56 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 Stöber 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 intermediate and the overall rate of particle growth is

Monodisperse colloidal silica is of great practical as well limited by the hydrolysis of the alkoxide.2,5,7 Subsequent
as fundamental interest. As a result, its method of chemical processes are relatively fast, and growth proceeds
preparation has attracted much attention in the past.1-9 by continuous addition of monomers.2,5,7 An alternative
A very common process has been the base-catalyzed view is that the hydrolysis is fast and some later step in
hydrolysis of silicon alkoxides. The Stöber method1 using the condensation process is the rate-limiting factor, and
ammonia and tetraethyl orthosilicate (TEOS) has been small primary particles are continuously nucleated which
widely used for the preparation of monodisperse silica subsequently coalesce to form larger particles.4 Static light
particles in the size range 20-1000 nm.2,4 Several scattering studies concluded that the growth proceeds
authors4,6,7 have described the general scheme of this through a surface reaction-limited condensation of hy-
chemical synthesis involving hydrolysis and condensation drolyzed monomers.2 Cryo-TEM investigations6 of reaction
of TEOS. Both stages of the reaction occur in alcohol intermediates postulated that the hydrolyzed monomers
solutions containing ammonia. The size and the polydis- react to form polymeric microgels which collapse upon
persity of silica particles depend on the reaction conditions attaining a critical size and cross-linking. The collapsed
such as the pH, reagent concentrations, and so forth.2,4,7 particles densify by condensation, and these dense seed
In the past, considerable effort has been made to unravel particles grow by surface addition of hydrolyzed monomers
the basic rate-limiting step involved in the entire reaction. or polymers.
These studies used a variety of techniques: NMR,2,6,7 More recent Si NMR investigation7 of the reaction
Raman spectroscopy,5 transmission electron micros- pathway showed that the precipitation of the doubly
copy,2,4,6 light scattering,2,3,5,7 and small-angle X-ray hydrolyzed monomer is a likely mechanism of nucleation
scattering (SAXS).8 The most probable rate-determining and the growth proceeds by aggregation. The balance
steps are the hydrolysis, the condensation, and the between rates of nucleation of primary particles and
aggregation. Spectroscopic studies revealed that only aggregation determines the final particle size. A more
singly hydrolyzed monomers are present as a reaction direct structural study by SAXS8 indicated that the initial
nuclei are highly ramified fractal structures that subse-
* Corresponding author. E-mail: narayan@esrf.fr. quently aggregate and condense to form more compact
† European Synchrotron Radiation Facility.
‡ King’s College London. objects. Subsequent ultra-SAXS investigation9 corrobo-
(1) Stöber, W.; Fink, A.; Bohn, E. J. J. Colloid Interface Sci. 1968, rated the earlier results and continuous nucleation
26, 62. mechanism. In these studies, the size of the first detected
(2) van Blaaderen, A.; van Geest, J.; Vrij, A. J. Colloid Interface Sci. primary particles was in the range of 16-20 nm.
1992, 154, 481.
(3) Phillipse, A. P. Colloid Polym. Sci. 1988, 266, 1174. Phillipse, A. The availability of high-brilliance synchrotron radiation
P.; Vrij, A. J. Chem. Phys. 1988, 87, 5634. sources permits time-resolved SAXS measurements on
(4) Bogush, G. H.; Tracy, M. A.; Zukoski, C. F. J. Non-Cryst. Solids extremely dilute dispersions with unprecedented resolu-
1988, 104, 95. Bogush, G. H.; Zukoski, C. F. J. Colloid Interface Sci.
1991, 142, 19. tion and dynamic range. In particular, it is now possible
(5) Matsoukas, T.; Gulari, E. J. Colloid Interface Sci. 1988, 124, 252; to investigate both the very early stages of the nucleation
1989, 132, 13. and the complete growth process in a single experiment.
