Oxygen Interactions with Silica Surfaces: Coupled Cluster and Density

Dec 4, 2012 - We consider oxygen interactions with realistic silica surfaces, including both experimentally observed nondefective surface reconstructi...
0 downloads 11 Views 3MB Size
Download PDF
Article pubs.acs.org/JPCC

Oxygen Interactions with Silica Surfaces: Coupled Cluster and Density Functional Investigation and the Development of a New ReaxFF Potential Anant D. Kulkarni,† Donald G. Truhlar,*,† Sriram Goverapet Srinivasan,‡ Adri C. T. van Duin,*,‡ Paul Norman,*,§ and Thomas E. Schwartzentruber*,§ †

Department of Chemistry, Supercomputing Institute, and Chemical Theory Center, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, United States ‡ Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States § Department of Aerospace Engineering and Mechanics, University of Minnesota, 110 Union St. SE, Minneapolis, Minnesota 55455-0153, United States S Supporting Information *

ABSTRACT: We consider oxygen interactions with realistic silica surfaces, including both experimentally observed nondefective surface reconstructions and experimentally observed surface defects. Nondefective models include clusters representing the site above a fully coordinated surface Si atom and bridging O atoms, and the defective models include clusters representing an under-coordinated Si defect, a nonbridging O defect, and a ring structure. Energies were obtained for the approach of atomic and molecular oxygen to these clusters in various configurations by using explicitly correlated CCSD(T)-F12b electronic structure theory and the Minnesota density functionals, which were found to be in good agreement. The Minnesota functionals were employed in binding energy calculations for all of the clusters, considering the singlet and triplet spin states for nondefective clusters and doublet and quartet spin states for defective clusters. We find that the chosen defects are energetically favorable sites for binding. The density functional energies were used to extend the empirical ReaxFFSiO potential for silica, which was previously parametrized for bulk silica polymorphs (van Duin et al. J. Phys. Chem. A, 2003, 107, 3803−3811), to model the gas−surface interactions represented by the defective and nondefective clusters presented here. Interaction energy predictions from ReaxFFGSI SiO agree very well with the density functional energies. ReaxFFGSI SiO can now be employed in reactive large-scale molecular dynamics simulations involving oxygen−silica gas−surface interactions such as oxide growth and the heterogeneous recombination of oxygen occurring on real silica surfaces.

1. INTRODUCTION The interaction of atomic and molecular oxygen with silica surfaces is of interest in many applications. Thin silica films formed by chemical vapor deposition in an oxygen discharge are important in microelectronics applications, where silica acts as an electric insulator between other components.1 A detailed understanding of oxygen-silica interactions would enable advances in the anisotropic dry-etching of silica surfaces for microelectronics.2,3 In addition, the synthesis, oxidation, and sintering of silica-based nanoparticles in plasma reactors is a large research field where an understanding of high-temperature oxygen-silica interactions is fundamental.4,5 Furthermore, the efficiency of low-pressure plasma reactors for producing atomic © XXXX American Chemical Society

oxygen is primarily limited by the heterogeneous recombination of atomic oxygen on silica based reactor walls.6 An accurate description of interactions between atomic and molecular oxygen with silica surfaces is also important in aerospace applications. Due to its low thermal conductivity, high melting temperature, and low catalytic activity, silica is a significant component in many reusable and ablative thermal protection systems for high-speed aerospace vehicles. For example, most current high-temperature oxidation-protection Received: August 31, 2012 Revised: November 14, 2012

A

dx.doi.org/10.1021/jp3086649 | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

observed both experimentally and by using previously available interatomic potentials. The ReaxFF force field is a classical potential parametrized from a training set of quantum chemical calculations.27 For silica−oxygen interactions, the ReaxFFSiO potential28 has been previously parametrized to reproduce the bulk phases of several polymorphs of SiO2. However, quantum chemical calculations of gas−surface interactions were not included in that parametrization. The goal of the present work is to carry out new density functional calculations (with more accurate density functionals than those mentioned above) to investigate the interaction of molecular and atomic oxygen with silica surfaces and to use the results to extend the ReaxFFSiO parametrization to accurately model oxygen−silica gas−surface interactions. This work is organized as follows. In section 2.1 we describe the density functional methods used, and in section 2.2 we describe the ReaxFF potential. The chemical systems studied are described in section 3, followed by the DFT results for these systems in section 4. The reparameterization of the ReaxFF potential to match the DFT results is described in section 5, followed by a summary in section 6.

