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Physicochemical Characterization of Silicalite-1 Surface and Its Implications on Crystal Growth Vladimiros Nikolakis,*,† Michael Tsapatsis,‡ and Dionisios G. Vlachos§ Foundation for Research and Technology Hellas, Institute of Chemical Engineering and High-Temperature Processes, (FORTH/ICE-HT) Stadiou Str, Platani, P.O. Box 1414, GR 26504 Patras, Greece, and Department of Chemical Engineering, 159 Goessmann Laboratory, University of Massachusetts Amherst, Amherst, Massachusetts 01003-3110, and Department of Chemical Engineering and Center for Catalytic Science and Technology (CCST), University of Delaware, Newark, Delaware 19716-3110 Received December 2, 2002. In Final Form: March 13, 2003 The value of the silicalite-1 colloidal crystal surface zeta potential was estimated from electrophoretic mobility measurements. Potassium nitrate and tetrapropylammonium bromide have been used as background electrolytes, and the pH was varied between 2.4 and 11.6. Comparison with similar results obtained with colloidal silica particles supports the hypothesis that both potassium and tetrapropylammonium ions can adsorb in the exposed silicalite-1 pores. The results were further analyzed with the triple layer surface complexation model that captured the observed zeta potential trends. The adjustable parameters of the model have been optimized by using a combination of factorial design, solution mapping, and linear regression. Furthermore, the model was used to study the effect of composition on the apparent activation energy. It is demonstrated that when surface complexation model predictions are used as input in the silicalite-1 growth model, there is qualitative agreement between growth model results and experimental observations. This is the first time that a detailed mechanism can explain issues such as the effect of composition on apparent activation energy.
Introduction Zeolites are crystalline, microporous aluminosilicate materials with well-defined pore structures. Tetrapropyllamonium (TPA)-silicalite-1 ([4(C3H7)N]Si96O192]) is a pure siliceous zeolite that has a pore network consisting of straight and zigzag channels with diameter ∼0.55 nm. Preparation of silicalite-1 continuous, thin, appropriately oriented films on porous supports is extremely important since they can be used as selective membranes.1 Unfortunately our ability to control silicalite-1 membrane characteristics by optimizing synthesis conditions is limited mainly by the incomplete understanding of silicalite-1 nucleation and growth mechanisms. This poor understanding has motivated extensive studies of TPA-silicalite-1 nucleation and growth with a variety of experimental methods. Small-angle X-ray scattering and dynamic light scattering data indicate that small colloidal particles (subcolloidal particles), having an estimated size of ∼2.8 nm, are present in the synthesis mixture under a wide range of compositions.2-7 Analysis * Corresponding author. E-mail:
[email protected]. Tel: ++302610965242. Fax: ++302610965223. † Institute of Chemical Engineering and High-Temperature Processes (FORTH/ICE-HT). ‡ University of Massachusetts Amherst. § University of Delaware. (1) Tsapatsis, M.; Xomeritakis, G.; Hillhouse, H.; Nair, S.; Nikolakis, V.; Bonilla, G.; Lai, Z. CATTECH 2000, 3 (2), 148-163. (2) de Moor, P.-P. E. A.; Beelen, T. P. M.; Komanschek, B. U.; Beck, L. W.; Wagner, P.; Davis, M. E.; van Santen, R. A. Chem.sA Eur. J. 1999, 5 (7), 2083-2088. (3) Watson, N. J.; Iton, E. L.; Keir, R. I.; Thomas, J. C.; Dowling, T. L.; White, J. W. J. Phys. Chem. B 1997, 101 (48), 10094-10104. (4) Ravishankar, R.; Kirschhock, C. E. A.; Knops-Gerrits, P. P.; Feijen, E. J. P.; Grobet, P. J.; Vanoppen, P.; De Schryver, F. C.; Mieche, G.; Fuess, H.; Schoeman, B. J.; Jacobs, P. A.; Martens, J. A. J. Phys. Chem. B 1999, 103, 4960-4964. (5) Schoeman, B. J. Microporous Mesoporous Mater. 1998, 22, 9-22. (6) Nikolakis, V.; Kokkoli, E.; Tirrell, M.; Tsapatsis, M.; Vlachos, D. G. Chem. Mater. 2000, 12 (3), 845-853.