(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 The primary goal of this work is to elucidate the structure
Interface Sci. 1997, 194, 78. of particles from the early nuclei to final stable colloids.
(8) Boukari, H.; Lin, J. S.; Harris, M. T. J. Colloid Interface Sci. Therefore, the paper reports data obtained for a selected
1997, 194, 311.
(9) Boukari, H.; Long, G. G.; Harris, M. T. J. Colloid Interface Sci. set of reaction parameters over different time windows
2000, 229, 129. and scattering vector ranges during the growth process.
10.1021/la015503c CCC: $22.00 © 2002 American Chemical Society
Published on Web 01/02/2002
Nucleation and Growth of Silica Colloids Langmuir, Vol. 18, No. 1, 2002 57

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 concen-
trations were chosen as an intermediate between those used in
earlier studies2-4,7,8 and to complete the whole growth process Figure 1. Typical 3-d representation of the time evolution of
within a short period when the sedimentation effect is not the SAXS intensity during the Stöber synthesis of silica
significant. particles. Measurements covered over 20 min corresponding to
The stopped-flow apparatus consisted of two pneumatically a sample-to-detector distance of 10 m.
driven syringes and a mixing chamber that is coupled to a thin-
walled flow-through capillary (2 mm diameter and wall thickness analytical form:
10 µm). To reduce the parasitic background, the capillary was
mounted in vacuum without any windows in the entire flight P(q) ) [3 (sin(qRS) - qRS cos(qRS))/q3RS3]2 (2)
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 Equations 1 and 2 imply that the intensity at q ) 0 is I0
the pneumatically driven piston. ) N(4/3πRS3)2(Fc - Fs)2. If the particle number and mass
SAXS is a powerful technique to probe the size, shape, and densities were conserved during the growth process, then
polydispersity of colloidal particles.10 The scattered intensity, I0/RS6 should remain constant. However, in real systems
I(q), is measured as a function of scattering wave vector, q ) there is a finite distribution of particle sizes and eq 1 has
(4π/λ) sin(θ/2), where λ is the wavelength of incident radiation to be weighted over the entire size distribution P(R).
and θ is the scattering angle. SAXS measurements were Experimentally, it has been found that the size distribution
performed on the ID2 beamline at the European Synchrotron of many colloidal systems can be adequately described by
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
the Schultz distribution function,13

[ ] [ ]
q e 6 nm-1) with sufficient intensity statistics, several different
sample-to-detector distances were used (1.5, 3, and 10 m). The (Z + 1)Z+1 (Z + 1)R
two-dimensional SAXS patterns were recorded with an image- P(R) ) RZ exp - /Γ(Z+1) (3)
intensified CCD camera.11 The incident and the transmitted
h
R h
R
fluxes were also simultaneously registered with each SAXS
pattern. Typically, a sequence of 120 frames was acquired after where Rh is the mean radius; Z is related to σR, the root-
each mixing. The dead time between the frames was varied in mean-square deviation of the radius, by σR ) R h /xZ+1;
a geometric progression. and Γ(Z) is the gamma function.
The standard data treatment involved various detector cor- In addition, for noninteracting systems the intensity at
rections for flat field response, spatial distortion, and dark current small q values (qRS < 1) is given by the Guinier
of the CCD, and normalization by the incident flux, sample approximation,10
transmission, exposure time and the angular acceptance of the
detector pixel elements.11 Further corrections, described else-
where,12 were necessary to account for the long tail of the point I(q) ) N(Fc - Fs)2V2 exp(-q2RS2/5) (4)
spread function of the image intensifier. The resulting normalized
two-dimensional images were azimuthally averaged to obtain From the limiting slope and the intercept of ln(I) versus
I(q) which essentially refers to the differential scattering cross q2, the radius and the molecular mass can be estimated.
section dΣ/dΩ per unit length in mm-1 sterad-1. However, slight interactions between particles can affect
The beam intensity was optimized in order to reduce the beam- I(q) in the small q region; thus, a more reliable method
induced degassing of the dissolved ammonia. During the early of estimating the radius and molecular weight is by fitting
stages, the measured I(q) at small q was dominated by this
the measured scattered intensity to the polydisperse
microbubble scattering if the full beam intensity (typically 1013
photons/s) was used. As a result, for the low q measurements spherical form factor over the whole measured q-range.
