- Email: [email protected]
The role of aging on the formation of porous silica
PREPARATION OF CATALYSTS VI Scientific Bases for the Preparation of Heterogeneous Catalysts G. Poncelet et al. (Editors) 9 1995 Elsevier Science B.V. All rights reserved.
33
The Role of Aging on the Formation of Porous Silica T.P.M. Beelen, W.H. Dokter, H.F. van Garderen, R.A. van Santen and E. Pantos a Schuit Institute of Catalysis, Eindhoven University of Technology, P.O. Box 513, 5600 MB EINDHOVEN, The Netherlands "Daresbury Laboratory, Daresbury, Warrington WA4 4AD, U.K.
Abstract. Porous silica gel has been prepared by acidification of water glass. To study aggregation, gelation and aging use has been made of 29Si-NMR to investigate silica transformations on molecular scale. Q* ratios were used to define distribution of silica in particles and gels. On colloidal scale both IH relaxation of water and small angle scattering (SAXS, SANS) was very informative, especially because changes in fractal dimension could be used to describe silica transformations during aggregation and aging. Interpretation of fractal dimension in terms of aging mechanisms is performed by computer simulations of both aggregation/aging processes and calculation of the corresponding scattering spectra. Comparison of simulated spectra of aged silica, based on hypothetical aging mechanisms, with experimental spectra emphasized the important role of formation of rings on local scale. In freeze-dried silicas pore distributions were investigated with both neutron scattering (SANS) and physisorption (BET), revealing different pore structures, both in growth and form, after aging at 80~ and aging catalyzed by fluorine. 1. INTRODUCTION. Amorphous silica gels exhibit a large diversity in structural properties. To be used as a supporting agent in heterogeneous catalysis, high specific Surface and high stability is necessary. Moreover, for many applications in selective catalysis a tailormade porous structure is necessary or very desirable. When silica is prepared by acidification of water glass (alkali solution of silica), polycondensation reactions occur between dissolved oligomeric silica species, resulting in (sub)colloidal particles [1]. These primary particles combine to very ramified aggregates, a process described by diffusion or reaction limited cluster-cluster aggregation with power-law dependent density (fractals) [2,3]. After gelation the fractal structure is still preserved at sub-micrometer scale, while at l a r g e r scale Euclidean behaviour is observed. After drying, these systems often appear to be microporous because in general the fractal structures are too weak to resist capillary forces or even gravity and the fragile aggregates collapse during the drying process. Therefore, reinforcement of the weak and teneous structures aging processes is necessary [1,4]. During aging silica is redistributed in the gel. Although this redistribution is based on hydrolysis/recondensation reactions of silica monomers, oligomers or particles, depending on process parameters (temperature, concentration, pH, catalysts) many transformations and structures may be formed, resulting in a wide selection of porous
34 structures. The investigation of aging mechanisms is quite challenging. Although understanding aging reactions is necessary to prepare tailor-made porous silicas on a scientific basis, the choice of proper methods is difficult, especially because of the vulnerability of the fragile system only very few methods may be used, while the extended length scale (more than 4 decades: from sub-nanometer to a few microns) requirs the combination of several techniques. At molecular scale we have chosen NMR because recent developments in both 295iNMR and spin-spin relaxation on hydrogen atoms made applications for silicas in colloidal systems possible. For the colloidal scale both the availability of synchrotron radiation providing a high-brilliance source for x-rays and the development of highintensity neutron sources made scattering methods with x-rays (SAXS) and neutrons (SANS) very suitable and opened new possibilities for studying mass density distributions during aggregation and aging processes, using fractal concepts to quantify these transformations and mass distributions. Extremely helpful in interpretation of scattering results proved to be computer simulations, forming a bridge between experimental results and explanations based on simulations of transformations of silica during aging. With the combination of computer programs (GRASP and DALAI) both aggregation and aging and the corresponding scattering spectra can be simulated, allowing an immediate check of mechanistical hypotheses with experimental spectra. As will be shown in this paper, combination of scattering methods and simulation is a new and very promising tool to study transformations in colloidal systems and may be applied succesfully in investigations in the preparation of porous materials.
2. EXPERIMENTAL SECTION. Water glass solutions were prepared by dissolution of amorphous silica (Aerosil 200 and 380, gracefully obtained from Degussa AG) in sodium hydroxide (Merck p.a. using teflon or polyethylene beakers. In a typical experiment the overall molar composition was chosen to be SiO2 : NaOH : H20 = 3 : 2 : 125. Silica gels were prepared by acidification of the alkaline silica solutions. The water glass solution was dosed drop by drop with a Pasteur pipette to a solution of 1.0 M HC1 while stirring vigorously, until pH = 4.0 was reached and the stirring was stopped. Gelation time was definied by the period of time lapsed between the end of acidification and the moment when no meniscus deformation could be observed on twisting the beaker. To avoid evaporation, aging was performed in closed containers. When the catalytic influence of fluorine was investigated, before acidification appropriate quantities of NaF were added to the HC1 solution. To avoid collapse of the fragile structure during drying, freeze drying was applied. After precooling to -40~ for at least 3 hours, small samples of the frozen gel (typically 5 g wet gel) were connected to a Labconco Lab-top freeze dryer operating at 900 Pa and -75~ condensor temperature during 24-48 hours. To remove NaC1 the gels were washed with circa 250 ml doubly distilled water. Dried gels were characterized by physical adsorption/desorption of nitrogen (BET) after outgassing under vacuum for 16 hours at 180~ Sorption measurements were performed on a Carlo Erba Strumentazione Sorptomatic 1900 using liquid nitrogen as sorbent. Typical adsorption/desorption runs demanded 8 hours of analysis. Care was taken that the equilibrium pressure was reached before introduction or withdrawal of
35 a calibrated volume of nitrogen. 29Si-NMR experiments were performed on a Bruker CXP-300 FT-NMR instrument operating at 7.05 T at room temperature. Magic angle sample spinning (MAS) was applied to average any chemical shift anisotropy arising in gelated and freeze dried samples. Spin-spin relaxation times have been determined by the Carr-Purcell-Meiboom-Gill 90~176 sequenze at a frequenzy of 20 MHz using a Bruker Minispec pcl00 at a field strength of 0.47 T. The operational temperature was 40~ in order to prevent temperature changes due to external influences. All samples were stored at 40~ The magnetization curve was analyzed using a monoexponential fit. A multiexponential technique yielded no perceivable improvement of the quality of the fit. SAXS experiments were performed at the Synchrotron Radiation Source at Daresbury Laboratories (United Kingdom) using NCD beamline 8.2. Wet gels and solutions were measured in closed cells with mylar windows (spacing 0.2 - 0.5 mm), dried gels were fixed at cellotape. With wavelength fixed at 0.15 nm, variation of camera length (sample to detector distance) between 1.0 and 4.0 m and appropriate positioning of the beamstop, the Q-range between 0.05 and 2.5 nm ~ could be covered. To enhance sensitivity at low Q a quadrant detector was used. Satisfactory signal to noise ratios were obtained with acquisition times between 1 and 5 minutes. Subtraction of parasitic (slits) and background scattering (water solution, mylar windows, cellotape) was applied using the procedure introduced by Vonk [5], adapted to fractal systems. SANS experiments were performed at the Rutherford Appleton Laboratory, ISIS facility, Abingdom, U.K. Pulsed neutrons with wavelengths between 0.22 - 1.0 nm were used in the LOQ diffractometer (time-of-flight) and were recorded on a 64 cm diameter position sensitive detector at 4.3 m from the sample. Scattering vectors between 0.05 and 2.3 nm ~ were obtained, providing information on distance scales from roughly 2 to 100 nm in a single measurement. Wavelength dependent corrections for sample transmission and detector efficiency have been included in the data reduction procedure to obtain a composite cross section in absolute units. In the cases where contrast variation was used, dried silica samples were impregnated with a H 2 0 / D 2 0 mixture (63 vol% D20) to obtain matching conditions.
3. RESULTS AND DISCUSSION.
3.1 Polymerization. Silica is prepared by acidification of water glass, a concentrated solution of silica in water at high pH (pH = 12-14). In water glass, monomeric silica is present as a mixture of ions of silicic acid [1]: Si(OH) 4
~
Si(OH)30-
+ H §
,~
....
~
Si
44- +
4H §
Due to condensation/hydrolysis reactions also dimers and oligomers are present:
36 -Si
-
O-
+
HO
-
Si-
'~
=Si
-
0
-
Si-
+
OH-
with three horizontal bars at Si representing bonds with OH, O or -O-Si-- groups. Because the Si-O-Si angle can very easily be varied between 90 ~ and 150 ~ [6] also 3, 4, 5, or higher membered rings are formed, being precursors for three-dimensional structures as the prismatic hexamer or the cubic octamers. Investigation of the composition of water glass by 29Si NMR is a very appropriate method, because the electron distribution near the silicon nucleus in different surroundings may be easily discerned, especially the chemical shift for the different Q* types of Si atoms. The Q~ nomenclature [7] is based on the number of siloxane bridges Si-(O-Si -- )~ : n = 0, 1, 2, 3 or 4) with Q0, representing monosilicic acid, up to Q4 for fully condensed siloxanes. More than 20 different silica anions have been identified by 29Si-NMR in water glass [8,9]. This situation is even further complicated by the products of condensation/hydrolysis reactions between the numerous species and the dynamic equilibria between them. Because both the pI~ values of the many kinds of --SiOH groups [1] and the reaction rates between the oligomeric species show appreciable differences, small changes in pH, concentration, temperature or the addition of small amounts of cations result in different compositions of water glass. A typical example is the influence of quaternary ammonium ions: tetramethylammoniumhydroxide strongly favours the presence of cubic octamers [ 10,11]. Decreasing the pH of a water glass solution favours condensation over hydrolysis, resulting in bigger oligomers or polymers. Due to the flexible Si-O-Si angles and the resulting tendency for ring formation and cross-linking, three-dimensional polymers are formed. Moreover, because activation energy of hydrolysis or solvolysis reactions is much lower for single bonded groups (Q~) compared to fully condensed species (Q4), the dynamic condensation/hydrolysis equilibria favour ultimately the formation of three-dimensional networks of Q4-type silica atoms. This results in roughly spherical particles with - S i - O H and --Si-O only at the surface, with pH and to a lesser extent also concentration and temperature controlling the -=Si-O/~-Si-OH ratio and therefore reactivity. Also growth of these primary particles depends strongly on surface charge and the catalytic influence of hydroxyl anions (pH) on condensation/hydrolysis reactions, resulting in a maximum radius ranging from 1-2 nm at pH = 2 to 100/zm at pH = 8 [1]. Due to stabilisation by surface charge, in the pH range 710 even stable sols may be formed if the concentration of electrolyte is less than 0.1 M and at low silica concentrations [1].
