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Master behavior for gelation in a sol-gel process under different temperature and pH conditions
Journal of Non-Crystalline Solids 163 (1993) 90-96 North-Holland
JoUrNAL or
NON-CRYSTALLINESOLIDS
Master behavior for gelation in a sol-gel process under different temperature and pH conditions R. Arroyo a R. Rodrlguez
b a n d P. S a l i n a s a
a Departamento de Qufmica and b Departamento de F[siea, Universidad Autdnoma Metropolitana-lztapalapa, Apdo. Postal 55-534, Mdxico, D.F. 09340, Mexico
Received 15 January 1993 Revised manuscript received 3 May 1993
A master behavior for gelation in a sol-gel process as function of temperature and pH is reported in this paper. The sol-gel system was kept at reflux temperature until it reached steady state; then it was cooled to room temperature and the pH was adjusted to some value with in a specific range. Once the pH was adjusted, the temperature of the reaction was set to some value, and the system carried to gelation. The particle size profile of sols was obtained as a function of the reaction time using dynamic light scattering. It was from these gelation profiles obtained under different temperature conditions that a master behavior was obtained. With these master curves, it was possible to build a super-master curve which allows prediction of gelation profiles for systems where both the temperature and pH have been specified. Two predictions for systems with different values of temperature and pH led to excellent agreement between experimental and predicted behavior.
1. Introduction T h e silica s o l - g e l m e t h o d has b e c o m e very i m p o r t a n t in glass t e c h n o l o g y b e c a u s e it allows novel m a t e r i a l s with specific physical a n d c h e m i cal p r o p e r t i e s [1-3] to b e p r e p a r e d . G l a s s e s with high p u r i t y a n d h o m o g e n e i t y m a y b e m a d e at low t e m p e r a t u r e a n d a l m o s t any m e t a l m a y b e incorp o r a t e d by a d d i n g an a p p r o p r i a t e salt [1] a n d o r g a n i c p o l y m e r chains [3-5]. G e l a t i o n t i m e is o n e o f t h e m o s t i m p o r t a n t q u a n t i t i e s m e a s u r e d in a s o l - g e l system [6-8]. G e l a t i o n t i m e d e p e n d s on t e m p e r a t u r e , p H , c h e m i c a l c o m p o s i t i o n a n d catalyzing agent. S e v e r a l m e t h o d s have b e e n d e s i g n e d to d e t e r Correspondence to: Dr R. Rodrlguez, Departamento de Fisica, Universidad Aut6noma Metropolitana-Iztapalapa, Apdo. Postal 55-534, M~xico, D.F. 09340, Mexico. Tel.: +52-5 686 0322. Telefax: + 52-5 686 8999.
m i n e g e l a t i o n t i m e in a s o l - g e l system. It is usual to d e t e r m i n e g e l a t i o n t i m e by m e a s u r i n g the t i m e r e q u i r e d to the system surface to r e m a i n s t e a d y while the c o n t a i n e r was t i l t e d for 2 min [7]. G e l a tion time was also d e t e r m i n e d by m e a s u r i n g t h e t i m e r e q u i r e d for solution visc, 'ity to r e a c h an a r b i t r a r y value ( a p p r o x i m a t e l y ~qO00 Poise) [8]. T h e d y n a m i c light s c a t t e r i n g ( D L S ) .'~chnique has b e e n u s e d to c h a r a c t e r i z e reactio, p r o d u c t s in t h e s o l - g e l p r o c e s s [9,10]. W i t h this tec~,nique it was p o s s i b l e to o b t a i n sol p a r t i c l e size d u r i n g the e n t i r e s o l - g e l r e a c t i o n [11,12]. This t e c h n i q u e is a p p r o p r i a t e to follow g e l a t i o n kinetics of sols in solution, b e c a u s e it allows m e a s u r e m e n t o f sol size as a f u n c t i o n o f the r e a c t i o n t i m e [6]. It is k n o w n t h a t a catalyst can d r a m a t i c a l l y i n f l u e n c e t h e g e l a t i o n p r o c e s s [6,8]. T h e g e l a t i o n p r o c e s s e s o f m e t a l alkoxides involve hydrolysis a n d p o l y m e r i z a t i o n reactions. T h e v a r i a t i o n o f t h e g e l a t i o n t i m e c a n n o t b e e x p l a i n e d solely on
0022-3093/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
R. Arroyo et al. / Master behavior for gelation
the basis of pH and the relative dissociation of the catalyst. The reaction mechanism involved with each catalyst must also be considered [8]. The gelation process is important because it is possible to relate the catalytic mechanism of the gelation process with the gel microstructure and properties. The way the chemical reaction is catalyzed determines, to some extent, what type of structure will be obtained, because the hydrolysis and polycondensation reactions depend strongly on if the system is acid- or base-catalyzed [13-15]. The hydrolysis rate is increased with an acid catalyst. It has been postulated [13-15] that a fine network structure of linear chains is formed when the gel is acid-catalyzed. In the low pH regime, linear chain growth seems to be preferred. This may be the result of higher reactivities at chain ends, promoting linear chain growth due to a lower mass density, allowing easier approach of reactive groups. In the case of an alkali catalyst, the rate of hydrolysis is apparently low. When the sol-gel process is base-catalyzed, the hydrolysis reaction is enhanced, producing many sol particles which grow in size and number as the sol-gel transition takes place. More dense colloidal particles with large interstices are produced in this case. The purpose of this work was to investigate the gelation profile under different chemical conditions, once the sol particle size has reached a constant value. We found different gelation profiles as a function of the pH and temperature of the reaction and it was possible to obtain a master behavior for these gelation profiles.