(sample-to-detector distance of 10 m) the beam intensity was For the Schultz distribution, there exists an analytical
reduced by a factor of 20 and the exposure time varied from 0.05 expression13 for the scattered intensity and this expression
to a few seconds. 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 Results
noninteracting spherical particles is given by10 Typical time evolution of SAXS intensity during the
Stöber growth process is depicted in Figure 1 as a 3-d plot
I(q) ) N(Fc - Fs)2V2 P(q) (1) of I versus q and time. Similar features were observed in
data sets acquired under different conditions. The oscil-
where N is the particle number density, Fc and Fs are the lations in the intensity at the later stages of the growth
average electron densities of the particle and the solvent, process readily indicate the development of the form factor
respectively, V ) 4/3πRS3 is the volume, and P(q) is the of spherical particles as given by eq 2. The maxima and
form factor of a sphere of radius RS. P(q) has the following the minima progressively shifted to the low-q region
signifying the growth of the particles. During the so-called
(10) Modern Aspects of Small-Angle Scattering; Brumberger, H., Ed.; induction time, the intensity evolved marginally only in
NATO ASI Series; Kluwer Academic Publishers: Dordrecht, 1995. the intermediate q-range. Figure 2 shows the evolution
(11) Narayanan, T.; Diat, O.; Boesecke, P. Nucl. Instrum. Methods
Phys. Res., Sect. A 2001, 467, 1005. of intensity over this q-range. The continuous lines depict
(12) Pontoni, D.; Narayanan, T.; Rennie, A. R. J. Appl. Crystallogr.,
submitted. (13) Kotlarchyk, M.; Chen, S.-H. J. Chem. Phys. 1983, 79, 2461.
58 Langmuir, Vol. 18, No. 1, 2002 Pontoni et al.

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 Figure 4. The SAXS intensity at different stages of growth for
analyzable data correspond to nuclei of radius about 3 nm a sample-to-detector distance of 10 m. The continuous lines are
formed within 1 min after mixing. The data at 35 s indicate the fits to the polydisperse sphere form factor. The high-q region
residual noise after the subtraction of background (∼3 × 10-3 shows Porod behavior. The overprediction of the fit at small q’s
mm-1). 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 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 Figure 5. The time variation of fitted polydispersity and I0/R6
continuous lines are fits to the polydisperse sphere scattering during the growth process in Figure 1. The average number
function. The inset depicts the change in fitted I0/R6 at the and mass densities of particles remain constant after the initial
initial stage of the growth signifying a drastic decrease in the stage.
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 Figure 6. A double log representation of the time evolution
fit to eq 1 weighted by eq 3, and Porod behavior is evident of the mean radius of the particles during the growth process.
in the high-q part of the scattering curves. The deviation The legends indicate sample-to-detector distances and acquisi-
from the fitted lines at small q’s is a signature of tion times for the corresponding scattering patterns. The
interactions between particles since eq 1 does not include straight lines with slopes of 1 and 1/2 are only guides to the eye.
the structure factor of interparticle potential. The inset
in Figure 4 depicts the residual of the fit, ∆I ) I (fitted) polydispersity decreased to about 10% at the late stage
- I (experimental), at q ) 0.02 nm-1 normalized by the of the growth. The time dependence of the fitted radius
corresponding R6. Therefore, positive ∆I values imply is depicted in Figure 6. The fitted radius increased linearly
repulsive interaction between particles. However, the with time at the early stage of growth followed by a smooth
initial negative ∆I cannot be fully attributed to attractive crossover to a smaller exponent between 1/2 and 1/3. The
interactions or concentration fluctuations because some significance of this behavior is discussed in the next
residual scattering by the degassed ammonia microbub- section. The fitted radius for t < 100 s deviated from the
bles cannot be excluded. power law.