systems for leading edges on hypersonic vehicles involve silicabased or silica-forming coatings (e.g., the reinforced carbon− carbon systems used on the Space Shuttle and the X-43A research aircraft vehicle). Furthermore, natural silica oxides (SiO2) form on SiC, Si3N4, and most ultra high temperature ceramic (UHTC) composite systems under conditions similar to those of earth re-entry.7,8 One significant contribution to the heating on thermal protection systems can come from the chemical reactions occurring on the surface of the vehicle. During atmospheric reentry, a strong bow shock forms in front of the vehicle, leading to temperatures of several thousands of degrees Kelvin in the gas between the shock and the surface of the vehicle. Such high temperatures cause vibrational excitation and dissociation of diatomic gas molecules, and under the low gas densities characteristic of re-entry, the gas can reach the surface of the vehicle in a dissociated, nonequilibrium state. In many cases, the surface of the vehicle acts as a catalyst for the exothermic recombination of dissociated species, increasing the overall heating on the thermal protection system of the vehicle. 9 It has been shown that this heterogeneous recombination can contribute up to 30% of the total heat load for Earth reentry.10 Despite a large body of experimental work6,7,11−14 (also see the summary paper of Bedra and BalatPichelin15) the fundamental processes occurring on silica surfaces exposed to atomic and molecular oxygen are still uncertain. Molecular dynamics (MD) can be used to provide insight into the mechanisms that contribute to heterogeneous recombination. The accuracy of such MD simulations depends on a description of the chemical structures present on a realistic surface as well as the ability of the chosen interatomic potential to describe the potential energy surfaces of the interaction of atomic and molecular oxygen with these structures. Previous studies in this area have been carried out for the interaction of atomic and molecular oxygen with the (001) cleaved β-cristobalite surface16−20 and for the interaction of atomic oxygen with the cleaved (001) β-quartz surface.21,22 In one series of studies,16−19 the authors used quantum chemical calculations (PW91 density functional calculations) to generate potential energy surfaces for the interactions of O and O2 with the surface. The potential energy surfaces were fit with a corrugation-reducing procedure, allowing the authors to carry out quasiclassical trajectory calculations for a number of reactions. In another series of studies20−22 the authors used an empirical interatomic potential (based on PBE0 density functional calculations in one work22) to describe the interaction of oxygen with the surface. In these studies the authors used semiclassical dynamics simulations in which phonons on the surface were quantized and the gas-phase atoms were treated classically. In both series of studies the authors used idealized cleaved crystal surfaces. However, cleaved silica surfaces are covered in highly reactive dangling bonds and tend to reconstruct to lower energy states, minimizing the number of under-coordinated atoms on the surface. For example, there are ab initio MD simulations showing that the (011) α-quartz surface undergoes significant reconstructions at 300 K.23 Additionally, there are density functional and MD results24,25 supported by experimental evidence26 showing that the (001) α-quartz surface reconstructs to form a well-ordered (1 × 1) pattern below 300 K. Therefore, these cleaved, unreconstructed chemical structures are not representative of real silica surfaces. In the present study we will focus on the interaction of atomic and molecular oxygen with realistic, stable surface configurations that have been

