Monte Carlo Simulation of Silica Surface Dehydroxylation under

The effect of the nature and the state of the surface of highly dispersed silicon, aluminum, and titanium oxides on their sorption characteristics. V...
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Monte Carlo Simulation of Silica Surface Dehydroxylation under Nonisothermal Conditions† V. I. Bogillo,‡ L. S. Pirnach,‡ and A. Dabrowski*,§ Institute of Surface Chemistry of NAS, 252022 Kiev, Ukraine, and Faculty of Chemistry, Maria Curie-Sklodowska University, 20031 Lublin, Poland Received December 20, 1995. In Final Form: June 25, 1996X The influence of distance between OH groups and lattice disorder of silica surface on the peak characteristics in the TPD (temperature programmed desorption) spectra of water desorption as well as on the coverage dependence of desorption activation energy has been investigated by the Monte Carlo simulation. The experimental TPD spectra of water desorption from different silica samples and coverage dependencies of desorption activation energy have been compared. The BOC-MP approach has been used to calculate the activation energies for possible associative desorption reactions which are realized during the dehydroxylation. It was established that most activation energies for associative desorption lie in the same region as those estimated from the TPD spectra.

Introduction Thermal dehydroxylation of inorganic oxides surface, as silica,1,2 alumina,3 and titania4,5 has a great effect on reactivity of their active sites, the concentration, and surface topography. The dehydroxylation is one of the most studied reactions on the silica surface.1,2,6-28 The thermal stability of hydroxyl groups on the silica surface * Author to whom correspondence should be addressed. † Presented at the Second International Symposium on Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids, held in Poland/Slovakia, September 4-10, 1995. ‡ Institute of Surface Chemistry of NAS. § Maria Curie-Sklodowska University. X Abstract published in Advance ACS Abstracts, September 15, 1996. (1) Iller, R. K. The Chemistry of Silica; Wiley: New York, 1979. (2) Hair, M. I. Infrared Spectra of Surface Compounds; Wiley: New York, 1975. (3) Knozinger, H.; Ratnasamy, P. Catal. Rev.-Sci. Eng. 1978, 17, 31. (4) Suda, Y.; Moromoto, T. Langmuir 1987, 3, 786. (5) Malet, P.; Munuera, G. J. Chem. Soc., Faraday Trans. 1 1989, 85, 4157. (6) Sindorf, D. W.; Maciel, G. E. J. Am. Chem. Soc. 1983, 105, 1487. (7) White, R. L.; Nair, A. Appl. Spectrosc. 1990, 44, 69. (8) Garafalini, S. H. J. Non-Cryst. Solids 1990, 120, 1. (9) Feuston, B. P.; Garafalini, S. H. J. Appl. Phys. 1990, 68, 4830. (10) Peri, J. B.; Hensley, A. L., Jr. J. Phys. Chem. 1968, 72, 2926. (11) Peri, J. B. J. Phys. Chem. 1966, 70, 2937. (12) Volkov, A. V.; Kiselev, A. V.; Lygin, V. I.; Ryabenko, E. A.; Shalumov, B. Z.; Shimichev, V. S. Kolloidn. Zh. 1979, 41, 323. (13) (a) Chuiko, A. A.; Gorlov, Yu. I. Chemistry of Silica Surface: Surface Structure, Active Sites and Adsorption Mechanisms; Naukova Dumka: Kiev, 1992. (b) Chuiko, A. A. React. Kinet. Catal. Lett. 1993, 50, 1. (14) Dunken, H.; Flammersheim, H. J.; Franke, S.; Wittkoff, H. Z. Chem. 1985, 25, 93. (15) Ryabenko, E. A.; Shalumov, B. Z.; Bessarabov, A. M.; Dyakonov, S. S.; Baykov, Yu. Zh. Fiz. Khim. 1985, 59, 219. (16) Zhuravlev, L. T. Pure Appl. Chem. 1989, 61, 1969. (17) Krylova, I. V.; Filonenko, A. P.; Sitonite, Yu. P. Zh. Fiz. Khim. 1967, 41, 2839. (18) Young, G. J. J. Colloid Sci. 1958, 13, 67. (19) Huhn, H. J. J. Therm. Anal. 1988, 33, 851. (20) Vansant, E. F.; Van Der Voort, P.; Vrancken, K. C. Characterization and Chemical Modification of the Silica Surface; Elsevier: Amsterdam, 1995. (21) Gavrilyuk, K. V.; Gorlov, Yu. I.; Nazarenko, V. A.; Chuiko, A. A.; Melnichenko, G. N. Teor. Experim. Khim. 1983, 19, 364. (22) Branda, M. M.; Montani, R. A.; Castellani, N. J. Surf. Sci. 1995, 341, 295. (23) Ustyuzhanin, P. F. PhD Dissertation, Institute of Surface Chemistry of NAS, Kiev, Ukraine, 1990. (24) Lygin, V. I.; Serazetdinov, A. D.; Chertyhina, O. I. Zh. Fiz. Khim. 1989, 63, 2948. (25) Gibbs, G. V. Am. Mineral. 1982, 67, 421. (26) Kolobova, O. I.; Kuznetsov, A. I.; Lygin, V. I.; Serazetdinov, A. D. Zh. Fiz. Khim. 1988, 62, 2109.

