J. Phys. Chem. B 2005, 109, 3893-3897
3893
A Nonisothermal Study of the Kinetics of the Nanoporosity Elimination in Sonogels-derived Silica Xerogels Dimas R. Vollet,* Wadley C. de Castro, Dario A. Donatti, and Alberto Iban˜ ez Ruiz Unesp - UniVersidade Estadual Paulista, IGCE, Departamento de Fı´sica, Cx.P. 178, 13500-970 Rio Claro, Sa˜ oPaulo, Brasil ReceiVed: October 14, 2004; In Final Form: December 31, 2004
A nonisothermal study of the kinetics of the nanoporosity elimination in monolithic silica xerogels, prepared from acid and ultrasound catalyzed hydrolysis of tetraethylortosilicate (TEOS), has been carried out by means of in situ linear shrinkage measurements performed with different heating rates. The study could be applied up to almost R ∼ 0.6 of the volume fraction R of eliminated pores. The activation energy was found increasing from about 3.2 × 102 kJ/mol for R ∼ 0.06 up to about 4.4 × 102 kJ/mol for R ∼ 0.44. The sintering process accompanying the nanopore elimination in this set of xerogels is in agreement with a viscous flux sintering process with the hydroxyl content diminishing with the volume fraction of eliminated pores. All the volume fraction of eliminated pores versus temperature (T) curves can be matched onto a unique curve with an appropriate rescaling of the T axis, independent of the heating rate. This scaling property suggests that the path of sintering seems the same, regardless of the heating rate; the difference is that the rate is faster at higher temperature.
Introduction A large variety of glasses and glass ceramics have been obtained by sol-gel process from the hydrolysis and polycondensation of tetraethoxysilane (TEOS).1 Because water and TEOS are immiscible, a mutual solvent such as ethanol is usually employed as a homogenizing medium for the TEOS hydrolysis in the conventional sol-gel method. Sonochemistry is an alternative method to promote hydrolysis of solventless TEOS-water immiscible mixtures in the presence of the catalyst.2-4 The structure and properties of the final product have been found to be strongly dependent on the conditions of preparation.2,5 Wet sonogels frequently exhibit structure consisting of a continuous solid network embedded in an up to almost 98% volume fraction liquid phase. Drying is the most critical step of the sol-gel processing in obtaining monolithic dried gels.6 Supercritical drying (aerogels), freeze-drying (cryogels), and evaporation drying (xerogels) are the usual methods in the production of dried gels.1 The structure and properties of xerogels have attracted the attention of several researchers for a wide variety of applications. Silica xerogels have been considered as appropriate matrices for the preparation of complex-centers doped materials for a variety of metallic ions7,8 and encapsulation of a variety of organic2,9,10 and inorganic compounds,3,11 with interesting optical and/or electronic properties. The characteristic interconnected mesoporous structure of xerogels has as well as been considered as an important transport medium for a variety of applications such as controlled-release carrier implantable materials for low molecular weight drugs in medicine12,13 and as substitute materials for membrane processes in fuel cells.14 Thus, the * Corresponding author: FAX +55-19 3526 2237; e-mail: vollet@ rc.unesp.br
nanoporous structure, the stability of the nanopores and the kinetics of pore elimination are naturally a matter of interest for control purposes in xerogel production. Silica xerogels prepared from acid and ultrasound catalyzed hydrolysis of TEOS exhibit, between about 570 and 1070 K (∼300 and ∼800 °C), a fairly stable nanoporous structure15,16 composed of pores having fully random shape, size, and distribution. The pore mean size and the specific surface area were evaluated as 1.3 nm and 600 m2/g, as determined through the DAB model17 by small-angle X-ray scattering, and 1.9 nm and 400 m2/g, as determined through the BET method by nitrogen adsorption.17 The difference between the values obtained from these techniques is that the BET method is not be so well suited to microporous solids.18 The pore size distribution from nitrogen adsorption isotherms has been found in the range of pore-width below about 5 nm, the incremental pore volume increasing exponentially in the micropore region.17 However, the total pore volume as measured by the volume of nitrogen adsorbed at the nitrogen saturation pressure is in agreement with the value measured directly from mass and volume determinations. This means that the pores of the xerogel structure are interconnected. Such a nanoporous structure is readily eliminated16,17 at temperatures higher than about 1170 K (∼900 °C), probably above of the glass transition temperature of the xerogels. It has been found that the nanoporosity elimination in the sonogelderived xerogels under an isothermal hold gives place in such a mechanism that the pore volume fraction and the specific surface are diminished while the pore mean size is kept constant.17 In this work, we present an in-situ study carried out by means of dilatometric thermal analysis of the nonisothermal kinetics of the nanoporosity elimination in silica xerogels prepared from acid and ultrasound catalyzed hydrolysis of TEOS.