2. METHODOLOGY 2.1. Density Functional Calculations. The singlet (S) and triplet (T) potential energy curves were studied for clusters with an even number of electrons, and the doublet (D) and quartet (Q) states were studied for clusters with an odd number of electrons. The reason for these choices is as follows: When O or O2 is far from the surface of a system with an even number of electrons, the lowest-energy state is a triplet; however, when it is close to the surface the lowest energy state is a singlet. The ReaxFF force field is fit, at any geometry, to the lowest-energy state; therefore we calculate both the singlet and triplet energies at every geometry, and a fit is made to the lower energy. However, for some of our surface models, the system has an odd number of electrons; in such cases the lowestenergy state could be either a doublet or a quartet and so we calculate both states at each geometry and use the lower energy for fitting the ReaxFF force field. We consider two density functionals, namely M06-L29 and M06-2X,30 which have been well validated for a diverse set of problems, and have been shown to be more accurate than density functionals previously applied to the present problem (PW91, PBE0).30−33 Further validation for the present systems is provided below. We employ two basis sets, def2-SVP34 and def2-TZVP,34 and consider three density functional model chemistries, namely M06-L/T, M06-L/T+S, and M06-2X/T+S, where Y/T denotes a calculation with density functional Y with basis def2-TZVP on all atoms and Y/T+S denotes a calculation with density functional Y with basis def2-TZVP on Si and O and basis def2SVP on H. We also use the ma-TZVP35 and maug-cc-pVTZ36 basis sets for testing basis set effect in some systems. Gaussian 0937 was used for the geometry optimization as well as potential energy curve calculations with normal tight convergence in the self-consistent-field iterations. The integration grid employed is an ultrafine pruned grid with 99 radial shells and 590 angular points per shell, as defined in Gaussian 09. For benchmarking our density functional results we also use the explicitly correlated CCSD(T)-F12b method38 as implemented in Molpro.39 CCSD(T)-F12b calculations include both configuration state functions formed from one-electron basis functions and configuration state functions containing the B

dx.doi.org/10.1021/jp3086649 | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

Figure 1. (a) Cleaved (001) α-quartz surface. (b) Reconstructed (001) α-quartz surface. Surfaces as displayed are optimized with the ReaxFFSiO potential. Oxygen atoms are red, and silicon atoms are gray.

correlating factor F, which is exp(−βr12), where β is a parameter and r12 is the distance between two electrons. For energy computations involving clusters with an even number of electrons, the singlet energy is computed using the broken symmetry approach.40−42 The corrected singlet energy43 is ES =

2⟨E BS − E T⟩ ⟨S2⟩HS − ⟨S2⟩BS

+ ET

bond formation and bond dissociation realistically. This formulation allows ReaxFF to describe under- and overcoordinated systems properly. The bond orders are combined with functions of valence coordinates such as bond angles and torsion angles so that the energy contributions from bonding terms vanish on bond dissociation. The ReaxFF potential uses a central field formalism wherein nonbonded interactions, namely Coulomb and van der Waals interactions, are calculated between every atom pair. Excessively short range interactions are avoided by using a shielding term in the energy expression for the nonbonded interactions. Atomic charges are calculated using the geometry-dependent charge calculation scheme (EEM scheme) of Mortier et al.53 Instead of Ewald summation to calculate long-range Coulomb interactions, ReaxFF uses a seventh-order taper function with an outer cutoff radius of 10 Å. The system energy in ReaxFF is calculated as the sum of a number of energy terms according to

(1)

where EBS is the energy of the broken-symmetry singlet, ET is the triplet energy, S is total electron spin, ⟨S2⟩BS is the S2 expectation value for the broken-symmetry singlet, and ⟨S2⟩HS is the S2 expectation value for the triplet. For energy computations involving clusters with odd numbers of electrons, the corrected doublet energy using the broken symmetry approach is given by E D = E HS −

3(E HS − E LS) ⟨S2⟩HS − ⟨S2⟩LS

Esys = E bond + Eover + Eunder + E lp + Eval + Epen + Etors

(2)

+ Econj + EvdWaals + ECoulomb

where ELS is the energy of the broken-symmetry doublet, EQ is the quartet energy, ⟨S2⟩LS is the S2 expectation value for the broken-symmetry doublet, and ⟨S2⟩HS is the S2 expectation value for the quartet. Potential energies are computed using

ΔEM = EM (R ) − E0

(4)