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has been investigated both experimentally1,2,6-7,12-23 and theoretically.8-11,13a,24,26-28 Kinetics of this process was studied under the isothermal conditions using IR spectroscopy on loss of the OH groups1,12 as well as by thermodesorption of structural water under the nonisothermal conditions (TPD).13b,14,16-23 The topochemical kinetic models are commonly used for calculation of the activation parameters.12 The second reaction order was observed for the silica dehydroxylation from the treatment of TPD spectra using the Freeman and Carroll and Kissinger methods.16 It was established that both the apparent thermodesorption activation energy and preexponential factor increase with the decrease of silica surface coverage (Θ). The main types of OH groups on the silica surface are postulated to be vicinal, geminal, or isolated.1,2 Such factors as siloxane ring size, degree of the ring opening, number of OH groups per surface silicon site, and surface curvature influence the extent of hydrogen bonding of the surface OH groups, average distance between them, and temperature of their removal from the silica surface. From the analysis of second moment and width of 1H signal of adsorbed water at 93 K on the silica gel surface preheated at Tp ) 500 K in vacuum, it follows that three types of silanol groups are present on the surface: (1) single OH groups (ΘOH ) 0.25) with the distance between neighboring protons dH-H ) 0.50-0.52 nm; (2) paired OH groups with dH-H ) 0.25-0.26 nm and those separated by dH-H ) 0.500.52 nm (ΘOH ) 0.30); (3) clusters of OH groups formed by three and more silanols with dH-H ) 0.25-0.26 nm (ΘOH ) 0.45).29 Recently,30 the surface Cab-O-Sil HS5 at different Tp was characterized via single and multiple quantum 1H NMR spectroscopy. It was established that the small clusters of closely-placed OH groups (six to seven) exist on the surface. The geminal groups are postulated to be possible sites for the clusters. In addition, the 1H combined rotation and multiple pulse spectroscopy (CRAMPS) approach has distinguished the isolated silanols and clustered OH groups. The clustered OH groups were shown to disappear after evacuation at 773 K.31 (27) Gorlov, Yu. I.; Zayats, V. A.; Chuiko, A. A. Teor. Exper. Khim. 1986, 22, 533. (28) Kuznetsov, A. I.; Lygin, V. I.; Serazetdinov, A. D.; Riabenko, E. A.; Chertihkina, O. I. Fiz. Khim. Glasses 1990, 16, 9. (29) (a) Kilividze, V. I. Dokl. Akad. Nauk SSSR 1964, 157, 157. (b) Kilividze, V. I.; Kiselev, V. F. Probl. Kinet. Catal. 1968, 12, 302. (30) Hwang, S. J.; Uner, D. O.; King, T. S.; Pruski, M.; Gerstein, B. C. J. Phys. Chem. 1995, 99, 3697.

