adsorption of water on tio2 and sno2 surfaces:...

ADSORPTION OF WATER ON TiO2 AND SnO2 SURFACES:MOLECULAR DYNAMICS STUDY

Lukáš VLČEKa1,b* and Peter T. CUMMINGSa2,ca Department of Chemical Engineering, Vanderbilt University, Nashville, TN 37235-1604, U.S.A.;e-mail: 1 [email protected], 2 [email protected]

b Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic,165 02 Prague 6, Czech Republic

c Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge,TN 37831-6492, U.S.A.

Received January 8, 2008Accepted April 15, 2008

Published online May 9, 2008

Dedicated to Professor William R. Smith on the occasion of his 65th birthday.

The structure and thermodynamics of water adsorbed at the (110) surface of rutile (α-TiO2)and cassiterite (α-SnO2) were studied by means of molecular dynamics simulations withatomic interactions represented by a classical forcefield based on the SPC/E model of water.To investigate the effect of surface water dissociation on the adsorption of additional layersof water, two extreme cases of completely hydroxylated and nonhydroxylated surfaces wereconsidered. Axial density distributions and adsorption Helmholtz free energies of water fordifferent types of surfaces were compared and related to thermal gravimetric analysis datafrom literature. We found that the dissociation of water in the first layer considerablychanges the affinity of additional water to the surface, weakening hydrogen bonding be-tween the first and second layer and strengthening cohesion between the second and thirdlayer. Comparison with the experimental measurements of adsorption indicates that waterdissociates on cassiterite while it stays associated on rutile. The degree of dissociation in thefirst layer is not strongly affected by the adsorption of additional water.Keywords: Adsorption; Metal oxide; Rutile; Cassiterite; Water; Free energy; Chemical poten-tial; Simulation.

Metal oxide surfaces can be characterized by their ability to form strongchemical and hydrogen bonds with water molecules and other polar parti-cles. An example of the strength and importance of these interactions canbe a water-induced phase transition from rutile to anatase in TiO2nanoparticles1. The complex chemistry of the interface involving water dis-sociation, protonation of surface groups, and ion surface complexation is ofmajor interest to surface scientists and considerable effort has been devoted

Collect. Czech. Chem. Commun. 2008, Vol. 73, No. 4, pp. 575–589

Adsorption of Water on TiO2 and SnO2 Surfaces 575

© 2008 Institute of Organic Chemistry and Biochemistrydoi:10.1135/cccc20080575

to experimental study2–4, molecular simulations5–7, and the development oftheoretical models8–10.

In a series of recent papers we used molecular dynamics (MD) simulationsto investigate the structure and electrostatic properties of the electric dou-ble layer formed at the interface of rutile and cassiterite with bulk waterand electrolyte solutions11–13. One of the main observations was the domi-nant role of hydrogen bonding influencing all studied properties. The stiffhydrogen bond network anchored to the crystal surface extends several wa-ter layers into the solution and dictates the extent and location of ion ad-sorption, orientation of local electric fields, and overall dynamics in theinterface. Water dynamics at metal oxide surfaces was further investigatedin a combined neutron scattering (QENS) – MD study of adsorption at rutileand cassiterite nanoparticles14. The amount of adsorbed water was deter-mined from the thermal gravimetric analysis (TGA) and mass spectroscopy(MS), and subsequent MD simulations showed that at ambient conditionswater adsorbs in three distinct layers. The analysis of diffusion revealed thatthe dynamic relaxation in each layer has its typical timescale: up to tens ofpicoseconds in the third (outermost) layer, hundreds of picoseconds in thesecond (middle) layer, and microseconds or longer in the first layer.