A detailed description of each of these terms and their energy expressions can be found in the original work.54 The ReaxFF potential has been shown to accurately model a diverse array of chemically reacting systems, including gas− surface interfaces. For example, ReaxFF MD simulations of the trapping probability of low-incident-energy ( 0) parabola, the procedure uses extrapolation (or interpolation) to find the optimum parameter value within a user-input set range. On the other hand, if the program identifies a “concave down” (a < 0) parabola, the procedure chooses the best of the three parameter values. Using the best parameter value thus identified, a fourth ReaxFF run is performed after which the procedure moves on to the next parameter defined in the “params” file. In order to take into account the strong interparameter correlation in ReaxFF, multiple copies of the list of parameters to be optimized are placed in the “params” file so that the force field optimization program can visit any parameter more than once and optimize it while the other parameters take on their most recent values. The “params” file for the optimization of the ReaxFFSiO potential to describe gas−surface interactions included Si and O atom parameters, Si−O and O−O bond parameters, Si−O− Si, O−Si−O, O−O−Si, and Si−Si−O angle parameters. A detailed description of these parameters and the ReaxFFSiO potential energy equations can be found elsewhere.27,28 The inverse weights for various clusters in the training set were assigned carefully to ensure that the parameter optimization is able to generate a force field that can describe the energetics of the above clusters without causing much change in the description of other structures from the earlier ReaxFFSiO training set. Being a classical potential, ReaxFF does not use electronic degrees of freedom; for this reason, the ReaxFF potentials are always parametrized to reproduce the energy of the lowest-lying spin state of any configuration. Accordingly, for each of the above clusters, the energy of the lowest lying spin state (triplet/singlet for nondefective clusters and doublet/ quartet for defective clusters) was taken as the DFT value against which the ReaxFFSiO parameters were optimized. For clusters with an even number of electrons, this fit follows the triplet surface at large distances and transitions to the singlet surface at shorter distances, which involve strong bonding interactions (see Figures 8−11). For clusters with an odd number of electrons, the lowest lying potential energy curves all follow the doublet surface (shown in Figures 12−19), with the ReaxFF

I

dx.doi.org/10.1021/jp3086649 | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

Therefore the ReaxFFGSI SiO potential provides the same accuracy as the ReaxFFSiO potential for the silica systems described above while better describing the interaction of molecular and atomic oxygen with defects on silica surfaces.

