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Master behaviour for gelation in fluoride-catalyzed gels
Materials Letters 15 ( 1992) 242-247 North-Holland
Master behaviour for gelation in fluoride-catalyzed R. Rodriguez,
gels
M. Flores
Departamento de Fisica,
UniversidadAutdnoma Metropolitana-Iztaplapa, Apdo. Postal 55-534, Mexico, D.F. 09340, Mexico
J. G6mez and V.M. Castafio Institute de Fisica. Universidad National Autdnoma dekfkxico, Apdo. Postal 20-364. Mexico, D.F. 01000, Mexico
Received 29 September 1992
Master behavior for the gelation time in a sol-gel system catalyzed with ammonium fluoride is reported. This method allows for the determination in a reproducible way of the gelation profile in a sol-gel system, when the amount of this salt is known. The silica gel was prepared by mixing tetraethyl orthosilicate, water and ethanol; the reaction was carried out under reflux conditions. The kinetics of aggregation of silica particles was followed by using a dynamic light scattering technique, from the beginning of the chemical reaction. The unstable behaviour of the reaction at the beginning of the process was obtained in all cases. After this unstable regime, the system reaches a steady-state regime characterized by a constant value of the particle size. When the system approaches gelation, the particle size grows fast and this rate of growth depends on the pH of the system.
1. Introduction Silica sol-gel method has become very important in glass technology because it allows one to obtain glasses with specific physical and chemical properties. Besides the fact that it is possible to obtain glasses with high purity and homogeneity at low temperature, it is possible to incorporate into the glass almost any kind of metal by adding an appropriate salt [ 11. Furthermore, it is possible to incorporate, into the glass, organic polymers to obtain hybrid materials [2,3]. Gelation time is one of the most important quantities that are measured in a sol-gel system. This quantity depends on many physical and chemical parameters like temperature, pH, chemical composition, etc. It was usual to determine the gelation time by measuring the time required for the system surface to remain steady while the container was tilted for 2 min [ 41. Later, the gelation time was determined by measuring the time required for the viscosity of the solution to reach an arbitrary value (approximately 10000 P) [ 5 1. Dynamic light scattering ‘(DLS) technique has been used lately to determine the size of sols in solution [ 6,7], through the deter242
mination of the diffusion coeficient of the particles. Due to this, this technique is also appropriate for following the kinetics of gelation of sols in solution. The gelation process of metal alkoxides involves both hydrolysis and polymerization reactions; the way the catalysts affect these reactions is complex, depending not only upon pH but also the reaction mechanism of each catalytic agent [ 5 1. For a fluoride-catalyzed reaction, the anion must play an important role in the gelation process because, under the same conditions, the gelation times for bromideand iodide-catalyzed gels were three orders of magnitude greater than for the case of the fluoride [ 5 1. The fluoride salts produce rapid gelation in a silica sol system. It has been proposed [ 8 ] that hydrolysis reactions are probably responsible for the rapid gelation kinetics of fluoride-catalyzed gels. In this reaction, a fluoride anion approaches a molecule of TEOS forming a highly unstable pentacovalent intermediate. This complex rapidly decomposes forming a partially fluorinated silicon alkoxide and in the presence of H30+ yields byproducts of water and alcohol. Another complex is formed in the presence of water that decomposes into partially hydrated sili-
0167-577x/92/$ 05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.
Volume t 5, number 4
December 1992
MATERIALS LETTERS
con alkoxide plus regenerated fluoride and hydronium. Even this process will continue until all the ethoxide bonds are replaced by hydroxyl groups; the polymerization reaction will begin before all the TEOS was fully hydrated. The fluoride anion catalyzes both the hydrolysis and polymerization reactions. Iler [ 9 ] postulated that the effectiveness of fluoride in the polymerization reaction is due to the smaller ionic radius of the fluoride anion versus that of the hydroxyl group; then F- can increase the coordination of silicon above four. Other anions such as Cl-, Br-, I-, SOY, NO,, etc. are all larger than the hydroxyl group and are much less effective than this in catalyzing the reaction. Then, the fluoride-catalyzed gels exhibit rapid gelation due to nucleophilic substitution of fluoride anion and subsequent rapid hydrolysis and polymerization of the reaction sites. Only a few parts per million of fluoride can dramatically affect the rate of reaction [ 7 1. Because many of the properties of the fluoride-catalyzed gels are similar to those of basecatalyzed gels, it has been suggested that the roles of OH- and F- are similar. Trying to relate the catalytic mechanism of the gelation process with the resulting microst~cture and properties of the gels, it has been postulated that a fine network structure of linear chains exists in acidcatalyzed gels, and more dense colloidal particles with large interstices between them for base-catalyzed gels [ IO-1 21. The materials obtained with ammonium fluoride-catalyzed gels are white and opaque; the opacity of these gels may be due to the colloidal nature of the gel, as would be expected from a basic solution.