© 1997 American Chemical Society

Silica Surface Dehydroxylation

Hence, one could expect the influence of geometric heterogeneity of the silica surface OH groups and their topography on kinetics of their thermal desorption. One reason of such nonuniformity at high surface coverage can be the lateral interactions between the nearestneighboring OH groups in the above mentioned patches on an amorphous silica surface. The Monte Carlo study of Lennard-Jones gas adsorption on the amorphous surface demonstrated that adsorption isotherms are very sensitive to the effect of geometric heterogeneity.32 Previously it was established that the broadening of the distribution function on the distance and decrease of the average distance between the nearest neighbors on an amorphous surface, taking into consideration the repulsive interaction between them, leads to broadening of the distribution function on the apparent rate constants of chemisorption on an amorphous heterogeneous surface.33 A similar effect of surface amorphization would be expected for desorption kinetics. The Monte Carlo method is mostly used for the simulation of thermodesorption processes proceeding on the single crystal surface.10,11,34-37 In the present work this method has been used for simulation of water thermodesorption from both single crystal and amorphous silica surface under the nonisothermal conditions. The aim of this work has been to investigate by the Monte Carlo method the possible effects of varying the distance between OH groups with consideration of lateral repulsive dipole-dipole interaction between them and disordering the lattice on the peak characteristics of TPD spectra as well as on the coverage dependence of desorption activation energy. Mainly, these effects can be exhibited for the clusters of closely-spaced OH groups on the surface. The experimental TPD spectra of water desorption from different silica samples have been compared, and connection between desorption activation energies obtained from these spectra and those computed by the quantum chemistry methods for possible reactions during silica dehydroxylation has been discussed. Results and Discussion i. Monte Carlo Simulations. It was assumed that the single crystal silica surface contains only single OH groups, uniformly placed at each second Si atom (111 face of β-crystobalite). The average distance between neighboring OH groups (r) has been varied in the range from 0.3 to 0.7 nm.1,2,13a,38 Such a short distance (r ) 0.3 nm) between neighboring OH groups is, of course, not realistic for the fully uniformly hydroxylated surface (average number of OH groups per surface area is 4.6 OH/nm2 16). However, this distance may occur in the clusters of closelyspaced groups.29-31 Disordering of the lattice has been simulated by the random increase of OH groups coordinates in the ranges (X - ζr/2; X + ζr/2) and (Y - ζr(31/2)/2; Y + ζr(31/2)/2) where ζ is the degree of lattice disorder varied in the range 1 > ζ g 0. A dipole-dipole repulsion between the neighboring OH groups (W, in kJ mol-1) in (31) Bronnimann, C. E.; Zeigler, R. C.; Maciel, G. E. J. Am. Chem. Soc. 1988, 110, 2023. (32) Benegas, E. I.; Pereyra, V. D.; Zgrablich, G. Surf. Sci. 1987, 187, L647. (33) Bogillo, V. I.; Shkilev, V. P. Langmuir 1996, 12, 109. (34) Sales, J. L.; Zgrablich, G. Surf. Sci. 1987, 187, 1. (35) Nicholson, D.; Parsonage, N. G. Computer Simulation and the Statistical Mechanics of Adsorption; Academic Press: London, 1982. (36) Binder, K. Monte Carlo Methods in Statistical Physics, 2nd ed.; Topics in Current Physics; Springer: Belin, Heidelberg, 1986; Vol. 7. (37) Sales, J. L.; Unac, R. O.; Gardiulo, M. V.; Bustos, V.; Zgrablich, G. Langmuir 1996, 12, 95. (38) Kiselev, A. V.; Lygin, V. I.; Shapalin, K. L. Zh. Fiz. Khim. 1985, 59, 1521.

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accordance with the relation W ) 2µOH2/(4π0r3) ) 0.1746/ r3 39 (W, in kJ mol-1; r, in nm), (where µOH ) 1.51 D, dipole moment of surface OH group) has been taken into consideration in the calculations. The interaction between OH groups at the surface heating leads to dehydroxylation via the associative desorption mechanism