An important limitation of most classical simulations is the inability tomodel chemical reactions, such as the dissociation of chemisorbed water.While dissociable models of water and interfaces have been created15–17,they are not particularly good at reproducing phase equilibria or dynamicproperties, which are crucial for our study. Chemical reactions were typi-cally modeled by quantum chemical (ab initio) simulations, which pro-vided important insights into the stability of various surface structures anddissociation pathways5,18,19. The extent of ab initio calculations is, how-ever, severely constrained. Given the extremely slow diffusion modes of thesurface water it is not clear whether quantum chemical simulations withtheir limited system size (10–100 molecules) and timescale (1–10 ps) can ex-plore all relevant configurations. Increasing the size of the system to in-clude all the important features of hydrogen bonding observed in MDsimulations is practically beyond the capabilities of today’s computationalsystems.

The presented study is a natural continuation of our molecular simula-tions outlined above. We investigate the effect of water dissociation on theadsorption Helmholtz free energy. The results are related to the structure ofgrowing layers of adsorbed water and compared to experimental data fromthe thermal gravimetric analysis. Indirectly, the results can also provide


576 Vlček, Cummings:

information on the influence of adsorbed water on the dissociation–association equilibria in the first layer.

CALCULATIONS

To study water adsorbed at metal oxide surfaces we used classical moleculardynamics simulations. The forcefield was based on the SPC/E model ofwater20, which was chosen because of its ability to accurately reproduce thephase envelope of bulk water, as well as the liquid water structure,diffusivity, and dielectric properties over a wide range of temperatures anddensities. The potential model for bulk metal oxides, surface groups, andtheir interactions with SPC/E water was developed on the basis of DFT cal-culations21,22. Non-Coulombic interactions between metal oxide atoms in-cluding surface hydroxyl groups were fitted with the Buckingham potentialand interactions of metal oxides with water were fitted with theLennard–Jones potential23. The forcefield parameters and (110) surface geo-metries for rutile and cassiterite systems are summarized in ref.11 and ref.13,respectively. To make the simulations faster and consistent with earlierstudies11,13, we followed the same approach and fixed all solid phase atomsin space except those of the protolyzable surface oxygens. Bulk metal oxidegeometry was set according to experimental data from X-ray spectroscopyand the positions of atoms in the relaxed surface layers were taken from theDFT calculations21,22. Because our forcefield does not allow modeling waterdissociation directly, we constructed two types of surfaces, here callednonhydroxylated and hydroxylated, with the degree of dissociation presetto 0 and 100%, respectively. The nonhydroxylated surface consisted only ofmetal oxide atoms, which interacted with SPC/E molecules throughnon-bonded interactions. The hydroxylated surface also contained theproducts of water dissociation: terminal and bridging hydroxyls (Fig. 1).

The simulations were carried out in the NVT ensemble with temperatureset to 300 K. The system consisted of two metal oxide plates with 0–504 wa-ter molecules between them. The crystal phase was constructed from a basicunit of 4 metal and 8 oxygen atoms replicated six times in x and y direc-tions (parallel to the surface) and twice in z direction. The distance betweenthe plates was more than 40 Å to prevent significant interaction betweenthe opposite surfaces. Long-range Coulombic forces were computed usingthe three-dimensional Ewald summation with a two-dimensional correc-tion (EW3DC)24. A vacuum gap, required by the method, between outersides of the cassiterite plates was about 1.5 times the distance between thesurfaces, resulting in the size of the simulation box in z direction about 150 Å.



The real space cutoff distance was set to 12.66 Å, maximal reciprocal vectornumber k = 5, and parameter α = 0.244 Å–1. A fourth-order predictorcorrector method and quaternion formalism was used to integrate equa-tions of motion in the liquid phase. The motion of surface oxygens and hy-droxyls with constrained chemical bonds was computed using the SHAKEalgorithm25. The temperature of water was held constant by the Nose–Hooverthermostat26 and the surface groups were thermostatted through theinteraction with molecular water. Each simulation started from a pre-equilibrated configuration with water already adsorbed on the surface, thesystem was further equilibrated for more than 500 ps, and production runscovered more than 1.5 ns with a time step of 1.0 fs.