exception of the T4-O+O cluster (Figure 14), which follows both doublet and quartet surfaces. For a full description of chemical reactions, it may be necessary to develop a potential parametrization that describes multiple electronic energy states as well as probabilities of transitions between the states. This is illustrated in Figure 14 by the ReaxFFGSI SiO fit for the T4-O+O cluster, which follows both the doublet and quartet surfaces and inherently assumes that the oxygen atom makes an electronic energy state transition along this path. In reality, some oxygen atoms following this path may remain solely on the doublet or quartet potential energy surface. This may have consequences for the energetics of oxygen atoms interacting with this surface defect; oxygen atoms following the minimum energy surface do not cross any energy barrier, whereas oxygen atoms following the doublet surface experience a barrier of ∼0.6 eV followed by a potential energy minimum, and oxygen atoms following the quartet surface experience a purely repulsive interaction. Nevertheless, a potential that is fit to the minimum energy profile is a valuable first step in describing oxygen interactions with realistic sites on silica surfaces. The energy predictions from ReaxFFSiO and the newly parametrized ReaxFFGSI SiO along with the DFT values are shown in Figures 8−12 and 13−19. It is evident from the plots that ReaxFFGSI SiO is in much better agreement with the DFT values than ReaxFFSiO. Notably, among the defective structures, ReaxFFGSI SiO is able to predict the correct energy profile for T4O+O (Figure 14), T4-O2∥ (Figure 15), T4-O2⊥ (Figure 16), and ring structure (Figure 11). Among the nondefective clusters, the energy profile predicted by ReaxFFGSI SiO for the T2B1+O (Figure 9) and T5-S1+O (Figure 10) clusters is much less repulsive than the energy predicted by ReaxFFSiO. ReaxFFGSI SiO predicts a small attractive well between 1.9 and 3 Å for the T2-B1+O cluster. Though ReaxFFGSI SiO is in very good agreement with DFT, there are a few minor instances where ReaxFFGSI SiO is still unable to fully predict the DFT energy values. For instance, ReaxFFGSI SiO is unable to exactly reproduce the barrier for the approach of O2 molecule in the T4-O2∥ cluster (see Figure 15). In addition, ReaxFFGSI SiO predicts the minimum energy to occur at a distance of 2.0 Å for the T4-O2∥ cluster, whereas DFT predicts the minimum energy to occur at a distance of 1.7 Å. Though the energy profile for the T4-O+O cluster has been improved considerably from that predicted by GSI ReaxFFSiO, the potential well as predicted by ReaxFFSiO potential is still shallow in comparison to the DFT values (see Figure 14). In general this potential is in good agreement with DFT for the configurations within its training set, which encompass a wide range of geometries relevant to gas−surface interactions on silica surfaces. We have performed extensive validations of the ReaxFFGSI SiO potential outside of its training set to verify it is accurate and well behaved. For example, we have validated that the ReaxFFGSI SiO potential is as accurate as the ReaxFFSiO potential at reproducing the bulk structures of a number of forms of silica, including α/β-quartz28 and amorphous silica.64 Additionally, we have found that the ReaxFFGSI SiO potential correctly predicts the structure of the reconstructed (001) α-quartz surface24 and the structure of under-coordinated silicon atom defects and nonbridging oxygen atom defects observed in previous ReaxFF MD simulations of amorphous silica surfaces.64 In MD simulations of oxygen interactions with amorphous silica surfaces, we have GSI potential predicts no energy verified that the ReaxFFSiO discontinuities or structures inconsistent with previous simulations of such surfaces and experimental evidence.

6. SUMMARY We present density functional computations of gas−surface interactions between oxygen and realistic silica surfaces. Experimentally observed defective and nondefective silica surface structures are studied, and DFT is used to compute binding energies of oxygen atoms and molecules with these structures. In order to test the applicability of the Minnesota density functionals used in the DFT studies, energy values based on the explicitly correlated CCSD(T)-F12b model were computed for selected clusters. The comparison of the results for these smaller model systems indicated that the binding energy trends predicted by Minnesota density functionals are in close agreement with those predicted by the CCSD(T)-F12b model. We found that the DFT predicted potential energy curves for smaller (T1 and T2) and larger (T4, T5, and T8) versions of representative clusters were energetically almost identical, so the results presented here should not be dependent on cluster size. The bond dissociation energy of O2 predicted by the present approach was 5.37 eV, in good agreement with the experimental value (5.12 eV). The DFT energies presented here provide a database of energies for the interaction of atomic and molecular oxygen with realistic defects on silica surfaces as well as with undefected reconstructed surfaces. These DFT energies were utilized to develop the ReaxFFGSI SiO force field, based on ReaxFFSiO,54 to describe oxygen-silica gas−surface interaction. ReaxFFGSI SiO was demonstrated to reproduce the DFT-based potential energy curves for various clusters satisfactorily. This force field can be used for accurate largescale MD simulations of oxygen−silica gas−surface interactions.

■

ASSOCIATED CONTENT

S Supporting Information *

Cartesian coordinates of structures, tables of potential energy curves, and a file with the new interatomic potential. This potential file is formatted so it can be directly used by the Serial ReaxFF Molecular Dynamics code or by LAMMPS, the publicly available molecular dynamics code from Sandia (http://lammps.sandia.gov). This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (D.G.T.); [email protected] (A.C.T.v.D.); [email protected] (P.N.); schwartz@aem. umn.edu (T.E.S.). Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was sponsored by the Air Force Office of Scientific Research under AFOSR-MURI Grant FA9550-10-1-0563 and under AFOSR Grant FA9550-09-1-0157. The views and conclusions contained herein are those of the author and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the AFOSR or the U.S. Government. J

dx.doi.org/10.1021/jp3086649 | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