2>Si-OH f >Si-O• + >Si• + H2O

(1)

and to subsequent formation of strained siloxane bridges

>Si-O• + >Si• f >Si-O-Si
473 K the first peak was identified as type 2. One to three peaks are commonly observed in the TPD spectra. Their position and relative intensity depend on the heating rate. The Ed and Ad were calculated in the cited studies using Polanyi-Wigner,17 Kissinger,16 and Freeman-Carroll16,23 methods. In order to compare these spectra, the Ed values (given in brackets in Table 1) have been calculated using Tm and β parameters by simple Redhead’s peak maximum method42 for the first- and second-order kinetics at two Ad values (1013 and 1018 s-1). As can be seen from Table 1, the first peak in the TPD spectra is observed in the region 353-376 K. This peak is related to the desorption of physically adsorbed water from the silica surface. It must be emphasized that the calculated values in the original studies of Ad values for this process (2.8 × 104 s-1,14 3.6 × 105 s-1,22 0.8-47 s-1 16) are much smaller than the vibrational frequency, 1013 s-1. One of the reasons for such small preexponential factors may be including the readsorption in the thermodesorption process.43 However, this process is more favorable in the desorption from microporous solids. The pyrogenic silicas (Aerosil and Cab-O-Sil) are nonporous, whereas aerosilogel has uniform large pores with a diameter of 5.1 nm.16 Then, the dramatic decrease in Ad may be explained by limitations of Polanyi-Wigner, Kissinger, and Freemen-Carroll methods for the independent Ad determination on the heterogeneous surface.44 The calculated Ed1 values in refs 16 and 17 are lower than the values for the latent heat of water liquefaction (∆HL ) 44 kJ mol-1). This seems contrary to the conditions of the TPD experiment with registration of desorption products by the mass spectrometry method, when the (42) Redhead, P. A. Vacuum 1962, 12, 203. (43) Gorte, R. J. J. Catal. 1982, 75, 164. (44) de Jong, A. M.; Niemantsverdriet, J. W. Surf. Sci. 1990, 233, 355.

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Table 1. Experimental Data for Thermodesorption Spectra of Water from the Silica Surfacea desorption activation parameters sample silica gel Aerosil Aerosil Aerosil Cab-O-Sil Aerosilogeld porous silica film Aerosil pyrogenic silica Aerosil Kieselgel 60

type of peak

Tm (K)

1 2 2 1 2 1 1/2 3 2 3 1 2 1 2 3 1 2 3 1/2 2 1 1/2 3 1 2

353 563 520 362 >600 363 473 743 633 733 400-600 600-1100 376 535 677 371 560 760 453 533 323 458 573 350 700

β (K s-1) 0.167 0.25 0.167

Ed (kJ mol-1)

Ad (s-1)

27.2 79.5 45.4

2.84 × 104

0.25 6.0 0.097 1.0 1.0 0.02 0.167 0.167

72c 97c 26-44 87-205 69 95

3.6 × 105 3.6 × 105 0.8-47 104-5 × 107

(Ed1; Ed2)b 100; 139 161; 214 147; 195 102; 136 >172; 228 102; 136 133; 178 212; 282 164; 223 191; 259 115; 152 175; 231 101; 136 145; 195 185; 248 100; 134 152; 205 209; 280 137; 179 162; 212 91; 121 131; 173 164; 218 99; 132 202; 267

method, ref MS 17 MS 21 DSC 14 MS 13b IGC 22 MS16 MS 23 MS 23 DTG 18 DTG 19 DTG 20

a T and β are the temperature of peak’s maximum and heating rate; E and A are the desorption activation energy and preexponential m d d factor calculated in the cited studies. b Ed1 and Ed2 are the desorption activation energies estimated using Readhead’s method at n ) 1 for the first peak and n ) 2 for the other one at initial ΘOH ) 1 and at the pre-exponential factors 1013 s-1 (Ed1) and 1018 s-1 (Ed2), respectively. c Desorption activation energies were estimated from the quantum chemical data in ref 22. d The regions of change of T , E , and A as m d d a function of temperature of silica surface pretreatment.

