The structure of subcolloidal zeolite precursor nanoparticles

Studies in Surface Science and Catalysis, volume 154 E. van Steen, L.H. Callanan and M. Claeys (Editors) © 2004 Elsevier B.V. All rights reserved.

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THE STRUCTURE OF SUBCOLLOIDAL ZEOLITE PRECURSOR NANOPARTICLES Fedeyko, J., Sawant, K., Kragten, D., Vlachos, D. and Lobo, R.F. Center for Catalytic Science and Technology, Department of Chemical Engineering, University of Delaware, Newark, DE 19713 USA. ABSTRACT Subcolloidal zeolite precursor nanoparticles are studied through a combination of experimental and modeling techniques to determine the structure of the nanoparticles. ^^Si nuclear magnetic resonance (NMR) spectra of the nanoparticles in solution show that most of the silicon is incorporated into the nanoparticles and that the particles consist of primarily Q^ and Q^ species. The continuum analysis of small angle neutron scattering (SANS) data reveals that the nanoparticles have, most likely, an ellipsoidal shape and this conclusion is supported by a simulated annealing algorithm which combines both experimental data sets (NMR and SANS) and produces particles of an ellipsoidal shape. Keywords: simulated annealing, silicalite-1, small-angle neutron scattering, structure determination INTRODUCTION Upon mixing a solution of tetrapropylammonium hydroxide (TPAOH) and tetraethylorthosilicate (TEOS) at room temperature, a segregation of the solution into two metastable phases is observed. A continuous water-rich phase is formed containing most of the water and a small amount of Si02 and TPAOH. At the same time, the silica is microsegregated into nanoparticles (~ 4 nm) that contain most of the silica, a large fraction of the TPAOH and a small amount of water. It has been shown that the rate of growth of zeolites is controlled by the addition of these subcolloidal silica nanoparticles to the growing surface. The presence of these nanoparticles prior to and during crystal growth has been reported by several groups [1,2,3,], however, many characteristics such as the particle shape, particle size distribution, and fundamental properties such as the average composition, internal structure and charge remain unknown. Controlling the crystal shape and the rate of growth of zeolite crystals is crucial to the development of useful zeolite membranes for gas separations but to address this problem a better understanding of these zeolite-precursor nanoparticles is necessary. The study of nanoparticle shape is of particular importance in the development of growth models describing the formation of the final zeolite structures. We previously completed a study of the nanoparticles in their extracted form [4] and determined that these particles had no internal well-defined order and did not have a uniform particle shape. During our study, we discovered that the extraction process significantly changed the nanoparticles by causing aggregation and condensation of the Si02. To avoid the limitations associated with particle extraction, we have focused our current study on the nanoparticles in the growth solution. We apply two characterization techniques which recover structural information without the requirement of modifying the growth solution significantly, ^^Si nuclear magnetic resonance spectroscopy (NMR) and small-angle neutron scattering (SANS). The data obtained from these techniques are then combined through simulated annealing to determine the final shape of the nanoparticle. SANS is a essential technique when studying systems of dispersed particles and has been applied to a wide range of systems including polymers, aerogels, proteins and heated solutions of the subcolloidal zeolite nanoparticles [5]. The equation used to describe the intensity of dispersed systems is I(s) = (p.P(s)S(s)

(1)

where cp is the number density of scattering objects in the solvent, s is the scattering vector, P(s) is the form factor describing the scattering from an object, and S(s) is the structure factor describing the distribution of the objects in the solvent. An accurate description of the form factor can lead to the determination of the object's shape and internal structure. To eliminate the dependence of the structure factor on the scattering

1268 vector, allowing for a direct study of the form factor, SANS measurements must be operated at dilute concentrations of the nanoparticles [6]. With the elimination of structure factor dependence, the intensity measurements of the nanoparticle suspensions can now directly lead to particle shape. With no a priori knowledge of the particles general shape, the first step to determining particle shape is usually Kratky plots which are derived from Mclaurin expansions of the Debye equation centered around the scattering vector, s = 0 [6]. The application of Kratky plots can narrow the search field to one of three ideal possibilities, an infinitely flat plate, an infinitely long cylinder and a spheroid. In addition to providing an approximation for the shape, Kratky plots will also yield information about the particle's radius of gyration, Rg, which can be applied during particle modeling. To further elucidate the final particle shape, we applied the pair distance distribution function, PDDF [6]. The PDDF represents the set of volume element distances within a particle by scaling a correlation function, y(r), by the distances between volume elements, r. PDDF(r) = y(r) • r^

(2)

