J. Phys. Chem. C 2007, 111, 18155-18158
18155
Modeling Aqueous Silica Chemistry in Alkali Media Miguel J. Mora-Fonz, C. Richard A. Catlow, and Dewi W. Lewis* Department of Chemistry, UniVersity College London, 20 Gordon Street, London WC1H 0AJ, United Kingdom ReceiVed: September 6, 2007
A method for modeling the reactions of siliceous species is presented, which allows chemically accurate deprotonation and dimerization energetics to be calculated, at conditions reflecting those of high pH hydrothermal zeolite synthesis. The free energies of condensation reactions leading to silicate species up to the linear tetramer are considered at room temperature and at 450 K.
The precise mechanism of zeolite formation is far from being completely understood, a consequence of the complex reaction space and the difficulties in probing this chemistry under reaction conditions. Notwithstanding such problems, the initial processes of nucleation and subsequent crystallization under such hydrothermal conditions have been widely studied,1,2 and key pre-nucleation species have been identified.3,4 We have also recently demonstrated how computational methods can contribute to an understanding of the reactivity of silicate oligomers in the formation of specific “zeolitic” building units, with the aim of establishing a more general picture of nucleation.5 However, key to progress in this area is establishing whether computational models and methods are both accurate and also reflect, as closely as possible, the conditions present during synthetic and natural zeolite formation. Silicic acid (Si(OH)4), the monomeric silicate molecule, is the simplest but, perhaps, the most important species involved in the formation of zeolite nucleation centers. Little zeolite nucleation is noted under neutral conditions,2 and zeolite syntheses are typified by high pH (ca. 10-14). Two processes, in particular, are therefore vital in controlling the subsequent chemistry: deprotonation of the monomer, Si(OH)4 + OH- f Si(OH)3O- + H2O (and further deprotonations of the resulting anion), and dimerization by condensation of both neutral and anionic species, for example, 2Si(OH)4 f (OH)3-Si-O-Si(OH)3 + H2O. Experimental measurements of monomer deprotonation and dimerization energies have been reported and summarized by Iler6 and Brinker,7 with McCormick8 reviewing more recent measurements. Theoretical calculations have also been performed using a variety of different models.9-14 The complexity of silicate chemistry limits the experimental studies to only a few species, specifically the monomer and dimer, as many different reactions occur once polymerization is initiated, the individual speciation of which proves almost impossible. Similarly, computational methods have also been restricted by their relative high cost and also lack, in some instances, the incorporation of descriptions of solvent and pH effects. Here, we describe how a dielectric solvent model combined with explicit hydration allows DFT methods to describe accurately the chemistry of small silicate oligomers, exemplified here by Si(OH)4 and (OH)3-Si-O-Si-(OH)3, under conditions typical of zeolite formation. Specifically, we report the energet* Corresponding author. Tel.: +44 20 7679 4779. Fax: +44 20 7679 7463. E-mail:
[email protected].
ics of the deprotonation of both the monomer and the dimer, together with those of the dimerization, trimerization, and tetramerization reactions at 298 and 450 K. We also validate our method with the well-characterized water autoprotolysis reaction. The calculations were performed using DMOL,3 version 2.2,15 using a double numeric basis set plus polarization (DNP) and the BLYP functional. A description of the water solvent is included via the COSMO16 approach, with initial gas-phase optimized structures being reoptimized in the presence of the solvation model. Molecular dynamics using DFT forces are also used to ensure initial models do not become trapped in local minima. The Gibbs free energy is calculated by combining the electronic energy (BLYP/DNP), zero-point energy, together with the rotational, vibrational, and translational contributions to the energy, using standard statistical mechanics methods at 298 K (the temperature of most of the experimental measurements) and 450 K (characteristic of zeolite synthesis). Improvements to this initial solvated model are made by the inclusion of sodium counterions in the charged clusters, together with the addition of some explicit (together with the continuum description of COSMO) water molecules in the first coordination sphere of all of the species considered, to represent more completely the most important short-range interactions. Details of the number of explicit water molecules used for individual species are reported in Table 1, which gives the free energies calculated together with values derived from experimental pKa or equilibrium constants reported in the cited literature. Examples of the models used are shown in Figure 1. The reliability of the methodology is established by considering the autoprotolysis of water. It is clear that describing this reaction either (most simplistically) by “gas-phase” models or even with the inclusion of a COSMO solvation model drastically overestimates the free energy change. However, the inclusion of some explicit water molecules improves the description, giving the free energy within 4 kJ mol-1 of experiment. The experimental value is obtained using what we consider the most reliable current estimates of the entropies of the solution species given by Aue et al.,17 specifically that there is no difference in entropy between a solvated water and a hydronium ion. Inclusion of a full explicit hydration sphere does not appear necessary, as sufficient water is present to allow formation of the stabilized complexes, with three and four water molecules for the H+ and OH- ions, respectively. These complexes, OH-(H2O)4 and H3O+(H2O)3, are found to be the most prevalent
10.1021/jp077153u CCC: $37.00 © 2007 American Chemical Society Published on Web 11/15/2007
18156 J. Phys. Chem. C, Vol. 111, No. 49, 2007
Mora-Fonz et al.