water is evaporated at very low pressures (P < 1 × 10-4 Torr) even at room temperature, and Ed for this process coincides with ∆HL. Then, the desorption activation energy of water desorption in the range 350-380 K must be much higher than the ∆HL value. The reason for appearance of the peak in the range 350-380 K may be decomposition of strong hydrogen-bonding (H) or donoracceptor complexes (DA) of water with OH groups or lattice defects (strained siloxane bridges) on the silica surface. The possible region of desorption activation energies can be estimated from the experimental differential adsorption heats of water at low surface coverage (60-80 kJ mol-1 46 and 67-105 kJ mol-1 47) or from the quantum chemical calculations of these complexes (for H complex 2>SiOH‚‚‚ OH2, ∆E ) 60 kJ mol-1;46 for DA complex H2SiO2SiH2‚‚‚H2O, ∆E ) 130-158 kJ mol-1 48). These energies of complexes formation are close to those calculated in Table 1 Ed = 100 kJ mol-1 at Ad ) 1013 s-1. As follows from ref 16, the apparent desorption activation energy increases with a decrease in the surface coverage of silica with physically adsorbed water. This increase is close to the observed changes in differential heat of adsorption of water vapor45 and indicates high heterogeneity of the water surface complexes. The second peak in the TPD spectra of water from silica surface is observed in the region 520-633 K. As concluded (45) Fubini, B.; Bolis, V.; Cavenago, A.; Garrone, E.; Ugliengo, P. Langmuir 1993, 9, 2712. (46) Nonaka, A.; Ishizaki, E. J. Colloid Interface Sci. 1977, 62, 381. (47) Ferrari, A. M.; Garrone, E.; Spoto, G.; Ugliengo, P.; Zeccina, A. Surf. Sci. 1995, 323, 151. (48) Brinker, C. J.; Bunker, B. C.; Tallant, D. R.; Ward, K. J. J. Chim. Phys. 1986, 11-12, 851. (49) Oestrieke, D.; Yang, W. H.; Kirkpatrick, R. J.; Herrig, R. L.; Navrotsky, A.; Montez, B. Geochim. Cosmochim. Acta 1987, 51, 2199. (50) O’Keeffe, M.; Gibbs, G. V. J. Chem. Phys. 1984, 81, 876. (51) Gun’ko, V. M. Kinet. Catal. 1990, 31, 570. (52) Bogillo, V. I.; Gun’ko, V. M. Langmuir 1996, 12, 109. (53) Sauer, J.; Ahlrichs, R. J. Chem. Phys. 1990, 93, 2575. (54) Paukshtis, E. A.; Soltanov, R. I.; Yurchenko, E. N. React. Kinet. Catal. Lett. 1981, 16, 93.

in ref 16, the physically adsorbed water is practically completely removed at the temperature of silica surface pretreatment near 473 K in vacuum. The sharp change occurs in the order of water desorption from n ) 1 to n ) 2 at this temperature.16 The second reaction order confirms the associative desorption of the surface silanol groups. The estimated Ed for Tm values of second and third peaks at Ad ) 1013 and 1018 s-1 are presented in Table 1. The calculated Ed values (at Ad ) 1013 s-1) range from 130 to 210 kJ mol-1. As pointed out in ref 16, this temperature region is characterized by a considerable increase in the desorption activation energy with a decrease in the silica surface coverage with OH groups. However, only a limited region of dependence of Ed versus ΘOH can be constructed on the basis of Ed values from ref 16. Hence, we have determined the distribution function on the Ed value (Figure 5b) and dependencies of Ed versus ΘOH (Figure 6) on the basis of the TPD spectrum presented in ref 16 (Figure 6a), solving the integral equation for nonisothermal desorption kinetics from the heterogeneous surface in the condensation approximation.55 The dependencies of Ed versus ΘOH were calculated at ΘOH ) 1 and at three values of the preexponential factor: Ad ) 1013 s-1, 10-18 s-1, and Ad value connected with the desorption activation energy by the isokinetic relationship (ln Ad ) Ed/RTc + B, where Tc ) 2400 K and B ) 26.4). In addition, the Ed versus ΘOH dependencies from the original paper16 and the monograph20 are presented in Figure 6. It can be seen that the shapes of both the TPD peak and broad distribution curve are almost equal (Figure 5a,b). All Ed values in Table 1 for the second and third peaks estimated at Ad ) 1013 s-1 (Ed ) 130-210 kJ mol-1 and at Ad ) 1018 s-1 (170-280 kJ mol-1) fall on the dependencies of Ed versus ΘOH (ΘOH ) 0.08-0.5) calculated at these preexponential factors. The Ed versus ΘOH dependence, calculated under the assumption that (55) Bogillo, V. I.; Shkilev, V. P. Submitted for publication in Adsorpt. Sci. Technol.