■

Article

(38) Knizia, G.; Adler, T. B.; Werner, H. J. J. Chem. Phys. 2009, 130, 054104. (39) Werner, H.-J.; Knowles, P. J.; Lindh, R.; Manby, F. R.; Schütz, M.; Celani, P.; Korona, T.; Mitrushenkov, A.; Rauhut, G.; Adler, T. B.et al. Molpro computer program; 2009.1 ed., 2009. (40) Noodleman, L.; Peng, C. Y.; Case, D. A.; Mouesca, J. M. Coord. Chem. Rev. 1995, 144, 199−244. (41) Herebian, D.; Wieghardt, K. E.; Neese, F. J. Am. Chem. Soc. 2003, 125, 10997−11005. (42) Soda, T.; Kitagawa, Y.; Onishi, T.; Takano, Y.; Shigeta, Y.; Nagao, H.; Yoshioka, Y.; Yamaguchi, K. Chem. Phys. Lett. 2000, 319, 223−230. (43) Cramer, C. J.; Truhlar, D. G. Phys. Chem. Chem. Phys. 2009, 11, 10757−10816. (44) Bedra, L.; Rutigliano, M.; Balat-Pichelin, M.; Cacciatore, M. Langmuir 2006, 22, 7208−7216. (45) Rutigliano, M.; Zazza, C.; Sanna, N.; Pieretti, A.; Mancini, G.; Barone, V.; Cacciatore, M. J. Phys. Chem. A 2009, 113, 15366−15375. (46) Sanders, M. J.; Leslie, M.; Catlow, C. R. A. J. Chem. Soc., Chem. Commun. 1984, 1271−1273. (47) Tsuneyuki, S.; Tsukada, M.; Aoki, H.; Matsui, Y. Phys. Rev. Lett. 1988, 61, 869−872. (48) van Beest, B. W.; Kramer, G. J.; van Santen, R. A. Phys. Rev. Lett. 1990, 64, 1955−1958. (49) Burchart, E. D.; Verheij, V. A.; Vanbekkum, H.; Vandegraaf, B. Zeolites 1992, 12, 183−189. (50) Belonoshko, A. B.; Dubrovinsky, L. S. Geochim. Cosmochim. Acta 1995, 59, 1883−1889. (51) Ermoshin, V. A.; Smirnov, K. S.; Bougeard, D. Chem. Phys. 1996, 209, 41−51. (52) Roder, A.; Kob, W.; Binder, K. J. Chem. Phys. 2001, 114, 7602− 7614. (53) Mortier, W. J.; Ghosh, S. K.; Shankar, S. J. Am. Chem. Soc. 1986, 108, 4315−4320. (54) van Duin, A. C. T.; Strachan, A.; Stewman, S.; Zhang, Q.; Xu, X.; Goddard, W. A., III J. Phys. Chem. A 2003, 107, 3803−3811. (55) Valentini, P.; Schwartzentruber, T. E.; Cozmuta, I. J. Chem. Phys. 2010, 133, 084703. (56) Khalilov, U.; Pourtois, G.; van Duin, A. C. T.; Neyts, E. C. J. Chem. Phys. C 2012, 116, 8649−8656. (57) Khalilov, U.; Neyts, E.; Pourtois, G.; van Duin, A. C. T. J. Chem. Phys. C 2011, 115, 24839−24848. (58) Khalilov, U.; Pourtois, G.; Duin, A. C. T. v.; Neyts, E. C. Chem. Mater. 2012, 24, 2141−2147. (59) Chenoweth, K.; Cheung, S.; van Duin, A. C.; Goddard, W. A., III; Kober, E. M. J. Am. Chem. Soc. 2005, 127, 7192−7202. (60) Buehler, M. J.; Tang, H.; van Duin, A. C.; Goddard, W. A., III Phys. Rev. Lett. 2007, 99, 165502. (61) Sen, D.; Cohen, A.; Thompson, A. P.; Van Duin, A.; Goddard, W. A., III; Buehler, M. J. MRS Proc. 2010, DOI: 10.1557/PROC-1272PP04-13. (62) Ning, N.; Calvo, F.; van Duin, A. C. T.; Wales, D. J.; Vach, H. J. Phys. Chem. C 2008, 113, 518−523. (63) Neyts, E. C.; Khalilov, U.; Pourtois, G.; van Duin, A. C. T. J. Phys. Chem. C 2011, 115, 4818−4823. (64) Fogarty, J. C.; Aktulga, H. M.; Grama, A. Y.; van Duin, A. C.; Pandit, S. A. J. Chem. Phys. 2010, 132, 174704. (65) Pitman, M. C.; van Duin, A. C. J. Am. Chem. Soc. 2012, 134, 3042−3053. (66) Manzano, H.; Moeini, S.; Marinelli, F.; van Duin, A. C. T.; Ulm, F.-J.; Pellenq, R. J. M. J. Am. Chem. Soc. 2011, 134, 2208−2215. (67) Cacciatore, M.; Rutigliano, M. J. Thermophys. Heat Transfer 1999, 13, 195−203. (68) Rutigliano, M.; Zazza, C.; Sanna, N.; Pieretti, A.; Mancini, G.; Barone, V.; Cacciatore, M. J. Phys. Chem. A 2009, 113, 15366−15375. (69) Warren, W. L.; Kanicki, J.; Rong, F. C.; Poindexter, E. H. J. Electrochem. Soc. 1992, 139, 880−889. (70) Underhill, P. R.; Gallon, T. E. Vacuum 1981, 31, 477−481.