of the synthesis mixture with 1H-29Si cross-polarized magic angle spinning NMR indicates that the subcolloidal particles are preorganized inorganic-organic composite structures.4,8 All studies so far conclude that growth appears to be activated and that the size of the crystals, once nucleated, increases linearly with time without any new crystals been formed. The apparent activation energy depends on composition and ranges between ∼30 and ∼100 kJ/mol.3,6,7,9,10 Colloid silicalite-1 crystal growth has recently6 been explained by an aggregation mechanism, with ratelimiting step being the addition of subcolloidal particles onto the crystal surface.11 This mechanism is similar to the aggregative growth mechanism for the formation of amorphous silica particles, proposed by Bogush and Zukoski,11 where silica particles are considered to grow from nucleated primary particles of constant size. Silicalite-1 growth rate and activation energy predicted by this mechanism depend on the zeolite interparticle interactions that can be effectively described by a DLVOtype potential. Such a potential requires as input parameters the surface zeta potential (to describe electrostatic interactions) and the value of Hamaker constant (to describe van der Waals interactions). The most important parameter of that mechanism though, as determined by sensitivity analysis,6 is the silicalite-1 crystal surface electrostatic potential (zeta potential). The actual value of the potential depends on composition and temperature and determines both the growth rate and (7) Twoney, T. A. M.; MacKay, M.; Kuipers, H. O. C. E.; Thompson, R. W. Zeolites 1994, 14, 162-168. (8) Burkett, S. L.; Davis, M. E. J. Phys. Chem. 1994, 98, 4647-4653. (9) Schoeman, B. J.; Sterte, J.; Otterstedt, J. E. Zeolites 1994, 14, 568-575. (10) Iwasaki, A.; Hirata, M.; Kudo, I.; Sano, T. Zeolites 1996, 16, 35-41. (11) Bogush, G. H.; Zukoski, C. F. IV J. Colloid Interface Sci. 1991, 142 (1), 19-34.
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the activation energy. Even though it is possible to derive information about the particle zeta potential at low temperatures, an in situ experimental determination of the zeta potential value is difficult. Detailed models that successfully relate zeta potential with composition can allow extrapolation to different conditions where measurements are not feasible. To achieve this goal, it is necessary to identify and quantify the reactions and microprocesses that take place on the silicalite-1 surface. The electrochemical behavior of oxide surfaces immersed in electrolyte solution has been studied since the 1960s.12-14 The basic physicochemical methods used for linking the surface chemical reactions with measurable properties (i.e., surface charge density, zeta potential, etc.) as well as different models that are used to quantify the effect of solution chemistry (i.e., pH, ionic strength) on colloidal dispersions behavior have been reviewed by James.15 All studies indicate that proton adsorption/ desorption on the oxide surface is the primary regulating surface charge mechanism. Surface charge can further be regulated by the background electrolyte that can form ion pairs with the charged surface groups.13,16,17 Oxide acidbase properties and adsorption of organic and inorganic ions have been so far modeled using different surface complexation models (SCMs).13,14,16-22 These models take into account both the surface reactions, that are responsible for the development of the surface charge and also, to some extent, the molecular structure near the solid/ liquid interface (plane of adsorption and electric double layer). Despite their limitations,23 they have been widely used because they can fit experimental data and provide a convenient way for linking the oxide surface charge and potential with the solution properties. Knowledge of the charging properties can be a useful tool in linking the microscopic information of silicalite-1 crystal surface with macroscopic observations. For example an in situ calorimetric study showed that TPAsilicalite-1 growth is initially exothermic, but at some point it switches to endothermic accompanied with a sharp rise of the mother liquor pH. An explanation of the observed behavior will require a detailed knowledge of the silicalite1/mother liquor interfacial properties such as the mechanism of surface charging and TPA+ ion interaction with the crystal surface.24 Another interesting example is the variation of apparent activation energy with composition. As mentioned earlier activation energies in the range of ∼30 to ∼100 kJ/mol have been reported in the literature. These values have been obtained by monitoring size (12) Li, H. C.; de Bruyn, P. L. Surf. Sci. 1966, 5, 203-220. (13) Davis, J. A.; James, R. O.; Leckie, J. O. J. Colloid Interface 1978, 63 (3), 480-499. (14) Karthikeyan, K. G.; Elliot, H. A. J. Colloid