2. Experimental Silica particles were prepared by mixing 12 tool of ethanol reactive grade and 0.0025 mol of cobalt (II) acethyl-acetonate (Aldrich Chem. Co.) at room temperature until the salt was completely dissolved. This salt was added in order to accelerate the sol-gel reaction [11] and to include cobalt into the glass as a doping agent. After this, 4 mol CO 2 free tri-distilled water was added to the mixture without stopping the stirring. One mol of
91
tetraethyl ortosilicate (TEOS) (J.T. Baker) was added to the mixture. It has been reported [11,12] that, under similar conditions, the particle size profile shows a set of characteristic peaks in the early stage of the reaction. These correspond to unstable oscillations of the system due to the auto-catalytic nature of the reaction. After then, the profile reaches a condition where the size of sol particles remains particles remains practically constant with time. In this regime, the unstable damped oscillations disappear and the system reaches steady state. The relative scattered intensity (the ratio between the scattered and the incident intensities) grows practically linearly with the reaction time. Because the scattered intensity depends on the product of concentration and molecular weight of scattering particles, then, because the particle size is constant [11,12], it is the sol concentration which grows with time. This is the way the system reaches gelation. Because the main interest here is gelation, the first part of the particle size profile was not considered. We waited 165 min until the sol particle site reached a constant values before cooling the system to room temperature. Once the system reached room temperature, the pH of the solution was adjusted to a specific value in the range from 7.25 to 8.50 using a solution of ammonium hydroxide in ethanol (1 : 1 in volume). We chose this procedure because the pH is strongly dependent on the temperature and the specific time at which the pH is adjusted with respect to starting time of the reaction. Once the pH of the system was adjusted to a specific value, the sol solution was split in different reactors and heated to different temperatures, within the range from 23 to 76°C, until all reached gelation. Reactors were sampled regularly. Because the DLS technique measures the particle size profile through the determination of the diffusion coefficients of sols, and these coefficients depend linearly upon temperature (Einstein's relationship), every sample was cooled to room temperature. In this way, the chemical reaction was practically stopped within the times necessary to obtain a correlation function, and to guarantee a constant temperature during the 2-5
92
R. Arroyo et al. / Master behavior for gelation 0.4
min measuring time depending on the intensity of the scattered light. This procedure was repeated for different values of the p H for the same set of temperatures.
pH=8.50 T=23°C 0.3
o 2.1. Particle size measurements
DLS 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 [16]. The light scattering apparatus used to measure the particle size is very similar to that described elsewhere [17]. An argon ion laser (Lexel model 75) operating at l 0 = 488 nm was used as our light source with the light b e a m focused in the scattering cell with a b e a m diameter of 100 Ixm. A standard borosilicate glass cuvette of 10 m m 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 photomultiplier tube ( I T T model FW130) whose output went to a high bandwidth digital pre-amplifier, amplifier, discriminator and finally digital correlator ( L a n g l e y - F o r d model 1096). The data were fitted using the first two cumulants in an cumulant's expansion [18] of the time autocorrelation function. The solvent viscosity was chosen as 1.5256 cPoise because it was shown [12] that this value does not change in an appreciable way during the steady state regime, and the refractive index of the solvent was chosen as 1.3655.
3. Results
'~
0.2
0.1
0.0 200
250
300 Time (min)
350
400
Fig. 1. A particle size profile where the first part corresponds to a steady state characterized by a constant value of the size of sols. The last part of this profile corresponds to gelation where the particle size grows very fast with the reaction time.
of the reaction time. In fig. 2 it is possible to see the set of size profiles for five different temperatures corresponding to a p H adjusted to 8.50. In this figure, it is possible to observe the way the sol-gel systems reached gelation at different temperatures, for a p H value of 8.50. In order to obtain a master curve, all these curves were shifted with respect to the curve which corresponds to a temperature of 76°C, which was taken as the reference. In fig. 3 it is
0.8 e~ o
pH=8.5
76°C
0.8
L)
In fig. 1 it is possible to see typical particle size profile for a system with a p H of 8.50 and room temperature. The unstable behavior of the particle size profile is not shown. The first part of this profile corresponds to the steady state regime where the particle size remain practically constant with the time. The last part corresponds to the gelation regime where the size grows rapidly with time. For each p H value, the particle size profiles at different temperatures were plotted as a function
0.4 ~z
40°C
0.2
.