REFERENCES

(1) Granier, A.; Nicolazo, F.; Vallee, C.; Goullet, A.; Turban, G.; Grolleau, B. Plasma Sources Sci. Technol. 1997, 6, 147−156. (2) Hines, M. A. Annu. Rev. Phys. Chem. 2003, 54, 29−56. (3) Gupta, A.; Aldinger, B. S.; Faggin, M. F.; Hines, M. A. J. Chem. Phys. 2010, 133, 044710. (4) Kruis, F. E.; Fissan, H.; Peled, A. J. Aerosol Sci. 1998, 29, 511− 535. (5) Xiong, Y.; Pratsinis, S. E. J. Aerosol Sci. 1993, 24, 283−300. (6) Macko, P.; Veis, P.; Cernogora, G. Plasma Sources Sci. Technol. 2004, 13, 251−262. (7) Balat-Pichelin, M.; Badie, J. M.; Berjoan, R.; Boubert, P. Chem. Phys. 2003, 291, 181−194. (8) Alfano, D.; Scatteia, L.; Monteverde, F.; Beche, E.; Balat-Pichelin, M. J. Eur. Ceram. Soc. 2010, 30, 2345−2355. (9) Da Rold, G. G., C; Cavadias, S.; Amouroux, J. Adv. Mat. Res. 2010, 89−91, 136−141. (10) Barbato, M.; Reggiani, S.; Bruno, C.; Muylaert, J. J. Thermophys. Heat Transfer 2000, 14, 412−420. (11) Kim, Y. C.; Boudart, M. Langmuir 1991, 7, 2999−3005. (12) Carleton, K. L.; Marinelli, W. J. J. Thermophys. Heat Transfer 1992, 6, 650−655. (13) Cartry, G.; Duten, X.; Rousseau, A. Plasma Sources Sci. Technol. 2006, 15, 479−488. (14) Marschall, J., 1997 National Heat Transfer Conference, Baltimore, MD, 1997. AIAA Pap. No. 97-3879 (15) Bedra, L.; Balat-Pichelin, M. J. H. Aerosp. Sci. Technol. 2005, 9, 318−328. (16) Arasa, C.; Gamallo, P.; Sayos, R. J. Phys. Chem. B 2005, 109, 14954−14964. (17) Arasa, C.; Busnengo, H. F.; Salin, A.; Sayos, R. Surf. Sci. 2008, 602, 975−985. (18) Arasa, C.; Moron, V.; Busnengo, H. F.; Sayos, R. Surf. Sci. 2009, 603, 2742−2751. (19) Moron, V.; Gamallo, P.; Martin-Gondre, L.; Crespos, C.; Larregaray, P.; Sayos, R. Phys. Chem. Chem. Phys. 2011, 13, 17494− 17504. (20) Cacciatore, M.; Rutigliano, M.; Billing, G. D. J. Thermophys. Heat Transfer 1999, 13, 195−203. (21) Bedra, L.; Rutigliano, M.; Balat-Pichelin, M.; Cacciatore, M. Langmuir 2006, 22, 7208−7216. (22) Zazza, C.; Rutigliano, M.; Sanna, N.; Barone, V.; Cacciatore, M. J. Phys. Chem. A 2012, 116, 1975−1983. (23) Lopes, P. E. M.; Demchuk, E.; Mackerell, A. D. Int. J. Quantum Chem. 2009, 109, 50−64. (24) Chen, Y.