Journal of Sol-GelScienceand Technology,4, 99-105 (1995) © 1995KluwerAcademicPublishers,Boston. Manufacturedin The Netherlands.

A Calorimetric Study of the Ultrasound-Stimulated Hydrolysis of Solventless TEOS-Water Mixtures D.A. DONATTI AND D.R. VOLLET

Departamento de F&ica, Universidade Estadual Paulista, UNESP, Campus de Rio Claro, Cx.P. 178, 13500-970, Rio Claro (SP), Brazil Received February 23, 1994; accepted September 14, 1994

Abstract. The kinetics of ultrasound-stimulated and HCl-catalyzed hydrolysis of solventless TEOS-water mixtures was studied as a function of temperature ranging from 10°C up to 65°C by means of flux calorimelxy measurements. A specially designed device was utilized for this purpose. The exothermic peak arising few minutes after sonication began has been attributed mainly to the hydrolysis reaction. The overall hydrolysis process, which was measured through the irradiation time up to the hydrolysis peak, was found to be thermally activated, with an apparent activation energy A E = 36.4 kJ/mol. The alcohol produced at the early hydrolysis due to sonication seems to further enhance the reaction, via a parallel autocatalytic path, which is controlled by a faster pseudo second order rate constant (k'). Our modeling yielded k' = 6.3 x 10 -2 M-lmin -1 at 20°C, which is in a reasonable agreement with the literature, and an activation energy A E = 40.4 kJ/mol for the specific process of hydrolysis in presence of alcohol. Keywords: 1

hydrolysis, TEOS, sonication, calorimetry, rate constants

Introduction

A large variety of glasses and glass-ceramics has been obtained by sol-gel process by using tetraalkoxysilanes as raw material through hydrolysis and condensation reactions [1, 2]. The simplest kinetics for sol-gel reactions is formulated by considering only the concentrations of alkoxy, silanol and Si-O-Si bond [3]. The reactions for hydrolysis, water producing condensation and alcohol producing condensation are assumed to describe the overall kinetics of the system through the rate constants kH, kcw and kcA, respectively [3]. In acid and base conditions, hydrolysis seems to occur by nucleophilic attack of the water oxygen on the silicon atom [1]. Hydrolysis of silanes is specially facilitated by the presence of homogenizing agents such as alcohol and acetone [1]. The alkyl chain length and degree of branching of alkoxy group retard the hydrolysis of alkoxysilanes [1]. Most of the kinetics studies has been concerned with the alkoxide-alcohol-water system [2, 3, 4, 5, 6]. Several works [2, 3, 4] in TMOS-methanol-water systems have shown that the rate of hydrolysis reaction is much faster than the sum of the rates of both the water and alcohol producing condensation reactions. Therefore,

hydrolysis is not the rate limiting step in the overall reaction up to gelation. The overall hydrolysis and polycondensation rate constants are evaluated considering the time evolution of the gelation time [2, 7]. Sonication is an alternative method to accelerate the hydrolysis of alkoxides without using alcoholic solvent of the alkoxide-water system [8, 9, 10]. The gelation time is a function of the hydrolysis and polycondensation rate constants of the mixtures during and after the external action. Alcohol produced immediately after the start of hydrolysis helps in the mutual dissolution of alkoxide (TEOS for example) and water, increasing the reaction rate during the external action at this stage [9]. While hydrolysis of TEOS is even catalyzed by ultrasounds, as seen by the higher reactivity of the sono-solution, high speed stirring provokes increase of the polycondensation rate [9]. So, the sonogel process of solventless TEOS-water mixtures in acid conditions seems to be mainly based on the formation of silanol groups at the stage of the irradiation of the mixture and subsequent condensation reaction [9]. In the present work, the kinetics of the ultrasoundstimulated and HCl-catalyzed hydrolysis of the solventless TEOS-water mixtures is studied as a function of the temperature by means of flux calorimetry

100

Donatti and Vollet

I

measurements. In addition, a model for the hydrolysis constant rates is presented to explain the experimental data.

t I ° o

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(d , ,dt/y \

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=£5_-5--

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2.1

Materials and starting mixtures m50

Tetraethylorthosilicate (TEOS) (Wacker 97%), distilled and deionized water and HC1 (Merck 37%) were used to prepare two-phase TEOS-water-HC1 mixtures of constant volume (23.4 ml) in a molar ratio 1:6.6:0.053, respectively. Ethanol (Merck PA) was used as described in a few experiments in order to elucidate some questions.