dissolved. After this, 22.0 ml of high-purity tetraethyl orthosilicate (TEOS) (Fisher Co.) was added to the mixture without stopping the stirring. Once the mixture was homogeneous, we began to heat the system until it reached the reflux temperature, which was approximately 75 *C. Once the chemical reaction started, we began to take out samples at regular periods of time. Because the dynamic light scattering technique measures the diffusion coefftcient of sols, and this coefficient depends linearly on temperature (Einstein’s relationship), each sample that was taken out from the reactor was cooled to room temperature. In this way we practicaily stopped the chemical reaction within the time necessary to obtain a correlation function, and to guarantee a constant temperature during the measuring time (which was between 2 and 5 min). A typical correlation function is shown in fig. 1; it was taken at a scattering angle of 90” for a standard experiment at reflux temperature. The sample time for this correlation function was 5.0 x 1Om5s and the accumulation time was 120 s. 2.2. Particle size measurement Because the solution concentration and the particle size are in the right range for use of the dynamic light scattering technique (DLS), this has been used extensively to measure the size of particles suspended or dissolved in a liquid through a determination of the diffusion coefficient of the particle [ 131. I
/
2. Experimental 2.1. Sample preparation Approximately 72.8 ml of sol was prepared by mixing 6.8 ml of CO,-free tri-distilled water, with 44.0 ml of ethanol reactive grade and ammonium fluoride (Baker Co.), all at room temperature. The fluoride salts are the catalysts that accelerate the chemical reaction; this ammonium salt was added to the system in the range from 1.5 to 3.0 mg. This mixture was stirred until the fluoride was completely
0.0
IO”
1.0
IO
1
z 0 I(11
time iminl
Fig. 1. A typical time autocorrelation function for a sol-gel system with 1.5 mg of ammonium fluoride. The sample time was 2.0 x 1O-* s, and the accumulation time 120 s.
243
Volume 15, number 4
MATERIALS LETTERS
The light scattering apparatus used to measure the particle size is very similar to that described elsewhere [ 14’1.An argon-ion laser (LEXEL model 75) oprating at A0= 488 nm was used as our light source; the light beam was focused in the scattering cell with a beam diameter of 100 pm. A standard borosilicate glass cuvette of 10 mm light path, was used as a scattering cell, and in all experiments the scattering angle was 90”. The scattered light was collected by an optical system and focused onto a fast PMT (ITT model FW130) whose output went to a large-bandwidth digital pre-amplifier, amplifier, discriminator and finally the signal was processed by a digital correlator (Langley-Ford model 1096). The data were fitted using the first two cumulants in a cumulant’s expansion [ 15 ] of the time autocorrelation function. The solvent viscosity was chosen as 1.5256 CP because it was shown [ 161 that this value does not change in an appreciable way in the early stage of the reaction, and the refractive index of the solvent was chosen as 1.3655 [ 161.