~
°C
0,0 100
200 Time (min)
300
400
Fig. 2. A set of gelation profiles is shown for different values of temperature. In this case the pH of the system was adjusted to 8.5.
R. Arroyo et al. / Master behavior for gelation 0.8 ¸
93
0.8pH=8.5
) pH=8.50
0.6
~H=8.25 pH=8.00
0.6-
e-
p._-7 50
O
¢9
0.4
"~ 0.4"
0.2
0.2.
pH=7.75
N
0 0
100
200
300
400
0
100
Time (min)
200
3(10
400
Time (rain)
Fig. 3. T h i s plot shows a m a s t e r curve o b t a i n e d by shifting the curves s h o w n in fig. 2. T h e s a m e scale in t i m e as in fig. 2 was u s e d to see the effect of the shifting process.
possible to observe all curves collapsed in one curve which is called a master curve. T h e shifting factors required to overlap all the profiles shown in fig. 2 are plotted in fig. 4. T h e same p r o c e d u r e was carried out for the o t h e r p H values; for each p H value, a master curve can be o b t a i n e d following the same procedure as m e n t i o n e d before. In fig. 5 are plotted all the m a s t e r curves, where the p H values assigned to each one are shown in c o r r e s p o n d i n g master curve.
Fig. 5. A set of m a s t e r curves, o b t a i n e d in the same way as the curve s h o w n in fig. 3, for d i f f e r e n t v a l u e s of pH.
The inverse of the shifting factors, required to obtain all these master curves, are plotted in fig. 6 as a function of pH, for different temperatures. Using this plot, it was possible to obtain a set of curves which represents the inverse of the shifting factors as a function of temperature for different p H values; this is shown in fig. 7. It is possible to follow the same procedure to build a single master curve, for the set of curves shown in fig. 5. These curves were shifted with respect to the curve corresponding to p H = 8.50.
4.5 1.8.
T=23°C 3.5 T=30°C T=35°C
"7
kL
2.5
13t
T-_40oc
Lr. 1.5
T=55°C T_-~oc
1.05
T=76°C 05
0.8; 20
7
30
40 50 60 Temperature (°C)
70
80
Fig. 4. T h e inverse of the shifting factors u s e d to o b t a i n the m a s t e r curve are p l o t t e d as a function of the t e m p e r a t u r e .
7.5
8
8.5
pH
Fig. 6. T h e inverse of the shifting factors r e q u i r e d to o b t a i n the m a s t e r curves s h o w n in fig. 5 are p l o t t e d as a function of p H for d i f f e r e n t t e m p e r a t u r e s .
R. Arroyo et al. / Master behavior for gelation
94 4.5.
0.8 • * , o
3.5. "7 ~
pH=8.50 pH=8 .25 pH=8.00 pH=7.75
0.6
£
2.5.
0.4
1.5.
0.2
j
U.,
0.5. 20
40
60
80
0
100
Temperature (°C) Fig. 7. The inverse of the shifting factors required to obtain the master curves shown in fig. 5 are plotted as a function of temperature for different values of pH.
In this way it was possible to build a super-master curve. In this super-master curve is included all information about the gelation profile for a given p H and t e m p e r a t u r e of the system. In fig. 8 it is possible to observe the inverse of the shifting factors used to build the super-master curve as a function of p H for all temperatures. The supermaster curve obtained by collapsing the master curves shown in fig. 5 is shown in fig. 9. It is important to note in this figure that not all the master curves have the same value for the steady
200 Time (rain)
300
400
Fig. 9. The super-master curve obtained by shifting the master curves shown in fig. 5 with respect to the curve corresponding to a pH of 8.50.
state particle size. In order to prove the utility of this procedure, several systems with different values of t e m p e r a t u r e and p H were examined. One of these systems was carry out to gelation with a temperature of 35°C and a p H of 8.33. In fig. 10, it is possible to observe the experimental data taken under these conditions and the prediction obtained from the super-master curve. Another prediction was obtained for a system with a temperature of 60°C and a p H of 7.69. In fig. 11 it is possible to see the experimental data and the
0.4 1.30
-1.25
Experimental Data Prediction
pH=8.33 T=35°C
0.3
£
1.20 '7
',~
0.2
1.15
1.10
0.1
1.05
0.0 1.00
•
7.5
7.75
8
8.25
8.5
8.75
pH
Fig. 8. The inverse of the shifting factors required to obtain the super-master curve are plotted as a function of pH.
0
100
200
300
400
Time (min) Fig. 10. A comparison between the prediction obtained from the super-master curve and the experimental data, for a system with a pH of 8.33 and a temperature of 35°C.