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Figure 6. Dependencies of the apparent desorption energy on the silica surface coverage calculated using the condensation approximation on the basis of TPD spectrum presented in ref 16 ((1-3)) at initial ΘOH ) 1 and at Ad ) 1013 s-1 (1), Ad ) 10-18 s-1 (2), Ad ) exp(Ed/20.0 + 26.4 (3), from ref 16 (4); from ref 20 (5), and from MC simulations, taking into consideration the repulsion between the nearest neighbors at r ) 0.3 nm in the patches of closely-placed OH groups (6).

Figure 5. (a) Thermodesorption spectra of water from the aerosilogel sample reproduced from ref 16 at β ) 0.097 K s-1 and surface pretreatment in vacuum at 473 K (1) and 673 K (2). (b) Distribution curve of aerosilogel surface on the water desorption activation energy calculated from spectrum 1 in Figure 5a using the condensation approximation at Ad ) 1013 s-1.

compensation relationship exists between ln Ad and Ed, intersects both curves at Ad ) 1013 s-1 and 1018 s-1 and it gives rise to the maximum Ed at ΘOH ) 0 and minimum Ed at ΘOH ) 1 among these curves. It should be mentioned that the preexponential factors for the process of associative desorption of water from silica surface obtained in ref 22 (3.6 × 105 s-1) and in ref 16 (103 to 5 × 107 s-1) are 104-108 times lower than the lower limit of Ad predicted by TS theory for these processes.45 The possible explanation of such lower Ad values may be decrease of Ad with increasing the coverage due to the repulsive interaction between the nearest neighbors at high coverages or effects of surface reconstruction which are more important at the small coverages of silica surface. However, the TS theory predicts only the 102 times decrease of Ad value at the transition from ΘOH ) 0 to 1 in the case of repulsive interaction.56 On the other hand, many models of surface reconstruction also predict the coverage dependence of the Ad value for desorption.56 The coverage dependence of the Arrhenius parameters in this process usually is expressed via a chemical potential of adsorbed species. (56) Zhdanov, V. P. Surf. Sci. Rep. 1991, 12, 185.

The clear dependence of the chemical potential of OH groups on the ΘOH is quite possible, since rates of both rehydroxylation and dehydroxylation processes of silica surface are very sensitive to the change of ΘOH value.16,57 However, the coverage dependencies predicted are weak compared to the experimental data. Then, one may not exclude that Ad values obtained in ref 16 are due to the systematic errors of the Freeman-Carroll method employed. The effects of lateral interaction between OH groups on the silica surface are more likely at ΘOH g 0.5, when the patches with closely-placed OH groups exist on the surface in a considerable concentration. The results of MC simulation can be compared with the experimental data for this region of surface coverage. Assuming the patchwise topography of the OH groups (two kinds of sites with Ed1 , Ed2 and 1:1 ratio of patches with closely placed OH groups (1) to those with a much larger distance between these groups (2), we obtained the dependence Ed versus ΘOH for water desorption taking into consideration the repulsion between the nearest neighbors at r ) 0.3 nm (Figure 6). It can be seen that this dependence lies in the region of the experimental curves at ΘOH g 0.5. iii. Comparison of Quantum Chemical and Experimental Desorption Activation Energies for Dehydroxylation of Silica Surface. The detailed study of a mechanism of silica surface dehydroxylation requires the knowledge of activation energies for its elemental stages. Such data are known from the quantum chemical calculations of model clusters of OH silica groups and products of their dehydroxylation. The enthalpies of some possible mono- and bimolecular reactions of silica surface which are possible during the dehydroxylation are presented in Table 2. It can be seen that the condensation of closely-spaced OH groups at a distance between neighboring Si atoms near 0.3 nm is very favorable. However, most of the quantum chemical calculations of small clusters of silica OH groups performed by the nonempirical method do not take into account the possible (57) Zhuravlev, L. T. Colloids Surf. 1993, 74, 71.