Interface 1999, 220, 88-95. (15) James, R. O. Characterization of colloids in aqueous systems. In Ceramic Powder Science; Messing, G. L., Mazdiyansi, K., Haber, R. A.; Eds.; American Ceramic Society: Westerville, OH, 1987; pp 349410. (16) Yates, D. E. The structure of the oxide/aqueous electrolyte interface; PhD Thesis, University of Melbourne, 1975. (17) Lutzenkirchen, J.; Mangico, P.; Behra, P. J. Colloid Interface 1995, 170, 326-334. (18) Rutland, M. W.; Pashley, R. M. J. Colloid Interface 1989, 130 (2), 448-456. (19) Venema, P.; Hiemstra, T.; van Riemsdijk, W. H. J. Colloid Interface 1996, 181, 45-49. (20) Lutzenkirchen, J. J. Colloid Interface 1999, 217, 8-18. (21) Katz, L. E.; Hayes, K. F. J. Colloid Interface 1995, 170, 477490. (22) Katz, L. E.; Hayes, K. F. J. Colloid Interface 1995, 170, 491501. (23) Zuyi, T.; Taiwei, C.; Weijuan, L. J. Colloid Interface 2000, 232, 174-177. (24) Yang, S. Y.; Navrotsky, A. Chem. Mater. 2002, 14 (6), 28032811.
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changes either of spherical crystals6,9,25 or of specific silicalite-1 planes.10,26 The reaction mixtures had different composition and used a variety of silica sources. A direct comparison of the results requires knowledge of a detailed growth mechanism that takes into account the composition dependent interfacial properties of the silicalte-1 crystal. Composition variations of the reaction mixture will alter the silicalite-1 crystal surface charge resulting in subsequent variations of the zeta potential and apparent activation energy of growth. In this report electrophoretic mobility measurements are used to estimate the silicalite-1 zeta potential over a wide pH range, in the presence of simple (KNO3) and organic (tetrapropylammonium bromide) electrolytes. The triple layer, surface complexation model is subsequently used to quantify the zeta potential-composition relationship. Zeta potential predictions at different compositions are used as input parameters in the aggregation growth model, the results of which are compared with experiments providing an explanation for the effect of composition on the apparent activation energy. Finally, model limitations are discussed. Experimental Section Nanoparticle Synthesis. A suspension of silicalite seeds was first prepared by dissolving tetraethyl orthosilicate (TEOS >98%, Aldrich) in a tetrapropylammonium hydroxide (TPAOH, 1.0 M Aldrich) solution. The molar composition of the resulting clear mixture was 25 SiO2:5 TPAOH:100 EtOH:1450 H2O that is known to synthesize uniform silicalite crystals colloidal suspension.27 After synthesis the silicalite crystals were washed by repeated centrifugation until the pH of the supernatant liquid was less than 8. Then they were air-dried, calcined at 450 °C for ∼24 h, and redispersed by sonication resulting in an aqueous suspension of ∼5 g/L. A monodisperse suspension of amorphous silica particles was also prepared using a modification of the Stober method presented by Rutland et al.18 In particular, 60 mL of ethanol and 20 mL of 14.5 M ammonia were mixed and stirred for few minutes. Then 5 mL of TEOS was added, and the mixture was stirred at room temperature for about 1 h. Next, the mixture was diluted with water and boiled almost to dryness in order to remove ammonia and ethanol. The silica particles were finally collected and redispersed in water by sonication. Electrophoretic Mobility Measurements. Samples for electrophoretic mobility measurements were prepared by diluting 2.5 mL of the dense nanoparticle suspension in 50 mL of electrolyte solutions placed in PTE bottles. Tetrapropylammonium bromide (TPABr 98%, Aldrich) and potassium nitrate (Fisher Scientific) were used as background electrolytes. The pH was controlled by using potassium hydroxide (Fisher Scientific), tetrapropylammonium hydroxide (1.0 M solution in water, Aldrich), or hydrobromic acid (HBr 48%, Aldrich). The electrophoretic mobility of samples was measured at 25 °C by using a Brookhaven Instruments Corporation ZetaPlus, zeta potential analyzer. The electrophoretic mobility was converted to zeta potential by using the Smoluchowski equation28
ζ ) µη/o
(1)
where η is the viscosity of the solution, µ is the measured electrophoretic mobility, is the dielectric constant of the solution, and o is the dielectric permittivity of the free space. Seeded Growth Experiments. The effect of composition on the seeded silicalite-1 growth rate and activation energy has (25) Twomey, T. A. M.; Mackay, M.; Kuipers, H. P. C. E.; Thompson, R. W. Zeolites 1994, 14, 162-168. (26) Cundy, C. S.; Lowe, B. M.; Sinclair, D. M. Faraday Discuss. 1993, 95, 235-252. (27) Hedlund, J.; Mintova, S.; Sterte, J. Microporous Mesoporous Mater. 1999, 28 (1), 185-194. (28) Hunter, J. R., Foundations of colloid science; Clanderon Press: Oxford, 1989; Vol. II.