TABLE 1: Free Energies of Reaction at 298 and 450 K (kJ mol-1) in the Gas Phase and COSMO Solvation (COSMO) as Compared to Silicates Species up to the Tetramer with Experimental Results (expt)a free energy (∆G)/kJ mol-1 298 K reaction water autoprotolysis monomer I monomer II dimer I dimer II dimerization
trimerization tetramerization
H3O+ + OH- f H2O + H2O H3O+(H2O)3 + OH-(H2O)4 f (H2O)4 + (H2O)5 M + OH- f M- + H2O M + NaOH f MNa + H2O M + NaOH(H2O)3 f MNa(H2O)3 + H2O M- + OH- f M2- + H2O MNa + NaOH f MNa2 + H2O MNa(H2O)3 + NaOH(H2O)3 f MNa2(H2O)6 + H2O D + OH- f D- + H2O D + NaOH f DNa + H2O D + NaOH(H2O)3 f DNa(H2O)3 + H2O D- + OH- f D2- + H2O DNa + NaOH f DNa2 + H2O DNa(H2O)3 + NaOH(H2O)3 f DNa2(H2O)6 + H2O M + M(H2O) f D(H2O) + H2O M + M f D + H2O M + MNa(H2O)3 f DNa(H2O)3 + H2O M + MNa f DNa + H2O M + M- f D- + H2O M + DNa f TrNa + H2O M + DNa(H2O)3 f TrNa(H2O)3 + H2O M + TrNa f TNa + H2O M + TrNa(H2O)3 f TNa(H2O)3 + H2O
gas
COSMO
-1013 -509 -226 -90 -27 285 -64 -47 -296 -100 -27 119 -73 -28 -10 -13 -12 -23 -83 -42 -43 -16 -18
-258 -97 -61 -49 -29 2 -43 -17 -91 -79 -35 -25 -43 -25 -4 -2 -7 -32 -33 -16 -10 9 -10
exptb -10120,21 -336; -368 -188; -1722; -236 -388 -298 -78
450 K
298 K
COSMO
COSMO (Sefcik radii)
-261 -91 -64 -44 -30 2 -43 -14 -92 -76 -30 -23 -40 -24 -3 0 0 -31 -28 -8 -4 16 -6
-42 -29 0 -16 -64 -14
a Monomers I and II are the first and second deprotonation reactions for the monomer, respectively, with similar notation used for the dimer. For ease of comparison, those results for the most comprehensive model are in bold. Results are presented with standard COSMO atomic radii at both 298 and 450 K and for selected species at 298 K with the optimized radii given by Sefcik and Goddard13 (see text for further details). Monomer, dimer, trimer, and tetramer are symbolized by M, D, Tr, and T, respectively. b The experimental free energy for the proton transfer between two water molecules in solution is calculated from a thermodynamic cycle. The experimental enthalpy of formation of the species in the gas phase is taken from Dewar et al.,20 and the change in entropy for a proton transfer is considered zero, after Aue et al.17 The free energies of hydration are taken from Pearson.21
Figure 1. Models of the singly deprotonated monomer and dimer, and that of the doubly deprotonated dimer. The models depicted are the most comprehensive considered here, with three explicit water molecules and a Na+ ion coordinated to the deprotonated oxygen, together with a dielectric continuum model of the remaining solvent. We also considered the same silicate cluster but only surrounded by the continuum water model and also simply as gas-phase species (see Table 1). The structures shown are the energy minima for the models shown, and dotted lines indicate hydrogen bonds.
