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Langmuir 2002, 18, 56-59
Time-Resolved SAXS Study of Nucleation and Growth of Silica Colloids D. Pontoni,† T. Narayanan,*,† and A. R. Rennie‡ European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble Cedex, France, and Department of Chemistry, King’s College London, Strand, London WC2R 2LS, United Kingdom Received July 19, 2001. In Final Form: October 15, 2001 This paper reports a time-resolved small-angle X-ray scattering study of in situ Sto¨ber silica synthesis. The hydrolysis reaction is initiated by rapidly mixing equal amounts of alcoholic solutions of ammonia and tetraethyl orthosilicate, using a stopped-flow device coupled to a flow-through capillary cell. Measurements covered the scattering wave vector (q) range of 0.02 e q e 6 nm-1 and time (t) range of 0.1 e t e 1000 s. The combination of high sensitivity, low background, and high dynamic range of the experimental setup permitted observation of the primary particles of nucleation. During the entire growth process, the measured scattered intensity can be adequately described by a sphere scattering function weighted by a Schultz size distribution function. At the early stages of growth, the fitted radius increased linearly with time, subsequently crossing over to a smaller exponent of between 1/3 and 1/2. The observed behavior is consistent with an aggregation process involving primary particles of a few nanometers in size.
Introduction Monodisperse colloidal silica is of great practical as well as fundamental interest. As a result, its method of preparation has attracted much attention in the past.1-9 A very common process has been the base-catalyzed hydrolysis of silicon alkoxides. The Sto¨ber method1 using ammonia and tetraethyl orthosilicate (TEOS) has been widely used for the preparation of monodisperse silica particles in the size range 20-1000 nm.2,4 Several authors4,6,7 have described the general scheme of this chemical synthesis involving hydrolysis and condensation of TEOS. Both stages of the reaction occur in alcohol solutions containing ammonia. The size and the polydispersity of silica particles depend on the reaction conditions such as the pH, reagent concentrations, and so forth.2,4,7 In the past, considerable effort has been made to unravel the basic rate-limiting step involved in the entire reaction. These studies used a variety of techniques: NMR,2,6,7 Raman spectroscopy,5 transmission electron microscopy,2,4,6 light scattering,2,3,5,7 and small-angle X-ray scattering (SAXS).8 The most probable rate-determining steps are the hydrolysis, the condensation, and the aggregation. Spectroscopic studies revealed that only singly hydrolyzed monomers are present as a reaction * Corresponding author. E-mail:
[email protected]. † European Synchrotron Radiation Facility. ‡ King’s College London. (1) Sto¨ber, W.; Fink, A.; Bohn, E. J. J. Colloid Interface Sci. 1968, 26, 62. (2) van Blaaderen, A.; van Geest, J.; Vrij, A. J. Colloid Interface Sci. 1992, 154, 481. (3) Phillipse, A. P. Colloid Polym. Sci. 1988, 266, 1174. Phillipse, A. P.; Vrij, A. J. Chem. Phys. 1988, 87, 5634. (4) Bogush, G. H.; Tracy, M. A.; Zukoski, C. F. J. Non-Cryst. Solids 1988, 104, 95. Bogush, G. H.; Zukoski, C. F. J. Colloid Interface Sci. 1991, 142, 19. (5) Matsoukas, T.; Gulari, E. J. Colloid Interface Sci. 1988, 124, 252; 1989, 132, 13. (6) Bailey, J. K.; Mecartney, M. L. Colloids Surf. 1992, 63, 151. (7) Lee, K.; Look, J.-L.; Harris, M. T.; McCormick, A. V. J. Colloid Interface Sci. 1997, 194, 78. (8) Boukari, H.; Lin, J. S.; Harris, M. T. J. Colloid Interface Sci. 1997, 194, 311. (9) Boukari, H.; Long, G. G.; Harris, M. T. J. Colloid Interface Sci. 2000, 229, 129.