2.2

I---

48 I

I

I

0

2

4

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I

I

6

8

ZRRADIATION TIME (min) Fig. 1. The temperature as a function of the irradiation time for a mixture (23.4 ml) of TEOS-water-HCI (molar ratio 1:6.6:0.053) submitted to a constant power of ultrasonic irradiation. The surrounding bath temperature was held on 49.5°C.

Ultrasonic procedure

TEOS-water-HC1 mixtures were submitted to ultrasonic radiation by using a 20 kHz-600 W-VC 600 Sonics & Materials apparatus equipped with a titanium transducer of 13 mm diameter driven by an electrostrictive device. The ultrasound power (P) was kept at a constant value around 60 W and the sonication took place in a cylindrical container 40 mm diameter made of 0.7 mm thickness stainless steel. The external temperature (Te) of the container was controlled by a high water flux (7.5 l/min) from a thermostated bath (MLW/MK70) through an environmental holder. About half a minute after sonication, the inner temperature of the system reaches a steady value around 5°C above Te. So, a heat flow steady state has been stabilized for several temperatures in the range from 10°C up to 65°C under the same constant ultrasound power delivered to the system. Departures of this heat flow steady state represent a measurement of some reaction heat. The inner mixture temperature was measured "in situ" by means of a Chromel/Constantan thermocouple as a function of the time of irradiation and the bath temperature, and recorded in a xt apparatus (Philips/PM8010). Figure 1 shows a typical temperature (T) vs. irradiation time (t) pattern carried out in such conditions. The thermal peak as appearing in Fig. 1 around t = tp corresponds to a reaction evolution with the time. Figure 1 defines the parameters (AT)R = TR - - Te and ( A T ) p = Tp - Te, where TR and Tp are the inner temperature in the steady state associated to the reactant and product of the reaction,

respectively, and also the parameter (dT/dt)t=o, the initial slope of the T vs. t curve at the beginning of the ultrasound action. (AT)R and (dT/dt)t=o were used to determine the calorimeter constant as shown in the next section.

2.3

Interpretation of the calorimetric data

Under a steady state of the heat flow as described in the previous section, the rate of the heat delivered to the system, Q by the ultrasonic tip probe, is given by:

0=

riP = k L S ( A T ) R

(1)

where ~]is the efficiency in which the ultrasound power P is converted into heat in the system, keq is an equivalent heat conductivity through the medium, L the effective length of the heat flow through the cross section area S, and (AT)R is the difference between the constant homogeneous temperature of the reactant mixture (TR) and its surrounding bath (Te). An additional instantaneous delivery of heat to the medium by an exothermic reaction, for example, increases the instantaneous temperature of the mixture by an amount ATt and Eq. (1) becomes

d C A H _ keq" S

rTP 4- - ~ -

--~ d

[(AT)R 4- ATt]

+ -~(Cp. AT,)

(2)

where (dC/dt) is the reaction rate, A H is the heat of reaction and Cp the heat capacity of the whole system.

Solventless TEOS-Water Mixtures A s s u m i n g Cp as constant along the reaction path and using Eq. (1), Eq. (2) can be cast as

dC d(ATt) - - = OelATt + o L 2 - dt dt

i

(5)

Experimental results and discussion

The position and the shape of the exothermic peak as appearing in Fig. 1 were found to be a function of the temperature. The values in the inverse of the peak time tp, as defined in Fig. 1, obey an Arrhenius relationship --or exp

tp

R

100

I

.E E

!=_ E v

rO

OAo

(6)

where A E is a apparent activation energy and R the gas constant. Figure 2(a) shows the data fitting the Eq. (6) in the studied temperature range. The value of the corresponding activation energy was found A E = 36.4 kJ/mol.