3. Results A typical particle size profile with 1.5 mg of ammonium fluoride is shown in fig. 2. This figure shows a nonlinear unstable oscillatory behavior at the beginning of the reaction. After this unstable behavior,
0
100
200 300 time (min)
400
the system reaches a steady-state regime that is characterized by the fact that the particle size remains practically constant for a long period of time, until the gelation condition is reached. In the gelation regime, particle size grows very fast with time. Because the unstable behavior of the reaction produces a variety of dissipative structures that are unstable, the standard deviation of the particle size distribution is an important quantity. As we mentioned before, the time correlation function was fitted by using a second-order cumulant’s expansion. The second cumulant is related to the variance of the particle size distribution function [ 15 ] of ~01s.In fig. 3 the standard deviation (the square root of the variance) as a function of the reaction time is shown. The relative scattered intensity (the ratio of the scattered and the incident intensities), which depends on the product of the concentration and the molecular weight of the scatterers, is plotted as a function of time in fig. 4. It can be seen that the relative scattered intensity begins to grow with the reaction time once the steady-state condition is reached. Because in this regime the particle size is constant, the relative scattered intensity can only grow because the sol’s concentration was increasing with time; this is the way the system approaches gelation. Fig. 5 shows the gelation profile for systems with different amounts of catalyst. As can be seen, the gelation time depends inversely on the mass of fluoride salt; the gelling time is reduced by increasing the amount of catalyst. The curves shown in fig. 5 were
500
Fig. 2. A typical particle size profile for a sol-gel system with 1.5 mg of the fluoride salt. The unstable regime at the beginning of the reaction, the steady-state regime that has a constant value for the particle size and the gelation of the sample where the particle size grows very fast can be seen.
244
December 1992
100
200 300 time (min)
400
500
Fig. 3. Standard deviation of the particle size distribution function versus reaction time for the same system as in fig. 2.
Volume
15,number 4
MATERIALS
*‘Mc
December
LETTERS
0.4
t
Master 0.3
3
0. I
0 300
200
IO0
Curve
f
2 i O.*
0
1992
0
400
I
I
I 00
200
300
Jo0
S(H)
time (mlnl
time (min) Fig. 4. Relative scattered intensity (the ratio between the scattered and the incident intensities) as a function of time. It corresponds to a system with 1.5 mg of salt.
Fig. 6. The curves plotted in fig. 5 were shifted in such a way as to overlap all curves in one which is called a master curve.
0.4
0.3
I3
0
t,‘,,‘,,““‘,“,“““,, I
0 0
I(Ml
200
3(H)
400
time Cnnn) Fig. 5. Gelation profile for systems with different amounts ofcatalyst plotted as a function of time; large gelation times correspond to small amount of fluoride salt and vice versa.
shifted to obtain a master curve for the gelation process. This master curve is shown in fig. 6. In this figure, the same time scale in the plot was used as in fig. 5 in order to see the effect of the shifting. To be able to predict gelling time in systems with different amounts of catalyst, it is necessary to obtain an empirical relation between the shifting factors and the corresponding amount of salt. This is shown in fig. 7 where it is possible to observe that the shifting factor depends nearly linearly (with a negative slope) on the mass of salt. A prediction for the gelling profile is shown in fig. 8; this was done for an amount of ammonium fluoride of 2.5 mg. The continuous curve corresponds to the prediction and
I .s
2
2.5
3
2.5
mass of salt (mg)
SO0
Fig. 7. Shifting factors required function of the mass of salt.
to obtain
the master
the discrete points to the experimental
curve as a
data.
4. Discussion We have found some periodic oscillations in the particle size profile in the early stage of the reaction. We attribute these oscillations to nonlinear instabilities, which are characteristic of this chemical reaction [ 161. The instabilities of the reaction due to nonlinear effects correspond to a large variety of possible structures and sizes of the ~01s. These instabilities are responsible for the oscillations in the particle size profile. These oscillations are due to a competition between the homogenization of the chemical components due to the free diffusion pro245
Volume
15, number
4
MATERIALS
LETTERS
December
1992
action. The shifting factors of the master curve follow a linear relationship with the mass of salt. The nearly linear dependence of the shifting factors on the mass of salt may be due to the fast gelation reaction, which is characteristic of fluoride-catalyzed reactions. With these curves, it was possible to predict the gelation of a sample with 2.5 mg of fluoride salt. The comparison between the predicted gelation curve and the experimental data is shown in fig. 8. From this plot it can be seen that the predicted curve is in good agreement with the experimental data. 0
20
40
60
80
100
time (min)
Fig. 8. The gelation time for a sample with a known amount of salt as predicted by using the master curve: (p) predicted gelation profile, (. . .) experimental data.