10.1021/jp0452960 CCC: $30.25 © 2005 American Chemical Society Published on Web 02/09/2005
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Figure 1. Monolithic silica xerogel samples as obtained after isothermal hold at 1023 K during 10 h (A) and after dilatometric tests performed with heating rates of 5 K/min (B) and 10 K/min (C).
Experimental Section Samples were prepared from the sonohydrolysis of mixtures of 25 mL of tetraethoxysilane (TEOS), 8 mL of distilled and dionized water, and 5 mL of 0.1 N HCl as a catalyst. The resulting pH of the mixture was about 1.5 to 2.0. The hydrolysis was promoted during 10 min under a constant power (60 W) of ultrasonic radiation. Next, water was added to the sol (the dilution is desired in order to favor the obtaining of monolithic xerogels after drying) and the pH was adjusted to 4.5 by addition of NH4(OH) to accelerate the gelation process. The final water/ TEOS molar ratio of the resulting sol was equal to 14.4. The sol was cast in sealed 1 cm diameter glass tubes and kept at 313 K for gelation and aging for 30 days. The tubes were opened and kept covered by a thin aluminum foil to allow the samples to dry very slowly for 20 days to obtain about 50mm height and 6-mm diameter monolithic cylindrical samples of the xerogels. The monolithic xerogels were slowly heated (with heating rates as small as 1 K/hour at low temperatures) under atmospheric conditions up to 1023 K for an isothermal hold during 10 h. The samples were cooled back to ambient temperature with the inertia of the turned-off oven to get monolithic cylindrical samples of xerogels, such as that shown in Figure 1A. The samples were submitted to dilatometric tests up to 1270 K with different heating rates under atmospheric conditions. The linear shrinkage (∆L/L0) of the samples was measured as a function of the temperature T (or the time t) for constant heating rates β ) dT/dt of 2, 5, 10, 12.5, and 15 K/min. The maximum measurable value of the linear shrinkage (∆L/L0) on the experimental dilatometric device is about 6%. Results Figure 2A shows the curves of the linear shrinkage (∆L/L0) as a function of the temperature T for monolithic xerogels after isothermal hold at 1023 K during 10 h, as measured by dilatometric tests under heating rates β ) dT/dt of 2, 5, 10, 12.5 and 15 K/min. We attribute the abrupt linear shrinkage at around 1070-1300 K (depending on the heating rate) to a quantitative measurement of the kinetics of the nanopore elimination process in the sonogel-derived silica xerogels.15-17 We have estimated that ∆T ∼ (cFR2/4k)β should be the temperature difference between the surface and the center temperature of a cylinder sample under a “steady state” heat flow with a heating rate β, where R is the sample radius, c the specific heat, F the density, and k the thermal conductivity. Assuming c ∼ 8 × 102 J/kg‚K and k ∼ 0.5 W/m‚K (the last as a typical value for nanoporous xerogels19), together with R ∼ 3 × 10-3 m and F ∼ 1.6 × 103 kg/m3 for our samples, we obtain ∆T ∼ 1.5 K for β ) 15 K/min, the most critical heating in our case, which is even a negligible value for the present purposes.
Figure 2. (A) Linear shrinkage (∆L/L0) as a function of temperature T as measured by dilatometric tests performed with different constant heating rates for monolithic xerogels after isothermal hold at 1023 K during 10 h. (B) Evaluated volume fraction of eliminated pores (R). The plateaus and the range of the abrupt variation in ∆L/L0 for the samples with 12.5 and 15 K/min in (A) were not plotted in (B).