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Table 2. Enthalpies for Some Reactions Involved in the Dehydroxylation of the Silica Surface Calculated by the Quantum Chemical Methods (∆H) and Activation Energies for Recombinative Water Desorption Estimated Using the BOC-MP Methods (Edes) reaction

∆H (kJ mol-1)

Edes (kJ mol-1)

method

1.Condensation of Closely-Spaced Geminal or Vicinal (Single) OH Groups -21 100 STO-3G 2Si(OH)4 f (HO)3Si-O-Si(OH) … 72 146 MINDO/3 OH OH HO OH O O O HO HO Si

Si

Si

Si

Si

rSi-Si ) 0.32 nm rSi-Si ) 0.36 rSi-Si ) 0.40 nm rSi-Si ) 0.44 nm rSi-Si ) 0.48 nm OH

Si

OH O

Si

O

OH

O Si

Si

25 13a

Si

-29 67 175 338 575 -48

95 144 198 279 398 86

MNDO/STO-3G

24 24 24 24 24 28

102 127

161 174

ab initio ab initio

48, 49 50

MNDO

28

MNDO, STO-3G MNDO, STO-3G MNDO ab initio ab initio

24 24 27 48, 49 50

cycle (Si3O3)

Si

formation of three-membered cycle The same HO

ref

2.Condensation of Two Vicinal Groups 67 144

O Si

Si O

(rSi-Si ) 0.365 nm in cycle) the same (rSi-Si ) 0.40 nm) C2v to Cg transition in the cycle formation of two-membered cycle the same

110 200 242 232 231

165 210 231 226 226

2>SiOH f Si• + >SiO• >Si• + SiO• f >Si+ + >SiO>Si• + >SiO• f >Si-O-Si< >Si+ + >SiO- f >Si-O-Si
Si(OH)2 f >Si)O the same the same >SiOH f >SiO• + H• the same >SiOH f >Si• + OH• the same >SiOH f >SiO- + H+ the same the same the same >SiOH f Si+ + OHthe same

4.Monomolecular Reactions 372 336 (Ed ) 240-270) 499 496 365 397 1450 1299 1531 1390 989 940

MNDO MNDO MNDO/H; AM1 MNDO MNDO MNDO MNDO MNDO MNDO ab initio frequency shifts MNDO MNDO

13a 26 51 26 52 26 52 26 52 53 54 26 52

effect of relaxation of solid silica matrix. The calculations of more extended clusters by the semiempirical methods (MINDO/3, MNDO) lead to the more positive reaction enthalpies. The ∆H value sharply increases with increasing the distance between Si atoms of interacted silanol groups. This may be one of the important reasons for broadening the distribution function on the water desorption activation energy. More than 100 kJ mol-1 is required for formation of a three-membered cycle in these reactions. The concentration of such cycles increases from 473 K to their maximum concentration at 873 K.58 The interaction of vicinal groups with formation of twomembered cycles is less favorable than the above process since the strain energy exceeds 230 kJ mol-1. Their concentration increases from 900 K up to melting and reconstruction of silica matrix with formation of larger cycles.58 It can be seen in Table 2, that the interaction of vicinal groups has a more positive enthalpy in comparison with that between closely-spaced OH groups. Also, the different monomolecular reactions of single and geminal groups are possible on the silica surface at high temper(58) Brinker, C. J.; Scherer, G. W. Sol-Gel Science; The Physics and Chemistry of Sol-Gel Processing; Academic Press, Inc: Boston, MA, 1990.

atures. The most favorable process is the dehydroxylation of the geminal group with the formation of surface dSidO groups. In most studies of water desorption from the silica surface it was proposed that the activation energy for the associative desorption coincides with enthalpy of the reaction.13a,22 However, most of the reactions presented in Table 2 have very low and even negative enthalpies, or, again, very high positive values. The data for activation barriers of silica dehydroxylation are lacking in the literature. Recently, for the associative desorption of water from the rutile(110) surface studied by the SINDO1 method it has been computed that ∆H ) 40 kJ mol-1 and Ed ) 95 kJ mol-1.59 Also, the large difference between Ed ) 222 kJ mol-1 and ∆H ) 43 kJ mol-1 was observed for the mica dehydroxylation.60 A very slow rate of rehydroxylation of the silica surface pretreated at high temperatures presents the additional argument for the discrepancy between Ed and ∆H in the water desorption from silica. The rehydroxylation of small cycles on the dehydroxylated surface will be a very fast reaction when the Ed and ∆H values coincide. However, it is well-known57 that this process occurs at T > 373 K and its rate sharply (59) Bredow, T.; Jug, K. Surf. Sci. 1995, 327, 398. (60) Kodama, H.; Brydon, J. E. Trans. Faraday Soc. 1968, 64, 3113.