cess, and a spatial localization due to local disturbances of the chemical processes because of the involvement of an autocatalytic reaction [ 17,18 1. The oscillations are completely reproducible [ 16 1. In fig. 4, we noted that after the particle size protile has reached the steady-state regime, the relative scattered intensity begins to grow with time. However, in this regime, the particle size remains almost constant for a long period of time. The same behavior was observed in all the experiments performed. Because the relative scattered intensity is proportional to the product of the molecular weight and the concentration of the sample [ 131, and because the particle size remains constant in the steady-state regime, an increase in the scattered intensity is attributed to an increase in the number of particles with time. This important result indicates how the sol’s suspension reaches the state of gelation. It is the number of particles rather than their size, which increases as the system approaches gelation. The shear viscosity in a sol solution before the system approaches gelation grows as a power law with the reaction time [ 191. However, the volume fraction of the sols may change by increasing particle size or by increasing the number of particles. Then we can say that the viscosity of the sol solution is increased, once the system reaches the steady state, not by changing particle sizes, but by increasing the number of sols in the system. A master curve was obtained by changing the amount of fluoride salt used as a catalyst in the re246
5. Conclusion Several typical sol-gel reactions were studied and in all cases unstable behavior in the early stage of the reactions was obtained. This behavior was associated with nonlinear instabilities due to the autocatalytic nature of the reactions. After this behavior, the systems reach a steady-state regime characterized by the fact that the particle size of sols remains practically constant. However, the relative light scattered intensity grows with time, which means that the number of sols also grows with time. At the end, the particle size profile shows very fast growth which corresponds to gelation. For this behavior it was possible to obtain a master behavior that allows one to make a prediction of the gelation time once the amount of ammonium fluoride is known.
References [ 1] L.L. Hench and J.K. West, Chem. Rev. 90 ( 1990) 33. [ 2 ] H. Schmidt, in: Better ceramics through chemistry, eds. C.J. Brinker, DE. Clark and D.R. Ulrich (North Holland, Amsterdam, 1984). [ 31 G. Phillip and H. Schmidt, J. Non-Cryst. Solids 63 ( 1984) 283. [4] P. Yu, H. Liu and Y. Wang, J. Non-Cryst. Solids 52 (1982) 511. [ 51 E.J.A. Pope and J.D. Mackenzie, J. Non-Cryst. Solids 87 (1986) 185. [6] A.H. Boonstra, T.P.M. Meeuwsen, J.M.E. Baken and G.V.A. Aben, J. Non-Cryst. Solids 109 (1989) 153. [ 71 J.E. Moreira, M.L. Cesar and M.A. Aegerter, J. Non-Cryst. Solids 121 (1990) 394. [ 81 K.A. Adrianov, Metal organic polymers (Wiley, New York, 1965). [ 91 R.K. Iler, The chemistry of silica (Wiley, New York, 1979).
Volume 15, number 4
MATERIALS LETTERS
[ 10 ] C.J. Brinker, K.D. Keefer, D.W. Shaefer and C.S. Ashley, J. Non-Cryst. Solids 48 (1982) 47. [ 111 M. Yamane and T. Kojima, J. Non-Cryst. Solids 44 ( 198 1) 181. [ 121 L.C. Klein and G.J. Garvey, J. Non-Cryst. Solids 38&39 (1980) 45. [ 13 ] B.J. Beme and R. Pecora, Dynamic light scattering (Wiley, New York, 1976). [ 141 R. Rodriguez, Rev. Mex. Fis. 38 (1992) 450. [ 151 D.F. Koppel, J. Chem. Phys. 57 (1972) 4814.
December 1992
[ 161 A. Ruben and R. Rodriguez, J. Non-Cryst. Solids, to be published. [ 171 P. Glansdorff and I. Prigogine, Thermodynamic theory of structure, stability and fluctuations (Wiley-Interscience, New York, 1971). [ 181 A.M. Zhaboutinski, Oscillations in biological and chemical systems (Academy of Sciences, M&cow, 1967); Russ. J. Phys. Chem. 42‘( 1968) 1649. [ 191 L.C. Klein and G.J. Garvey, Soluble silicates (American Chemical Society, New York, 1982) pp. 293-303.