intermediate and the overall rate of particle growth is limited by the hydrolysis of the alkoxide.2,5,7 Subsequent chemical processes are relatively fast, and growth proceeds by continuous addition of monomers.2,5,7 An alternative view is that the hydrolysis is fast and some later step in the condensation process is the rate-limiting factor, and small primary particles are continuously nucleated which subsequently coalesce to form larger particles.4 Static light scattering studies concluded that the growth proceeds through a surface reaction-limited condensation of hydrolyzed monomers.2 Cryo-TEM investigations6 of reaction intermediates postulated that the hydrolyzed monomers react to form polymeric microgels which collapse upon attaining a critical size and cross-linking. The collapsed particles densify by condensation, and these dense seed particles grow by surface addition of hydrolyzed monomers or polymers. More recent Si NMR investigation7 of the reaction pathway showed that the precipitation of the doubly hydrolyzed monomer is a likely mechanism of nucleation and the growth proceeds by aggregation. The balance between rates of nucleation of primary particles and aggregation determines the final particle size. A more direct structural study by SAXS8 indicated that the initial nuclei are highly ramified fractal structures that subsequently aggregate and condense to form more compact objects. Subsequent ultra-SAXS investigation9 corroborated the earlier results and continuous nucleation mechanism. In these studies, the size of the first detected primary particles was in the range of 16-20 nm. The availability of high-brilliance synchrotron radiation sources permits time-resolved SAXS measurements on extremely dilute dispersions with unprecedented resolution and dynamic range. In particular, it is now possible to investigate both the very early stages of the nucleation and the complete growth process in a single experiment. The primary goal of this work is to elucidate the structure of particles from the early nuclei to final stable colloids. Therefore, the paper reports data obtained for a selected set of reaction parameters over different time windows and scattering vector ranges during the growth process.
10.1021/la015503c CCC: $22.00 © 2002 American Chemical Society Published on Web 01/02/2002
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The measured structural parameters are used to deduce the particle morphology and growth law. Experimental Section The chemicals, TEOS (Fluka), 25% ammonia solution (Prolabo), and absolute alcohol (Prolabo), were used as purchased. The growth process was initiated by mixing two stock solutions of ammonia and TEOS in ethanol in equal volumes. The resulting concentrations of the reacting mixtures were [TEOS] ) 0.09 mol/ L, [NH3] ) 1.45 mol/L, and [H2O] ) 4.15 mol/L. These concentrations were chosen as an intermediate between those used in earlier studies2-4,7,8 and to complete the whole growth process within a short period when the sedimentation effect is not significant. The stopped-flow apparatus consisted of two pneumatically driven syringes and a mixing chamber that is coupled to a thinwalled flow-through capillary (2 mm diameter and wall thickness 10 µm). To reduce the parasitic background, the capillary was mounted in vacuum without any windows in the entire flight path of the incident and transmitted beams. The combined mixing and transfer dead times were less than 10 ms. The data acquisition is hardware triggered at the end of the movement of the pneumatically driven piston. SAXS is a powerful technique to probe the size, shape, and polydispersity of colloidal particles.10 The scattered intensity, I(q), is measured as a function of scattering wave vector, q ) (4π/λ) sin(θ/2), where λ is the wavelength of incident radiation and θ is the scattering angle. SAXS measurements were performed on the ID2 beamline at the European Synchrotron Radiation Facility, Grenoble, France.11 The incident X-ray wavelength was 0.1 nm. To cover a wide q-range (0.02 nm-1 e q e 6 nm-1) with sufficient intensity statistics, several different sample-to-detector distances were used (1.5, 3, and 10 m). The two-dimensional SAXS patterns were recorded with an imageintensified CCD camera.11 The incident and the transmitted fluxes were also simultaneously registered with each SAXS pattern. Typically, a sequence of 120 frames was acquired after each mixing. The dead time between the frames was varied in a geometric progression. The standard data treatment involved various detector corrections for flat field response, spatial distortion, and dark current of the CCD, and normalization by the incident flux, sample transmission, exposure time and the angular acceptance of the detector pixel elements.11 Further corrections, described elsewhere,12 were necessary to account for the long tail of the point spread function of the image intensifier. The resulting normalized two-dimensional images were azimuthally averaged to obtain I(q) which essentially refers to the differential scattering cross section dΣ/dΩ per unit length in mm-1 sterad-1. The beam intensity was optimized in order to reduce the beaminduced degassing of the dissolved ammonia. During the early stages, the measured I(q) at small q was dominated by this microbubble scattering if the full beam intensity (typically 1013 photons/s) was used. As a result, for the low q measurements (sample-to-detector distance of 10 m) the beam intensity was reduced by a factor of 20 and the exposure time varied from 0.05 to a few seconds.