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depends on the concentration of OH groups. In order to estimate the activation barriers of the oxides dehydroxylation, we have used the bond order conservation Morse potential (BOC-MP) method for the associative desorption61

Ed )

QOHQH 2(QOH + QH)

+ 0.5∆H

(8)

where ∆H is the reaction enthalpy and QOH and QH are the chemisorption energy of OH and H species, respectively. The QOH and QH quantities were estimated from the Si-O and O-H bond dissociation energies:52 QOH ) 397 kJ mol-1; QH ) 496 kJ mol-1. The calculated Ed values for possible reactions during the silica dehydroxylation are presented in Table 2. Using the ∆H ) 40 kJ mol-1 for dehydroxylation of the rutile surface59 and Ti-O and O-H bond dissociation energies for the OH groups of titania clusters from ref 52, QOH ) 140 kJ mol-1 and QH ) 438 kJ mol-1, the Ed ) 126 kJ mol-1 was calculated from eq 8. This value is close to Ed ) 95 kJ mol-1, which was calculated by the SINDO1 method, and to the experimental activation energies of water desorption from the titania surface (95-123 kJ mol-1 59). As can be seen from Table 2, the most calculated Ed values for the bimolecular reactions of dehydroxylation, with the exception of interaction of OH groups on the Si‚‚‚ Si distance more than 0.4 nm, lie in the same region as those estimated from the TPD spectra (Table 1 and Figure 5b). The first set of the reactions of closely-spaced OH group condensation has much lower Ed values (average value is near 150 kJ mol-1) in comparison with the second group of vicinal group condensation (average value is near 200 kJ mol-1). For example, the experimental TPD spectrum in Figure 5a can be simulated using the biGaussian distribution on Ed at the 1:5 ratio for the first (1) and second (2) peaks in the distribution and at β ) 0.097 K s-1, Ad ) 1013 s-1, average desorption energies: Ed1 ) 160 kJ mol-1, Ed2 ) 200 kJ mol-1, and the mean square deviations of the energies: σEd1 ) 0.1Ed1 and σEd2 ) 0.2Ed2 (Figure 7). Generally, the detailed description of the experimental TPD spectra is made difficult by the fact that far too many simultaneous and consecutive reactions possessing the different activation energies and initial reagent concentrations are possible during silica surface dehydroxylation. The present data demonstrate the reasons for possible heterogeneity of silica surface dehydroxylation and observed shape of the TPD spectra. (61) (a) Shustorovich, E. Adv. Catal. 1990, 37, 101. (b) Shustorovich, E.; Bell, A. T. Surf. Sci. 1992, 279, 355.

Figure 7. TPD spectrum simulated using the bi-Gaussian distribution on desorption activation energy at the 1:5 ratio of first (1) and second (2) peaks in the distribution and at β ) 0.097 K s-1, Ad ) 1013 s-1: average desorption energies, Ed1 ) 160 kJ mol-1, Ed2 ) 200 kJ mol-1; mean square deviations of the energies, σEd1 ) 0.1Ed1 and σEd2 ) 0.2Ed2.

Conclusions Our calculations have demonstrated the possible effects of lateral repulsive dipole-dipole interactions between the closely-spaced OH groups, disordering of the solid lattice and nonactivated surface diffusion on the position and shape of temperature-programmed desorption spectra of water from the single crystal and amorphous silica surface and on the dependencies of the apparent desorption activation energy on the surface coverage. The experimental TPD spectra of water desorption from different silica samples and dependencies of the apparent desorption activation energy on the surface coverage have been compared. The BOC-MP approach has been used for estimation of the activation energies for possible associative desorption reactions which are realized during the silica surface dehydroxylation. It was established that most predicted activation energies lie in the same region as those estimated from the TPD spectra. Acknowledgment. Useful discussions with Mr. V. P. Shkilev and Professor V. A. Pokrovskij are gratefully acknowledged. V.I.B. also thanks the International Science Foundation for the partial financial support of this work. LA951561K