247
Master behaviour for gelation in fluoride-catalyzed R. Rodriguez,
gels
M. Flores
Departamento de Fisica,
UniversidadAutdnoma Metropolitana-Iztaplapa, Apdo. Postal 55-534, Mexico, D.F. 09340, Mexico
J. G6mez and V.M. Castafio Institute de Fisica. Universidad National Autdnoma dekfkxico, Apdo. Postal 20-364. Mexico, D.F. 01000, Mexico
Received 29 September 1992
Master behavior for the gelation time in a sol-gel system catalyzed with ammonium fluoride is reported. This method allows for the determination in a reproducible way of the gelation profile in a sol-gel system, when the amount of this salt is known. The silica gel was prepared by mixing tetraethyl orthosilicate, water and ethanol; the reaction was carried out under reflux conditions. The kinetics of aggregation of silica particles was followed by using a dynamic light scattering technique, from the beginning of the chemical reaction. The unstable behaviour of the reaction at the beginning of the process was obtained in all cases. After this unstable regime, the system reaches a steady-state regime characterized by a constant value of the particle size. When the system approaches gelation, the particle size grows fast and this rate of growth depends on the pH of the system.
1. Introduction Silica sol-gel method has become very important in glass technology because it allows one to obtain glasses with specific physical and chemical properties. Besides the fact that it is possible to obtain glasses with high purity and homogeneity at low temperature, it is possible to incorporate into the glass almost any kind of metal by adding an appropriate salt [ 11. Furthermore, it is possible to incorporate, into the glass, organic polymers to obtain hybrid materials [2,3]. Gelation time is one of the most important quantities that are measured in a sol-gel system. This quantity depends on many physical and chemical parameters like temperature, pH, chemical composition, etc. It was usual to determine the gelation time by measuring the time required for the system surface to remain steady while the container was tilted for 2 min [ 41. Later, the gelation time was determined by measuring the time required for the viscosity of the solution to reach an arbitrary value (approximately 10000 P) [ 5 1. Dynamic light scattering ‘(DLS) technique has been used lately to determine the size of sols in solution [ 6,7], through the deter242
mination of the diffusion coeficient of the particles. Due to this, this technique is also appropriate for following the kinetics of gelation of sols in solution. The gelation process of metal alkoxides involves both hydrolysis and polymerization reactions; the way the catalysts affect these reactions is complex, depending not only upon pH but also the reaction mechanism of each catalytic agent [ 5 1. For a fluoride-catalyzed reaction, the anion must play an important role in the gelation process because, under the same conditions, the gelation times for bromideand iodide-catalyzed gels were three orders of magnitude greater than for the case of the fluoride [ 5 1. The fluoride salts produce rapid gelation in a silica sol system. It has been proposed [ 8 ] that hydrolysis reactions are probably responsible for the rapid gelation kinetics of fluoride-catalyzed gels. In this reaction, a fluoride anion approaches a molecule of TEOS forming a highly unstable pentacovalent intermediate. This complex rapidly decomposes forming a partially fluorinated silicon alkoxide and in the presence of H30+ yields byproducts of water and alcohol. Another complex is formed in the presence of water that decomposes into partially hydrated sili-
0167-577x/92/$ 05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.
Volume t 5, number 4
December 1992
MATERIALS LETTERS
con alkoxide plus regenerated fluoride and hydronium. Even this process will continue until all the ethoxide bonds are replaced by hydroxyl groups; the polymerization reaction will begin before all the TEOS was fully hydrated. The fluoride anion catalyzes both the hydrolysis and polymerization reactions. Iler [ 9 ] postulated that the effectiveness of fluoride in the polymerization reaction is due to the smaller ionic radius of the fluoride anion versus that of the hydroxyl group; then F- can increase the coordination of silicon above four. Other anions such as Cl-, Br-, I-, SOY, NO,, etc. are all larger than the hydroxyl group and are much less effective than this in catalyzing the reaction. Then, the fluoride-catalyzed gels exhibit rapid gelation due to nucleophilic substitution of fluoride anion and subsequent rapid hydrolysis and polymerization of the reaction sites. Only a few parts per million of fluoride can dramatically affect the rate of reaction [ 7 1. Because many of the properties of the fluoride-catalyzed gels are similar to those of basecatalyzed gels, it has been suggested that the roles of OH- and F- are similar. Trying to relate the catalytic mechanism of the gelation process with the resulting microst~cture and properties of the gels, it has been postulated that a fine network structure of linear chains exists in acidcatalyzed gels, and more dense colloidal particles with large interstices between them for base-catalyzed gels [ IO-1 21. The materials obtained with ammonium fluoride-catalyzed gels are white and opaque; the opacity of these gels may be due to the colloidal nature of the gel, as would be expected from a basic solution.