The adsorption Helmholtz free energy can be defined as the minimum ofthe excess Helmholtz energy across the interface. There are several ap-proaches to the calculation of free energies and related entropic quantities,each suitable for a different situation. The methods of thermodynamic inte-gration and free energy perturbations are well suited for dense homoge-neous systems. Alternatively, free energy profiles can also be explored bythe calculation of the potential of mean force, combined with umbrellasampling27. Anisotropic and heterogeneous systems, however, pose a seri-ous challenge for these methods because they typically explore the phasespace by small increments and cannot effectively visit all relevant regionswhen the degeneracy of an isotropic system is removed. A very efficientmethod for such situations is the Widom test particle insertion method28,in which a particle whose chemical potential or free energy is calculated



FIG. 1Structure of nonhydroxylated and hydroxylated (110) surfaces of cassiterite. Legend: metal(yellow), oxygen (red), hydrogen (white), bridging oxygen (B), terminal oxygen (T), hydrogenbonds (green), and chemisorption (blue)

but which is not a part of the equilibrated system, is randomly inserted intothe system and excess Helmholtz free energy is calculated as

A k T u k T k T pV NexB B B= − ⟨ − ⟩ + −ln exp [ / ] / (1)

where the first term on the right side is excess chemical potential and u isthe interaction energy of the test particle with the equilibrated system. Forthe test particle method to be efficient, high probability of successful testinsertions without an overlap is essential. This condition is usually well sat-isfied for small molecules and low-density systems offering suitable cavities.A variant of the method with more efficient search for cavities in densersystems has recently been used to study the adsorption and solvation ener-gies at the interface of water vapor with ice and liquid water29,30. Unlike inthe bulk, the structure of adsorbed water is open, increasing thus the proba-bility of a successful particle insertion. The sampling is further facilitated bythe fact that the lowest excess free energy can be expected at the open sur-face of adsorbed layers where the new incoming molecules usually attach.Our test simulations showed that due to the diffuse character of outer layersand the lattice-like structure of the first layer, we can effectively use simplerandom insertions without the need for special cavity search described inrefs29,30. To compensate for a relatively lower acceptance ratio of insertionsinto the deeper layers, we first sampled this region with trial insertions ofwater molecule cores (coinciding with oxygen atoms) to find suitable cavi-ties. After a successful insertion of the core, 20 random orientations weregenerated to sample the local environment in search for hydrogen bonds.Each unsuccessful insertion of the core was counted as 20 unsuccessfulinsertions of full water molecules. There were 200 random oxygen atom po-sitions generated every time step and the total number of random particleinsertions in the dense regions during 1.5 ns runs totaled to approximately3 × 109. The combination of the open surface structure and more frequentsampling of inner layers contribute to the reliability of the method and rel-atively low statistical errors. Our previous study of the dynamics of ad-sorbed water showed that the slowest diffusion relaxation time ofmolecules in the second layer is in the order of hundreds of picoseconds14,which should insure that our simulations spanning at least 1.5 ns will sam-ple a representative set of configurations. Diffusion relaxation times in thefirst layer were estimated to be around 1 µs for rutile and even longer forcassiterite, which seems to be too slow for the timespan of our simulations.



The treatment of the adsorption in the first layer is discussed in the follow-ing section.

RESULTS AND DISCUSSION

To investigate the gradual growth of adsorbed water layers, we calculatedthe density profiles, excess chemical potentials, and Helmholtz free ener-gies of water at different surface coverages. These quantities are closely re-lated as the excess free energy determines where additional water willadsorb, and the close relationship can also be used to check the correctnessof the data. The results are interpreted with respect to the thermal gravi-metric analysis experiments published in ref.14 and the question of waterdissociation discussed in refs11,13, which were the primary motivation forthis work.