3.2 Aggregation. At low pH or after screening by electrolytes of negative surface charge, silica particles may form interparticle bonds due to condensation reactions between -SiOH and -SiO- groups on different primary particles. Because the distribution of reactive groups on the surface of the particles is stochastic, directions of particle-particle bonds are rather arbitrary and therefore particle-particle interactions result in teneous aggregates with an amorphous structure. Interactions are not restricted to particleparticle or particle-aggregate bonds, but also interactions between aggregates or clusters of particles are possible, leading to highly ramified and extended aggregates. Polymerization or particle formation and aggregation, however, are no strict sequential processes: both are based on the same (condensation) reaction and
37 therefore are to be considered as competitive processes. Moreover, because OH- is both a reagent and a catalyst for the condensation/hydrolysis reaction, reaction rates at low pH are much lower than at high pH and are comparable to diffusion rates of small particles. Therefore, before elementary particles have been grown to maximum size, aggregates may be formed by either reaction limited or diffusion limited clustercluster aggregation, depending on the ratio between reaction and diffusion rates [2]. If the acidified water glass solution contains sufficient silica, the growing aggregates ultimately contact each other forming a percolating system: the gel. Especially at low pH (small particles) the gel can be visualized as a teneous network of interconnected aggregates with the silica density mainly concentrated in the centra of the aggregates. The branches of the aggregates are relatively thin threads composed of chains of silica particles [12]. Voids between the aggregates or within the branches of the aggregates are still filled with a solution containing silica as monomers, oligomers, elementary particles and small aggregates. After the gelation point this silica is added gradually to the thin threads, reinforcing the weak gelatinous system (to be discussed in 3.6). 3.3 Fractals. To characterize stochastic processes as aggregation and gelation and subsequent transformations during aging, fractal concepts are almost indispensible. Introduced to the scientific community rather recently (Mandelbrot's "The Fractal Geometry of Nature" was published in 1977 [13]), many phenomena in physics, chemistry and biology can be described using fractal principles, including aggregation [2,14]. To explain basic principles of fractal analysis we will use 2-dimensional models of aggregates depicted in figure 1. Figure la. Fractal aggregate, constructed by computer simulated diffusion limited aggregation. Fractal dimension ,~ . D = 1.44
x.X
...:.~: :.:.:.:
:.:. :~ ~:.:
:.:.p:"" ~.,....:
~p:" 9~,.~:
.•.:~-': oO%.SC- -1,..
:.:'--:.: :r
9.:.-:..: .f 9 :':.3": :':...:'." * "~::",..:': :':.2: ;9
9
o %,.~-o
,~
i~
9149 o
.-..-'~: :,:'.~.:
;5
~o
~%hoo
:,:'~,:
, o-9 o-~
.j%~oo
..,:"...:
Figure lb. Deterministic Vicsek fractal constructed of 1, 5, 25 and 125 basic units respectively. Fractal dimension D = 1.465
38 In figure la an aggregate is shown with a mass density gradient: mass distribution in the center is distinctly different (higher average density) compared with the mass density in the periphery. As will be shown in the next paragraphs this mass distribution and its gradient is determined by the physics of the aggregation process and therefore related with the process parameters. Moreover, the aggregate is (in statistical sense) self-similar: the same gradient in density distribution is observed on different length scales, resulting in a characteristic quantity or variable for the density gradient: the fractal dimension. This concept is more easy to understand with the growth of an "artificial aggregate" in figure lb, known as Vicsek's 2d deterministic fractal [14,15]. As shown, this can been constructed by adding repeatedly the figure to its corner points, each iteration resulting in a threefold increase in size R. The "mass" M (= number of points), however, is increasing only fivefold at each step (instead of ninefold according to Euclidean geometry), resulting in the relation M --- R D with D = log5/log3 = 1.465 as can be shown easily [14]. Contrary to mass-size relations in (two-dimensional) Euclidian geometry with M -- R 2, in Vicsek's fractal one is dealing with a non-integer ("fractar') dimension (D = 1.465) for this relation. Concerning the mass distribution fractal systems show a typical behaviour: mass density is not a constant, but is depending on R or any other representative length scale. So, contrary to Euclidian systems as both non-fractal porous and non-porous materials, one can observe a non-zero mass density gradient, described by the fractal dimension D. In non-deterministic fractal systems like the aggregate in figure la, the mass density also decreases with increasing R, but now D (determined with statistical methods [2]) is 1.44 (the corresponding aggregate in 3-dimensional space has D = 1.81). Although shape and morphology are quite different, the fractal dimension D and therefore the decrease in mass density are almost the same in figure la and lb. With the concept of fractal dimension, differences or similarities in mass density distributions between aggregates may be quantified, such as changes due to growth and aging. Therefore the fractal dimension can be considered to be an important parameter to describe aggregation, gelation and aging phenomena in silicas, comparable to other system parameters as, for example, density or porosity.
3.4 Small Angle Scattering. To study growth of primary particles and subsequent aggregation and gelation of these particles in wet systems, most techniques can not be applied. Methods based on NMR or other spectroscopic techniques give information only at atomic or molecular scale and not at (sub)colloidal scale (1 - 100 nm). Moreover, methods requiring the removal of fluids prior to analysis can be discarded because the ramified and fragile structure may be changed or even destroyed during sample preparation. Finally, as shown in the preceding section on fractals, methods have to be found providing information on mass distributions and fractal dimension. Methods based on scattering of radiation satify these requirements. Although scattering of visible light can only be used for transparant systems, scattering of x-rays and neutrons can be applied both for transparent and opaque systems allowing the in situ study of silicas from acidification of water glass up to the dried systems. Because constructive interference between scattered radiation is only possible at interfaces between phases with different electron density (x-rays) or different nuclei (neutrons), it is possible with scattering of radiation to obtain information concerning both the size of primary particles or clusters of particles and the size and fractal mass density of aggregates. To measure aggregates or particles at colloidal scale, however, due to
39 the Bragg relation the interference of x-rays or neutrons can only be observed at very small angles (typically less than 1~ and therefore use has been made of SAXS (Small Angle X-ray Scattering) and SANS (Small Angle Neutron Scattering). High intensity sources, necessary for in situ dynamical experiments, are available at the Synchrotron Radiation Source 'Daresbury Laboratory, UK) and the pulsed neutron source at ISIS (Rutherford Appleton Laboratory, UK) respectively. quadrant or SAXS detector
incoming beam
beam
Figure 2. Schematic picture of set-up of SAXS measurements.
stop
In figure 2 the set-up of a SAXS measurement is sketched. The available 20 -range is determined by the choice of the sample-detector distance (camera length), the height of the beam stop of the primary beam and the height and sensitivity of the detector. To eliminate the dependence on wavelength, the intensity I of the scattered radiation is expressed as function of the scattering vector Q with magnitude IQI = Q = (21r/X)sin20. Because Q -- 1/d (Bragg's Law), the Q-range and therefore also the d-range are determined by the same parameters determining the 20-range, with a long camera length corresponding with measurements at relatively low Q and high d (big particles) values and the other way round for short camera lengths. With variation of camera length between 1 and 4 meters colloidal systems between 1 and 50 nm may be studied. With SANS the camera length is fixed, but the pulsed time-of-flight system provides measurements in roughly the same colloidal range. A very important feature of SAXS and SANS is the direct information concerning fractal properties. Because the number of elementary particles N(R) in a fractal aggregrate is given by N(R) -- (R/R0) D with R0 = radius of primary particle, it can be proved [18,19,20] that I(Q) -- Q-D resulting in a straight line with slope = -D in a log(I)-log(Q) plot. See figure 3. (,,)
(b)
:
log
(c)
- RQ
I
Figure 3. (a) Logaritmic scaling of an aggregate, part of an aggregate, primary particle and part of a primary particle. (b) Log(I)-Log(Q) plot on the same scale and corresponding with (a). R~ and Ro in (a) are approximations for the radius of gyration of the aggregate and the primary particle as measured in (b).