dissolved. After this, 22.0 ml of high-purity tetraethyl orthosilicate (TEOS) (Fisher Co.) was added to the mixture without stopping the stirring. Once the mixture was homogeneous, we began to heat the system until it reached the reflux temperature, which was approximately 75 *C. Once the chemical reaction started, we began to take out samples at regular periods of time. Because the dynamic light scattering technique measures the diffusion coefftcient of sols, and this coefficient depends linearly on temperature (Einstein’s relationship), each sample that was taken out from the reactor was cooled to room temperature. In this way we practicaily stopped the chemical reaction within the time necessary to obtain a correlation function, and to guarantee a constant temperature during the measuring time (which was between 2 and 5 min). A typical correlation function is shown in fig. 1; it was taken at a scattering angle of 90” for a standard experiment at reflux temperature. The sample time for this correlation function was 5.0 x 1Om5s and the accumulation time was 120 s. 2.2. Particle size measurement Because the solution concentration and the particle size are in the right range for use of the dynamic light scattering technique (DLS), this has been used extensively to measure the size of particles suspended or dissolved in a liquid through a determination of the diffusion coefficient of the particle [ 131. I
/
2. Experimental 2.1. Sample preparation Approximately 72.8 ml of sol was prepared by mixing 6.8 ml of CO,-free tri-distilled water, with 44.0 ml of ethanol reactive grade and ammonium fluoride (Baker Co.), all at room temperature. The fluoride salts are the catalysts that accelerate the chemical reaction; this ammonium salt was added to the system in the range from 1.5 to 3.0 mg. This mixture was stirred until the fluoride was completely
0.0
IO”
1.0
IO
1
z 0 I(11
time iminl
Fig. 1. A typical time autocorrelation function for a sol-gel system with 1.5 mg of ammonium fluoride. The sample time was 2.0 x 1O-* s, and the accumulation time 120 s.
243
Volume 15, number 4
MATERIALS LETTERS
The light scattering apparatus used to measure the particle size is very similar to that described elsewhere [ 14’1.An argon-ion laser (LEXEL model 75) oprating at A0= 488 nm was used as our light source; the light beam was focused in the scattering cell with a beam diameter of 100 pm. A standard borosilicate glass cuvette of 10 mm light path, was used as a scattering cell, and in all experiments the scattering angle was 90”. The scattered light was collected by an optical system and focused onto a fast PMT (ITT model FW130) whose output went to a large-bandwidth digital pre-amplifier, amplifier, discriminator and finally the signal was processed by a digital correlator (Langley-Ford model 1096). The data were fitted using the first two cumulants in a cumulant’s expansion [ 15 ] of the time autocorrelation function. The solvent viscosity was chosen as 1.5256 CP because it was shown [ 161 that this value does not change in an appreciable way in the early stage of the reaction, and the refractive index of the solvent was chosen as 1.3655 [ 161.