10

~---(a ° ~

x

0.05

3'0 3',

32

313 A

3;

3.6

--?- (fo ~1)

(4)

but ATt is the temperature above Te. Since ATt = 0 at t = 0, then (5) yields r l P = Cp(dATt/dt)t=o = Cp(dT/dt)t=o at t = 0. A n d because ATt = (AT)R = constant for t > t,. then (dATt/dt)t>t, = 0 and therefore (5) yields r i p = (keqS/L)(AT)R for t > ts. The elimination of riP from the two last equations yields (o~2/oq) = (AT)R/(dT/dt),=o. The measured mean value o f (~2/~1) was 0.16 rain.

3

i

50~-~

29

Equation (4) gives the reaction fraction f as a function of the reaction time t' since the calorimeter constant (~2/~1) is known. To compute the latter, an Eq. analogous to Eq. (2) m a y be written for the stage from the initio of the ultrasound action (t = 0) up to the initio of the steady state associated to the reactant mixture (t = &., for example), under the absence of any reaction, so that

+ Cpd(ATt)d---~

i

0.50

(~)A~

riP = keqSATtL

i

1O 0

(3)

where Oil = (keqS/LAH) and ~2 = (Cp/AH). Integrating Eq. (3) along the reaction time (t') from initial conditions t t = 0, where C = 0 and ATt = 0, up to t' = ty, where C = A0 (the initial quantity to react) and ATt; = 0, and by defining the quantity f = C/Ao as the reaction fraction, we obtain:

fo" AT, dt + f = fo ~ ATtdt

[

101

Fig. 2. Experimental data fitting the Arrhenius equation. (a) The inverse of the peak time (1/tp) = (1.66 x 105 rain-I) exp(-4.38 x 103/T). (b) The rate constant k = (1.72 x 105 M -2 min-1).exp(-4.87 x 103/T).

I

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1

o 42

o v

uJ 40 rr

<~38 IM

L, JO_ 3 6 i ~E

t.

LLI

E---5 4

-I

0

I

2 4 6 8 IRRADIATION TIME (min)

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10

Fig. 3. Effect of the addition (at the point tA) of an equivalent amount of pre-heated (34.5°C) acidified water (8.4 ml of 0.04 N HC1) to a solution of TEOS (15 ml) and ethanol (7 ml), along the course of the irradiation. The peak at tA has been found when water is added to pure ethanol under the same conditions.

Such exothermic peak was attributed mainly to the reaction of hydrolysis of the ultrasound-stimulated system based on the following reasons: i) The literature [3] states that hydrolysis in TMOS/methanol solution occurs very rapidly with exothermic heat release, and the condensation rates are much slower than hydrolysis. Also the hydrolysis is retarded with alkyl chain length [1]. ii) Figure 3 shows that such peak just appears when an equivalent quantity of acidified water is added to a TEOS/ethanol solution along the course of irradiation. The sharp exothermic peak as appearing at the point tA, at the instant of the water addition in Fig. 3, corresponds to an alcohol/water mixture

102

Donatti and Vollet

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. . . . . .

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0

1

t

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in situ ~r~Jt

X.

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4 6 8 10 t2 t4 IRRADIATION TIME ( rain )

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Fig. 4. Effect of the additions ofpre-heated (34.5°C) 0.1 N NH4OH at the points tl (3.4 ml) and tz (1.0 ml) along the irradiation process, after the hydrolysis peak occurs.