Figure 1. Typical 3-d representation of the time evolution of the SAXS intensity during the Sto¨ber synthesis of silica particles. Measurements covered over 20 min corresponding to a sample-to-detector distance of 10 m.
analytical form:
P(q) ) [3 (sin(qRS) - qRS cos(qRS))/q3RS3]2
(2)
Equations 1 and 2 imply that the intensity at q ) 0 is I0 ) N(4/3πRS3)2(Fc - Fs)2. If the particle number and mass densities were conserved during the growth process, then I0/RS6 should remain constant. However, in real systems there is a finite distribution of particle sizes and eq 1 has to be weighted over the entire size distribution P(R). Experimentally, it has been found that the size distribution of many colloidal systems can be adequately described by the Schultz distribution function,13
P(R) )
[
] [
(Z + 1)Z+1 R h
RZ exp -
]
(Z + 1)R R h
/Γ(Z+1) (3)
where R h is the mean radius; Z is related to σR, the rooth /xZ+1; mean-square deviation of the radius, by σR ) R and Γ(Z) is the gamma function. In addition, for noninteracting systems the intensity at small q values (qRS < 1) is given by the Guinier approximation,10
I(q) ) N(Fc - Fs)2V2 exp(-q2RS2/5)
(4)
From the limiting slope and the intercept of ln(I) versus q2, the radius and the molecular mass can be estimated. However, slight interactions between particles can affect I(q) in the small q region; thus, a more reliable method of estimating the radius and molecular weight is by fitting the measured scattered intensity to the polydisperse spherical form factor over the whole measured q-range. For the Schultz distribution, there exists an analytical expression13 for the scattered intensity and this expression was used to fit the experimental data. In the following sections, the fitted mean radius is represented as R.
Data Analysis In the small-angle region, I(q) of a suspension of uniform noninteracting spherical particles is given by10
I(q) ) N(Fc - Fs)2V2 P(q)
(1)
where N is the particle number density, Fc and Fs are the average electron densities of the particle and the solvent, respectively, V ) 4/3πRS3 is the volume, and P(q) is the form factor of a sphere of radius RS. P(q) has the following (10) Modern Aspects of Small-Angle Scattering; Brumberger, H., Ed.; NATO ASI Series; Kluwer Academic Publishers: Dordrecht, 1995. (11) Narayanan, T.; Diat, O.; Boesecke, P. Nucl. Instrum. Methods Phys. Res., Sect. A 2001, 467, 1005. (12) Pontoni, D.; Narayanan, T.; Rennie, A. R. J. Appl. Crystallogr., submitted.
Results Typical time evolution of SAXS intensity during the Sto¨ber growth process is depicted in Figure 1 as a 3-d plot of I versus q and time. Similar features were observed in data sets acquired under different conditions. The oscillations in the intensity at the later stages of the growth process readily indicate the development of the form factor of spherical particles as given by eq 2. The maxima and the minima progressively shifted to the low-q region signifying the growth of the particles. During the so-called induction time, the intensity evolved marginally only in the intermediate q-range. Figure 2 shows the evolution of intensity over this q-range. The continuous lines depict (13) Kotlarchyk, M.; Chen, S.-H. J. Chem. Phys. 1983, 79, 2461.