3. Results A typical particle size profile with 1.5 mg of ammonium fluoride is shown in fig. 2. This figure shows a nonlinear unstable oscillatory behavior at the beginning of the reaction. After this unstable behavior,
0
100
200 300 time (min)
400
the system reaches a steady-state regime that is characterized by the fact that the particle size remains practically constant for a long period of time, until the gelation condition is reached. In the gelation regime, particle size grows very fast with time. Because the unstable behavior of the reaction produces a variety of dissipative structures that are unstable, the standard deviation of the particle size distribution is an important quantity. As we mentioned before, the time correlation function was fitted by using a second-order cumulant’s expansion. The second cumulant is related to the variance of the particle size distribution function [ 15 ] of ~01s.In fig. 3 the standard deviation (the square root of the variance) as a function of the reaction time is shown. The relative scattered intensity (the ratio of the scattered and the incident intensities), which depends on the product of the concentration and the molecular weight of the scatterers, is plotted as a function of time in fig. 4. It can be seen that the relative scattered intensity begins to grow with the reaction time once the steady-state condition is reached. Because in this regime the particle size is constant, the relative scattered intensity can only grow because the sol’s concentration was increasing with time; this is the way the system approaches gelation. Fig. 5 shows the gelation profile for systems with different amounts of catalyst. As can be seen, the gelation time depends inversely on the mass of fluoride salt; the gelling time is reduced by increasing the amount of catalyst. The curves shown in fig. 5 were
500
Fig. 2. A typical particle size profile for a sol-gel system with 1.5 mg of the fluoride salt. The unstable regime at the beginning of the reaction, the steady-state regime that has a constant value for the particle size and the gelation of the sample where the particle size grows very fast can be seen.
244
December 1992
100
200 300 time (min)
400
500
Fig. 3. Standard deviation of the particle size distribution function versus reaction time for the same system as in fig. 2.
Volume
15,number 4
MATERIALS
*‘Mc
December
LETTERS
0.4
t
Master 0.3
3
0. I
0 300
200
IO0
Curve
f
2 i O.*
0
1992
0
400
I
I
I 00
200
300
Jo0
S(H)
time (mlnl
time (min) Fig. 4. Relative scattered intensity (the ratio between the scattered and the incident intensities) as a function of time. It corresponds to a system with 1.5 mg of salt.
Fig. 6. The curves plotted in fig. 5 were shifted in such a way as to overlap all curves in one which is called a master curve.
0.4
0.3
I3
0
t,‘,,‘,,““‘,“,“““,, I
0 0
I(Ml
200
3(H)
400
time Cnnn) Fig. 5. Gelation profile for systems with different amounts ofcatalyst plotted as a function of time; large gelation times correspond to small amount of fluoride salt and vice versa.
shifted to obtain a master curve for the gelation process. This master curve is shown in fig. 6. In this figure, the same time scale in the plot was used as in fig. 5 in order to see the effect of the shifting. To be able to predict gelling time in systems with different amounts of catalyst, it is necessary to obtain an empirical relation between the shifting factors and the corresponding amount of salt. This is shown in fig. 7 where it is possible to observe that the shifting factor depends nearly linearly (with a negative slope) on the mass of salt. A prediction for the gelling profile is shown in fig. 8; this was done for an amount of ammonium fluoride of 2.5 mg. The continuous curve corresponds to the prediction and
I .s
2
2.5
3
2.5
mass of salt (mg)
SO0
Fig. 7. Shifting factors required function of the mass of salt.
to obtain
the master
the discrete points to the experimental
curve as a
data.
4. Discussion We have found some periodic oscillations in the particle size profile in the early stage of the reaction. We attribute these oscillations to nonlinear instabilities, which are characteristic of this chemical reaction [ 161. The instabilities of the reaction due to nonlinear effects correspond to a large variety of possible structures and sizes of the ~01s. These instabilities are responsible for the oscillations in the particle size profile. These oscillations are due to a competition between the homogenization of the chemical components due to the free diffusion pro245
Volume
15, number
4
MATERIALS
LETTERS
December
1992
action. The shifting factors of the master curve follow a linear relationship with the mass of salt. The nearly linear dependence of the shifting factors on the mass of salt may be due to the fast gelation reaction, which is characteristic of fluoride-catalyzed reactions. With these curves, it was possible to predict the gelation of a sample with 2.5 mg of fluoride salt. The comparison between the predicted gelation curve and the experimental data is shown in fig. 8. From this plot it can be seen that the predicted curve is in good agreement with the experimental data. 0
20
40
60
80
100
time (min)
Fig. 8. The gelation time for a sample with a known amount of salt as predicted by using the master curve: (p) predicted gelation profile, (. . .) experimental data.