./
0.4
Experimental Data Prediction 0.3 e0.2
R. Arroyo et al. / Master behavior for gelation
pH=7.69
T=~°C
0.1
0.0 t 00
200
300
400
Time (min) Fig. 11. A comparison between the experimental data and the predicted behavior for a system with a pH of 7.69 and a temperature of 60°C.
predicted gelation profile obtained from the super-master curve.
4. Discussion The DLS technique is appropriate to determined the gelation profile of a sol-gel system in the early stage of gelation. When the particle size of sols begins to be very large and the sol solution becomes optically opaque, the standard DLS technique is not longer valid, and it is necessary to switch to technique such as diffusion wave spectroscopy. As mentioned above the steady state particle size value for the particle size does not have to be the same for systems with different values of p H or temperature. W h e n the super-master curve was built, only the rising part of the profile was overlapped. Master curves are very useful because they allow prediction of behavior of similar systems when one or more p a r a m e t e r s are changed. The t e m p e r a t u r e was varied from room to boiling temperatures, which is a range where many s o l gel reactions are carried out. T h e p H was varied from 7.50 to 8.50. For p H values > 8.50 and high temperatures, the gelation process was too fast to
95
be followed by DLS, and for p H lower than 7.50 and low temperatures gelation time was longer than 90 h. The inverse of shifting factors as a function of t e m p e r a t u r e show two different regimes. In figs. 4 and 7 it is possible to observe that, for temperatures below 50°C, these factors are almost linear with temperature. Above this temperature, the system shows another regime where the inverse of the factors are also linear with temperature, but with a different slope. Ample evidence suggests [19] that these regimes correspond to either diffusion or reaction-limited processes. For low temperatures, the reactivity of the system is lower than at higher temperature; then the diffusion processes control sol aggregation to produce the gel. For high temperatures, the reactivity of the chemical reactions is higher, and convective flows appear which produce a transport of mass which is faster than that produced by diffusion. In this case, the process is controlled by reaction rate. Two predictions were made for systems with high value of p H (8.33) and low t e m p e r a t u r e (35°C) and vice versa (pH = 7.69 and T = 60°C). In both cases, the experimental result was in good agreement with predicted gelation profile. The largest difference between them is about 10 min for a gelation time of around 300 min. This means that the error introduced by the use of the super-master curve in the prediction of the gelation profile is about 3%.
5. Conclusions It is important to know the gelation profile of sol-gel systems for different values of external parameters, because the morphology of the end material is determined, to a great extent, by the way the system approach gelation. In this paper, the feasibility of use of the master curve to predict the gelation profile for systems where the t e m p e r a t u r e and p H has been specified is shown. The predicted gelation profiles are in good agreement with experimental data.
96
R. Arroyo et al. / Master behavior for gelation
References [1] L.L. Hench and J.K. West, Chem. Rev. 90 (1990) 33. [2] L.C. Klein and G.J. Garvey, Soluble Silicates (American Chemical Society, Washington, 1982) ch. 18, p. 293. [3] C.J. Brinker and G.W. Scherer, Sol-Gel Science. The Physics and Chemistry of Sol-Gel Processing (Academic Press, New York, 1989). [4] H. Schmidt, in: Better Ceramics Through Chemistry, ed. C.J. Brinker, D.E. Clark and D.R. Ulrich (North-Holland, New York, 1984) p. 327. [5] G. Phillip and H. Schmidt, J. Non-Cryst. Solids 63 (1984) 283. [6] R. Rodrlguez, M. Flores, J. G6mez and V. Castafio, Mater. Lett. 15 (1992) 242. [7] P. Yu, H. Liu and Y. Wang, J. Non-Cryst. Solids 52 (1982) 511. [8] E.J.A. Pope and J.D Mackenzie, J. Non-Cryst. Solids 87 (1986) 185.
[9] A.H. Boonstra, T.P.M. Meeuwsen, J.M.E. Baken and G.V.A. Aben, J. Non-Cryst. Solids 109 (1989) 153. [10] J.E. Moreira, M.L. Cesar and M.A. Aegerter, J. NonCryst. Solids 121 (1990) 394. [11] R. Arroyo and R. Rodrlguez, J. Non-Cryst. Solids 151 (1992) 229. [12] R. Rodr~guez, R. Arroyo and P. Salinas, J. Non-Cryst. Solids 159 (1993) 73. [13] C.J. Brinker, K.D. Keefer, D.W. Shaefer and C.J. Ashley, J. Non-Cryst. Solids 48 (1982) 47. [14] M. Yamame and T. Kojima, J. Non-Cryst. Solids 44 (1981) 181. [15] L.C. Klein and G.J. Garvey, J. Non-Cryst. Solids 38&39 (1980) 45. [16] B.J. Berne and R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976). [17] R. Rodrlguez, Rev. Mex. Fis. 38 (1992) 450. [18] D.F. Koppel, J. Chem. Phys. 57 (1972) 4814. [19] E.J.A. Pope and J.D. Mackenzie, J. Non-Cryst. Solids 101 (1988) 212.