The volume fraction R of eliminated pores at time t (or temperature T since β ) constant) is defined as R ) (∆V/Vp), where ∆V is volume contraction of the sample at time t and Vp the total pore volume of the sample. According to data from nitrogen adsorption measurements,17 the starting xerogels after isothermal hold at 1023 K for 10 h present Vp ) 0.17 cm3/g, which yields a pore volume fraction φ of about 0.27, assuming the value 2.2 g/cm3 for the skeletal density of the xerogels, as frequently quoted for fused silica. Under the assumption of isotropic volume shrinkage in the nanopore elimination process, the fraction R of the eliminated porosity at time t can be cast in terms of the linear shrinkage (∆L/L0) as
R)
∆V 1 ∆V 3 ∆L ) ) Vp φ V0 φ L0
(1)
The introduction of the variable R is justified because it accounts directly for the volume fraction of eliminated pores, which is hardly viewed directly from ∆L/L0. The magnitude and the characteristic of interconnection of the initial porosity φ have been well established by two independent experimental methods: measuring the volume of nitrogen adsorbed at the nitrogen saturation pressure17 and measuring the pore volume directly from mass and volume determinations. Anyway, R is mathematically equivalent to the linear shrinkage, and the proportionality constant between R and ∆L/L0 introduced in eq 1 does not affect the results in the following analyses. Figure 2B shows the values of the volume fraction R of eliminated pores as a function of temperature T for different heating rates β. The plateau at about 6% linear shrinkage (Figure 2A) is due to the maximum measurable value on the experimental device in measuring shrinkage events. For the samples with heating rates of 12.5 and 15 K/min, there is a discontinuity in the first derivate of the liner shrinkage curves at around 2% linear shrinkage (before the experimental limit of 6% linear shrinkage has been attained), yielding a very sharp and abrupt apparent linear contraction. This may be due to the appearance of cracks in the samples submitted to the heating rates of 12.5 and 15 K/min. In this work, we are referring up to about 60% of the pore elimination for samples with heating rates of 2, 5,
Kinetics of the Nanoporosity Elimination
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Figure 3. Plots showing that the values of the dR/dT slopes depend on the fraction R but not on the heating rate β, suggesting a scaling property of the system.
and 10 K/min, and only up to about 20% of the pore elimination for samples with heating rates of 12.5 and 15 K/min (Figure 2B). Cracking may be caused by relief of stresses due to differential strain induced by nonhomogeneous thermal expansion in the porous medium under heating. It depends on the pore size and the porosity and would be favored under higher heating rates. The nanopore elimination rate dR/dt can be obtained from the slopes dR/dT of the curves of Figure 2B as dR/dt ) βdR/ dT, where β ) dT/dt is the heating rate. Figure 3 shows dR/dT evaluated from the slopes of the curves of Figure 2B. The curves dR/dT obtained for different heating rates fall all in a single curve that depends exclusively on the volume fraction R of eliminated pores, at least up to R ∼ 0.6. We have obtained from linear fitting that the function dR/dT ) (0.060 K-1)R1.32 describes well the data of Figure 3, independent of the heating rate β, and thus accounts for a scaling property of the system. This means that all the ∆L/L0 versus T curves can be matched onto a unique curve with an appropriate rescaling of the T axis. Thus, the path of the sintering seems the same, regardless of the heating rate; the differences are that the rate is faster at higher temperature. It would definitely be interesting to check whether this scaling property persists if a given value of ∆L/L0 is obtained for a more complex path than linear heating, for instance with initial isothermal stages of various duration followed by linear heating with a single β. However, isothermal holds in the range of the abrupt increase in the linear shrinkage rate may not be completely equivalent to be directly compared to constantheating-rate studies.
Figure 4. Arrhenius plots of β(dR/dT). The slopes of the straight lines and thus the apparent energy of activation of the process are different for different R values.