Structure of Adsorbed Water

Figures 2 and 3 present the oxygen density profiles of adsorbed water onthe four types of studied surfaces; each plot shows simulation data for vari-ous amounts of adsorbed water (surface coverage) up to 3.5 water moleculesper surface unit. In all cases water gradually forms three distinct layers seenin the distributions as three maxima (peaks) separated by two minima.

At hydroxylated surfaces (Figs 2b and 3b) the bond of the first layer tothe surface is permanent by definition, with a fixed oxygen–metal atom dis-tance. It is manifested as a very high and narrow peak around 2 Å from thesurface plane. For steric reasons no other molecules can enter this region.A surface covered with a monolayer of dissociated water offers two mainkinds of H-bonding opportunities for water from outer layers: the hydrogenatom of a bridging hydroxyl and the oxygen atom of a terminal hydroxyl(see Fig. 1). Hydrogens of terminal hydroxyls are typically bonded to neigh-boring hydroxyls and, therefore, not available for other molecules. The to-tal number of H-bonds available for the second layer is two per surface unitbut some second-layer molecules can participate in two bonds with the sur-face, which results in the total occupancy less than 2. The integration ofthe second peak yielded approximately 1.6 water molecules per surfaceunit. It can be also noticed that the second peak is highest for the systemwith 2.5 adsorbed layers, which is approximately two full layers. The lower-ing of the second peak at higher coverages can be explained by strongbonding with the third layer, which weakens bonding with the first layer.Larger lattice parameters of cassiterite leave more space between the rows of



terminal and bridging hydroxyls and allow second-layer molecules to approachthe surface closer than at rutile. The third layer can be identified as a shortand wide but clearly defined peak at about 6 Å from the surface. The existenceof a density maximum at such a distance from the surface suggests orderingof water molecules and strong bonding to the second layer.



FIG. 2Oxygen density profiles of water adsorbed at rutile for different surface coverages from up to3.5 molecules per surface unit. Top: nonhydroxylated surface, bottom: hydroxylated surface

The plots of density profiles for nonhydroxylated surfaces (Figs 2a and 3a)show that water is built up layer by layer, first filling up the top layer beforeadsorbing in a new one. Such behavior indicates large differences in the af-finity of individual layers to the surface and weakening of this strengthwith each additional layer. From the viewpoint of the thermal gravimetric



FIG. 3Oxygen density profiles of water adsorbed at cassiterite for different surface coverages from upto 3.5 molecules per surface unit. Top: nonhydroxylated surface, bottom: hydroxylated surface

analysis, it may be expected that the adsorbed water will desorb over a widerange of temperatures. Integration of the first peak of the distributionshows that there is at most one water molecule per surface unit and, oncethere is enough water on the surface to form a monolayer, the first layer ismost of the time fully occupied. It is known from previous studies that thefirst-layer molecules are chemisorbed to surface metal atoms18,19. Associatedwater in the first layer leaves bridging oxygens unprotonated and availablefor forming strong hydrogen bonds with molecules in the second layer,which is thus very stable as implied by the corresponding high and narrowpeaks, and confirmed by the thermodynamic calculations described below.This kind of strong hydrogen bonds cannot be formed at hydroxylated sur-faces (Figs 2b and 3b), at which the bridging oxygens are protonated. At thesurface coverage corresponding to approximately three water molecules persurface unit the oxygen density distribution in the first two layers is essen-tially the same as at the interface with bulk water investigated in our previ-ous study11,13. The first two adsorbed layers are apparently very rigid andtheir structure does not depend on bonding to outer water molecules. Thethird layer appears to be very diffuse, without a distinct structure and onlyweakly attached to the surface.

Thermodynamics of Adsorption

The profiles of excess chemical potential of water at metal oxides tell uswhether and where water will adsorb. We know from the results of the TGAexperiments (Figs 4 and 5 of ref.14) that at ambient condition water adsorbsin three layers and the last water (first layer) desorbs at temperatures rang-ing from about 190 °C for rutile to 300 °C for cassiterite. Because the high-est coverage considered in this study corresponds to <80% relativehumidity at 300 K, we may expect that the adsorption Helmholtz energyfor this coverage will be lower than (but relatively close to) the values ofthe excess chemical potential of pure SPC/E water, which is approximately27 kJ/mol 31.