JoUrNAL or
NON-CRYSTALLINESOLIDS
Master behavior for gelation in a sol-gel process under different temperature and pH conditions R. Arroyo a R. Rodrlguez
b a n d P. S a l i n a s a
a Departamento de Qufmica and b Departamento de F[siea, Universidad Autdnoma Metropolitana-lztapalapa, Apdo. Postal 55-534, Mdxico, D.F. 09340, Mexico
Received 15 January 1993 Revised manuscript received 3 May 1993
A master behavior for gelation in a sol-gel process as function of temperature and pH is reported in this paper. The sol-gel system was kept at reflux temperature until it reached steady state; then it was cooled to room temperature and the pH was adjusted to some value with in a specific range. Once the pH was adjusted, the temperature of the reaction was set to some value, and the system carried to gelation. The particle size profile of sols was obtained as a function of the reaction time using dynamic light scattering. It was from these gelation profiles obtained under different temperature conditions that a master behavior was obtained. With these master curves, it was possible to build a super-master curve which allows prediction of gelation profiles for systems where both the temperature and pH have been specified. Two predictions for systems with different values of temperature and pH led to excellent agreement between experimental and predicted behavior.
1. Introduction T h e silica s o l - g e l m e t h o d has b e c o m e very i m p o r t a n t in glass t e c h n o l o g y b e c a u s e it allows novel m a t e r i a l s with specific physical a n d c h e m i cal p r o p e r t i e s [1-3] to b e p r e p a r e d . G l a s s e s with high p u r i t y a n d h o m o g e n e i t y m a y b e m a d e at low t e m p e r a t u r e a n d a l m o s t any m e t a l m a y b e incorp o r a t e d by a d d i n g an a p p r o p r i a t e salt [1] a n d o r g a n i c p o l y m e r chains [3-5]. G e l a t i o n t i m e is o n e o f t h e m o s t i m p o r t a n t q u a n t i t i e s m e a s u r e d in a s o l - g e l system [6-8]. G e l a t i o n t i m e d e p e n d s on t e m p e r a t u r e , p H , c h e m i c a l c o m p o s i t i o n a n d catalyzing agent. S e v e r a l m e t h o d s have b e e n d e s i g n e d to d e t e r Correspondence to: Dr R. Rodrlguez, Departamento de Fisica, Universidad Aut6noma Metropolitana-Iztapalapa, Apdo. Postal 55-534, M~xico, D.F. 09340, Mexico. Tel.: +52-5 686 0322. Telefax: + 52-5 686 8999.
m i n e g e l a t i o n t i m e in a s o l - g e l system. It is usual to d e t e r m i n e g e l a t i o n t i m e by m e a s u r i n g the t i m e r e q u i r e d to the system surface to r e m a i n s t e a d y while the c o n t a i n e r was t i l t e d for 2 min [7]. G e l a tion time was also d e t e r m i n e d by m e a s u r i n g t h e t i m e r e q u i r e d for solution visc, 'ity to r e a c h an a r b i t r a r y value ( a p p r o x i m a t e l y ~qO00 Poise) [8]. T h e d y n a m i c light s c a t t e r i n g ( D L S ) .'~chnique has b e e n u s e d to c h a r a c t e r i z e reactio, p r o d u c t s in t h e s o l - g e l p r o c e s s [9,10]. W i t h this tec~,nique it was p o s s i b l e to o b t a i n sol p a r t i c l e size d u r i n g the e n t i r e s o l - g e l r e a c t i o n [11,12]. This t e c h n i q u e is a p p r o p r i a t e to follow g e l a t i o n kinetics of sols in solution, b e c a u s e it allows m e a s u r e m e n t o f sol size as a f u n c t i o n o f the r e a c t i o n t i m e [6]. It is k n o w n t h a t a catalyst can d r a m a t i c a l l y i n f l u e n c e t h e g e l a t i o n p r o c e s s [6,8]. T h e g e l a t i o n p r o c e s s e s o f m e t a l alkoxides involve hydrolysis a n d p o l y m e r i z a t i o n reactions. T h e v a r i a t i o n o f t h e g e l a t i o n t i m e c a n n o t b e e x p l a i n e d solely on
0022-3093/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
R. Arroyo et al. / Master behavior for gelation
the basis of pH and the relative dissociation of the catalyst. The reaction mechanism involved with each catalyst must also be considered [8]. The gelation process is important because it is possible to relate the catalytic mechanism of the gelation process with the gel microstructure and properties. The way the chemical reaction is catalyzed determines, to some extent, what type of structure will be obtained, because the hydrolysis and polycondensation reactions depend strongly on if the system is acid- or base-catalyzed [13-15]. The hydrolysis rate is increased with an acid catalyst. It has been postulated [13-15] that a fine network structure of linear chains is formed when the gel is acid-catalyzed. In the low pH regime, linear chain growth seems to be preferred. This may be the result of higher reactivities at chain ends, promoting linear chain growth due to a lower mass density, allowing easier approach of reactive groups. In the case of an alkali catalyst, the rate of hydrolysis is apparently low. When the sol-gel process is base-catalyzed, the hydrolysis reaction is enhanced, producing many sol particles which grow in size and number as the sol-gel transition takes place. More dense colloidal particles with large interstices are produced in this case. The purpose of this work was to investigate the gelation profile under different chemical conditions, once the sol particle size has reached a constant value. We found different gelation profiles as a function of the pH and temperature of the reaction and it was possible to obtain a master behavior for these gelation profiles.