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Figure 2. SAXS intensity at different stages of the growth for a sample-to-detector distance of 1.5 m. The continuous curves are fits to the polydisperse sphere form factor. The earliest analyzable data correspond to nuclei of radius about 3 nm formed within 1 min after mixing. The data at 35 s indicate the residual noise after the subtraction of background (∼3 × 10-3 mm-1).
Figure 3. Time evolution of SAXS intensity following the initial induction period. The sample-to-detector distance was 3 m, and the acquisition time was 0.2 s. The late stage behavior of intensity is essentially the same as depicted in Figure 1. The continuous lines are fits to the polydisperse sphere scattering function. The inset depicts the change in fitted I0/R6 at the initial stage of the growth signifying a drastic decrease in the number density of scattering objects.
the fits to the sphere scattering function (eq 1) weighted by the Schultz distribution function (eq 3). This indicates that the initial nuclei are more like spherical droplets. In addition, fits to eq 1 imply Porod behavior:10 particles are dense and have a sharp interface. Figure 3 presents the evolution of intensity immediately after the induction period. The spherical form factor became evident after about 120 s, and the continuous lines are fit to the polydisperse sphere form factor. The inset illustrates the variation of the fitted I0/R6 ratio after the initial nucleation stage. The scattered intensity from the dispersion over the small q region during the different stages of the reaction is shown in Figure 4. The continuous lines are fit to eq 1 weighted by eq 3, and Porod behavior is evident in the high-q part of the scattering curves. The deviation from the fitted lines at small q’s is a signature of interactions between particles since eq 1 does not include the structure factor of interparticle potential. The inset in Figure 4 depicts the residual of the fit, ∆I ) I (fitted) - I (experimental), at q ) 0.02 nm-1 normalized by the corresponding R6. Therefore, positive ∆I values imply repulsive interaction between particles. However, the initial negative ∆I cannot be fully attributed to attractive interactions or concentration fluctuations because some residual scattering by the degassed ammonia microbubbles cannot be excluded. Figure 5 shows the time evolution of the fitted I0/R6 ratio and the polydispersity for the data presented in Figure 1. After the initial nucleation stage (see also the inset in Figure 3), the ratio I0/R6 remained nearly constant over the whole reaction signifying constant particle number (N) and mass densities (∝ Fc - Fs). The fitted
Pontoni et al.
Figure 4. The SAXS intensity at different stages of growth for a sample-to-detector distance of 10 m. The continuous lines are fits to the polydisperse sphere form factor. The high-q region shows Porod behavior. The overprediction of the fit at small q’s in the late stage of growth is attributed to the effect of repulsive interactions between the colloidal particles. For a comparison, the inset shows the deviation (∆I) at q ) 0.02 nm-1 normalized by the corresponding R6.
Figure 5. The time variation of fitted polydispersity and I0/R6 during the growth process in Figure 1. The average number and mass densities of particles remain constant after the initial stage.
Figure 6. A double log representation of the time evolution of the mean radius of the particles during the growth process. The legends indicate sample-to-detector distances and acquisition times for the corresponding scattering patterns. The straight lines with slopes of 1 and 1/2 are only guides to the eye.
polydispersity decreased to about 10% at the late stage of the growth. The time dependence of the fitted radius is depicted in Figure 6. The fitted radius increased linearly with time at the early stage of growth followed by a smooth crossover to a smaller exponent between 1/2 and 1/3. The significance of this behavior is discussed in the next section. The fitted radius for t < 100 s deviated from the power law. Discussion The time-resolved SAXS data of Sto¨ber silica growth presented in the previous section demonstrate that the scattered intensity over the entire growth process is well described by a model of polydisperse spheres of uniform
Nucleation and Growth of Silica Colloids
density. This is in contrast to the fractally rough colloids14 found in slow growth. For the reaction conditions used in this study, the induction time associated with the nucleation of particles is fairly short ( 1. However, with a vanishing repulsive barrier, the long-ranged dispersion forces can bring down W to