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been examined by in situ dynamic light scattering. Two different molar compositions were examined: (A) 40 SiO2/9 TPAOH/9500 H2O; (B) 40 SiO2/9 TPAOH/9 TPABr/9500 H2O. The details of the experiment have already been presented in a previous publication.6
Modeling of the Oxide/Solution Interface Surface Reactions. Previous studies on oxides (e.g., alumina, titania, silica, etc.)13,17,29-31 indicate that the surface charge is due to the existence of surface hydroxyl groups (SOH). Surface charge can be generated either by a dissociation reaction of the surface hydroxyl hydrogen, resulting in a negative charged surface site (SO-) or by H+ adsorption on a surface hydroxyl resulting in a positive surface site (SOH2+). In addition other ions present in solution might specifically adsorb on charged sites by forming “ion pairs” 16 or “surface complexes”.13 The reactions mentioned above for a surface immersed in a NaCl electrolyte solution can be expressed as follows K1
Figure 1. Description of the solid/liquid interface according to the Stern-Grahame model.35
R1: SOH 798SO- + H+s
ionic surfactants on the particle surface is due to both electrostatic and alkyl chain hydrophobic interactions.12,18,34 Silicalite is a purely siliceous zeolite, and thus, its surface charging is expected to be similar to that of silica or quartz particles. However, silicalite has a pore network of molecular dimensions that is absent from the other siliceous materials. The pores exposed on the surface can act as pockets where different ions can adsorb. This can be taken into account by considering the following reaction
K2
R2: SOH + H+s 798 SOH2+ K3
R3: SOH + Na+s 798 SONa + H+s K4
R4: SOH + H+s + Cl-s 798 SOH2Cl where the subscript s indicates that the species surface concentrations have to be considered. The concentration of an ion A next to the surface is related to the bulk concentration [A+] by the Boltzmann distribution32
[A+]s ) [A+]e-(eψs/kT)
(2)
where ψs is the potential at the surface, e is the electron charge, k is the Boltzmann constant, and T is the temperature. The surface charging of amorphous or quartz silica in different electrolyte solutions has been studied by several research groups.12,18,29,30,33 The results from all those studies indicate that siliceous surfaces are negatively charged in the presence of common electrolytes (e.g., NaCl, KNO3, KCl, Ba(NO3)2, La(NO3)3, etc.). The absolute value of their surface charge decreases with decreasing pH, approaching zero at a pH between 2 and 3. Very small ( 1, indicating that they are hydrophobic compounds.41 For that reason, TPA+ ions are expected to adsorb on the silicalite surface, adding a positive charge to it. Similar results have been obtained for the zeta potential of silica particles in the presence of TPA+ ions as a function of pH (Figure 5). The silica surface has a positive zeta potential at low pH, but its magnitude is significantly (41) Tamaki, K. Bull. Chem. Soc. Jpn. 1974, 47 (11), 2764-2767.