Here we focus on fitting the PDDF directly through modeling techniques as well as comparing the ideal solutions of the PDDF determined in previous works to the system. The combination of the SANS analysis and ^^Si NMR through the simulated annealing algorithm will allow for the quantitative description of the external structure of these nanoparticles without biasing the result with preconceived models. EXPERIMENTAL SANS measurements are performed on homogeneous solutions of nanoparticles prepared following the procedure of Nikolakis et al. [7], which consists of a mixture of molar ratios 40 Si02: 9 TPAOH: 9500 H2O: 160 EtOH. Specifically, 40% TPAOD in deuterated water is diluted with deionized D2O to the desired final concentration and allowed to stir for 30 minutes. TEOS (Aldrich) is then added dropwise to the solution and the final mixture is stirred for 12 hours at room temperature. 40 wt.% TPAOD is synthesized by mixing TPABr (Aldrich) with deuterated water and adding silver oxide (Aldrich). Dynamic light scattering measurements on the solution indicates the particles are between 5-10 nm in diameter. Solution ^^Si NMR spectra are performed on nanoparticle solutions prepared following the procedure of Ravishankar et al. [8], in which, 9.0 g of TEOS is added dropwise to 7.9 g of 40 wt.% TPAOH (Alfa Aesar). The mixture is stirred for 30 minutes followed by the addition of 9.0 g of deionized water. The final homogeneous solution is stirred for an additional 12 hours. These higher concentrations are required to obtain reasonable signal to noise ratios. Nikolakis et al. [7], in a study of the growth of silicalite seeds, determined that the concentration of silica did not affect the growth rate. We assume that this observation applies and that the nanoparticles do not change in size and shape by changing concentration allowing for a study of both dilute and slightly more concentrated nanoparticle suspensions. ^^Si NMR spectroscopy Solution ^^Si NMR spectra were recorded using a Bruker AMX 360 MHz spectrometer operating at a resonance frequency of 71.549 MHz with samples held in Teflon tubes (conventionally used as liners for 5 mm glass NMR sample tubes) without spinning at room temperature. Teflon sample tubes were used to prevent the contribution to the ^^Si NMR signal from conventional Si-containing glass NMR sample tubes. A 5 mm QNP broadband probe head was used for these experiments with an inverse gated coupling pulse program with a relaxation time of 60 s and a pulse length of 11 |is. The spectral width scanned was 400 or 200 ppm centered around 0 ppm with number of scans ranging from 62 to 3500 corresponding to instrument times varying from a few hours to 60 hour experiments. All experiments employed a fixed set of magnet-shim parameters optimized for the specific probe. Deuterium oxide (D2O, Aldrich, 98 atom % D) was used as a solvent to provide an internal NMR lock. The spectra were referenced to 2, 2-dimethyl-2silapentane-5 sulfonate (DSS) saturated in D2O and deconvoluted and fit with simulations using the GRAMS/32(S) Spectral Notebase^'^ Version 4.10 Level 1 software. In spite of using Teflon instead of glass NMR sample tubes, in all the solution ^^Si NMR spectra a broad peak appears at ~ 111.81 ppm from unavoidable Si-containing glass inserts surrounding the magnetic coils in the probe and treated as instrument background. To establish the shape and peak position of this background and to confirm that there is no contribution from the synthesized solutions, the spectrum of a solution with no TEOS was subtracted as background.

1269 Small angle neutron scattering SANS measurements were performed on the NG3 small-angle diffractometer at NIST. Two different sample to detector distances were used, 13 m and 2.2 m. Each data set was corrected to account for scattering from the sample holder and to eliminate machine background as well as converted to an absolute scale. A set of contrast matching experiments were conducted varying the ratio of D2O/H2O in solution. Five different solutions 0, 25, 50, 75, and 98 wt.% D2O were prepared to determine a scattering length density of the particle, which was found to be 2.2x10"^ A'^. Kratky plots and PDDF analyses are carried out on the 98% D2O sample which has the largest signal to noise ratio. SIMULATIONS We have adapted a systematic simulated annealing optimization method to determine nanoparticle shape from the SANS and NMR results. In this technique nanoparticles composed of Si02 only are constructed on the computer and quenched slowly from sufficiently high temperatures. During the quenching process, the units (building blocks) making up the structure move according to certain rules and these moves are accepted using a Metropolis algorithm. Given its statistical mechanics basis, this method searches the phase space effectively and thermal fluctuations can drive the system uphill in energy (or uphill in any other objective function used) resuhing in high probability of finding the global minimum, i.e., the structure that best fits the data. In this manner, unbiased solutions with possible non-regular geometric shapes can result. The building unit for the model consists of "spheres" of Si02. This selection simplifies the calculation of the PDDF and Rg without causing the loss of significant information from the scattering of the individual silicon and oxygen atoms as well as allowing the study of large atomic systems rapidly. The building units are considered hard spheres with a hard sphere diameter of 2.85 A. Initially, 400 building units are placed randomly in a cubic simulation box of 80 A. The objective function, F, F = . 1 ^ wj * (Q^ - Q^'^P )^ + wj^ 1-0