(d)
"-" Ro
-Di
(a)
(d)' ( e ) ~ ~' IlRG
i
llRo
log
" Q
40 Because in fractal aggregates the fractal region is restricted both by the size of the aggregate (upper size Rg) and the size of the primary particle (lower size R0) also the straight line in the log(I)-log(Q) plot has a limited length. The cross-over at the low-Q limit is representative of the size of the fractal aggregate Rg (more accurately: radius of gyration) and the cross-over at the high-Q limit is representative of the radius of the primary particle. The region Q > Q(R0) is the Porod region with slope = -4 in the case of monodisperse and non-fractal primary particles [20,21,22]. As can be concluded from this discussion, log(I)-log(Q) plots of SAXS or SANS spectra may produce inmediately the most important parameters describing growth and development of (fractal) aggregates. The width of the "Q-window", however, in many silica systems is too small to show the full fractal curve. This is often due to the large extension of the fractal range. For example, with the combination of SAXS, USAXS (Ultra Small X-Ray Scattering) and STXM (Scanning Transmission X-Ray Microscopy) we could show that the scale of the fractal range could be observed from approximately 0.5 nm up to 10/~m [23], more than 4 decades! 3.5 Simulation
Since the pioneering work by Jullien et al and Meakin in 1983, computer simulations of fractal growth have given an extremely important contribution to the development and understanding of fractal concepts in growing aggregates (for a review see [2] and [24]). Although the calculation of fractal dimensions or the position of the high- and low-q limits of the fractal region can not be performed using first principles, large scale computer simulations have proven to be very useful in studying the transformation of a "solution" (sol) of particles into a continuous threedimensional network (gel) and to find relations between physical parameters and fractal properties of aggregating, gelating and aging systems. For example, it is rather difficult to predict a priori the change in fractal dimension due to hydrolysis and recondensation of primary particles or small clusters in aggregates or due to growth of primary particles by ring formation [2,25,26]. The concept of diffusion-limited cluster-cluster aggregation (DLCA) is very useful and applied in many simulations. In this type of simulation process, particles are placed in a box and subjected to Brownian (random walk) movements. Aggregation (clustering) may occur when two or more particles/clusters come within the vicinity of each other and the combined cluster continues the random walk. The simulation is stopped at the gelation point (percolating system) or when all particles are combined in one final aggregate. The fractal dimension of the DLCA aggregates is approximately 1.8. In the case when the reactivity is not limited by diffusion, but by the rate of reaction between colliding particles or clusters of particles, the aggregation process becomes reaction limited (RLCA). Although the ramified aggregates appear to be rather similar to the DLCA aggregates, the fractal dimension is increased to 2.1. This can be explained by the observation that during growth the majority of particles, approaching the aggregate, collide with the outermost particles or branches. In this way the inner part of the aggregate is screened rather effectively. However, if only a small percentage of the collisions is successful and results in the formation of a bond, some particles may pass the screening outermost branches and react with branches in the core of the aggregate, resulting in a more compact structure with a smaller mass gradient and higher fractal dimension. Recent calculations [3] have shown that by using differences in reactivity in relation to local coordination a continuous array of D
41 values may be found, limited by D --, 3 (dense structures). Because during aggregation, gelation and aging of silica also a great variety of D values has been found using SAXS or SANS, computer simulation might be an important technique for the interpretation these data. For this reason we developed GRASP, an off-lattice box program for formation of aggregates using cluster-cluster aggregation, combining DLCA and RLCA. The aggregates obtained were introduced to DALAI, a program to calculate SAXS or SANS spectra from the coordinates of scattering particles. The spectra produced by the G R A S P / D ~ combination can be used not only to test the influence of physical parameters upon the SAXS spectrum and to compare the simulated with the experimental spectra, but also to measure the fractal properties dimension D and the radius of gyration Rg of a simulated aggregate easily and reliably [15]. 3.6 Aging. After acidification, aggregation and gelation silica gel is still far from thermodynamic equilibrium. By the dynamic condensation/hydrolysis equilibria a continuous process of dissolving and recondensation of monomers or oligomers of silica will change the network. Due to the difference in surface energy, silica at highly curved surfaces (convex surfaces) will dissolve relatively easy and recondensate preferentially in the "necks" between particles or in the crevices in the centre of the aggregates (concave surfaces). This effect (Ostwald ripening) decreases the number of small particles and smoothens the chains or surfaces of the gel network and is the main contribution to the aging process [1]. During aging the gel network is reinforced considerably and will be stronger in withstanding better the capillary forces during drying resulting in a porous structure of the dried silica. Without sufficient aging the weak gel structure shall collapse during drying and only a microporous silica would be produced [4,27,28]. The influence of aging on local (atomic) scale can be studied by NMR. In 295iNMR the Q3/Q4 ratio, indicative for the ratio between surface and bulk Si atoms, decreases considerably during aging [9] and is in agreement with the model of transfer of Si from convex surfaces to gaps or necks between particles. The decrease in surface area is also observed by the change in spin-spin relaxation ('1"2) of hydrogen 3.50
3.50
regation 3.10
3.10
E
2.70
2.70
~
2.30
2.30
1.90
1.90
F/Si > 0
0
FISi > 0 FISi - 0
Gelation point 1.50 -1.50
. -0.80
.
. -0.10
. 0.60
1.30
2.00
log (Time (hrs))
Figure 4a. Spin-spin relaxation time T2 during aggregation, gelation and aging. pH = 4, conc.(SiO2) = 0.73 M, F/Si - 0.0
1.50 -1.50
. -0.80
.
. -0.10
. 0.60
1.30
2.q
log (Time (hrs))
Figure 4b. As 4a except for F/Si ratios circles: F/Si=0.00; triangles: F/Si=0.01 diamonds: F/Si=0.03; squares: F/Si=0.10
42 atoms of water influenced by the silica surface [29,30,31]. This method is based on the decrease of "['2 when free water is influenced or weakly bonded to a silica surface. As shown in figure 4a, after the steep decrease of I"2 due to the formation of aggregates the curve increases during aging, indicating a (slow) decrease of surface area. If aging is accelerated by addition of fluorine (fluorine ions are a catalyst for hydrolysis/ condensation reactions [1]), the decrease of silica surface is also enhanced (figure 4b). See reference [29] for more details concerning use of relaxation methods to study aging or pore formation. 5 4-1.4- h r s . -
" ..........
~
:3" a
5.0
hrs.
~ -1.9
v
v 0
2 0.5 hrs.
0 -0.80 ,
I
-0.52
I
I
-0.24-
0.04-
=
,
l
0.52
0.60
log ( Q (nm-~)) Figure 5. SAXS spectra of silica with fluorine during aggregation and aging at various times. Gelation point at 0.8 hrs. Conc(SiO2) = 0.73 M, pH = 4.0, F/Si = 0.01. SAXS spectra also confirm Ostwald ripening during aging. In figure 5 three SAXS curves in a log(I)-log(Q) plot are shown at various aging times. The spectra after 0.5 and 5 hours show only the fractal region, the Q values related with aggregate size and size of the primary particles being outside the Q-window of the SAXS apparatus. Therefore, the radius of the primary particles has to be smaller than 1 nm. After 41.4 hrs aging, however, the cross-over between fractal region and Porod region is observed at approximately Q = 0.5 nm 4, corresponding with R0 -~ 5 nm. Ostwald ripening has increased the radius of the building blocks of the aggregates (the primary particles) by at least a factor of 5 [29]. These figures are confirmed by experiments in aggregates from acidified potassium water glass, resulting in Ro ~ 4.5 nm after 1 month aging and also catalysed by fluorine [9]. Aging at pH = 7-8 even shows R0 = 10 nm [9], but probably before aging primary particles have been much larger at this pH compared to pH = 4 [29]. Both aging experiments and SAXS spectra, however, strongly indicate that aging is much more complicated and can not be described using Ostwald ripening alone. For example, in wet gels a considerable shrinking and discharge of water during aging is also observed. To explain this phenomenon one has to assume changes in the structure at a relatively big scale compared to smoothing of branches by hydrolysis/recondensation equilibria. Moreover, in many experiments SAXS spectra
43 show a decrease of the fractal dimension during aging although both from intuition and from simulations [3,25,26] an increase had to be expected during restructuring. To relate hypothetical aging mechanisms with information obtained from SAXS spectra computer simulations proved to be extremely informative. To explain the growth of primary particles and the (slight) decrease of the fractal dimension during aging, an aging mechanism was postulated. This was based on the solvolysis of primary particles at the periphery of the.aggregates (dissolution of the outermost branches), migration by diffusion towards the center of the aggregates and recombination in the inner crevices. Simulations with the GRASP/DALAI combination, however, showed very clearly that solvolysed particles will probably will never arrive at the center of the aggregates: during the random walk they will stick on the ramified branches. Even worse, if no preference for hydrolysis is given to the outermost particles, the aggregates become more ramified during aging. Much more succesfull were recent simulations based upon ring formation [32]. In this model single bonded particles were allowed to perform small movements with respect to each other, resulting in reinforcement of the thin branches by the formation of rings. In figure 6 fractal dimensions are shown, extracted from the SAXS spectrum which was calculated from the simulated aggregates before and after aging according to local ring formation. The fractal dimension D = 1.45 before aging has decreased to 1.26 at low Q (large scale effects) and increased to 1.87 at high Q (local effect). Recently we confirmed these results with SAXS experiments on aging silica [33]. In figure 7 the experimental log(I)-log(Q) plots show the same pattern: the fractal dimension D = 2.2 (corresponding with D = 1.45 in 2 dimensions) after short aging, shows a decrease at low Q and an increase at high Q after prolonged aging. These results can be explained assuming different effects of local reorganizations at small and large length scales. See figure 8. At small scale (scale a) the density of silica has increased resulting in a lower density gradient and therefore an increase in le+08
"
-
i
-
-
-
w
-
-
-
/i
-
J
-
!
.
.
I
,
,
1e+07
le+06
%
N~\
o,-,~
t000o0 N
",
Op = i.87
10000 Ro
1 0 0 0
0.0(31
9
9
I
0.01
9
,
,
I
-
.
9
0.1
9
I
t
9
.
10
10{3
q
Figure 6. Simulated SAXS curves before and after aging by local ring formation.
44 1.00
2.05
-q.,= "-I
0.40 v
>., 09 t,.(11 t,-
-0.20
L..,
"~*-t Q4 =o~.o ~~"="'~o,..~.o,,..
/
-0.80
_..,.
r 0
2.35
2.2
o
-1.40
--,,,, . -2.00 -1.50
. . . . . . . . .
I
- 1.30
1
_
- 1.10
I
I
-0.90
-0.70
.*
-0.50
log Q (~-1)
Figure 7. SAXS curves of silica gels aged for various times" (a) 1 week, (b) 2.5 months, (c) 5 months. Conc.(SiO2) = 0.73 M (4 wt%), pH = 4.0.
non-aged
aged
C
Figure 8. Pictural view of aging by local increase in density. fractal dimension. At large scale (scale c), however, mass is even more concentrated in the "linear" branches without changing the overall morphology and therefore resulting in an increase of the mass gradient and corresponding decrease of D. Although we do not believe ring formation is the only aging mechanism, the agreement with fractal properties of aged systems indicates that ring formation problably makes an important contribution to aging. 3.7 Pore formation.