2. Experimental Silica particles were prepared by mixing 12 tool of ethanol reactive grade and 0.0025 mol of cobalt (II) acethyl-acetonate (Aldrich Chem. Co.) at room temperature until the salt was completely dissolved. This salt was added in order to accelerate the sol-gel reaction [11] and to include cobalt into the glass as a doping agent. After this, 4 mol CO 2 free tri-distilled water was added to the mixture without stopping the stirring. One mol of
91
tetraethyl ortosilicate (TEOS) (J.T. Baker) was added to the mixture. It has been reported [11,12] that, under similar conditions, the particle size profile shows a set of characteristic peaks in the early stage of the reaction. These correspond to unstable oscillations of the system due to the auto-catalytic nature of the reaction. After then, the profile reaches a condition where the size of sol particles remains particles remains practically constant with time. In this regime, the unstable damped oscillations disappear and the system reaches steady state. The relative scattered intensity (the ratio between the scattered and the incident intensities) grows practically linearly with the reaction time. Because the scattered intensity depends on the product of concentration and molecular weight of scattering particles, then, because the particle size is constant [11,12], it is the sol concentration which grows with time. This is the way the system reaches gelation. Because the main interest here is gelation, the first part of the particle size profile was not considered. We waited 165 min until the sol particle site reached a constant values before cooling the system to room temperature. Once the system reached room temperature, the pH of the solution was adjusted to a specific value in the range from 7.25 to 8.50 using a solution of ammonium hydroxide in ethanol (1 : 1 in volume). We chose this procedure because the pH is strongly dependent on the temperature and the specific time at which the pH is adjusted with respect to starting time of the reaction. Once the pH of the system was adjusted to a specific value, the sol solution was split in different reactors and heated to different temperatures, within the range from 23 to 76°C, until all reached gelation. Reactors were sampled regularly. Because the DLS technique measures the particle size profile through the determination of the diffusion coefficients of sols, and these coefficients depend linearly upon temperature (Einstein's relationship), every sample was cooled to room temperature. In this way, the chemical reaction was practically stopped within the times necessary to obtain a correlation function, and to guarantee a constant temperature during the 2-5
92
R. Arroyo et al. / Master behavior for gelation 0.4
min measuring time depending on the intensity of the scattered light. This procedure was repeated for different values of the p H for the same set of temperatures.
pH=8.50 T=23°C 0.3
o 2.1. Particle size measurements
DLS 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 [16]. The light scattering apparatus used to measure the particle size is very similar to that described elsewhere [17]. An argon ion laser (Lexel model 75) operating at l 0 = 488 nm was used as our light source with the light b e a m focused in the scattering cell with a b e a m diameter of 100 Ixm. A standard borosilicate glass cuvette of 10 m m 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 photomultiplier tube ( I T T model FW130) whose output went to a high bandwidth digital pre-amplifier, amplifier, discriminator and finally digital correlator ( L a n g l e y - F o r d model 1096). The data were fitted using the first two cumulants in an cumulant's expansion [18] of the time autocorrelation function. The solvent viscosity was chosen as 1.5256 cPoise because it was shown [12] that this value does not change in an appreciable way during the steady state regime, and the refractive index of the solvent was chosen as 1.3655.
3. Results
'~
0.2
0.1
0.0 200
250
300 Time (min)
350
400
Fig. 1. A particle size profile where the first part corresponds to a steady state characterized by a constant value of the size of sols. The last part of this profile corresponds to gelation where the particle size grows very fast with the reaction time.
of the reaction time. In fig. 2 it is possible to see the set of size profiles for five different temperatures corresponding to a p H adjusted to 8.50. In this figure, it is possible to observe the way the sol-gel systems reached gelation at different temperatures, for a p H value of 8.50. In order to obtain a master curve, all these curves were shifted with respect to the curve which corresponds to a temperature of 76°C, which was taken as the reference. In fig. 3 it is
0.8 e~ o
pH=8.5
76°C
0.8
L)
In fig. 1 it is possible to see typical particle size profile for a system with a p H of 8.50 and room temperature. The unstable behavior of the particle size profile is not shown. The first part of this profile corresponds to the steady state regime where the particle size remain practically constant with the time. The last part corresponds to the gelation regime where the size grows rapidly with time. For each p H value, the particle size profiles at different temperatures were plotted as a function
0.4 ~z
40°C
0.2
.