,,=, 3 4 I--

38

i

36 i

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0

Fig. 6. Effect of ethanol additions, at the arrows along the irradi-

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Te (%) Fig. 5. The temperature excess held on the steady states associated to the reactant mixture, (AT)R, and the reaction product, (AT)p, with respect to the bath temperature (Te).

reaction since the same shape and size peak is found when water is added to pure ethanol in the same conditions. So, peak at tA does not correspond to any hydrolysis reaction. iii) It is well known [11] that the increase of pH up to 5.5 intensifies the polycondensation reaction up to gelation, after the acid hydrolysis occurs. Figure 4 shows no relevant thermal peak arising with the additions of 0.1 N NH4OH solution at the instants ta (3.4 ml) and t2 (1.0 ml) that could be associated with condensation reactions. The small sharp peaks at the position ta and t2 in Fig. 4, associated with the basecified water additions, look like the earlier peak of the alcohol/water mixture in Fig. 3. The system of the Fig. 4 gelled "in situ" almost instantaneously after the total quantity of base (4.4 x 10 .3 moles) was added.

ation process of TEOS-water-HC1 mixtures, on the thermal peak of the hydrolysis. (a) no additions; (b) 3.0 ml; (c) 7.0 ml.

The temperature difference between the system and its surrounding bath, of both steady states existing before [(AT)R] and after [(AT)p] the hydrolysis reaction, were generally found to be rather different one from the other and both dependent on the temperature. Figure 5 shows that (AT)p and (AT)R diminish with increasing temperature, the latter less than the former. Variation of these parameters could be associated with changes in the thermal properties of the medium as r/ or (o~2/cq) in Eqs. (1) and (4). The thermal properties of the reactant mixture depend on the temperature alone since its composition was kept constant. Such properties of the reaction products seem to be a function of either the temperature or the composition of the product or both. Therefore the reaction product might not be exactly the same for all temperature. These differences may be caused by either a dissimilar reaction degree of hydrolysis or a partial condensation reaction, whose extension would depend on the temperature or even on the earlier hydrolyzation. However, as suggested before, condensation does not seem to contribute substantially to measurable exothermic release of heat. Figure 6 shows the effect of additing ethanol along the irradiation process on the thermal peak of the hydrolysis. The reaction shifts towards shorter irradiation times, and the peak rise to its maximum is more accentuated as more alcohol is added. So, hydrolysis by ultrasound process seems to be accelerated by ethanol presence. The rate increasing could be associated to the

Solventless TEOS-Water Mixtures ethanol homogenizing effect. The diminution of the drop rate of the peak from its maximum with ethanol addition, as inferred from Fig. 6, can be associated to a dilution effect, since the volume of the system has been increased with the additions.

4

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v Lt.

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The acid hydrolysis of TEOS may be formulated as

-4

SiOR + H20 -~ SiOH + ROH -6

dC = koAB (7) dt Assuming that tile production of alcohol accelerates the reaction as suggested in the previous section, and adopting a parallel path without assuming any particular mechanism, one could suppose a parallel autocatalytic reaction as

0

i

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i

2

4

6

£EACTION TIME (rain)

Fig. 7. Data of the function F ( f ) as determined from the experimental data f of 39°C, fitting the Eq. (10) for determination of the rate constants ko and k.

with:

F(f) = ln f + ( l r-@r) l n ( 1 - f ) -(l~lr)ln(~

where k' would be a pseudo-second order rate constant obeying the following rate equation (8)

where k' = kD would depend on the alcohol concentration. In his model k would be interpreted as a third order rate constant. By adding both parallel rate Eqs. (7) and (8), and by expressing the time dependent compositions D, A and B in terms of C as D=C,A=Ao-CandB=B0-C, whereAoand B0 are the respective initial compositions, the total rate equation becomes

dC dt

- - = k(X + C)(Ao - C)(Bo - C)

(9)

where )~ = ko/k. The integration of Eq. (9) under the condition )~ << 1 with the substitution of the reaction fraction f = C/Ao (see Appendix I), yields the following linear relationship on the reaction time t'

F(f) =kAoBot'-ln(@)

S-)

(11)

and with r = Bo/Ao. k and k0 are obtained from the slope (o~)and the intercept (I) of the F ( f ) vs. t' plot as:

SiOR + H20 + ROH k~ SiOH + 2ROH

dC - - = k'aB = kDAB dt

I

4

A simple model for the ultrasound-stimulated rate constants

where R respresents the ethyl group and ko is a second order rate constant. Assigning the concentration of SiOR, H20, SiOH and ROH by A, B, C and D, respectively, the rate equation for SiOH or ROH production is

i

103

(10)

k =

O~

AoBo

(12)

and k0 =

exp(I)

