning Electron Microscopy (FESEM) in a Hitachi S5200 microscope. Cross sectional views were obtained by cleaving the silicon substrates.

  a substrate and a transparent layer of different refraction index[START_REF] Sánchez-Valencia | Preillumination of TiO2 and Ta2O5 Photoactive Thin Films As a Tool to Tailor the Synthesis of Composite Materials[END_REF] .

3. 2 .

 2 Theoretical results and discussion.Once a suitable set of interatomic potentials is obtained, we created the unit cells that model the systems of interest. The simplest cell to study the adsorption of rhodamines is a bare surface formed by a slab of TiO 2 in vacuum. We generated a 17 Å slab exposing the (101) surface of anatase TiO 2 , with a (6 a x x 8 a y ) periodic replication of the elementary experimental cell of dimensions a x =5.44 Å and a y =3.776 Å. The simulation cell contains 10 Ti atoms and 20 O atoms, giving a total of 480 Ti atoms and 960 O atoms. The dimensions of the unit cell are 32.66 Å x 30.2 Å x 50 Å, and the angle between a x and a y is 110.30º. There is a vacuum gap of 33 Å between the slabs. The charges on the Ti and O atoms are 2.196e and -1.098e respectively. Since we are interested in studying the effect of pH on the adsorption energy (E ad ) of rhodamines, we also generated three unit cells to model different values of pH: 1) hydroxylated surface under neutral conditions, 2) hydroxylated surface under acidic conditions and 3) hydroxylated surface under basic conditions. Surface 1 is created by adding an H atom to each bridging O atom and a hydroxyl

  shows a snapshot of the simulation of the adsorption of rhodamine 6G on a fully hydroxylated surface, modelling the surface for neutral conditions. As shown in Table4(where the values of the energies of adsorption of the two rhodamine molecules on the four types of surfaces are shown), under basic conditions the adsorption energy of rhodamine 6G is -46.5 kcal/mol. Under neutral conditions E ad decreases to -28.6 kcal/mol, and under acidic conditions it decreases further to -7.1 kcal/mol. The latter value is negative, suggesting that there might be some adsorption of rhodamine 6G under acidic conditions, in disagreement with what is experimentally observed. This apparent contradiction might be due to the simplicity of the model. E ad is calculated as the difference in energy between two states. One state consists of two systems, the isolated TiO 2 surface and the isolated rhodamine molecule. The other state consists of the rhodamine molecule adsorbed onto the surface. A more accurate value of E ad would be obtained if the interaction of the rhodamine molecule with water molecules would have been taken into account accurately. The interaction rhodamine-water would cause a decrease of the adsorption energies of the two rhodamine molecules under all pH conditions. For this reason, this initial study only provides qualitative information about the adsorption energy, predicting relative energetic differences, not the actual absolute values of adsorption energy.The dynamics of the rhodamine 6G molecule adsorbed onto the different surfaces shows significant variations.

  cannot get closer to the hydroxyl groups of the surface, this effect results in an increase of the adsorption angle β, i.e. the position of the N3 atom is lower than that of the rest of the molecule. This particular geometrical arrangement has the net effect of creating an attraction between two positively charged systems.

Figure 1 Figure 1 ¶Figure 2 a)Formatted

 112 Figure 1

4 UV 28 Figure 5

 4285 Figure 4

Figure 8 Figure 9

 89 Figure 8Average values of the angles α and β during the simulations.

-2 nm -1 10 -12 ]

		pH =3.8	pH=5.5	pH=6.6
	TiO 2 -Rh6G	0	2.87	13.07
	TiO 2 -Rh800	5.82	4.12	7.85

Table 2

 2 Values of some of the important geometrical features of the (101) hydroxylated anatase surface, obtained with DFT and with the interatomic potentials developed by Predota et al.[START_REF] Predota | Electric Double Layer at the Rutile (110) Surface. 1. Structure of Surfaces and Interfacial Water from Molecular Dynamics by Use of ab Initio Potentials[END_REF][START_REF] Bandura | Derivation of Force Field Parameters for TiO 2 -H 2 O Systems from ab Initio Calculations[END_REF] , including the new terms that improve the description of the O-H bonds for this particular surface.

	23,28	126.2º	1.93Å 1.01Å 0.97Å 2.73Å 127.8º 119.8º
	Plus added terms.
	DFT	122.3º	1.87Å 0.98Å 0.98Å 2.49Å 126.2º 118.3º

Table 3

 3

Table 4

 4 Energies of adsorption, E ad , of the two rhodamine molecules studied on the (101) surface of anatase. All energies are in kcal/mol.

	Deleted: ¶
	Atom name	... [2]

Table 3

 3 Atomic charges and DREIDING force field types of the atoms of rhodamine 6G shown in Figure3a.

			Page Break
		Force Field			Force Field
	Atom name	type	Charge	Atom name	type	Charge
	C1	C_R	0.18	H3	H_	0.074
	C2	C_R	0.057	C24	C_3	-0.008
	C3	C_R	-0.365	H4	H_	0.078
	C4	C_R	0.181	C25	C_3	0.046
	C5	C_R	-0.061	C26	C_3	-0.161
	C6	C_R	-0.058	N3	N_1	-0.417
	O1	O_R	-0.183	H5	H_	0.059
	C7	C_R	0.242	H6	H_	0.069
	C8	C_R	0.033	H7	H_	0.094
	C9	C_R	-0.064	H8	H_	0.055
	C10	C_R	-0.137	H9	H_	0.054
	C11	C_R	0.005	H10	H_	0.053
	C12	C_R	0.14	H11	H_	0.029
	C13	C_R	-0.344	H12	H_	0.038
	N1	N_R	-0.002	H13	H_	0.09
	C14	C_1	0.417	H14	H_	0.028
	C15	C_3	-0.131	H15	H_	0.074
	C16	C_3	-0.137	H16	H_	0.1
	C17	C_3	-0.016	H17	H_	0.05
	C18	C_3	-0.06	H18	H_	0.058
	N2	N_R	0.085	H19	H_	0.027
	C19	C_3	-0.143	H20	H_	0.059
	C20	C_3	0.016	H21	H_	0.042
	H1	H_	0.211	H22	H_	0.098
	C21	C_3	-0.017	H23	H_	0.048
	C22	C_3	0.018	H24	H_	0.043
	H2	H_	0.209	H25	H_	0.075
	C23	C_3	-0.011	H26	H_	0.082

Table 4

 4

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