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smaller than the one of silicalite (difference of 30-40 mV). The observed positive zeta potential indicates that TPA+ adsorbs on the siliceous surfaces. In addition, the fact that the silica zeta potential is smaller indicates that the zeolite surface pores can be considered as adsorption sites. Parameter Estimation and Triple Layer Model Results. To describe the observed experimental behavior, the adjustable parameters of the triple layer model have to be determined (K1, K2, K5, C1, C2, SiOH surface site density, and pore surface density). The values for the silanol and pore surface site densities were estimated from crystallographic data. Even though large silicalite-1 crystals are coffin shaped (the external surfaces observed are {100}, {010}, and {101}), scanning electron microscopy indicates that the crystals used in the electrophoretic mobility measurements can be considered as spherical. For that reason, the silanol and pore surface site densities have been considered to be the average of the corresponding surface site densities of each crystallographic plane, which can be estimated by considering more detailed microscopic information available for each plane. Silicalite-1 crystal has a three-dimensional pore network of straight and sinusoidal channels. The crystal unit cell consists of a large number of 96 Si atoms, indicative of the complexity of the structure. The straight channels are perpendicular to the {010} plane, the sinusoidal channels run across the {100} plane, whereas the {101} plane does not have channels perpendicular to the surface. Furthermore, the density of free silanol groups facing perpendicular to the surface is different for each crystallographic plane. In a zeolite crystal though, each crystallographic plane does not necessarily terminate at the end of a unit cell; thus the surface site density has been calculated for several possible terminal configurations that were created by removing SiO2 layers from the unit cell surface. The only constrain was that each created surface does not have any broken silicon five-member rings. The {100} and {010} surfaces created had three different terminal configurations (regarding the SiOH density), while the {101} surface had only two. In addition the terminating surfaces of the {101} plane had both SiOH and Si(OH)2 groups. The surface site density used in the fitting procedure was 4.16 SiOH groups per nm2 and was the average of the corresponding values for each plane. The Si(OH)2 silanol groups of the{101} surface were considered as SiOH. Silicate oligomer deprotonation constants found in the literature 42 show that the equilibrium deprotonation constant of the first silanol does not depend strongly on the degree of silica condensation. In addition to that, it is about 10 times larger than the corresponding one for the deprotonation of the second silanol group. Thus it can be concluded that the later assumption is not expected to introduce significant errors in the calculations. The effect of the surface silanol density value uncertainty has been also been examined and will be discussed later. In a similar way, the average pore surface site density was estimated as 0.64 pores per nm2. The rest of the parameters (K1, K3, K5, C1, and C2) are optimized in two steps. First they are manually adjusted so that the model predictions agree reasonably well with the experiments at 0.01 M TPABr. Sensitivity analysis is then used to identify the most important parameters at different conditions (e.g., pH, ionic strength). Sensitivity analysis involves perturbation of a parameter from its initial value and estimation of the corresponding change (42) Sefcik, J.; McCormick, A. V. AIChE J. 1997, 43 (11), 27732784.
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Nikolakis et al. Table 1. Values of Parameters Used in the Modelsa pK1 ) 5.82 pK2 ) 12.27 pK5 ) -5.81
C1 ) 2.12 F‚m-2 C2 ) 0.12 F‚m-2
a The silanol surface site density used is 4.16 SiOH sites‚nm-2 and the pore site density is 0.64 pores‚nm-2.
Figure 6. Normalized changes in zeta potential from sensitivity analysis conducted (a) at four different pH values and an ionic strength of 0.01 and (b) at four different ionic strengths and a pH ) 9. In all cases the perturbation was 10%.
in the model predictions. The corresponding relative change (|(yperturbed - yo)/yo|) for each parameter as a function of pH at constant ionic strength (I ) 0.01) and as a function of ionic strength at pH 9 is presented in Figure 6. As can be seen in Figure 6a, the most sensitive parameters of the model change with pH. At low pH (∼2) the model is more sensitive to the value of pK5 and insensitive of the values of pK1 and pK3. On the other hand, at high pH (∼11), the values of pK1 and pK3 are the most important ones. In Figure 6b the effect of the parameters in the higher pH regime is further investigated as a function of ionic strength. The model appears to be more sensitive to the value of the equilibrium constant pK1 for the surface silanol dissociation irrespective of the ionic strength. On the other hand, the second more sensitive variable changes with composition. At high ionic strengths, the equilibrium constant pK2 for the cation complexation on SiO- site is the second most sensitive parameter, whereas at low ionic strengths it is the equilibrium constant pK5 for the cation complexation on the pores. The sensitivity analysis results indicate that we can estimate the parameter values by selectively fitting different groups of parameters at conditions that maximize their effect in the output of the model. Since a direct optimization is difficult, an indirect approach was employed. This approach involves a combination of factorial design, solution mapping, and linear regression and has already been used to analyze complex gas phase or surface reaction mechanisms.43,44 A brief description of the methodology will follow. The solution of the model equations is decoupled from the optimization by deriving simple empirical expressions (i.e., polynomials) for the model response (zeta potential) as a function of the most sensitive parameters. At each experimental condition, the zeta potential is calculated for a set of values (43) Frenklach, M.; Miller, D. L. AIChE J. 1985, 31, 498. (44) Aghalayam, P.; Park, Y. K.; Vlachos, D. G. AIChE J. 2000, 46 (10), 2017-2029.