* (Rg - Rgexp )^ ^ ^ m\^Y

* ^ i = 1

^P^DF . - PDDF

)^

0)

H

is then calculated for the initial arrangement. The first term accounts for the differences between the experimental and model NMR spectra where Q" represents the connectivity of the building units. This connectivity is simulated by setting a bonding region between 2.85-3.4 A. Any two units with a distance within this range are considered bound in the calculation of the Q values. The next term represents the difference between the radii of gyration values, while the final term accounts for the differences in fitting the pair distance distribution function. The fitting of the distance distribution function involves the normalization of the experimental distance distribution function to a maximum value of 1. The function is then discretized into 26 points each of which represents a fraction of distances located with a certain length range relative to the maximum number of distances. The model performs a grouping of unit-unit distances based on the same 26 set distances and normalized in the same fashion to allow for the direct comparison of PDDFs. Since the values of each term differ significantly, weighting functions, w, are applied to ensure that each term has the same order of magnitude in the final objective function and can be varied between simulation runs to test the importance of each parameter at reaching a defined shape. The annealing process begins at a dimensionless temperature of 5000 and is lowered to 10 during the simulation. An annealing schedule was developed with two steps. The first eliminates the dependence of the initial condition by performing Monte Carlo moves at high temperatures (between 5000 and 3000) in which almost all moves are accepted shuffling the positions of the units in the box. During this period, 500 Monte Carlo moves are performed at each 1 degree decrease in temperature. Each move during the entire simulation selects a unit at random and moves it a random distance in x, y, and z. After the initialization period, the step size for each temperature decrease is reduced to 0.01 and the number of Monte Carlo moves per step is increased to between 1400 and 2000. The acceptance or rejection of a move is based on the impact each has on the objective function. After each move, the Rg, PDDF and Q values are recalculated to account for variations caused by moving a specific unit. Moves leading to the overlapping of the hard spheres, an overcoordination of the Si02 units or the formation of three member rings are rejected. Three member rings occur when two Si02 units within bonding range share another unit within the bonding range. All other moves have their objective functions calculated with decreases in the objective function automatically accepted. Any increase in the objective function may be accepted by comparing the corresponding Boltzmann factor to a random number.

1270 RESULTS Solution ^^Si NMR The in situ solution ^^Si NMR spectrum of the solution of nanoparticles, the simulation of the experimental spectrum and further analysis performed on the experimental data are shown in Figure 1. Initially, the ^^Si NMR experiment on a Teflon NMR sample tube containing only D2O was measured and the spectrum obtained is shown in Figure la. This spectrum shows a broad peak at ~ -111.81 ppm due to the Si-containing inserts in the probe head, referred to as the instrument background. The in situ solution ^^Si NMR spectrum of the synthesis solution of nanoparticles, as recorded, is shown in Figure lb. The broad peak is attributed to the instrument background. (Although this peak overlaps with the Q"^ range, the absence of additional peaks in this range with significantly higher signal to noise ratios led to the conclusion that negligible fraction of Q'^s exist.) Apart from the instrument background, this spectrum shows two distinct broad peaks in the ranges of-103 to -107 ppm and -93 to -98 ppm, which were assigned as Q^ and Q^ respectively [9]. The inset in Figure 1 highlights the presence of several sharp peaks superimposed on the broad peak assigned as Q^. Similar sharp peaks are observed along with the broad peak assigned as Q^ and smaller peaks also appear in the range attributed to Q^s. These peaks can be attributed to the silicate species present in solution (as opposed to in the nanoparticle phase) [10]. The presence of smaller silicon species is ignored during our later analyses of the nanoparticle suspension for two reasons. First, the area under the show peaks is relatively insignificant when compared to the broad peaks. Also, the lack of any peak for Q^ proves that little silicon remains in solution as monomers. The simulation of the spectrum is shown in Figure Ic and the components of the simulated background are shown in Figure Id. The spectrum of the synthesis solution of nanoparticles after subtracting the simulated instrument background is shown in Figure le and the simulation of this spectrum, from which the relative ratios of the species present is obtained by calculating the areas under the peaks, is shown in Figure If The fractions of Q" in the synthesis solution containing the nanoparticles are 78% Q^ and 22% Q^ which are then used as the first input to the simulated annealing algorithm.