~
°C
0,0 100
200 Time (min)
300
400
Fig. 2. A set of gelation profiles is shown for different values of temperature. In this case the pH of the system was adjusted to 8.5.
R. Arroyo et al. / Master behavior for gelation 0.8 ¸
93
0.8pH=8.5
) pH=8.50
0.6
~H=8.25 pH=8.00
0.6-
e-
p._-7 50
O
¢9
0.4
"~ 0.4"
0.2
0.2.
pH=7.75
N
0 0
100
200
300
400
0
100
Time (min)
200
3(10
400
Time (rain)
Fig. 3. T h i s plot shows a m a s t e r curve o b t a i n e d by shifting the curves s h o w n in fig. 2. T h e s a m e scale in t i m e as in fig. 2 was u s e d to see the effect of the shifting process.
possible to observe all curves collapsed in one curve which is called a master curve. T h e shifting factors required to overlap all the profiles shown in fig. 2 are plotted in fig. 4. T h e same p r o c e d u r e was carried out for the o t h e r p H values; for each p H value, a master curve can be o b t a i n e d following the same procedure as m e n t i o n e d before. In fig. 5 are plotted all the m a s t e r curves, where the p H values assigned to each one are shown in c o r r e s p o n d i n g master curve.
Fig. 5. A set of m a s t e r curves, o b t a i n e d in the same way as the curve s h o w n in fig. 3, for d i f f e r e n t v a l u e s of pH.
The inverse of the shifting factors, required to obtain all these master curves, are plotted in fig. 6 as a function of pH, for different temperatures. Using this plot, it was possible to obtain a set of curves which represents the inverse of the shifting factors as a function of temperature for different p H values; this is shown in fig. 7. It is possible to follow the same procedure to build a single master curve, for the set of curves shown in fig. 5. These curves were shifted with respect to the curve corresponding to p H = 8.50.
4.5 1.8.
T=23°C 3.5 T=30°C T=35°C
"7
kL
2.5
13t
T-_40oc
Lr. 1.5
T=55°C T_-~oc
1.05
T=76°C 05
0.8; 20
7
30
40 50 60 Temperature (°C)
70
80
Fig. 4. T h e inverse of the shifting factors u s e d to o b t a i n the m a s t e r curve are p l o t t e d as a function of the t e m p e r a t u r e .
7.5
8
8.5
pH
Fig. 6. T h e inverse of the shifting factors r e q u i r e d to o b t a i n the m a s t e r curves s h o w n in fig. 5 are p l o t t e d as a function of p H for d i f f e r e n t t e m p e r a t u r e s .
R. Arroyo et al. / Master behavior for gelation
94 4.5.
0.8 • * , o
3.5. "7 ~
pH=8.50 pH=8 .25 pH=8.00 pH=7.75
0.6
£
2.5.
0.4
1.5.
0.2
j
U.,
0.5. 20
40
60
80
0
100
Temperature (°C) Fig. 7. The inverse of the shifting factors required to obtain the master curves shown in fig. 5 are plotted as a function of temperature for different values of pH.
In this way it was possible to build a super-master curve. In this super-master curve is included all information about the gelation profile for a given p H and t e m p e r a t u r e of the system. In fig. 8 it is possible to observe the inverse of the shifting factors used to build the super-master curve as a function of p H for all temperatures. The supermaster curve obtained by collapsing the master curves shown in fig. 5 is shown in fig. 9. It is important to note in this figure that not all the master curves have the same value for the steady
200 Time (rain)
300
400
Fig. 9. The super-master curve obtained by shifting the master curves shown in fig. 5 with respect to the curve corresponding to a pH of 8.50.
state particle size. In order to prove the utility of this procedure, several systems with different values of t e m p e r a t u r e and p H were examined. One of these systems was carry out to gelation with a temperature of 35°C and a p H of 8.33. In fig. 10, it is possible to observe the experimental data taken under these conditions and the prediction obtained from the super-master curve. Another prediction was obtained for a system with a temperature of 60°C and a p H of 7.69. In fig. 11 it is possible to see the experimental data and the
0.4 1.30
-1.25
Experimental Data Prediction
pH=8.33 T=35°C
0.3
£
1.20 '7
',~
0.2
1.15
1.10
0.1
1.05
0.0 1.00
•
7.5
7.75
8
8.25
8.5
8.75
pH
Fig. 8. The inverse of the shifting factors required to obtain the super-master curve are plotted as a function of pH.
0
100
200
300
400
Time (min) Fig. 10. A comparison between the prediction obtained from the super-master curve and the experimental data, for a system with a pH of 8.33 and a temperature of 35°C.