Figure 7. Measured (symbols) zeta potential of silicalite seeds compared with best fits of the triple layer surface model (lines) versus pH for (a) 0.001 M TPABr, (b) 0.01 M TPABr, (c) 0.1 M TPABr, and (d) versus TPABr concentration at pH ) 2.6, 7.5, 9.2, and 11.4. The doted lines show the effect of surface silanol density uncertainty. The parameters used are shown in Table 1.
of the most sensitive adjustable parameters, as determined through factorial design.45 This technique has been developed to determine the optimal set of experiments when the measured quantity strongly depends on more than one unknown parameter. After the coefficients of the second-order degree polynomials are obtained, the optimal adjustable parameters have been estimated by fitting the polynomial response to the experimental points. Polynomials as a function of C2 and K5 at low pH and as a function of C1, K1, and K3 at high pH were first derived and then fitted to the experimental data. In particular, the values of C2 and pK5 were estimated by fitting the zeta potential as a function of ionic strength at pH ) 2.6, and those of pK1, pK3, and C1 were fitted at pH ) 11.4. This approach is justified from the sensitivity analysis results (see Figure 6) presented earlier. The optimized values of the parameters are presented in Table 1. The results of the analysis with the triple layer surface complexation model are shown in Figure 7. The model can successfully describe the zeta potential changes as function of pH and ionic strength. The agreement is better at the larger ionic strengths, which are of greater interest since they are closer to the silicalite-1 synthesis conditions. Although the model does not perfectly fit the experimental data, the agreement is reasonably good to justify its use for qualitative predictions. Doted lines in snapshots a-c of Figure 7 depict the surface silanol density uncertainty effect in the model results. They have been calculated using the average number of the maximum (5.74 nm-2) and minimum (3.16 nm-2) surface silanol densities of each (45) Box, G. E. P.; Draper, N. R. Empirical model-building and response surfaces; Wiley: New York, 1987.
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Table 2. Linear Growth Rates of Seeded Growth at Different Temperatures and Comparison of Experimental and Predicted Activation Energies for Compositions A and Ba linear growth rates (nm‚h-1) temp, °C
composition A
composition B
66 76 90
1.6 3.8 17.2
2.0 4.3 10.7
exptl predicted
composition A 98.27 (6.96) 97
activation energy (kJ/mol) composition B 72.14 (2.32) 41
a The value in the parentheses is the standard deviation of the fit of experimental data. The growth model predictions were made for ψA ) -47.92 mV and ψB) -37.34 mV. The Hamaker constant in both cases was 1.5 × 10-20 J and the Debye length was 3.4 nm for composition A (40 SiO2/9 TPAOH/9500 H2O) and 3.0 nm for composition B (40 SiO2/9 TPAOH/9 TPABr/9500 H2O).