cess, and a spatial localization due to local disturbances of the chemical processes because of the involvement of an autocatalytic reaction [ 17,18 1. The oscillations are completely reproducible [ 16 1. In fig. 4, we noted that after the particle size protile has reached the steady-state regime, the relative scattered intensity begins to grow with time. However, in this regime, the particle size remains almost constant for a long period of time. The same behavior was observed in all the experiments performed. Because the relative scattered intensity is proportional to the product of the molecular weight and the concentration of the sample [ 131, and because the particle size remains constant in the steady-state regime, an increase in the scattered intensity is attributed to an increase in the number of particles with time. This important result indicates how the sol’s suspension reaches the state of gelation. It is the number of particles rather than their size, which increases as the system approaches gelation. The shear viscosity in a sol solution before the system approaches gelation grows as a power law with the reaction time [ 191. However, the volume fraction of the sols may change by increasing particle size or by increasing the number of particles. Then we can say that the viscosity of the sol solution is increased, once the system reaches the steady state, not by changing particle sizes, but by increasing the number of sols in the system. A master curve was obtained by changing the amount of fluoride salt used as a catalyst in the re246
5. Conclusion Several typical sol-gel reactions were studied and in all cases unstable behavior in the early stage of the reactions was obtained. This behavior was associated with nonlinear instabilities due to the autocatalytic nature of the reactions. After this behavior, the systems reach a steady-state regime characterized by the fact that the particle size of sols remains practically constant. However, the relative light scattered intensity grows with time, which means that the number of sols also grows with time. At the end, the particle size profile shows very fast growth which corresponds to gelation. For this behavior it was possible to obtain a master behavior that allows one to make a prediction of the gelation time once the amount of ammonium fluoride is known.
References [ 1] L.L. Hench and J.K. West, Chem. Rev. 90 ( 1990) 33. [ 2 ] H. Schmidt, in: Better ceramics through chemistry, eds. C.J. Brinker, DE. Clark and D.R. Ulrich (North Holland, Amsterdam, 1984). [ 31 G. Phillip and H. Schmidt, J. Non-Cryst. Solids 63 ( 1984) 283. [4] P. Yu, H. Liu and Y. Wang, J. Non-Cryst. Solids 52 (1982) 511. [ 51 E.J.A. Pope and J.D. Mackenzie, J. Non-Cryst. Solids 87 (1986) 185. [6] A.H. Boonstra, T.P.M. Meeuwsen, J.M.E. Baken and G.V.A. Aben, J. Non-Cryst. Solids 109 (1989) 153. [ 71 J.E. Moreira, M.L. Cesar and M.A. Aegerter, J. Non-Cryst. Solids 121 (1990) 394. [ 81 K.A. Adrianov, Metal organic polymers (Wiley, New York, 1965). [ 91 R.K. Iler, The chemistry of silica (Wiley, New York, 1979).
Volume 15, number 4
MATERIALS LETTERS
[ 10 ] C.J. Brinker, K.D. Keefer, D.W. Shaefer and C.S. Ashley, J. Non-Cryst. Solids 48 (1982) 47. [ 111 M. Yamane and T. Kojima, J. Non-Cryst. Solids 44 ( 198 1) 181. [ 121 L.C. Klein and G.J. Garvey, J. Non-Cryst. Solids 38&39 (1980) 45. [ 13 ] B.J. Beme and R. Pecora, Dynamic light scattering (Wiley, New York, 1976). [ 141 R. Rodriguez, Rev. Mex. Fis. 38 (1992) 450. [ 151 D.F. Koppel, J. Chem. Phys. 57 (1972) 4814.
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[ 161 A. Ruben and R. Rodriguez, J. Non-Cryst. Solids, to be published. [ 171 P. Glansdorff and I. Prigogine, Thermodynamic theory of structure, stability and fluctuations (Wiley-Interscience, New York, 1971). [ 181 A.M. Zhaboutinski, Oscillations in biological and chemical systems (Academy of Sciences, M&cow, 1967); Russ. J. Phys. Chem. 42‘( 1968) 1649. [ 191 L.C. Klein and G.J. Garvey, Soluble silicates (American Chemical Society, New York, 1982) pp. 293-303.
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