Figure 5 shows the time evolution of the fitted I0/R6
ratio and the polydispersity for the data presented in Discussion
Figure 1. After the initial nucleation stage (see also the The time-resolved SAXS data of Stöber silica growth
inset in Figure 3), the ratio I0/R6 remained nearly constant presented in the previous section demonstrate that the
over the whole reaction signifying constant particle scattered intensity over the entire growth process is well
number (N) and mass densities (∝ Fc - Fs). The fitted described by a model of polydisperse spheres of uniform
Nucleation and Growth of Silica Colloids Langmuir, Vol. 18, No. 1, 2002 59

density. This is in contrast to the fractally rough colloids14 fresh nuclei cannot be ruled out since the measured
found in slow growth. For the reaction conditions used in intensity is completely dominated by the larger growing
this study, the induction time associated with the nucle- particles. In fact, the deduced morphology of the particles
ation of particles is fairly short (<60 s). Presumably, during suggests that the growth is likely to have proceeded by
this time sufficient hydrolyzed monomers were formed the addition of the primary nuclei onto these larger
but SAXS is not sensitive to this first step. Subsequently, particles. At this stage, the size distribution approaches
I(q) in the intermediate q-range (0.1 < q < 0.5 nm-1) began an invariant form as indicated in Figure 5. The decrease
to evolve, and it is attributed to the formation of primary in growth rate at later stages can be attributed to the
nuclei. At the same time, there was not any observable depletion of the primary nuclei in the reservoir.3 The
change in the intensity over the high q-range, typically observed behavior is in agreement with previous studies
1-6 nm-1. Within the statistical uncertainties, the scat- which concluded that the rate-limiting step is the hy-
tering from these primary nuclei is better described by a drolysis reaction and the growth proceeds by an aggrega-
polydisperse sphere form factor of radius ∼3 nm (see the tion mechanism involving primary particles.2,6,7
fitted curve for t ) 65 s in Figure 2) than by a fractal After the initial nucleation stage, the growth is pre-
structure function, indicating that they have droplet-like sumably accomplished by the coalescence/coagulation of
form. These small nuclei rapidly coalesced to form larger primary nuclei with colloidally stable larger particles.
particles, and in this process their number density sharply Therefore, the Smoluchowski rate equation16,18,19 can be
decreased as is evident in the inset of Figure 3. In the used to rationalize the observed growth laws. This rate
subsequent stages of growth, presumably freshly formed equation can describe both gelling and nongelling growth
primary nuclei coalesced with larger particles, thus processes.18 In the nongelling case, typically R ∼ tz/D, where
resulting in dense compact particles. z ) 1/(1 - λ) with λ being the homogeneity exponent of the
After the initial nucleation stage, the radius of the reaction kernel.18 Nongelling systems pertain to λ e 1,
particles increased linearly with time. The polydispersity with λ ) 0 and 1 for diffusion-limited and reaction-limited
of the system decreased until it reached a steady value of aggregation, respectively.19 The observed linear regime
about 10%. In the classical Lifshitz-Slyozov15 nucleation corresponds to λ ) 2/3, implying compact particles and
and growth process, one would expect a power law of either straight-line ballistic motion between aggregating par-
1
/2 or 1/3 during the early stage of nucleation depending on ticles.20 This is consistent with a scenario where particles
the degree of supersaturation (high or low, respectively). attract each other without an intervening repulsive
This suggests that the early stage growth of silica particles barrier. The later behavior refers to λ between 0.33 and
is faster than a purely diffusion-controlled process and 0 and the growth mechanism crossover toward a diffusion
cannot be readily explained by classical theory of nucle- type behavior. The colloidal stability is attained in this
ation and growth. Faster growth rates are usually seen crossover region when the electrostatic repulsive barrier
in the presence of gravity-induced hydrodynamic flows,16 is developed.