Although during aging reorganizations of silica reinforce the ramified and teneous network, it is difficult to show formation of pores during aging with SAXS or SANS. According to the Babinet principle [17], the dispersed component in a two-phase system is scattering and in wet gels therefore always scattering by silica is recorded.
45 On the contrary, in dried gels the pores are the dispersed component and therefore pores had to be investigated by SAXS and SANS only in freeze-dried gels. As shown [4,29], freeze-drying was necessary to avoid collapse of the ramified system by capillary forces during drying, especially in gels with short aging times. Because with SANS contrast variation using HzO/D20 mixtures could be applied, with this method we were also able to prove scattering was caused by pores and not by silica [22]. Log(I)-log(Q) plots of SANS spectra of aged and freeze-dried silicas showed rather low fractal dimensions (D = 1.4 - 1.5). See figure 9 for a typical spectrum. The low fractal dimension corresponds very well to an aging mechanisms according to figure 8, because the decreasing volume density of pores from the core to the outer parts of the aggregates may be expected if the main branches are preferentially reinforced, creating many pores near the centre [22]. In figure 10 the relation between D and the distribution of pores is explained in 2-dimensional examples.
5.00 >.,
1.,_50
09 c (1.) c-
o-~ o
-1.4
0.00
-1.50
-2.40
-1.80
-1.20
-0.60
Jog e Figure 9. SANS spectrum of dried gel after aging for 1 hour at 80~ D=
1
D=
1.5
in wet gel state. D=2
.' . ) r ~ %
.. \
/ 9 .,,~ ~ . y . . . /
\ \' . "o' . "' o. ' ' _ ' :/ . ' 7 Figure 10. 2-dimensional models of pore distribution depending on D. D = 1: high pore density gradient and highest density at the center. D = 1.5: moderate pore density gradient. D = 2 (Euclidean geometry): no pore density gradient.
46 As already published [1,4,12,29] accelaration of gelation and aging by fluorine results both in different SAXS spectra of wet systems and in different surface area and pore structure of dried gels. In figure 11 we have compared systematically aging with fluorine and aging at 80 ~ Pore radii have been measured both with SANS (using
90 o<( oo D
=..-
60
-8 C) 9
5O
o rl
0
1100
2200
Aging time
5500
(rain.)
Figure 11. Pore radii determined by SANS (squares) and BET (diamonds) after aging at 80~ (open symbols) and with fluorine (closed symbols). 500 z',-
300
(o)
375
(b)
200
250 >
100
125 0
0.00
0.25
0.50
PlPo (')
0.75
1.00
0 0.00
0.25
0.50
O. 75
1.00
P/Po (')
Figure 12. Adsorption/desorption hysteresis curves for gel aged at 80~ aged with fluorine (right).
(left) and gel
the low-Q cross-over point in the log(I)-log(Q) plot) and with physisorption (BET) as a function of aging. The gels at 80 ~ showed reasonable agreement between the pore sizes obtained from scattering data and from BET. The deviations may be explained by assuming the presence of non-interconnected pores. Clearly the deviations are much bigger in the fluorine catalysed system. This bad conformity can probably be assigned to the presence of slit-like pores as can be deducted from the
47 adsorption/desorption hysteresis curve (figure 12) according to the classification of de Boer (type B) [35]. The radius determined with BET is the distance between the walls of the slit, but with SANS we are measuring the radius of gyration with contributions also of the depth of the slit. Therefore SANS-radius > BET-radius, in accordance with results presented in figure 11. 4. Conclusions.
To study aggregation, gelation and aging of silica, prepared by acidification of water glass, both NMR and scattering spectroscopy proved to be very efficient methods. With 29Si-NMR reactions at molecular scale could be studied using shifts in Qn ratios. Especially Q3/Q4 (ratio between surface- and bulk-silica) was very useful describing aging reactions. On colloidal scale 'H-relaxation time (T2) of water could be used to characterize silica conversions, with T2 decreasing during aggregation and increasing again by loss of silica area during aging. Studying aggregation and aging on colloidal scale SAXS was very informative, with the fractal dimension D representing silica transformations. To interpretate changes of D during aging, computer simulations were indispensable providing calculations of simulated spectra corresponding to various possible aging mechanisms. In dried and porous silicas care has to be taken in comparing SANS and BET results because radius of gyration (SANS) and pore radius (BET) might be different, depending on the shape of the pores. Acknowledgements.
Financial support (W.H.D. and H.F.v.G.) was given by the Dutch Department of Economic Affairs, as part of the "IOP-Katalyse" programme. Beam time both at Daresbury Laboratory and Rutherford Appleton Laboratory were provided by the SERC/NWO agreement on use of synchrotron radiation and pulsed neutron source respectively. We thank Drs. Wim Bras (NWO/SERC) for his assistance at SAXS and dr. Richard Heenan (SERC) for his assistance at SANS. Minispec experiments were performed at Bruker Spectrospin N.V., Wormer, The Netherlands and we appreciate the assistance of Piet Ruigrok.
REFERENCES.
[1] [2] [3] [4]
[5] [6] [7]
R.K. Iler, "The Chemistry of Silica", John Wiley & Sons Inc., New York, 1979. R. Jullien and R. Botet, "Aggregation and Fractal Aggregates", World Scientific, Singapore, 1987. M. Kalalla, R.Jullien and B. Cabane, J.Phys.II(France), 2 (1992) 7 P.W.J.G. Wijnen, T.P.M. Beelen, C.P.J. Rummens, H.C.P.L. Saeijs, J.W. de Haan, L.J.M. van de Ven and R.A. van Santen, J.Coll.Interf.Sci., 145 (1991) 17. C.G. Vonk, J.Appl.Cryst., 6 (1973) 81 B.W.H. van Beest, J. Verbeek and R.A. van Santen, Catal.Lett.,_l (1988) 147 G. Engelhardt, H. Jancke, M. M~igi, T. Pehk and E. Lippmaa, J.Organo-Met. Chem., 28 (1971) 293
48
[81 [91 [10] [111 [121 [13] [141 [15] [16] [171
[~8] [191 [20] [21] [22] [23] [24]
[251 [26] [271 [281 [291 [30] [31]
[32] [34]
[35]
C.T.G. Knight, J. Chem. Soc., Dalton Trans. (1988) 1457. C.T.G. Knight, R.J. Kirkpatrick and E. Oldfield, J. Chem. Soc., Chem. Comm. (1989) 919. P.W.J.G. Wijnen, T.P.M. Beelen, J.W. de Haan, L.J.M. van de Ven and R.A. van Santen, Coll. Surf., 4__55(1990) 255. I. Hasegawa, S. Sakka, Y. Sugahara, K. Kuroda and C. Kato, J. Chem. Soc., Chem. Comm. (1989) 208. T.P.M. Beelen, P.W.J.G. Wijnen, C.P.J. Rummens and R.A. van Santen, "Better Ceramics through Chemistry IV", MRS Symp. Proc. 180, (1990) 273. B.B. Mandelbrot, "The Fractal Geometry of Nature", Freeman, New York, 1977. T. Vicsek, "Fractal Growth Phenomena" (2e Ed.), World Scientific, Singapore, 1992 H.F. van Garderen, W.H. Dokter, T.P.M. Beelen, R.A. van Santen and E.Pantos, to be published in Modell.Simul.Mater.Sci.Eng., 2 (3) May 1994 A. Guinier and G. Fournet, "Small-Angle Scattering of X-rays", J.Wiley and Sons, New York (1955) O. Glatter and O. Kratky, "Small Angle X-ray Scattering", Academic Press, London (1982) T. Freltoft, J.K. Kjems and S.K. Sinha, Phys.Rev.B, 33 269 J. Teixeira in "On Growth and Form", H.E. Stanley and N. Ostrowski, Eds., M. Nijhoff, Dordrecht (1986), 145. J.E. Martin and A.J. Hurd, J. Appl. Cryst., 2__9_0(1987) 61. J.D.F. Ramsay, Chem. Soc. Rev., 15 (1986) 335. W.H. Dokter, T.P.M. Beelen, H.F. van Garderen and R.A. van Santen, accepted for publication Symp.Proc. COPS III, Marseille 1993 T.P.M. Beelen, W.H. Dokter, H.F. van Garderen, R.A. van Santen, M.T. Browne and G.R. Morrison, "Better Ceramics through Chemistry V", MRS Symp. Proc. 271 (1992) 263. P. Meakin, Physica Scripta 46 (1992) 295 P. Meakin, J.Chem.Phys., 83 (1985) 3645 P. Meakin, J.Coll.Interf.Sci., 112 (1986) 187 L.L. Hench and J.K. West, Chem. Rev. 90 (1990) 33. C.J. Brinker and G.W. Scherer, "Sol-gel Science", Academic Press, San Diego, 1990. W.H. Dokter, H.F. van Garderen, T.P.M. Beelen, J.W. de Haan, L.J.M. van de Ven and R.A. van Santen, Coll. & Surf.A, 72 (1993) 165 D.P. Gallegos, D.M. Smith and C.J. Brinker, J.Coll.Interf.Sci., 124 (1988) 186 and references cited therein. C.L. Glaves, C.J. Brinker, D.M. Smith and P.J. Davis, Chem.Mat., 1 (1989) 34. H.F. van Garderen, E. Pantos, W.H. Dokter, T.P.M. Beelen, M.A.J. Michels, P.A.J. Hilbers and R.A. van Santen, submitted J.Chem.Phys. W.H. Dokter, T.P.M. Beelen, H.F. van Garderen and R.A. van Santen, submitted to "Better Ceramics through Chemistry vr', MRS Symp.Proc. (1994) J.C.P. Broekhof and R.H. van Dongen in "Physical and chemical Aspects of Adsorbents and Catalysts", B.G. Linssen (Ed.), Academic Press, London (1970), 1-59
33
The Role of Aging on the Formation of Porous Silica T.P.M. Beelen, W.H. Dokter, H.F. van Garderen, R.A. van Santen and E. Pantos a Schuit Institute of Catalysis, Eindhoven University of Technology, P.O. Box 513, 5600 MB EINDHOVEN, The Netherlands "Daresbury Laboratory, Daresbury, Warrington WA4 4AD, U.K.