Figure 1. In situ solution ^^Si NMR spectra of a Teflon NMR sample tube containing (a) D2O, (b) the synthesis solution of nanoparticles, (c) the simulation of the spectrum shown in (b), and (d) its components. The final spectrum after subtracting the instrument background and the simulation of that spectrum are shown in (e) and (f) respectively. The inset shows the presence of sharp peaks superimposed on the broad peak assigned as Q^

1271 Small angle neutron scattering Kratky plots Figure 2 illustrates the application of Kratky plots to the measured intensity of the nanoparticles in deuterium oxide. ^ ^

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Figure 2. Kratky plots of sphere, infinitely long cylinder and infinitely flat plate. The solid straight lines represent the three basic simplifications of the Debye equation expanded around s = 0; a sphere, an infinitely long cylinder, and an infinitely flat plate: Sphere

lnI(s)«lnI(0)-s^Rg^/3

(4)

Long Rod

In (I(s) • s) = In 1(0) - s'Rg V2

(5)

Flat Plate

In (I(s) • s^) = In 1(0) - s^Rg^

(6)

The dotted curves are the measured intensity with solvent background subtracted plotted in the same functional forms as each of the equations. In order to apply the approximations to develop the Kratky plots, the minimum value of s sampled must be less than TI/D, where D is the largest particle dimension [6]. For a nanoparticle with a largest dimension of 50 A, the minimum s must be less than 0.63 A \ The minimum s value of Figure 2 is 0.61 k-\ The primary information gathered from Figure 1 is that the particle shape is between a sphere and a cylinder since the theoretical linear fits of those models are closest to the actual experimental curves. Also, the radius of gyration is calculated from the corresponding equations for the cylinder and sphere and is between 13-19 A. The large range found for the radius of gyration leads us to apply a lower weighting to the Rg term of the objective function for the simulated annealing (see below). Pair distance distribution function Kratky plots are a quick method for determining the qualitative particle shape of nanoparticles. However to quantify their specific dimensions quantitatively, the pair distance distribution function is applied. Figure 3 contains four PDDF curves; the red squares represent our experimental PDDF, the blue line is an analytical solution for a sphere with diameter of 50 A, the green line represents a PDDF from an ellipsoidal model fit directly to the SANS intensity data, and the black triangles are the PDDF from the simulated annealing structure shown in Figure 4. The experimental PDDF was calculated by inverse Fourier transforming the experimental intensity (after subtracting the solvent background) performed using GIFT software developed by Glatter, et. al. [11]. The experimental PDDF clearly displays the properties of a particle with an ellipsoidal shape Glatter containing a larger maximum distance than the analytical sphere with the same maximum PDDF radius (see Glatter). The PDDF of the homogeneous ellipsoid further supports this observation as the two curves are practically identical except in the low distance region where the PDDF of the ellipsoid is slightly higher.

1272

r* experimental A simulated anneaSiog mod^l

r(A} Figure 3. Pair distance distribution functions of the experimental data, analytical sphere, theoretical ellipsoid and simulated annealing model. All curves are normalized to 1 at the maximum value of the PDDF. The ellipsoid dimensions and intensity measurements are determined using non-linear fitting solvers provided by NIST [12], which calculate a numerical solution of the form factor of an ellipsoid. Five parameters are required for the solver: the volume fraction of particles in solution, both radii of the ellipsoid, the sample background and the contrast, (the difference between the solvent and nanoparticle scattering length densities). Two of these variables must be held constant for an accurate solution to be reached. For the nanoparticles, the solution volume fraction was set to 0.006 based on estimates for the amount of nanoparticles with 5 nm diameters formed if all Si02 in the system is incorporated into nanoparticles. This assumption is supported by the lack of Q^ and Q^ peaks in the Figure 1 which would exist if monomers of silicon were present. The other variable fixed is the contrast. Both the scattering length density of the solvent and the nanoparticle were known after performing contrast matching experiments which led to a contrast value of-3.56x10'^ A"\ The solver was then able to calculate the solution background and ellipsoid radii which had values of 0.149 cm"\ 9.5 A and 34 A respectively. An analytical solution for the PDDF of a sphere was developed by Porod and only requires that the longest dimension of the nanoparticle be known [13]. In the analysis of Kratky plots, a longest dimension of 50 A represented the minimum s value of reliable data and was used as the longest dimension in the analytical calculation. During the simulated annealing process, the model's objective function is decreased from a relative value of 1.65x10^ to 44. The experimental Q values entered into the system are 0% Q^, 0.75% Q\ 22% Q^ 76.5% Q^ and 0.75% Q^ The model begins with all units in the Q° state, but reaches final Q values of 0% Q^ 0.75% Q\ 22.3% Q^ 76.2% Q^ and 0.75% Q\ In addition to fitting both the Q values and PDDF, the model also has a radius of gyration 14.7 A which falls within the expected range and an average Si-Si distance of 3.1 A, which also is within the range of most amorphous silica phases. Figure 4 shows three views of the actual Si02 and SiOH units of the model in its final annealed state. The particle is definitely ellipsoidal in shape with radii of 10 A and 22 A in good agreement with the theoretical ellipsoid.

