Ind. Eng. Chem. Res. 2004, 43, 4457-4464
4457
Reactive Phase Equilibria in Silica Aerogel Synthesis: Experimental Study and Prediction of the Complex Phase Behavior Using the PC-SAFT Equation of State Oliver Spuhl,† Stefanie Herzog,† Joachim Gross,‡ Irina Smirnova,*,† and Wolfgang Arlt† Fachgebiet Thermodynamik und thermische Verfahrenstechnik, Technische Universita¨ t Berlin, Strasse des 17 Juni 135, 10623 Berlin, Germany, and BASF AG, Conceptional Process Engineering, GIC/P-Q920, 67056 Ludwigshafen, Germany
Synthesis of silica aerogels can be markedly accelerated by adding carbon dioxide (CO2) during the sol-gel process. The optimization of the sol-gel process in the presence of CO2 requires the knowledge of the phase equilibrium of the reactants [tetraethyl orthosilicate (TEOS) and water (H2O)], the solvent, and CO2. The perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state is applied here to investigate the conditions under which an undesirable liquid demixing of that quaternary reactive mixture occurs. In this work pure-component parameters of the PC-SAFT equation of state for the solvent acetonitrile (ACN) and TEOS have been identified. Binary interaction parameters of all six related binary systems were determined. The phase behavior of three systems, which are not available in the literature, were studied experimentally: the vapor-liquid equilibria of the systems TEOS-CO2 and TEOS-ACN and the liquid-liquid equilibrium of the system ACN-H2O-TEOS. All four related ternary systems have been calculated at 293.15 K and 20 and 100 bar. The phase behavior of the quaternary system TEOS-H2O-ACN-CO2 is discussed. It is concluded that the addition of CO2 does not lead to a liquid demixing as long as the starting mixture of TEOS-H2O-ACN is homogeneous. Introduction Silica aerogels are ultralight, highly porous materials with an extremely low density. Because of their unique properties, like high transparency, low thermal conductivity, and large surface area, aerogels are used as insulating materials, catalyst support, sound absorbers, etc.1 Silica aerogels are usually synthesized by hydrolysis and the subsequent condensation of tetraethyl orthosilicate (TEOS). The reaction (the so-called solgel process) can be summarized as follows:
nSi(OC2H5)4 + 2nH2O 9 8 nSiO2 + 4nC2H5OH (1) cat. The reaction process leads to the formation of a gel phase (gelation). Both acids and bases can be used as catalysts for this reaction.2-5 Recently, it was proposed to use CO2 as a catalyst. It was demonstrated that the addition of supercritical CO2 during the sol-gel process accelerates the gelation.6 To convert a gel into an aerogel, the solvent must be removed from the gel. This can be done by extraction of the solvent with supercritical CO2.1,7 The extraction time is rather long and depends on the sample size and solvent amount. One of the possibilities of shortening the extraction time is to perform the reaction directly in supercritical CO28 without the use of any additional solvent. In this case two advantages are achieved simultaneously: no extraction of the solvent is needed,8 and the gelation time * To whom correspondence should be addressed. Tel.: +493031422755. Fax: +493031422406. E-mail: I.Smirnova@ vt.tu-berlin. † Technische Universita¨t Berlin. ‡ BASF AG.
is reduced.6 However, the limitation of such a process is that the reacting mixture must be homogeneous to achieve transparent aerogels of low density. It was demonstrated8 that it is impossible to get a homogeneous mixture of the reactants TEOS, H2O, and CO2 because of the poor miscibility of these substances. The miscibility can be improved by replacing water (H2O) with formic acid, but in this case the properties of the obtained gels would be significantly changed.8 Another way to avoid demixing of the initial solution is to add some organic solvent to the ternary system TEOSH2O-CO2. The amount of solvent must be sufficient to get a homogeneous system. To determine the required amount of solvent, the phase equilibrium of the quaternary system TEOS-H2O-CO2-organic solvent should be known. However, the experimental study of the phase equilibrium in quaternary systems is extremely time-consuming. An additional difficulty results from the hydrolysis of TEOS (reaction 1), which takes place during the experiments. New compounds (ethanol and oligomers) appear in the system because of the reaction and taint the results. To avoid this, it is advantageous to calculate the phase behavior of such systems. The purpose of this study is to predict the liquidliquid-phase equilibrium in the quaternary reactive system TEOS-H2O-CO2-organic solvent using the perturbed-chain statistical associating fluid theory (PCSAFT) equation of state (EOS).9 Acetonitrile (ACN) has been chosen as the organic solvent. The prediction of the phase behavior of a quaternary system with the PCSAFT EOS requires information about the phase behavior of the corresponding binary systems. The binary interaction parameters of the PC-SAFT equation should be fitted to the experimental data of binary systems.