At hydroxylated surfaces (Figs 4b and 5b), the first layer of water is disso-ciated and chemically bonded to metal oxide atoms. The Helmholtz energyof chemical bonding can be, in principle, obtained from ab initio calcula-tions and is not investigated here. For steric reasons it is not possible to in-sert additional molecules to the fully occupied first layer and the excessHelmholtz energy reaches extremely large values. A distinct and importantfeature of the adsorption Helmholtz energies at hydroxylated surfaces istheir small dependence on the surface coverage, especially for occupancy



between 1.0 and 2.5 molecules per surface unit. This implicates that oncetemperature or vapor pressure reaches a certain value, all water beyond thefirst layer will desorb. This behavior is especially distinct for thehydroxylated rutile surface. (Here we suppose that the structure of the ad-sorbed layers is not qualitatively changed at higher temperatures. The rigid-ity and regular pattern dictated by the static crystal surface makes such a



FIG. 4Excess chemical potential profiles of water adsorbed at rutile for different surface coveragesfrom up to 3.5 molecules per surface unit. Top: nonhydroxylated surface, bottom: hydroxylatedsurface

proposition reasonable.) If water adsorbs at rutile dissociatively, fastdesorption of outer two layers should be observed in the TGA experiments,but this is not the case. On the other hand, such a behavior was observed inexperiments with cassiterite. This result is consistent with our earlier obser-vation that the first layer desorbs from cassiterite at much higher tempera-tures, which was interpreted as a sign of dissociative adsorption. It was notclear, however, whether the dissociative adsorption occurs only for a mono-



FIG. 5Excess chemical potential profiles of water adsorbed at cassiterite for different surfacecoverages from up to 3.5 molecules per surface unit. Top: nonhydroxylated surface, bottom:hydroxylated surface

layer or for all coverages. We may also notice in Table I that the adsorption freeenergy (the minimum of the Helmholtz energy profiles) at the hydroxylatedcassiterite for the highest coverage is approximately 27.6 ± 1.6 kJ/mol, whichis slightly lower than 25 kJ/mol found for solvation in pure SPC/E water31.Given that even higher coverage was observed in experiments (4.0 moleculesper surface unit) there is still capacity to adsorb additional water.

At nonhydroxylated surfaces, the adsorption of the first layer is mediatedby the nonbonded interactions of SPC/E molecules and can be thus investi-gated in the same way as the adsorption of higher layers. Despite very slowdynamics of the first layer and its high density, seen as a high peak in Figs 2aand 3a, it is relatively easy to determine the probability of the successfulinsertion of a test particle. Since there are only a limited number of surfacemetal atoms that can bind first-layer molecules and each metal atom canbind either zero or one water oxygen, it is easy to test the generated configu-rations for a suitable cavity. We notice that, starting at the coverage of fulltwo water layers, the first one is permanently occupied and does not offeropportunities for a successful insertion of a test particle. There are only rareoccasions when a first-layer molecule exchanges position with a second-layer molecule, during which time a successful insertion is conceivable butwas not observed. The relaxation time of such an exchange was estimatedto be about 1 µs for rutile and can be expected even longer for cassiterite,



TABLE IAdsorption Helmholtz energies (kJ/mol) of investigated surfaces at different coveragesa,b

Surfacecoveragea Aads (R, N) Aads (R, H) Aads (C, N) Aads (C, H)

0 80.7 – 96.9 –

0.5 67.2 (1.5) – 86.8 (0.2) –

1 62.8 (1.5) 30.8 (2.3) 77.8 (0.5) 52.0 (3.0)

1.5 58.0 (2.0) 30.8 (1.3) 61.0 (1.9) 40.4 (0.8)