species in such solutions.18,19 Little change in either geometry or energetics is found when further explicit water molecules are added. The first deprotonation energy (as pKa) of the monomer is the most reliably determined thermodynamic property of silicate oligomers. Thus, this value serves as a key reference in evaluating the reliability of any theoretical method whose aim is to investigate the self-assembly of silicate oligomers. From our results, it is evident that the gas-phase and the COSMO models are again inadequate to model correctly the monomer’s first deprotonation energy. Similarly, simply including the counterion (Na+) together with COSMO results in poor energet-
ics as compared to experiment. It is only when both explicit solvation and the Na+ counterion are included in our model, making the system considered overall neutral, that the experimental deprotonation energies are described accurately (within 4 kJ mol-1). While there is general agreement that deprotonation energies calculated with DFT-COSMO correlate well with experimental pKa and that it is possible to estimate pKa values by linear extrapolation,9,22,23 DFT-COSMO alone, using the standard atomic radii to compute the solvation cavity, is not considered able to reliably compute absolute pKa values.9 Here, however, through the inclusion of some explicit solvation and counterions,
Modeling Aqueous Silica Chemistry in Alkali Media good agreement with experiment is achieved. Thus, such an approach, whereby some, but not necessarily all, of the inner solvation sphere of a deprotonated species is considered, may be more generally applicable, as discussed further below. The presence of multiple species in solution makes accurate experimental determination of the pKa of the dimer significantly more difficult. Thus, values tend to be extrapolated from a composite value following a fitting procedure to determine the relative populations of the monomer and dimer.8 Again, there is good agreement (within 4 kJ mol-1) between our calculated deprotonation energies (once explicit hydration is considered) and the available experimental results, giving both added confidence in our method but also in the robustness of the experimental fitting procedure, in this case. Higher deprotonation energies have also been determined for the monomer together with the first and second deprotonation energies for the dimer.24 However, these rely increasingly on fitting procedures, where the concentrations of the more strongly deprotonated species and of the dimer species are very small as compared to the dominant singly and doubly deprotonated monomeric species. Hence, these values are likely to be less reliable. Nevertheless, it is clear that the first and second deprotonation energies of the dimer are well described with our method (Table 1), giving us increased confidence in modeling larger silicate species. The dimerization reaction is the fundamental reaction of silica chemistry. Again, the range of conditions (acidic, neutral, basic) and the difficulties in attempting to restrict further polymerization occurring make it a challenging reaction to study experimentally. The experimental estimate of the ∆G is = -7 kJ mol-1.8 In addition, there are a number of computed values: using DFT/TNP, Catlow et al.12 reported a gas-phase dimerization free energy of -9.2 kJ mol-1, while Tosell,11 using MP2/ 6-311+G(2d,p), reported a value of +24.7 kJ mol-1 in the gas phase but +8.8 kJ mol-1 when a G2/COSMO model is applied. Most recently, Trinh et al. reported a value of +9 kJ mol-1 for the neutral dimerization and -28 kJ mol-1 for the reaction of a monomer with a deprotonated monomer, both using B3LYP/ 6-31+G(d,p) with COSMO solvation.23 However, none of these studies consider explicit hydration. Our calculations reproduce well the experimental data for the dimerization reaction, both under neutral and under basic conditions. Note, that these calculations correctly reflect how an increase in pH makes polymerization more favorable. Moreover, we find the reaction of two deprotonated monomers (with cations and explicit water) to be slightly less favorable (-3.4 kJ mol-1), again reflecting experimental observation that very high pH does not necessarily result in increased polymerization. Thus, we believe that the combination of the DFT method used, together with a suitable explicit representation of the inner solvation sphere of the key species and a continuum representation of the remainder of the solvent, allows the aqueous chemistry of silicate oligomers to be modeled reliably. The effect of including explicit water molecules can be considered two-fold. First, they shield the highly charged regions from the continuum, allowing electrons to redistribute more “naturally”. Second, they result in an improvement in the description of the shape of the cavity in the dielectric continuum that is constructed by the COSMO methodology. COSMO uses atomic radii to construct the cavity,16 and the large difference in atomic size between neutral atoms and these charged and ionic species is significant and results in a poorer description of the surface of the molecule. Thus, addition of explicit water near such atoms, particularly bare O- and Na+, effectively