(13)

The values of the function F ( f ) were calculated from the experimental data which were determined through Eq. (4), for several temperatures. To determine f , the experimental data ATt in Eq. (4) were linearly extrapolated under the peak between the base lines at (AT)n and (AT)p. Figure 7 shows Eq. (10) fitting reasonably well the experimental data at 39°C. Table 1 shows the parameters ko and k obtained from such fitting for several temperature in the studied range. Figure 8 shows the experimental data f compared to the curves f vs. total irradiation time t, as plotted from the data of Table 1 through the Eqs. (10) and (11). We introduced F ( f ) solely as a device to fit the experimental data and determine the parameters k and ko. We did

104

Donatti and Vollet

Table 1.

The temperature dependence of the hydrolysis rate con-

stants. TR (°C)

k0 (M-lmin -1)

10.5 19.5 24.0 32.0 39.0 45.5 55.5 63.4

5.0 6.4 5.5 5.5 5.7 7.4 14.3 12.1

;

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x

x x x x x x ×

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0.8

k (M-2min -1) 5.8 10.6 12.1 19.4 28.0 45.7 61.5 86.3

i

x x x x x x x x

I

~.(:9~.-b

10-3 10-3 10.3 10 .3 10 .3 10.3 10.3 10.3

i

I

~c~O~-

(

1.1_

0.4

° o°

V-

0.0 0

5

i0 il5 210 215 IRRADIATION TIME (min)

3~0

55

Fig. 8. Experimental reaction fraction (dots), as a function of the irradiation time, compared to the curves as plotted from the data of the Table 1 through the Eqs. (10) and (11), for the reactant temperatures: (a) 10.5°C, (b) 19.5°C, (c) 24.0°C, (d) 32.0°C, (e) 39.0°C, (f) 45.5°C, (g) 55.5°C and (h) 63.5°C.

not find any theoretical model based on elementary assumptions that would allow us to associate the linearity observed in F ( f ) with some particular transformation mechanism. The values o f k in Table 1 obey the Arrehenius equation according to the fitting shown in Fig. 2(b). The corresponding activation energy is A E = 40.4 kJ/mol, which is about 10 percent greater than the value 36.4 kJ/mol for the overall process determined from tp. We take the value k = 1.1 x 10 .2 M -2 min -1 obtained at T ~ 20°C in the present work in order to compare our results with other data [11]. Obviously, the third order k values of the present work could not be directly compared with the second order rates of hydrolysis kn, which were obtained by Aelion et al. [11] for the TEOS-water system using ethanol as a

solvent. However, if we use their acid specific rate at 20°C (ksp -- 0.051 M - i s -1 [HC1] - t ) and our value for the acid concentration ([HC1] = 0.016 M), we obtain kn = 4.9 x 10 .2 M -1 rain - I . Assuming the alcohol composition in the present work varied from 0 ( f = 0) up to 11.5 M ( f = 1), which corresponds to 4 times the initial TEOS concentration, one should have 5.7 M as a mean value (D) for the alcohol concentration during the hydrolysis. Therefore, the value of the pseudo second order rate at 20°C of the present work should b e k ' = k D = 1.1 x 10 - 2 M - 2 m i n -1 x 5 . 7 M = 6.3 x 10 .2 M - l m i n - I , which is in reasonable agreement with the estimated value from reference [11]. The method associated to this model does not permit unequivocal determination of the dependence of k0 upon the temperature in Table 1. The mean value of k0 in the range of studied temperature was found to be 8.9 x 10 -4 M - I min -1 with a little dispersion. Really, k0 seems to behave as a start for the faster parallel autocatalytic reaction controlled by the rate constant k. We notice two main oscillations around the F(f) fitting line, when all studied temperatures are considered, see Fig. 8 (oscillations at the extremities where f -+ 0 or 1 would be spurious since F(f) is not defined there). We believe that the first oscillation (positive deviation), at the beginning of the hydrolysis rising peak, might be due to the alcohol enhanced specific catalytic strength due to initial stage heterogeneities (yielding larger initial rates), and the second one (negative deviation) might be associated to the loss of the specific catalytic strength by the alcohol as the reaction progresses (yielding minor rates) due to the high homogenization of the system in this stage. Anyway, as the range swept by F(f) covers 100% of the transformations (the medium might not be an inexhaustible mass source), and as vigorous agitation by ultrasound was kept during all the process, we cannot assure that the condition stated in the paper by Garcia Ruiz et al. [12] can be fulfilled, in order to associate the oscillations around the F(f) fitting line with an autocontrolled growth process.