Abstract. Porous silica gel has been prepared by acidification of water glass. To study aggregation, gelation and aging use has been made of 29Si-NMR to investigate silica transformations on molecular scale. Q* ratios were used to define distribution of silica in particles and gels. On colloidal scale both IH relaxation of water and small angle scattering (SAXS, SANS) was very informative, especially because changes in fractal dimension could be used to describe silica transformations during aggregation and aging. Interpretation of fractal dimension in terms of aging mechanisms is performed by computer simulations of both aggregation/aging processes and calculation of the corresponding scattering spectra. Comparison of simulated spectra of aged silica, based on hypothetical aging mechanisms, with experimental spectra emphasized the important role of formation of rings on local scale. In freeze-dried silicas pore distributions were investigated with both neutron scattering (SANS) and physisorption (BET), revealing different pore structures, both in growth and form, after aging at 80~ and aging catalyzed by fluorine. 1. INTRODUCTION. Amorphous silica gels exhibit a large diversity in structural properties. To be used as a supporting agent in heterogeneous catalysis, high specific Surface and high stability is necessary. Moreover, for many applications in selective catalysis a tailormade porous structure is necessary or very desirable. When silica is prepared by acidification of water glass (alkali solution of silica), polycondensation reactions occur between dissolved oligomeric silica species, resulting in (sub)colloidal particles [1]. These primary particles combine to very ramified aggregates, a process described by diffusion or reaction limited cluster-cluster aggregation with power-law dependent density (fractals) [2,3]. After gelation the fractal structure is still preserved at sub-micrometer scale, while at l a r g e r scale Euclidean behaviour is observed. After drying, these systems often appear to be microporous because in general the fractal structures are too weak to resist capillary forces or even gravity and the fragile aggregates collapse during the drying process. Therefore, reinforcement of the weak and teneous structures aging processes is necessary [1,4]. During aging silica is redistributed in the gel. Although this redistribution is based on hydrolysis/recondensation reactions of silica monomers, oligomers or particles, depending on process parameters (temperature, concentration, pH, catalysts) many transformations and structures may be formed, resulting in a wide selection of porous
34 structures. The investigation of aging mechanisms is quite challenging. Although understanding aging reactions is necessary to prepare tailor-made porous silicas on a scientific basis, the choice of proper methods is difficult, especially because of the vulnerability of the fragile system only very few methods may be used, while the extended length scale (more than 4 decades: from sub-nanometer to a few microns) requirs the combination of several techniques. At molecular scale we have chosen NMR because recent developments in both 295iNMR and spin-spin relaxation on hydrogen atoms made applications for silicas in colloidal systems possible. For the colloidal scale both the availability of synchrotron radiation providing a high-brilliance source for x-rays and the development of highintensity neutron sources made scattering methods with x-rays (SAXS) and neutrons (SANS) very suitable and opened new possibilities for studying mass density distributions during aggregation and aging processes, using fractal concepts to quantify these transformations and mass distributions. Extremely helpful in interpretation of scattering results proved to be computer simulations, forming a bridge between experimental results and explanations based on simulations of transformations of silica during aging. With the combination of computer programs (GRASP and DALAI) both aggregation and aging and the corresponding scattering spectra can be simulated, allowing an immediate check of mechanistical hypotheses with experimental spectra. As will be shown in this paper, combination of scattering methods and simulation is a new and very promising tool to study transformations in colloidal systems and may be applied succesfully in investigations in the preparation of porous materials.
2. EXPERIMENTAL SECTION. Water glass solutions were prepared by dissolution of amorphous silica (Aerosil 200 and 380, gracefully obtained from Degussa AG) in sodium hydroxide (Merck p.a. using teflon or polyethylene beakers. In a typical experiment the overall molar composition was chosen to be SiO2 : NaOH : H20 = 3 : 2 : 125. Silica gels were prepared by acidification of the alkaline silica solutions. The water glass solution was dosed drop by drop with a Pasteur pipette to a solution of 1.0 M HC1 while stirring vigorously, until pH = 4.0 was reached and the stirring was stopped. Gelation time was definied by the period of time lapsed between the end of acidification and the moment when no meniscus deformation could be observed on twisting the beaker. To avoid evaporation, aging was performed in closed containers. When the catalytic influence of fluorine was investigated, before acidification appropriate quantities of NaF were added to the HC1 solution. To avoid collapse of the fragile structure during drying, freeze drying was applied. After precooling to -40~ for at least 3 hours, small samples of the frozen gel (typically 5 g wet gel) were connected to a Labconco Lab-top freeze dryer operating at 900 Pa and -75~ condensor temperature during 24-48 hours. To remove NaC1 the gels were washed with circa 250 ml doubly distilled water. Dried gels were characterized by physical adsorption/desorption of nitrogen (BET) after outgassing under vacuum for 16 hours at 180~ Sorption measurements were performed on a Carlo Erba Strumentazione Sorptomatic 1900 using liquid nitrogen as sorbent. Typical adsorption/desorption runs demanded 8 hours of analysis. Care was taken that the equilibrium pressure was reached before introduction or withdrawal of
35 a calibrated volume of nitrogen. 29Si-NMR experiments were performed on a Bruker CXP-300 FT-NMR instrument operating at 7.05 T at room temperature. Magic angle sample spinning (MAS) was applied to average any chemical shift anisotropy arising in gelated and freeze dried samples. Spin-spin relaxation times have been determined by the Carr-Purcell-Meiboom-Gill 90~176 sequenze at a frequenzy of 20 MHz using a Bruker Minispec pcl00 at a field strength of 0.47 T. The operational temperature was 40~ in order to prevent temperature changes due to external influences. All samples were stored at 40~ The magnetization curve was analyzed using a monoexponential fit. A multiexponential technique yielded no perceivable improvement of the quality of the fit. SAXS experiments were performed at the Synchrotron Radiation Source at Daresbury Laboratories (United Kingdom) using NCD beamline 8.2. Wet gels and solutions were measured in closed cells with mylar windows (spacing 0.2 - 0.5 mm), dried gels were fixed at cellotape. With wavelength fixed at 0.15 nm, variation of camera length (sample to detector distance) between 1.0 and 4.0 m and appropriate positioning of the beamstop, the Q-range between 0.05 and 2.5 nm ~ could be covered. To enhance sensitivity at low Q a quadrant detector was used. Satisfactory signal to noise ratios were obtained with acquisition times between 1 and 5 minutes. Subtraction of parasitic (slits) and background scattering (water solution, mylar windows, cellotape) was applied using the procedure introduced by Vonk [5], adapted to fractal systems. SANS experiments were performed at the Rutherford Appleton Laboratory, ISIS facility, Abingdom, U.K. Pulsed neutrons with wavelengths between 0.22 - 1.0 nm were used in the LOQ diffractometer (time-of-flight) and were recorded on a 64 cm diameter position sensitive detector at 4.3 m from the sample. Scattering vectors between 0.05 and 2.3 nm ~ were obtained, providing information on distance scales from roughly 2 to 100 nm in a single measurement. Wavelength dependent corrections for sample transmission and detector efficiency have been included in the data reduction procedure to obtain a composite cross section in absolute units. In the cases where contrast variation was used, dried silica samples were impregnated with a H 2 0 / D 2 0 mixture (63 vol% D20) to obtain matching conditions.
3. RESULTS AND DISCUSSION.
3.1 Polymerization. Silica is prepared by acidification of water glass, a concentrated solution of silica in water at high pH (pH = 12-14). In water glass, monomeric silica is present as a mixture of ions of silicic acid [1]: Si(OH) 4
~
Si(OH)30-
+ H §
,~
....
~
Si
44- +
4H §
Due to condensation/hydrolysis reactions also dimers and oligomers are present:
36 -Si
-
O-
+
HO
-
Si-
'~
=Si
-
0
-
Si-
+
OH-
with three horizontal bars at Si representing bonds with OH, O or -O-Si-- groups. Because the Si-O-Si angle can very easily be varied between 90 ~ and 150 ~ [6] also 3, 4, 5, or higher membered rings are formed, being precursors for three-dimensional structures as the prismatic hexamer or the cubic octamers. Investigation of the composition of water glass by 29Si NMR is a very appropriate method, because the electron distribution near the silicon nucleus in different surroundings may be easily discerned, especially the chemical shift for the different Q* types of Si atoms. The Q~ nomenclature [7] is based on the number of siloxane bridges Si-(O-Si -- )~ : n = 0, 1, 2, 3 or 4) with Q0, representing monosilicic acid, up to Q4 for fully condensed siloxanes. More than 20 different silica anions have been identified by 29Si-NMR in water glass [8,9]. This situation is even further complicated by the products of condensation/hydrolysis reactions between the numerous species and the dynamic equilibria between them. Because both the pI~ values of the many kinds of --SiOH groups [1] and the reaction rates between the oligomeric species show appreciable differences, small changes in pH, concentration, temperature or the addition of small amounts of cations result in different compositions of water glass. A typical example is the influence of quaternary ammonium ions: tetramethylammoniumhydroxide strongly favours the presence of cubic octamers [ 10,11]. Decreasing the pH of a water glass solution favours condensation over hydrolysis, resulting in bigger oligomers or polymers. Due to the flexible Si-O-Si angles and the resulting tendency for ring formation and cross-linking, three-dimensional polymers are formed. Moreover, because activation energy of hydrolysis or solvolysis reactions is much lower for single bonded groups (Q~) compared to fully condensed species (Q4), the dynamic condensation/hydrolysis equilibria favour ultimately the formation of three-dimensional networks of Q4-type silica atoms. This results in roughly spherical particles with - S i - O H and --Si-O only at the surface, with pH and to a lesser extent also concentration and temperature controlling the -=Si-O/~-Si-OH ratio and therefore reactivity. Also growth of these primary particles depends strongly on surface charge and the catalytic influence of hydroxyl anions (pH) on condensation/hydrolysis reactions, resulting in a maximum radius ranging from 1-2 nm at pH = 2 to 100/zm at pH = 8 [1]. Due to stabilisation by surface charge, in the pH range 710 even stable sols may be formed if the concentration of electrolyte is less than 0.1 M and at low silica concentrations [1].