J. Phys. Chem. C, Vol. 111, No. 49, 2007 18157 places these atoms “inside” the molecule and reduces the errors in the cavity shape and size. Similar conclusions have been drawn before for silicates13 and for related systems, for example, concentrated aluminum hydroxide solutions.24,25 An alternative to the inclusion of explicit solvent, to improve quantitative agreement with experiment, is to refit the radii used.13 However, such a fitting procedure rescales the radii of all atoms of the same element. Here, the most significant change in atomic size is due to the deprotonation of the oxygen atoms in the silicate fragments. The semi-ionic nature of these species means that the charge is fairly well localized on this particular oxygen. Hence, rescaling the radius of all oxygen atoms is unrealistic. Furthermore, the fitted radii are dependent on the level of theory used,13 which will lead to some compromise in transferability. To illustrate that our method of inclusion of explicit water, which in essence ensures that changes in atomic size do not result in a poorer representation of the cavity, is both transferable and, indeed, gives better agreement with experiment, we present in Table 1 the results obtained without explicit water but with the Sefcik and Goddard13 COSMO radii. These authors used B3LYP 6-31G**+//6-31G** for their calculations, and they note that the fitted radii are therefore specific to this level of theory. Hence, our deprotonation energies using their radii but with the BLYP/DNP/COSMO method do not exactly reproduce the experimental values. On the contrary, when the Sefcik and Goddard radii are used together with explicit water, the results are almost comparable to our original results (and hence experiment). Thus, our hypothesis that the explicit water provides an effective shielding of the ionic species is supported. We acknowledge that the level of theory considered here should not, perhaps, be expected to give as good an agreement as found. Nevertheless, the method performs consistently for all of the species and conditions considered and at a relative low computational cost. Indeed, the inclusion of the combination of explicit and COSMO solvation appears to provide a good compromise between expense and accuracy. Note that, at this level of theory, the largest cluster presented here (the hydrated tetramer) requires 25 000 min on a 2.8 GHz Xeon processor, with 2 GB memory. Furthermore, little change is noted, for example, when the number of explicit waters is increased further here, nor when Car Parinello quantum molecular dynamics were used (at considerable higher cost) to consider aluminate species.25 Hence, the method, which allows us to consider conditions that are chemically relevant to zeolite synthesis, can, we believe, be applied with confidence to further silicate species. We show, for example, in Table 1 the results for the reactions discussed above at 450 K, a temperature akin to typical zeolite synthesis, and also for the trimerization and tetramerization reactions. Of note here is that there is little variation in the free energy of adding a monomer to a hydrated monomer, dimer, or trimer at 298 K. However, the formation of such small fragments through monomer addition is less favorable at elevated temperatures, suggesting that lower temperatures are required to initiate formation of larger silicates. Indeed, we note that room-temperature aging of synthesis gels is often critical to the successful formation of zeolite crystals. Further studies using this method will allow us to approach a more comprehensive description of the key reactions that occur during the pre-nucleation phase of zeolites and other silicates. Acknowledgment. We acknowledge Dr. Jo¨rg A. Becker and Dr. Ju¨rgen Woenckhaus for stimulating discussion regarding this work. M.J.M.-F. is greatly indebted to CONACYT Mexico and UCL for financial support. These calculations were
18158 J. Phys. Chem. C, Vol. 111, No. 49, 2007 performed on a computational resource provided by the EPSRC to D.W.L. through grant GR/S06233/01. References and Notes (1) Cundy, S. C.; Cox, A. P. Chem. ReV. 2003, 103, 663. (2) Cundy, C. S.; Cox, P. A. Microporous Mesoporous Mater. 2005, 82, 1. (3) Kinrade, S. D.; Knight, C. T. G.; Pole, D. L.; Syvitski, R. T. Inorg. Chem. 1998, 37, 4272. (4) Kirschhock, C. E. A.; Kremer, S. P. B.; Grobet, P. J.; Jacobs, P. A.; Martens, J. A. J. Phys. Chem. B 2002, 106, 4897. (5) Mora-Fonz, M. J.; Catlow, C. R. A.; Lewis, D. W. Angew. Chem., Int. Ed. 2005, 44, 3082. (6) Iler, R. K. The Chemistry of Silica: Solubility, Polymerization, Colloid and Surface Properties, and Biochemistry; Wiley: New York, 1979. (7) Brinker, C. J.; Scherer, G. W. Sol-Gel Science: The Physics and Chemistry of Sol-Gel Processing; Harcourt Brace Jovanovich: Boston, 1990. (8) Sefcik, J.; McCormick, A. V. AIChE J. 1997, 43, 2773. (9) Schuurmann, G. J. Chem. Phys. 1998, 109, 9523. (10) Pereira, J. C. G.; Catlow, C. R. A.; Price, G. D. Chem. Commun. 1998, 1387. (11) Tossell, J. A. Geochim. Cosmochim. Acta 2005, 69, 283. (12) Catlow, C. R. A.; Coombes, D. S.; Lewis, D. W.; Pereira, J. C. G. Chem. Mater. 1998, 10, 3249.
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