plane. It is clear that the effect is small and does not alter the conclusions drawn from the analysis above. Effect of Composition on Growth Rate and Activation Energy. Our recently proposed growth model, summarized in the Appendix, predicts that growth rates and activation energies for silicalite-1 vary with zeta potential due to a variation of electrostatic repulsion felt by growth units (subcolloidal particles) in their approach to a zeolite surface. From the analysis presented above, it is clear that the silicalite-1 crystal zeta potential depends on the TPA+ concentration. As a result, changes in the TPA+ concentration should be expected to affect both the growth rate and activation energy. Zeta potential predictions at the synthesis compositions can be used to compute growth rates at different temperatures using equations A1-A4 from the Appendix. Furthermore, by monitoring the crystal size changes with dynamic light scattering, it is possible to get the linear growth rates for each composition at different temperatures. Arrhenius fits of such simulation and experimental data provide an estimate of the apparent activation energy at each composition. The linear growth rates at different temperatures along with the experimental and the predicted activation energies for compositions A and B are presented in Table 2. As can be seen from Table 2, the apparent activation energy is smaller for composition B, where the TPA+ concentration is higher. Increasing the TPA+ concentration, at a constant pH, decreases the silicalite-1 zeta potential, which in turn decreases the value of the apparent activation energy. The predicted changes of the activation energy with composition qualitatively agree with the experimental values. Deviations between experiments and simulations can be attributed to the fact that the zeta potential values used in the growth model have been predicted at 25 °C and were considered temperature independent. Another important observation from Table 2 is that at lower temperatures the growth rate is higher for composition B, whereas at 90 °C composition A results in faster growth. To predict absolute values of the growth rate, it is necessary to know both the concentration and exact size of the subcolloidal particles (see eq A1). However, the subcolloidal particle formation mechanism, which is a more difficult problem, has not yet been solved; thus, it is not currently possible to make accurate predictions
about changes of their properties (i.e., size, concentration) with composition and temperature. Discussion of Surface Complexation Model Limitations. Unfortunately, analysis of the silicalite-1 zeta potential provides information only about the average properties of the surface. To make predictions about the behavior of each crystallographic plane, more detailed information is required. Multisite complexation (MUSIC) modeling, developed by Hiemstra et al.,46 can provide this type of information. The MUSIC model can give estimates of the surface complexation equilibrium constants considering the different types of hydroxyl groups known to occur on an oxide surface. The Gibbs free energy of protonation is considered as the sum of a local electrostatic part and a lumped term of the remaining contributions. The electrostatic contribution is calculated explicitly by taking into account the bond geometry as well as the interaction between the adsorbing ion with the surface oxygen and the underlying metal. The MUSIC model has been extended by Sverjensky et al.40 by adding to the electrostatic interaction term a contribution from the ion solvation estimated using the Born model of solvation. Even though the MUSIC model can give an estimate of the differences in the complexation equilibrium constants for the silicalite-1 surface silanol groups of each crystallographic plane, it is not expected to be able to predict differences of the TPA+ interaction with the surface pores. The Gibbs free energy of TPA+ adsorption is expected to vary since the pores of each plane facing the surface are different ({100} sinusoidal channels, {010} straight channels, {101} pores are not perpendicular to the surface). Even though surface complexation models employ a detailed description of the ion sorption on the functional groups of the surface, their results have always to be viewed with caution due to their underlying assumptions. While developed for a uniform infinite flat surface with noninteracting sites, they are usually applied to particulate systems. This assumption will hold only if the double layer thickness is much smaller than the particle radius. Fortunately this is true for the analysis presented here since the size of the colloid silicalite-1 crystals is ∼450 nm whereas the maximum double layer thickness for the conditions examined is ∼10 nm. In addition, the models do not capture multilayer adsorption, which might be taking place especially in systems that contain hydrophobic organic molecules. Even though TPA+ molecules have hydrophobic alkyl chains, they are water soluble; thus multiplayer adsorption on silicalite-1 surface is not expected to take place. Another limitation arises from the lack of detailed description of the real surface structure. As a result, lateral and stereochemical interactions are not taken into account. The contribution of the later ones might be significant if the TPA+ cation size is considered. In addition the distance between the complex and the surface might vary with composition. Recent studies (using extended X-ray adsorption fine structure) of lead adsorption to montomorillonite indicate that the plane of adsorption changes with pH and ionic strength.47 Furthermore, the zeta potential is considered to coincide with that at the outmost adsorption plane instead of the shear plane. Finally, it has to be mentioned, especially with the triple layer model, that there are more than one set of parameters that can fit a set of experimental data equally well.21,22 Due to the limitations mentioned above, the (46) Hiemstra, T.; van Riemsdijk, W. H.; Bolt, G. H. J. Colloid Interface Sci. 1989, 133 (1), 91-104. (47) Strawn, D. G.; Sparks, D. L. J. Colloid Interface 1999, 216, 257269.
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predictions made with the surface complexation models must be viewed more as qualitative trends rather than as quantitative data.
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of radius rs, is
dR Dco(R + rs) 4 ) πr 3 dt 3 s R2W
Conclusions
(A1)
The physicochemical characteristics of the silicalite-1 surface have been investigated by measuring the particle zeta potential in the presence potassium nitrate and tetrapropyllamonium bromide electrolytes. Positive zeta potentials have been observed at low pH values (pH