3.2 Aggregation. At low pH or after screening by electrolytes of negative surface charge, silica particles may form interparticle bonds due to condensation reactions between -SiOH and -SiO- groups on different primary particles. Because the distribution of reactive groups on the surface of the particles is stochastic, directions of particle-particle bonds are rather arbitrary and therefore particle-particle interactions result in teneous aggregates with an amorphous structure. Interactions are not restricted to particleparticle or particle-aggregate bonds, but also interactions between aggregates or clusters of particles are possible, leading to highly ramified and extended aggregates. Polymerization or particle formation and aggregation, however, are no strict sequential processes: both are based on the same (condensation) reaction and
37 therefore are to be considered as competitive processes. Moreover, because OH- is both a reagent and a catalyst for the condensation/hydrolysis reaction, reaction rates at low pH are much lower than at high pH and are comparable to diffusion rates of small particles. Therefore, before elementary particles have been grown to maximum size, aggregates may be formed by either reaction limited or diffusion limited clustercluster aggregation, depending on the ratio between reaction and diffusion rates [2]. If the acidified water glass solution contains sufficient silica, the growing aggregates ultimately contact each other forming a percolating system: the gel. Especially at low pH (small particles) the gel can be visualized as a teneous network of interconnected aggregates with the silica density mainly concentrated in the centra of the aggregates. The branches of the aggregates are relatively thin threads composed of chains of silica particles [12]. Voids between the aggregates or within the branches of the aggregates are still filled with a solution containing silica as monomers, oligomers, elementary particles and small aggregates. After the gelation point this silica is added gradually to the thin threads, reinforcing the weak gelatinous system (to be discussed in 3.6). 3.3 Fractals. To characterize stochastic processes as aggregation and gelation and subsequent transformations during aging, fractal concepts are almost indispensible. Introduced to the scientific community rather recently (Mandelbrot's "The Fractal Geometry of Nature" was published in 1977 [13]), many phenomena in physics, chemistry and biology can be described using fractal principles, including aggregation [2,14]. To explain basic principles of fractal analysis we will use 2-dimensional models of aggregates depicted in figure 1. Figure la. Fractal aggregate, constructed by computer simulated diffusion limited aggregation. Fractal dimension ,~ . D = 1.44
x.X
...:.~: :.:.:.:
:.:. :~ ~:.:
:.:.p:"" ~.,....:
~p:" 9~,.~:
.•.:~-': oO%.SC- -1,..
:.:'--:.: :r
9.:.-:..: .f 9 :':.3": :':...:'." * "~::",..:': :':.2: ;9
9
o %,.~-o
,~
i~
9149 o
.-..-'~: :,:'.~.:
;5
~o
~%hoo
:,:'~,:
, o-9 o-~
.j%~oo
..,:"...:
Figure lb. Deterministic Vicsek fractal constructed of 1, 5, 25 and 125 basic units respectively. Fractal dimension D = 1.465
38 In figure la an aggregate is shown with a mass density gradient: mass distribution in the center is distinctly different (higher average density) compared with the mass density in the periphery. As will be shown in the next paragraphs this mass distribution and its gradient is determined by the physics of the aggregation process and therefore related with the process parameters. Moreover, the aggregate is (in statistical sense) self-similar: the same gradient in density distribution is observed on different length scales, resulting in a characteristic quantity or variable for the density gradient: the fractal dimension. This concept is more easy to understand with the growth of an "artificial aggregate" in figure lb, known as Vicsek's 2d deterministic fractal [14,15]. As shown, this can been constructed by adding repeatedly the figure to its corner points, each iteration resulting in a threefold increase in size R. The "mass" M (= number of points), however, is increasing only fivefold at each step (instead of ninefold according to Euclidean geometry), resulting in the relation M --- R D with D = log5/log3 = 1.465 as can be shown easily [14]. Contrary to mass-size relations in (two-dimensional) Euclidian geometry with M -- R 2, in Vicsek's fractal one is dealing with a non-integer ("fractar') dimension (D = 1.465) for this relation. Concerning the mass distribution fractal systems show a typical behaviour: mass density is not a constant, but is depending on R or any other representative length scale. So, contrary to Euclidian systems as both non-fractal porous and non-porous materials, one can observe a non-zero mass density gradient, described by the fractal dimension D. In non-deterministic fractal systems like the aggregate in figure la, the mass density also decreases with increasing R, but now D (determined with statistical methods [2]) is 1.44 (the corresponding aggregate in 3-dimensional space has D = 1.81). Although shape and morphology are quite different, the fractal dimension D and therefore the decrease in mass density are almost the same in figure la and lb. With the concept of fractal dimension, differences or similarities in mass density distributions between aggregates may be quantified, such as changes due to growth and aging. Therefore the fractal dimension can be considered to be an important parameter to describe aggregation, gelation and aging phenomena in silicas, comparable to other system parameters as, for example, density or porosity.
3.4 Small Angle Scattering. To study growth of primary particles and subsequent aggregation and gelation of these particles in wet systems, most techniques can not be applied. Methods based on NMR or other spectroscopic techniques give information only at atomic or molecular scale and not at (sub)colloidal scale (1 - 100 nm). Moreover, methods requiring the removal of fluids prior to analysis can be discarded because the ramified and fragile structure may be changed or even destroyed during sample preparation. Finally, as shown in the preceding section on fractals, methods have to be found providing information on mass distributions and fractal dimension. Methods based on scattering of radiation satify these requirements. Although scattering of visible light can only be used for transparant systems, scattering of x-rays and neutrons can be applied both for transparent and opaque systems allowing the in situ study of silicas from acidification of water glass up to the dried systems. Because constructive interference between scattered radiation is only possible at interfaces between phases with different electron density (x-rays) or different nuclei (neutrons), it is possible with scattering of radiation to obtain information concerning both the size of primary particles or clusters of particles and the size and fractal mass density of aggregates. To measure aggregates or particles at colloidal scale, however, due to
39 the Bragg relation the interference of x-rays or neutrons can only be observed at very small angles (typically less than 1~ and therefore use has been made of SAXS (Small Angle X-ray Scattering) and SANS (Small Angle Neutron Scattering). High intensity sources, necessary for in situ dynamical experiments, are available at the Synchrotron Radiation Source 'Daresbury Laboratory, UK) and the pulsed neutron source at ISIS (Rutherford Appleton Laboratory, UK) respectively. quadrant or SAXS detector
incoming beam
beam
Figure 2. Schematic picture of set-up of SAXS measurements.
stop
In figure 2 the set-up of a SAXS measurement is sketched. The available 20 -range is determined by the choice of the sample-detector distance (camera length), the height of the beam stop of the primary beam and the height and sensitivity of the detector. To eliminate the dependence on wavelength, the intensity I of the scattered radiation is expressed as function of the scattering vector Q with magnitude IQI = Q = (21r/X)sin20. Because Q -- 1/d (Bragg's Law), the Q-range and therefore also the d-range are determined by the same parameters determining the 20-range, with a long camera length corresponding with measurements at relatively low Q and high d (big particles) values and the other way round for short camera lengths. With variation of camera length between 1 and 4 meters colloidal systems between 1 and 50 nm may be studied. With SANS the camera length is fixed, but the pulsed time-of-flight system provides measurements in roughly the same colloidal range. A very important feature of SAXS and SANS is the direct information concerning fractal properties. Because the number of elementary particles N(R) in a fractal aggregrate is given by N(R) -- (R/R0) D with R0 = radius of primary particle, it can be proved [18,19,20] that I(Q) -- Q-D resulting in a straight line with slope = -D in a log(I)-log(Q) plot. See figure 3. (,,)
(b)
:
log
(c)
- RQ
I
Figure 3. (a) Logaritmic scaling of an aggregate, part of an aggregate, primary particle and part of a primary particle. (b) Log(I)-Log(Q) plot on the same scale and corresponding with (a). R~ and Ro in (a) are approximations for the radius of gyration of the aggregate and the primary particle as measured in (b).