2 44.0 (3.5) 33.0 (1.7) 46.0 (2.0) 40.5 (2.0)

2.5 23.2 (1.3) 31.8 (4.0) 23.9 (0.8) 36.6 (2.0)

3.5 23.5 (1.3) 24.1 (2.1) 22.9 (1.9) 27.6 (1.6)

a R, C, N, and H denote rutile, cassiterite, nonhydroxylated and hydroxylated surfaces,respectively. b Standard deviations are given in parentheses. c Water molecules per surfaceunit.

for which the Helmholtz energy minimum reaches almost 100 kJ/mol 14.Such a finding is not surprising because the employed forcefield is basedon ab initio calculations that predict stronger bonding to the SnO2 surfaceand the tendency of water to dissociate. As it was noted in the discussion ofthe structural properties, associative adsorption leaves bridging oxygensunprotonated and available for strong hydrogen bonding with the secondlayer. The excess Helmholtz energy in the second layer ranges from about70 kJ/mol for a monolayer coverage to about 0 kJ/mol for full three-layercoverage observed experimentally, which reflects the high stability andcompactness of the layer compared to the second layer at hydroxylated sur-faces. The minimum of the Helmholtz energy profiles shifts to the thirdlayer only when the coverage exceeds that needed to completely fill twolayers. The Helmholtz energy of adsorption at rutile for the highest coverage(3.5 molecules per surface unit) can be estimated to be around 23.5 ± 1.7 kJ/mol,which is close to the value for solvation in pure SPC/E water31. Given thestatistical error of our calculations and possible deviation due to theforcefield, this value agrees very well (units of kJ/mol) with what can be ex-pected for 80% humidity at ambient conditions. As opposed to hydroxy-lated surfaces, the absolute value of adsorption Helmholtz energy growsrapidly as the surface coverage is decreased. Such a behavior should bereflected in the TGA desorption studies as a slow weight loss over a wide rangeof temperatures and was actually observed for rutile. This finding agreeswell with predictions based on smaller-scale ab initio calculations withmonolayer and bilayer coverages and also suggests that additional water doesnot have a dramatic influence on the dissociation in the first layer.

CONCLUSIONS

We have performed molecular simulations of water adsorbed on TiO2 andSnO2 surfaces and studied density profiles and adsorption Helmholtz ener-gies for a range of surface coverages from zero to values detected at ambientconditions. We have found that there are substantial differences betweenthe ways water adsorbs at surfaces depending on the degree of dissociationin the first layer. In the case of nondissociative surfaces, water adsorbs layerby layer with a relatively weak cohesion between the neighboring layers,which implies gradual adsorption/desorption over a wide range of tempera-tures or pressures. Such a behavior was observed for rutile nanoparticlesand is consistent with ab initio calculations predicting molecular adsorp-tion in the first layer. At dissociative surfaces, the first layer is adsorbed verystrongly while the second forms relatively weaker bonds with the surface



which are compensated by increased bonding with the third layer. Thistype of interactions corresponds to the desorption of outer two layers oc-curring in a limited range of temperatures or pressures, and the desorptionof the first layer at high temperatures. Thermal gravimetric analysis has de-tected this type of behavior for cassiterite nanoparticles, which is in agree-ment with the ab initio studies of water mono- and bilayers predicting thatadsorption at cassiterite is mostly dissociative. It also follows that additionallayers of adsorbed water do not have large influence on the dissociation–association equilibrium in the first layer.

This research was supported by the Division of Chemical Sciences, Geosciences and Biosciences,Office of Basic Energy Sciences, U.S. Department of Energy under contract DE-AC05-00OR22727, OakRidge National Laboratory, managed and operated by UT-Battelle, LLC. The computational resourceswere provided by the Computing Center for Research and Education at Vanderbilt University. Theauthors would like to thank Prof. Jorge Sofo from Pennsylvania State University for an inspiringdiscussion that led to this study.

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adsorption of water on tio2 and sno2 surfaces:...

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