5

Conclusion

The dynamic method of calorimetry by flux of heat, employed in this work, enabled us to study, in a simple way, the kinetics of the acid hydrolysis of solventless TEOS-water mixtures under ultrasound stimulation.

Solventless TEOS-Water Mixtures The alcohol produced at the early hydrolysis due to the sonication action, enhances the further hydrolysis through a parallel autocatalytic path, which is controlled by a faster pseudo second order rate constant. The overall hydrolysis process was found to be thermally activated, with an apparent activation energy of 36.4 kJ/mol. Presently, we are extending our study to probe the effect of both amount and type of catalytic acid, as well as the effect of the initial concentrations of both ethanol and water, on the ultrasound-stimulated TEOS hydrolysis.

105

Equation (I.2) can be modified to yield: In

Lr×\ Z / \Ao

x r- ~

=kt'

(I.5)

c and since By using (I.4) and the definition f = At--; ( ~ + f)a ~_ fa (except for f -+ 0), we obtain In f + ( 1r - - ~ ) l n ( 1 - f ) - l-r

= kAoBot'-ln(-~)

(I.6)

Appendix I which is the same one as Eq. (10) since F ( f ) is given by Eq. (11). F(f) is defined in the whole f-range except in the extremes where f --+ 0 and f --+ 1.

Equation (9) can be integrated as

fo c

dC

k

(4 + C)(Ao - C)(Bo - C)

dt

fOff

(I.1)

which yields

Acknowledgments Work supported by FAPESP and CNPq. Both authors thank Dr. M.A. Aegerter and Dr. M. Atik for acquainting them to the sol-gel process and the sonication technique.

(1.2) References

after the substitution 1 (4 + C ) ( A o - C ) ( B o - C) -

-

L+ C

+

~

Ao - C

+

-

-

Bo - C

(1.3)

where

1 .

(3- AoBo' y -

1

~1

AoBo (1 - r)

__1 Qr___~). AoBo

(I,4)

with r = Bo/Ao. Equations (I.4) are obtained after resolving the constraining equations from (I.3) under the assumption Z << 1.

l. C.J. Bfinker, J. Non-Cryst. Solids, 100, 31 (1988). 2. S.Y. Chang and T.A. Ring, J. Non-Cryst. Solids, 147&148, 56 (1992). 3. R.A. Assink and B.D. Kay, J. Non-Cryst. Solids, 99, 359 (1988). 4. E Brunet and B. Cabane, J. Non-Cryst. Solids, 163, 211 (1993). 5. W.G. Klemperer and S.D. Ramamurthi, J. Non-Cryst. Solid, 121, 16 (1990). 6. T. Lours, J. Zarzycki, A. Craievich, D.I. Dos Santos, and M. Aegerter, J. Non-Cryst. Solids, 100, 207 (1988). 7. G. Orcel and L. Hench, J. Non-Cryst. Solids, 79, 177 (1986). 8. M. Tarasevich, Am. Ceram. Bull., 63, 500 (1984). 9. M. Ramirez-Del-Solar, N. De La Rosa-Fox, L. Esquivias, and J. Zarzicky, J. Non-Cryst. Solids, 121, 40 (1990). 10. M. Atik, PhD Thesis, Montpellier University (1990). 11. R. Aelion, A. Loebel, and E Eirich, J. Am. Chem. Society, 72(12), 5705 (1950). 12. J.M. Garda-Ruiz, A. Santos, and E.J. Alfaro, J. Cryst. Growth, 84, 555 (1987).