./
0.4
Experimental Data Prediction 0.3 e0.2
R. Arroyo et al. / Master behavior for gelation
pH=7.69
T=~°C
0.1
0.0 t 00
200
300
400
Time (min) Fig. 11. A comparison between the experimental data and the predicted behavior for a system with a pH of 7.69 and a temperature of 60°C.
predicted gelation profile obtained from the super-master curve.
4. Discussion The DLS technique is appropriate to determined the gelation profile of a sol-gel system in the early stage of gelation. When the particle size of sols begins to be very large and the sol solution becomes optically opaque, the standard DLS technique is not longer valid, and it is necessary to switch to technique such as diffusion wave spectroscopy. As mentioned above the steady state particle size value for the particle size does not have to be the same for systems with different values of p H or temperature. W h e n the super-master curve was built, only the rising part of the profile was overlapped. Master curves are very useful because they allow prediction of behavior of similar systems when one or more p a r a m e t e r s are changed. The t e m p e r a t u r e was varied from room to boiling temperatures, which is a range where many s o l gel reactions are carried out. T h e p H was varied from 7.50 to 8.50. For p H values > 8.50 and high temperatures, the gelation process was too fast to
95
be followed by DLS, and for p H lower than 7.50 and low temperatures gelation time was longer than 90 h. The inverse of shifting factors as a function of t e m p e r a t u r e show two different regimes. In figs. 4 and 7 it is possible to observe that, for temperatures below 50°C, these factors are almost linear with temperature. Above this temperature, the system shows another regime where the inverse of the factors are also linear with temperature, but with a different slope. Ample evidence suggests [19] that these regimes correspond to either diffusion or reaction-limited processes. For low temperatures, the reactivity of the system is lower than at higher temperature; then the diffusion processes control sol aggregation to produce the gel. For high temperatures, the reactivity of the chemical reactions is higher, and convective flows appear which produce a transport of mass which is faster than that produced by diffusion. In this case, the process is controlled by reaction rate. Two predictions were made for systems with high value of p H (8.33) and low t e m p e r a t u r e (35°C) and vice versa (pH = 7.69 and T = 60°C). In both cases, the experimental result was in good agreement with predicted gelation profile. The largest difference between them is about 10 min for a gelation time of around 300 min. This means that the error introduced by the use of the super-master curve in the prediction of the gelation profile is about 3%.
5. Conclusions It is important to know the gelation profile of sol-gel systems for different values of external parameters, because the morphology of the end material is determined, to a great extent, by the way the system approach gelation. In this paper, the feasibility of use of the master curve to predict the gelation profile for systems where the t e m p e r a t u r e and p H has been specified is shown. The predicted gelation profiles are in good agreement with experimental data.
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R. Arroyo et al. / Master behavior for gelation
References [1] L.L. Hench and J.K. West, Chem. Rev. 90 (1990) 33. [2] L.C. Klein and G.J. Garvey, Soluble Silicates (American Chemical Society, Washington, 1982) ch. 18, p. 293. [3] C.J. Brinker and G.W. Scherer, Sol-Gel Science. The Physics and Chemistry of Sol-Gel Processing (Academic Press, New York, 1989). [4] H. Schmidt, in: Better Ceramics Through Chemistry, ed. C.J. Brinker, D.E. Clark and D.R. Ulrich (North-Holland, New York, 1984) p. 327. [5] G. Phillip and H. Schmidt, J. Non-Cryst. Solids 63 (1984) 283. [6] R. Rodrlguez, M. Flores, J. G6mez and V. Castafio, Mater. Lett. 15 (1992) 242. [7] P. Yu, H. Liu and Y. Wang, J. Non-Cryst. Solids 52 (1982) 511. [8] E.J.A. Pope and J.D Mackenzie, J. Non-Cryst. Solids 87 (1986) 185.
[9] A.H. Boonstra, T.P.M. Meeuwsen, J.M.E. Baken and G.V.A. Aben, J. Non-Cryst. Solids 109 (1989) 153. [10] J.E. Moreira, M.L. Cesar and M.A. Aegerter, J. NonCryst. Solids 121 (1990) 394. [11] R. Arroyo and R. Rodrlguez, J. Non-Cryst. Solids 151 (1992) 229. [12] R. Rodr~guez, R. Arroyo and P. Salinas, J. Non-Cryst. Solids 159 (1993) 73. [13] C.J. Brinker, K.D. Keefer, D.W. Shaefer and C.J. Ashley, J. Non-Cryst. Solids 48 (1982) 47. [14] M. Yamame and T. Kojima, J. Non-Cryst. Solids 44 (1981) 181. [15] L.C. Klein and G.J. Garvey, J. Non-Cryst. Solids 38&39 (1980) 45. [16] B.J. Berne and R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976). [17] R. Rodrlguez, Rev. Mex. Fis. 38 (1992) 450. [18] D.F. Koppel, J. Chem. Phys. 57 (1972) 4814. [19] E.J.A. Pope and J.D. Mackenzie, J. Non-Cryst. Solids 101 (1988) 212.