-W.; Cao, C.; Cheng, H.-P. Appl. Phys. Lett. 2008, 181911. (25) Rignanese, G. M.; Charlier, J. C.; Gonze, X. Phys. Chem. Chem. Phys. 2004, 6, 1920−1925. (26) Steurer, W.; Apfolter, A.; Koch, M.; Sarlat, T.; Sondergard, E.; Ernst, W. E.; Holst, B. Surf. Sci. 2007, 601, 4407−4411. (27) van Duin, A. C. T.; Dasgupta, S.; Lorant, F.; Goddard, W. A. J. Phys. Chem. A 2001, 105, 9396−9409. (28) van Duin, A. C. T.; Strachan, A.; Stewman, S.; Zhang, Q. S.; Xu, X.; Goddard, W. A. J. Phys. Chem. A 2003, 107, 3803−3811. (29) Zhao, Y.; Truhlar, D. G. J. Chem. Phys. 2006, 125, 194101. (30) Zhao, Y.; Truhlar, D. G. Theor. Chem. Acc. 2008, 120, 215−241. (31) Zhao, Y.; Truhlar, D. G. Acc. Chem. Res. 2008, 41, 157−167. (32) Zhao, Y.; Truhlar, D. G. Rev. Mineral. Geochem. 2010, 71, 19− 37. (33) Zhao, Y.; Truhlar, D. G. Chem. Phys. Lett. 2011, 502, 1−13. (34) Weigend, F.; Ahlrichs, R. Phys. Chem. Chem. Phys. 2005, 7, 3297−3305. (35) Zheng, J.; Xu, X.; Truhlar, D. Theor. Chem. Acc. 2011, 128, 295− 305. (36) Papajak, E.; Leverentz, H. R.; Zheng, J. J.; Truhlar, D. G. J. Chem. Theory Comput. 2009, 5, 1197−1202. (37) Frisch, M. J. et al. Gaussian 09, revision A.1; Gaussian Inc.: Walingford, CT, 2009. K

dx.doi.org/10.1021/jp3086649 | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

Article

(71) Levine, S. M.; Garofalini, S. H. J. Chem. Phys. 1987, 86, 2997− 3002. (72) Wilson, M.; Walsh, T. R. J. Chem. Phys. 2000, 113, 9180−9190. (73) Bunker, B. C.; Haaland, D. M.; Ward, K. J.; Michalske, T. A.; Smith, W. L.; Binkley, J. S.; Melius, C. F.; Balfe, C. A. Surf. Sci. 1989, 210, 406−428. (74) Rimola, A.; Ugliengo, P. J. Chem. Phys. 2008, 128, 204702. (75) Knizia, G.; Adler, T. B.; Werner, H. J. J. Chem. Phys. 2009, 130, 054104. (76) van Duin, M.; Polman, J. E.; De Breet, I. T.; van Ginneken, K.; Bunschoten, H.; Grootenhuis, A.; Brindle, J.; Aitken, R. J. Biol. Reprod. 1994, 51, 607−617.

L

dx.doi.org/10.1021/jp3086649 | J. Phys. Chem. C XXXX, XXX, XXX−XXX