(d)
"-" Ro
-Di
(a)
(d)' ( e ) ~ ~' IlRG
i
llRo
log
" Q
40 Because in fractal aggregates the fractal region is restricted both by the size of the aggregate (upper size Rg) and the size of the primary particle (lower size R0) also the straight line in the log(I)-log(Q) plot has a limited length. The cross-over at the low-Q limit is representative of the size of the fractal aggregate Rg (more accurately: radius of gyration) and the cross-over at the high-Q limit is representative of the radius of the primary particle. The region Q > Q(R0) is the Porod region with slope = -4 in the case of monodisperse and non-fractal primary particles [20,21,22]. As can be concluded from this discussion, log(I)-log(Q) plots of SAXS or SANS spectra may produce inmediately the most important parameters describing growth and development of (fractal) aggregates. The width of the "Q-window", however, in many silica systems is too small to show the full fractal curve. This is often due to the large extension of the fractal range. For example, with the combination of SAXS, USAXS (Ultra Small X-Ray Scattering) and STXM (Scanning Transmission X-Ray Microscopy) we could show that the scale of the fractal range could be observed from approximately 0.5 nm up to 10/~m [23], more than 4 decades! 3.5 Simulation
Since the pioneering work by Jullien et al and Meakin in 1983, computer simulations of fractal growth have given an extremely important contribution to the development and understanding of fractal concepts in growing aggregates (for a review see [2] and [24]). Although the calculation of fractal dimensions or the position of the high- and low-q limits of the fractal region can not be performed using first principles, large scale computer simulations have proven to be very useful in studying the transformation of a "solution" (sol) of particles into a continuous threedimensional network (gel) and to find relations between physical parameters and fractal properties of aggregating, gelating and aging systems. For example, it is rather difficult to predict a priori the change in fractal dimension due to hydrolysis and recondensation of primary particles or small clusters in aggregates or due to growth of primary particles by ring formation [2,25,26]. The concept of diffusion-limited cluster-cluster aggregation (DLCA) is very useful and applied in many simulations. In this type of simulation process, particles are placed in a box and subjected to Brownian (random walk) movements. Aggregation (clustering) may occur when two or more particles/clusters come within the vicinity of each other and the combined cluster continues the random walk. The simulation is stopped at the gelation point (percolating system) or when all particles are combined in one final aggregate. The fractal dimension of the DLCA aggregates is approximately 1.8. In the case when the reactivity is not limited by diffusion, but by the rate of reaction between colliding particles or clusters of particles, the aggregation process becomes reaction limited (RLCA). Although the ramified aggregates appear to be rather similar to the DLCA aggregates, the fractal dimension is increased to 2.1. This can be explained by the observation that during growth the majority of particles, approaching the aggregate, collide with the outermost particles or branches. In this way the inner part of the aggregate is screened rather effectively. However, if only a small percentage of the collisions is successful and results in the formation of a bond, some particles may pass the screening outermost branches and react with branches in the core of the aggregate, resulting in a more compact structure with a smaller mass gradient and higher fractal dimension. Recent calculations [3] have shown that by using differences in reactivity in relation to local coordination a continuous array of D
41 values may be found, limited by D --, 3 (dense structures). Because during aggregation, gelation and aging of silica also a great variety of D values has been found using SAXS or SANS, computer simulation might be an important technique for the interpretation these data. For this reason we developed GRASP, an off-lattice box program for formation of aggregates using cluster-cluster aggregation, combining DLCA and RLCA. The aggregates obtained were introduced to DALAI, a program to calculate SAXS or SANS spectra from the coordinates of scattering particles. The spectra produced by the G R A S P / D ~ combination can be used not only to test the influence of physical parameters upon the SAXS spectrum and to compare the simulated with the experimental spectra, but also to measure the fractal properties dimension D and the radius of gyration Rg of a simulated aggregate easily and reliably [15]. 3.6 Aging. After acidification, aggregation and gelation silica gel is still far from thermodynamic equilibrium. By the dynamic condensation/hydrolysis equilibria a continuous process of dissolving and recondensation of monomers or oligomers of silica will change the network. Due to the difference in surface energy, silica at highly curved surfaces (convex surfaces) will dissolve relatively easy and recondensate preferentially in the "necks" between particles or in the crevices in the centre of the aggregates (concave surfaces). This effect (Ostwald ripening) decreases the number of small particles and smoothens the chains or surfaces of the gel network and is the main contribution to the aging process [1]. During aging the gel network is reinforced considerably and will be stronger in withstanding better the capillary forces during drying resulting in a porous structure of the dried silica. Without sufficient aging the weak gel structure shall collapse during drying and only a microporous silica would be produced [4,27,28]. The influence of aging on local (atomic) scale can be studied by NMR. In 295iNMR the Q3/Q4 ratio, indicative for the ratio between surface and bulk Si atoms, decreases considerably during aging [9] and is in agreement with the model of transfer of Si from convex surfaces to gaps or necks between particles. The decrease in surface area is also observed by the change in spin-spin relaxation ('1"2) of hydrogen 3.50
3.50
regation 3.10
3.10
E
2.70
2.70
~
2.30
2.30
1.90
1.90
F/Si > 0
0
FISi > 0 FISi - 0
Gelation point 1.50 -1.50
. -0.80
.
. -0.10
. 0.60
1.30
2.00
log (Time (hrs))
Figure 4a. Spin-spin relaxation time T2 during aggregation, gelation and aging. pH = 4, conc.(SiO2) = 0.73 M, F/Si - 0.0
1.50 -1.50
. -0.80
.
. -0.10
. 0.60
1.30
2.q
log (Time (hrs))
Figure 4b. As 4a except for F/Si ratios circles: F/Si=0.00; triangles: F/Si=0.01 diamonds: F/Si=0.03; squares: F/Si=0.10
42 atoms of water influenced by the silica surface [29,30,31]. This method is based on the decrease of "['2 when free water is influenced or weakly bonded to a silica surface. As shown in figure 4a, after the steep decrease of I"2 due to the formation of aggregates the curve increases during aging, indicating a (slow) decrease of surface area. If aging is accelerated by addition of fluorine (fluorine ions are a catalyst for hydrolysis/ condensation reactions [1]), the decrease of silica surface is also enhanced (figure 4b). See reference [29] for more details concerning use of relaxation methods to study aging or pore formation. 5 4-1.4- h r s . -
" ..........
~
:3" a
5.0
hrs.
~ -1.9
v
v 0
2 0.5 hrs.
0 -0.80 ,
I
-0.52
I
I
-0.24-
0.04-
=
,
l
0.52
0.60
log ( Q (nm-~)) Figure 5. SAXS spectra of silica with fluorine during aggregation and aging at various times. Gelation point at 0.8 hrs. Conc(SiO2) = 0.73 M, pH = 4.0, F/Si = 0.01. SAXS spectra also confirm Ostwald ripening during aging. In figure 5 three SAXS curves in a log(I)-log(Q) plot are shown at various aging times. The spectra after 0.5 and 5 hours show only the fractal region, the Q values related with aggregate size and size of the primary particles being outside the Q-window of the SAXS apparatus. Therefore, the radius of the primary particles has to be smaller than 1 nm. After 41.4 hrs aging, however, the cross-over between fractal region and Porod region is observed at approximately Q = 0.5 nm 4, corresponding with R0 -~ 5 nm. Ostwald ripening has increased the radius of the building blocks of the aggregates (the primary particles) by at least a factor of 5 [29]. These figures are confirmed by experiments in aggregates from acidified potassium water glass, resulting in Ro ~ 4.5 nm after 1 month aging and also catalysed by fluorine [9]. Aging at pH = 7-8 even shows R0 = 10 nm [9], but probably before aging primary particles have been much larger at this pH compared to pH = 4 [29]. Both aging experiments and SAXS spectra, however, strongly indicate that aging is much more complicated and can not be described using Ostwald ripening alone. For example, in wet gels a considerable shrinking and discharge of water during aging is also observed. To explain this phenomenon one has to assume changes in the structure at a relatively big scale compared to smoothing of branches by hydrolysis/recondensation equilibria. Moreover, in many experiments SAXS spectra
43 show a decrease of the fractal dimension during aging although both from intuition and from simulations [3,25,26] an increase had to be expected during restructuring. To relate hypothetical aging mechanisms with information obtained from SAXS spectra computer simulations proved to be extremely informative. To explain the growth of primary particles and the (slight) decrease of the fractal dimension during aging, an aging mechanism was postulated. This was based on the solvolysis of primary particles at the periphery of the.aggregates (dissolution of the outermost branches), migration by diffusion towards the center of the aggregates and recombination in the inner crevices. Simulations with the GRASP/DALAI combination, however, showed very clearly that solvolysed particles will probably will never arrive at the center of the aggregates: during the random walk they will stick on the ramified branches. Even worse, if no preference for hydrolysis is given to the outermost particles, the aggregates become more ramified during aging. Much more succesfull were recent simulations based upon ring formation [32]. In this model single bonded particles were allowed to perform small movements with respect to each other, resulting in reinforcement of the thin branches by the formation of rings. In figure 6 fractal dimensions are shown, extracted from the SAXS spectrum which was calculated from the simulated aggregates before and after aging according to local ring formation. The fractal dimension D = 1.45 before aging has decreased to 1.26 at low Q (large scale effects) and increased to 1.87 at high Q (local effect). Recently we confirmed these results with SAXS experiments on aging silica [33]. In figure 7 the experimental log(I)-log(Q) plots show the same pattern: the fractal dimension D = 2.2 (corresponding with D = 1.45 in 2 dimensions) after short aging, shows a decrease at low Q and an increase at high Q after prolonged aging. These results can be explained assuming different effects of local reorganizations at small and large length scales. See figure 8. At small scale (scale a) the density of silica has increased resulting in a lower density gradient and therefore an increase in le+08
"
-
i
-
-
-
w
-
-
-
/i
-
J
-
!
.
.
I
,
,
1e+07
le+06
%
N~\
o,-,~
t000o0 N
",
Op = i.87
10000 Ro
1 0 0 0
0.0(31
9
9
I
0.01
9
,
,
I
-
.
9
0.1
9
I
t
9
.
10
10{3
q
Figure 6. Simulated SAXS curves before and after aging by local ring formation.
44 1.00
2.05
-q.,= "-I
0.40 v
>., 09 t,.(11 t,-
-0.20
L..,
"~*-t Q4 =o~.o ~~"="'~o,..~.o,,..
/
-0.80
_..,.
r 0
2.35
2.2
o
-1.40
--,,,, . -2.00 -1.50
. . . . . . . . .
I
- 1.30
1
_
- 1.10
I
I
-0.90
-0.70
.*
-0.50
log Q (~-1)
Figure 7. SAXS curves of silica gels aged for various times" (a) 1 week, (b) 2.5 months, (c) 5 months. Conc.(SiO2) = 0.73 M (4 wt%), pH = 4.0.
non-aged
aged
C
Figure 8. Pictural view of aging by local increase in density. fractal dimension. At large scale (scale c), however, mass is even more concentrated in the "linear" branches without changing the overall morphology and therefore resulting in an increase of the mass gradient and corresponding decrease of D. Although we do not believe ring formation is the only aging mechanism, the agreement with fractal properties of aged systems indicates that ring formation problably makes an important contribution to aging. 3.7 Pore formation.