0«0

Figure 4. Three views of a 400 Si02 unit model structure with ellipsoidal radii of 10 A and 22 A. Thefirsttwo images display the Si02 units alone and the third image has silicon, oxygen and hydrogen atoms replacing the Si02 units.

1273 The model successfully fits the experimental results leading to a prediction of particle shape, but is limited by some of our model assumptions. First, the model has three additional particles not connected to the final nanoparticle which would lead to the determination that the system is not completely monodisperse as assumed by both the Kratky plots and the non-linear ellipsoid fit. Polydispersity would normally lead to additional characteristics in the measured scattering intensity, as shown by Pederson in 1993 [14], such as local maxima and minima which do not exist in our scattering curve. As the average particle size increases, these local signals are smoothed and the curve appears to be monodisperse. Our average particle size, however, is small enough < 50A that we would expect to see these additional characteristics if polydispersity actually occurred, so the presence of these additional particles must not be ignored. One possibility for the presence of additional particles is the number of Si02 units (400 in the current model). Varying this value may change the level of polydispersity in the model and may lead to solutions without additional particles. Another limitation is that the model contains scattering information only from SiOi, while the contrast matching experiments indicate that the experimental scattering includes information about the structure directing agent, TPA, located on the particles surface. The addition of TPA to the model may lead to variations in particle shape and a description of the composition variations throughout the particle. Incorporation of these factors is being carried out and will be reported in the near future. CONCLUSIONS We have developed a methodology for determining the structure of nanoparticles of Si02 present during the first stages of silicalite-1 growth. The combination of both ^^Si NMR and SANS experimental results through simulated annealing has led to the determination of an ellipsoidal particle shape with radii of 10 A and 22 A which is in good agreement with SANS calculations of a theoretical ellipsoid with radii of 9 A and 34 A. Further SANS will have to be completed with the use of a deuterated structure directing agent to determine the composition of the particles and to develop a simulated annealing model which can determine the optimum positions of TPA^ and Si02 within the particle. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

Dokter, W., Beelen, T., van Garderen, H., van Santan, R., J. Appl. Cryst, 27 (1994), 901- 906. de Moor, P.P., Beelen, T., van Santan, R., J. Phys. Chem. B, 103 (1999), 1639-1650. Schoeman, B.J., Microporous Materials, 9 (1997), 267-271. Kragten, D., Fedeyko, J., Sawant, K., Rimer, J., Vlachos, D., Lobo, R., J. Phys. Chem. B, accepted 2003. Watson, J., Iton, L., Keir, R., Thomas, J., Bowling, T., White, J., J. Phys. Chem. B, 101 (1997), 10094-10104. Feigin, L., Svergun, D., Structure Analysis by Small-Angle X-Ray and Neutron Scattering, Plenum Press, (1987). Nikolakis, V., Kokkoli, E., Tirrell, M., Tsapatsis, M., Vlachos, D., Chem. Mater., 12 (2000), 845-853 Ravishankar, R.; Kirschhock, C. E. A.; Schoeman, B. J.; de Vos, D.; Grobet, P. J.; Jacobs, P. A.; Martens, J. A., 12th International Zeolite Conference, (1998), 1825-1832. Engelhardt, G., Michel, D., High-Resolution Solid-State NMR of Silicates and Zeolites; John Wiley & Sons Ltd.: Chichester, (1987). Knight, C. T. G.; Kinrade, S. D., J. Phys. Chem. B, 106 (2002), 3329 Clatter, O., Brunner-Popela, J., Weyerich, B., Fritz, G., Bergmann, A., General Indirect Fourier Transformation Version 5, (2000). Kline, S., SANS Data Reduction Software Version 4, (2001). Clatter, O., J. Appl. Cryst, 12 (1979), 166-175. Pederson, J., J. Appl. Cryst, 27 (1994), 595-608.