TABLE 1: Apparent Activation Energy E and Kinetic Factor Af(r) as a Function of the Volume Fraction r of Eliminated Pores in Sonogel-derived Xerogels R
E (102kJ/mol)
Af(R) (min-1)
0.06 0.11 0.17 0.22 0.33 0.44
3.2 ( 0.1 3.3 ( 0.1 3.6 ( 0.1 4.1 ( 0.2 4.0 ( 0.2 4.4 ( 0.2
∼2.5 1012 ∼1.3 1013 ∼1.6 1014 ∼4 1016 ∼2 1016 ∼1 1018
isothermally in an infinitesimal time dt, in which the reaction (or porosity elimination) rate dR/dt can be cast as21
dR E ) Af(R) exp dt RT
(
(2)
where R is the fraction of eliminated nanopores at time t, T the absolute temperature, E the activation energy, R the gas constant, and Af(R) a kinetic factor where A is a frequency factor and f(R) a function of the fraction of the eliminated porosity. Under the condition of constant heating rate (β ) dT/dt ) constant), eq 2 can be cast as
Discussion The densification process probed by the abrupt variation of ∆L/L0 in the range 1070-1300 K in this work could be assigned to the range associated with the final of region II and all region III, according to the classification adopted by Arau´jo et al.20 in their study of the tetramethoxysilane-derived sol-gel glass densification through constant-heating-rate techniques. The earlier stages of densification associated with their classification do not belong to the scope of this work because our xerogels have been previously treated at 1023 K for 10 h. Arau´jo et al.20 have concluded that sintering is the mechanism by which the linear shrinkage in the final of region II and all region III occurs. The reason for sintering mechanisms acting even at such low temperatures for pure silica is the decrease in the viscosity of the material due to the presence of hydroxyls. Nonisothermal kinetic methods are based on the assumption that the nonisothermal reaction (or porosity elimination) occurs
)
E dR ) Af(R) exp dT RT
β
(
)
(3)
The activation energy E can be directly evaluated from eq 3 by plotting log[β(dR/dT)] versus 1/T as evaluated for a given value of R (R ) constant) for different heating rates β. Under this condition, the plot log[β(dR/dT)] versus 1/T yields a straight line with slope equal to -E/R‚ln10 and intercept log[Af(R)]. Figure 4 shows the plots of log[β(dR/dT)] versus 1/T for R ) 0.06, 0.11, 0.17, 0.22, 0.33, and 0.44. Table 1 shows the activation energy E and the kinetic factor Af(R) evaluated from the linear fittings. The value for the activation energy was found increasing from about 3.2 × 102 kJ/mol for R ) 0.06 up to about 4.4 × 102 kJ/mol for R ) 0.44. We have found from linear fitting that E(R) ) (3.0 + 3.1R) × 102 kJ/mol is a reasonable function to describe the activation energy in the studied R range.
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The increase of the value of the activation energy associated to the nanopore elimination in the present xerogels is in agreement with the results expected for sintering processes in silica gels submitted to constant heating rates.1 It has been pointed out that the value of the apparent activation energy for sintering process of silica gels depends on the hydroxyl contents, which should change with temperature and time along a constant-heating-rate experiment.22 The value of the energy of activation for viscous flux sintering in silica-based materials is frequently quoted as about 4.8 × 102 kJ/mol, this value diminishing significantly with the hydroxyl group content.1 For instance, Arau´jo et al.20 have found (2.7 ( 0.3) × 102 kJ/mol for the activation energy at the beginning of region III (according to their classification), in which the hydroxyl content was significant. Values for the activation energy changing between 5 × 102 and 7 × 102 kJ/mol have also been reported1 for silica glasses, with hydroxyl contents changing from 0.12 to 0.0003 weight %. These values are somewhat higher than those of the present work. It may be due to the different hydroxyl contents, which are frequently higher in alkoxide-derived sonogels. The hydroxyl content, which affects the viscosity of the gels, has a rather complex dependence on the heating rate. The more rapidly heated sample retains more hydroxyls, which depress its viscosity, and the pore elimination rate is increased. On the other hand, excessively rapid heating unavoidably provokes differential stresses causing the gel to crack. The cracking process could also be an additional reason for the increase of the rate of the pore elimination since it could be changing the surrounding conditions for the sintering process. The kinetic factor Af(R) was found increasing from ∼1012 min-1 for R ) 0.06 up to ∼1018 min-1 for R ) 0.44 (Table 1). We do not expect f(R) increasing with R. For instance, for a typical n-order reaction (non autocatalytic reaction) we expect f(R) decreasing with R to account for the diminution of the reaction rate dR/dt as the reacted quantity R increases. Even though f(R) could be increasing with R (as in an autocatalytic reaction) in the present xerogels, because a particular variation in the pore size distribution or the existence of some relation between pore elimination and cracking process, we would not expect a change of such an order of magnitude. This suggests that the frequency factor A may be increasing with R, accompanying the activation energy behavior. The variation of the kinetic factor Af(R) with the advance of R can be determined from the experimental data through eq 3 using the function E(R) ) (3.0 + 3.1R) × 102 kJ/mol for the activation energy. Then,
( )
E(R) dR exp dT RT
Af(R) ) β
(4)