Although during aging reorganizations of silica reinforce the ramified and teneous network, it is difficult to show formation of pores during aging with SAXS or SANS. According to the Babinet principle [17], the dispersed component in a two-phase system is scattering and in wet gels therefore always scattering by silica is recorded.
45 On the contrary, in dried gels the pores are the dispersed component and therefore pores had to be investigated by SAXS and SANS only in freeze-dried gels. As shown [4,29], freeze-drying was necessary to avoid collapse of the ramified system by capillary forces during drying, especially in gels with short aging times. Because with SANS contrast variation using HzO/D20 mixtures could be applied, with this method we were also able to prove scattering was caused by pores and not by silica [22]. Log(I)-log(Q) plots of SANS spectra of aged and freeze-dried silicas showed rather low fractal dimensions (D = 1.4 - 1.5). See figure 9 for a typical spectrum. The low fractal dimension corresponds very well to an aging mechanisms according to figure 8, because the decreasing volume density of pores from the core to the outer parts of the aggregates may be expected if the main branches are preferentially reinforced, creating many pores near the centre [22]. In figure 10 the relation between D and the distribution of pores is explained in 2-dimensional examples.
5.00 >.,
1.,_50
09 c (1.) c-
o-~ o
-1.4
0.00
-1.50
-2.40
-1.80
-1.20
-0.60
Jog e Figure 9. SANS spectrum of dried gel after aging for 1 hour at 80~ D=
1
D=
1.5
in wet gel state. D=2
.' . ) r ~ %
.. \
/ 9 .,,~ ~ . y . . . /
\ \' . "o' . "' o. ' ' _ ' :/ . ' 7 Figure 10. 2-dimensional models of pore distribution depending on D. D = 1: high pore density gradient and highest density at the center. D = 1.5: moderate pore density gradient. D = 2 (Euclidean geometry): no pore density gradient.
46 As already published [1,4,12,29] accelaration of gelation and aging by fluorine results both in different SAXS spectra of wet systems and in different surface area and pore structure of dried gels. In figure 11 we have compared systematically aging with fluorine and aging at 80 ~ Pore radii have been measured both with SANS (using
90 o<( oo D
=..-
60
-8 C) 9
5O
o rl
0
1100
2200
Aging time
5500
(rain.)
Figure 11. Pore radii determined by SANS (squares) and BET (diamonds) after aging at 80~ (open symbols) and with fluorine (closed symbols). 500 z',-
300
(o)
375
(b)
200
250 >
100
125 0
0.00
0.25
0.50
PlPo (')
0.75
1.00
0 0.00
0.25
0.50
O. 75
1.00
P/Po (')
Figure 12. Adsorption/desorption hysteresis curves for gel aged at 80~ aged with fluorine (right).
(left) and gel
the low-Q cross-over point in the log(I)-log(Q) plot) and with physisorption (BET) as a function of aging. The gels at 80 ~ showed reasonable agreement between the pore sizes obtained from scattering data and from BET. The deviations may be explained by assuming the presence of non-interconnected pores. Clearly the deviations are much bigger in the fluorine catalysed system. This bad conformity can probably be assigned to the presence of slit-like pores as can be deducted from the
47 adsorption/desorption hysteresis curve (figure 12) according to the classification of de Boer (type B) [35]. The radius determined with BET is the distance between the walls of the slit, but with SANS we are measuring the radius of gyration with contributions also of the depth of the slit. Therefore SANS-radius > BET-radius, in accordance with results presented in figure 11. 4. Conclusions.
To study aggregation, gelation and aging of silica, prepared by acidification of water glass, both NMR and scattering spectroscopy proved to be very efficient methods. With 29Si-NMR reactions at molecular scale could be studied using shifts in Qn ratios. Especially Q3/Q4 (ratio between surface- and bulk-silica) was very useful describing aging reactions. On colloidal scale 'H-relaxation time (T2) of water could be used to characterize silica conversions, with T2 decreasing during aggregation and increasing again by loss of silica area during aging. Studying aggregation and aging on colloidal scale SAXS was very informative, with the fractal dimension D representing silica transformations. To interpretate changes of D during aging, computer simulations were indispensable providing calculations of simulated spectra corresponding to various possible aging mechanisms. In dried and porous silicas care has to be taken in comparing SANS and BET results because radius of gyration (SANS) and pore radius (BET) might be different, depending on the shape of the pores. Acknowledgements.
Financial support (W.H.D. and H.F.v.G.) was given by the Dutch Department of Economic Affairs, as part of the "IOP-Katalyse" programme. Beam time both at Daresbury Laboratory and Rutherford Appleton Laboratory were provided by the SERC/NWO agreement on use of synchrotron radiation and pulsed neutron source respectively. We thank Drs. Wim Bras (NWO/SERC) for his assistance at SAXS and dr. Richard Heenan (SERC) for his assistance at SANS. Minispec experiments were performed at Bruker Spectrospin N.V., Wormer, The Netherlands and we appreciate the assistance of Piet Ruigrok.
REFERENCES.
[1] [2] [3] [4]
[5] [6] [7]
R.K. Iler, "The Chemistry of Silica", John Wiley & Sons Inc., New York, 1979. R. Jullien and R. Botet, "Aggregation and Fractal Aggregates", World Scientific, Singapore, 1987. M. Kalalla, R.Jullien and B. Cabane, J.Phys.II(France), 2 (1992) 7 P.W.J.G. Wijnen, T.P.M. Beelen, C.P.J. Rummens, H.C.P.L. Saeijs, J.W. de Haan, L.J.M. van de Ven and R.A. van Santen, J.Coll.Interf.Sci., 145 (1991) 17. C.G. Vonk, J.Appl.Cryst., 6 (1973) 81 B.W.H. van Beest, J. Verbeek and R.A. van Santen, Catal.Lett.,_l (1988) 147 G. Engelhardt, H. Jancke, M. M~igi, T. Pehk and E. Lippmaa, J.Organo-Met. Chem., 28 (1971) 293
48
[81 [91 [10] [111 [121 [13] [141 [15] [16] [171
[~8] [191 [20] [21] [22] [23] [24]
[251 [26] [271 [281 [291 [30] [31]
[32] [34]
[35]
C.T.G. Knight, J. Chem. Soc., Dalton Trans. (1988) 1457. C.T.G. Knight, R.J. Kirkpatrick and E. Oldfield, J. Chem. Soc., Chem. Comm. (1989) 919. P.W.J.G. Wijnen, T.P.M. Beelen, J.W. de Haan, L.J.M. van de Ven and R.A. van Santen, Coll. Surf., 4__55(1990) 255. I. Hasegawa, S. Sakka, Y. Sugahara, K. Kuroda and C. Kato, J. Chem. Soc., Chem. Comm. (1989) 208. T.P.M. Beelen, P.W.J.G. Wijnen, C.P.J. Rummens and R.A. van Santen, "Better Ceramics through Chemistry IV", MRS Symp. Proc. 180, (1990) 273. B.B. Mandelbrot, "The Fractal Geometry of Nature", Freeman, New York, 1977. T. Vicsek, "Fractal Growth Phenomena" (2e Ed.), World Scientific, Singapore, 1992 H.F. van Garderen, W.H. Dokter, T.P.M. Beelen, R.A. van Santen and E.Pantos, to be published in Modell.Simul.Mater.Sci.Eng., 2 (3) May 1994 A. Guinier and G. Fournet, "Small-Angle Scattering of X-rays", J.Wiley and Sons, New York (1955) O. Glatter and O. Kratky, "Small Angle X-ray Scattering", Academic Press, London (1982) T. Freltoft, J.K. Kjems and S.K. Sinha, Phys.Rev.B, 33 269 J. Teixeira in "On Growth and Form", H.E. Stanley and N. Ostrowski, Eds., M. Nijhoff, Dordrecht (1986), 145. J.E. Martin and A.J. Hurd, J. Appl. Cryst., 2__9_0(1987) 61. J.D.F. Ramsay, Chem. Soc. Rev., 15 (1986) 335. W.H. Dokter, T.P.M. Beelen, H.F. van Garderen and R.A. van Santen, accepted for publication Symp.Proc. COPS III, Marseille 1993 T.P.M. Beelen, W.H. Dokter, H.F. van Garderen, R.A. van Santen, M.T. Browne and G.R. Morrison, "Better Ceramics through Chemistry V", MRS Symp. Proc. 271 (1992) 263. P. Meakin, Physica Scripta 46 (1992) 295 P. Meakin, J.Chem.Phys., 83 (1985) 3645 P. Meakin, J.Coll.Interf.Sci., 112 (1986) 187 L.L. Hench and J.K. West, Chem. Rev. 90 (1990) 33. C.J. Brinker and G.W. Scherer, "Sol-gel Science", Academic Press, San Diego, 1990. W.H. Dokter, H.F. van Garderen, T.P.M. Beelen, J.W. de Haan, L.J.M. van de Ven and R.A. van Santen, Coll. & Surf.A, 72 (1993) 165 D.P. Gallegos, D.M. Smith and C.J. Brinker, J.Coll.Interf.Sci., 124 (1988) 186 and references cited therein. C.L. Glaves, C.J. Brinker, D.M. Smith and P.J. Davis, Chem.Mat., 1 (1989) 34. H.F. van Garderen, E. Pantos, W.H. Dokter, T.P.M. Beelen, M.A.J. Michels, P.A.J. Hilbers and R.A. van Santen, submitted J.Chem.Phys. W.H. Dokter, T.P.M. Beelen, H.F. van Garderen and R.A. van Santen, submitted to "Better Ceramics through Chemistry vr', MRS Symp.Proc. (1994) J.C.P. Broekhof and R.H. van Dongen in "Physical and chemical Aspects of Adsorbents and Catalysts", B.G. Linssen (Ed.), Academic Press, London (1970), 1-59