which is very unlikely in this case. A faster growth than Conclusion
the Brownian diffusion limit is possible if the initial nuclei
are attracted together by long-ranged dispersion forces. Stopped-flow time-resolved SAXS is used to follow the
The cumulative effect of interactions and local hydrody- nucleation and growth process in Stöber silica synthesis.
namics can be expressed in terms of the stability factor The high brilliance of the X-ray beam combined with the
(W).17 The Brownian diffusion limit corresponds to W ) high-sensitivity detection permitted monitoring of the
1, and in general W > 1. However, with a vanishing complete process of nucleation to the formation of final
repulsive barrier, the long-ranged dispersion forces can stable particles. The classical theory of heterogeneous
bring down W to <1 resulting in a faster growth than the nucleation is not adequate to fully describe the nucleation
Brownian limit. At the later stages of growth, particles and growth process in Stöber silica synthesis. The observed
acquire sufficient electric charges to overcome the strong growth laws are consistent with an aggregation mecha-
dispersion forces. The Stöber silica is stabilized by the nism involving primary particles. The exponent describing
electric double layer formed by the surface silanol groups the power law growth depends on the interparticle
(SiO- Η+). The onset of repulsive interaction between the interactions. A crossover in the power law exponent
particles is evident in the inset of Figure 4. However, the demarcates the limiting stability of the suspension where
signature of initial attractive interactions in the small-q the electrostatic repulsion overcomes the long-ranged
data may have been camouflaged by the scattering from dispersion forces. The first observable nuclei seem to have
the unavoidable gas microbubbles present in the mixture. a dropletlike form. This morphology is consistent with a
scenario where one of the reaction intermediates is phase
The observed power law at the late stage approaches separating from the solution.6,7 The mass and the number
that of a diffusive type growth. This is in sharp contrast densities of dominantly growing particles remained
to that observed near a first-order phase transition with constant after the initial stage of growth suggesting that
a conserved order parameter, where the early stage is freshly formed nuclei coagulate with existing colloidally
usually diffusion limited and in the later stage the growth stable larger particles.
is accelerated by hydrodynamic flows.16 Throughout the
growth process, the deduced I0, which is proportional to Acknowledgment. We are grateful to S. Finet and J.
the square of the molecular mass, remained proportional Gorini for fabricating and extensively testing the stopped-
to R6 indicating that the particles are dense (dimension- flow device. The European Synchrotron Radiation Facility
ality D ) 3) and the number density of the dominantly is acknowledged for the provision of beam time and the
growing spheres is constant. However, the formation of financial support.
LA015503C
(14) Keefer, K. D.; Schaefer, D. W. Phys. Rev. Lett. 1986, 56, 2376.
(15) Lifshitz, I. M.; Slyozov, V. V. J. Phys. Chem. Solids 1961, 19, 35. (18) van Dongen, P. G. J.; Ernst, M. H. Phys. Rev. Lett. 1985, 54,
(16) Gunton, J. D.; San Miguel, M.; Sahni, P. S. In Phase Transitions 1396.
and Critical Phenomena; Domb, C., Lebowitz, J. L., Eds.; Academic (19) Ball, R. C.; Weitz, D. A.; Witten, T. A.; Leyvraz, F. Phys. Rev.
Press: London, 1983; Vol. 8, p 267. Lett. 1987, 58, 274. Broide, M. L.; Cohen, R. J. J. Colloid Interface Sci.
(17) Spielman, L. A. J. Colloid Interface Sci. 1970, 33, 562. Law, B. 1992, 153, 493.
M.; Petit, J.-M.; Beysens, D. Phys. Rev. E 1998, 57, 5782. (20) Oh, C.; Sorensen, C. M. J. Aerosol Sci. 1997, 28, 937.