Figure 5 shows the plots of Af(R) versus R for the different heating rates β. The scaling property dR/dT ) 0.060R1.32 was used in eq 4 to plot the curves in Figure 5, but it is not a necessary condition since we have the experimental dR/dT. The plots in Figure 5 fall all in the same curve for all the heating rates β, including the values of the Table 1. Then we have another independent scaling property of the system: the kinetic factor Af(R) can be matched onto a unique curve with an appropriate rescaling of T since R and T scales according to dR/dT ) 0.060R1.32. This result corroborates the suggestion that the path of sintering seems the same, regardless of the heating rate; the differences are that the rate is faster at higher temperature. Figure 5 also shows a slightly increase of the kinetic factor Af(R) at very small values of R. This may represent a true diminution of the function f(R) with the advancing of R. From
Figure 5. Kinetic factor Af(R) as a function of the fraction R of eliminated pores for different heating rates β. All the curves obtained at various heating rates fall on a unique curve. The points (0) represent Af(R) evaluated from the linear coefficients of the straight lines fitted in Figure 4.
the experimental data, we can determine the kinetic factor Af(R) as a function of R, but we could not probe, however, the evolution on the frequency factor A and on the function f(R) separately. Several studies1,22,23 using linear shrinkage measurements (∆L/L0) in the sintering of silica gels have assumed a power law approach (∆L/L0)-n, where n is a parameter which is a function of mechanism of transformation, as a measure of the function f(R). By substitution of f(R) ∼ R-n in eq 2 and recognizing that E . RT, the integration of eq 2 has been approximated by1
Rn+1 )
[
] ( )
2 1 ART (n + 1) E exp β E RT
(5)
so that, under the condition of constant T, a plot of lnR versus lnβ should yield a straight line with slope equal to -1/(n+1). However, the method fails in studying the present xerogels because A and E were found both as a function of R, thus the integration yielding eq 5 may not be quite suitable. Determinations of the evolution of f(R) would be useful because it could be associated with geometrical factors related to the size and distribution of pores and also with the cracking rate, which should have a complex dependence on the pore mean size and the porosity. It has been found,17 from isothermal hold experiments, that the pore elimination in sonogel-derived xerogels occurs in such a way that the pore volume and the specific surface area diminish, while the pore mean size is kept constant. Besides, the pore size distribution curves normalized by the total pore volume17 fall all onto a unique curve, independent of temperature and time of the isothermal hold in the temperature range of the nanopore elimination. These results support a mechanism of pore elimination in which certain volume fractions are left free of pores and other fractions untouched. Thus, other mechanisms could be actuating together with the viscous flow sintering. At the last, the cracking appearance should be changing the surrounding conditions for the sintering. It has also been pointed out22 that the removal of ultramicropores (present in these sonogel-derived xerogels) by viscous sintering is analogous to structural relaxation since ultramicropores are essentially indistinguishable from free volume. Additional information about the sintering mechanism could be obtained by comparing the present data with the existing sintering models1 such as Scherer’s cylinder model for
Kinetics of the Nanoporosity Elimination interconnected pores or Mackenzie-Shuttleworth for isolated pores. However, these models are more properly applied when sintering is performed isothermally in which the gel viscosity is single valued. Finally, we observed that all the samples were found foamed and bloated at the final of the test as shown in Figure 1 (B and C). The foaming phenomenon has been observed17 to occur close to the final fraction of the pore elimination, very far beyond the maximum R ∼0.6, to which the present study is referring. Then, the foaming/bloating phenomenon is off the point of the curves of Figure 2. However, it has also been found that foaming seems to be favored by isothermal holds.17 In fact, the sample heated at 5 K/min (Figure 1B) was found more bloated than that heated at 10 K/min (Figure 1C) at the final of the process. Conclusions The kinetics of the nanoporosity elimination in silica xerogels prepared from acid and ultrasound catalyzed hydrolysis of TEOS has been studied by a nonisothermal method of linear shrinkage using thermal dilatometric analysis. The value of the activation energy was found varying from about 3.2 × 102 kJ/mol for 6% of volume fraction of eliminated pores up to about 4.4 × 102 kJ/mol for 44% of volume fraction of eliminated pores. The sintering process accompanying the nanopore elimination in the present silica xerogels was found to be in agreement with a viscous flux sintering process with the hydroxyl group content diminishing with the fraction of eliminated pores. All the volume fraction R of eliminated pores versus temperature (T) curves can be matched onto a unique curve with an appropriate rescaling of the T axis, independent of the heating rate. This scaling property suggests that the path of sintering seems the same, regardless of the heating rate; the differences are that the rate is faster at higher temperature. Acknowledgment. Research partially supported by FAPESP, Brazil.
J. Phys. Chem. B, Vol. 109, No. 9, 2005 3897 References and Notes (1) Brinker, C. J.; Scherer, G. W. Sol-Gel Science: The Physics and Chemistry of Sol-Gel Processing; Academic Press: San Diego, 1990. (2) Litra´n, R.; Ramı´rez-del-Solar, M.; Blanco, E. J. Non-Cryst. Solids 2003, 318, 49. (3) Chen, W.; Zhang, J.; Cai, W. Scr. Mater. 2003, 48, 1061. (4) Donatti, D. A.; Vollet, D. R.; Iban˜ez Ruiz, A. J. Phys. Chem. B 2003, 107, 3091. (5) Huang, L. W.; Liang, K. M.; Cui, S. H.; Gu, S. R. Mater. Res. Bull 2001, 36, 461. (6) Scherer, G. W. J. Non-Cryst. Solids 1988, 100, 72. (7) Morita, M.; Kajiyama, S.; Rau, D.; Sakurai, T.; Iwamura, M. J. Lumin. 2003, 102-103, 608. (8) Sujatha Devi, P.; Ganguli, D. J. Non-Cryst. Solids 2004, 336, 128. (9) Litra´n, R.; Blanco, E.; Ramı´rez-del-Solar, M. J. Non-Cryst. Solids 2004, 333, 327. (10) Parvathy Rao, A.; Venkateswara Rao, A. Sci. Technol. AdV. Mater. 2003, 4, 121. (11) Feng, Y.; Yao, R.; Zhang, L. Physica B 2004, 350, 348. (12) Ahola, M.; Kortesuo, P.; Kangasnieme, I.; Kiesvaara, J.; Yli-Urpo, A. Int. J. Pharm. 2000, 195, 219. (13) Radin, S.; El-Bassyouni, G.; Vresilovic, E. J.; Schepers, E.; Ducheyne, P. Biomaterials 2005, 26, 1043. (14) Colomer, M. T.; Anderson, M. A. J. Non-Cryst. Solids 2001, 290, 93. (15) Vollet, D. R.; Donatti, D. A.; Iban˜ez Ruiz, A. J. Non-Cryst. Solids 2002, 306, 11. (16) Vollet, D. R.; Donatti, D. A.; Iban˜ez Ruiz, A.; da Silva, J. S. P. J. Phys. Status Solidi A 2003, 196, 379. (17) Vollet, D. R.; de Castro, W. C.; Donatti, D. A.; Iban˜ez Ruiz, A. J. Phys. Status Solidi A 2005, 202, 411. (18) Leofanti, G.; Padovan, M.; Tozzola, G.; Venturelli, B. Catal. Today 1990, 41, 207. (19) Jain, A.; Rogojevic, S.; Ponoth, S.; Gill, W. N.; Plawsky, J. L.; Simonyi, E.; Chen, Shyng-Tsong; Ho, P. S. J. Appl. Phys. 2002, 91, 3275. (20) Arau´jo, F. G.; LaTorre, G. P.; Hench, L. L. J. Non-Cryst. Solids 1995, 185, 41. (21) Wendlandt, W. W. Thermal Analysis (Chemical Analysis), Vol. 19; Elving, P. J.; Winefordner, J. D.; and Kolthoff, I. M.; John Wiley: New York, 1985; p.79. (22) Brinker, C. J.; Scherer, G. W.; Roth, R. P. J. Non-Cryst. Solids 1985, 72, 345. (23) Woolfrey, J. L.; Bannister, M. J. J. Am. Ceram. Soc. 1972, 55, 390.