10.1021/ie049893k CCC: $27.50 © 2004 American Chemical Society Published on Web 06/09/2004
4458 Ind. Eng. Chem. Res., Vol. 43, No. 15, 2004 Table 1. Data References for the Binary Systems no.
binary system
1
ACN-H2O
2 3 4 5 6
H2O-CO2 ACN-CO2 TEOS-CO2 ACN-TEOS TEOS-H2O
type of data VLE LLE VLE VLE VLE VLE LLE
data references 10 11 12 and 13 14 and 15 no data available no data available practically immiscible, reacting system2
An overview of the corresponding binary systems is given in Table 1. Table 1 shows that the phase behavior of binary systems 1-3 is known, whereas systems 4 and 5 have not yet been reported in the literature. It is known that TEOS-H2O is practically immiscible,2 but no exact data are available. Because the knowledge of the phase behavior of systems 4-6 is essential for the prediction of the phase behavior of the quaternary system TEOSH2O-CO2-ACN, it was necessary to investigate the phase equilibria of systems 4-6. The binary system TEOS-H2O is a reacting system, and therefore its phase behavior is difficult to determine experimentally. However, the binary interaction parameter of this system can be derived from the phase equilibrium data of the ternary system TEOS-H2O-ACN, when the hydrolysis rate of TEOS is slow enough to allow direct measurements (at low temperatures or high solvent concentrations). For this reason, the ternary system TEOS-H2O-ACN has been investigated. Experimental Methods Vapor-Liquid Equilibrium (VLE): TEOS-CO2. To measure the VLE of the binary system TEOS-CO2, a static synthetic method similar to that used by Meskel-Lesavre et al.16 was applied. The experimental setup consists of the high-pressure view cell with variable volume. The cell content can be stirred, and the volume of the cell can be varied from 80 to 140 ( 0.8 mL by shifting the piston. For the bubble-point measurements of the binary systems TEOS-CO2, the evacuated cell was loaded with a known amount of both substances and thermostated ((0.1 K). The mole fractions could be calculated with an accuracy of (3.5 × 10-4 mol/mol. The cell was pressurized so that the pressure was about 8 MPa above the expected bubble point. Subsequently, the stirrer was turned on, the piston was slowly moved out (velocity 0.18 mL/min), and the temperature and pressure were monitored. After constant pressure had been achieved, the piston was stopped and the P-V curve was derived from the experimental data. The break point in the P-V curve indicates the bubble pressure at a given composition.16 Each curve was registered three times, and the mean value of the bubble pressure was taken for evaluation. Additionally, the bubble formation was visually observed. Isosteric P-T data could be obtained by this method. VLE: ACN-TEOS. The VLE of the binary system ACN-TEOS was investigated using a static analytic method. The apparatus used is described in detail elsewhere.17 Briefly, pure degassed TEOS was filled into an evacuated static cell (550 cm3) and thermostated ((0.1 K). The pressure was measured with an accuracy of (0.5%.17 The predetermined amount of degassed ACN was injected step by step into the cell. After each
injection, the mixture was stirred, the cell was thermostated at least 40 min, and the pressure was monitored. After constant pressure had been reached, a liquidphase sample was withdrawn and analyzed by gas chromatography. Isothermal P-x data could be obtained by this method. Liquid-Liquid Equilibrium (LLE): H2O-ACNTEOS. The LLE of the ternary system H2O-ACNTEOS was studied by the isothermic titration method (Bancrofts method). Homogeneous binary mixtures ACN-TEOS (for the left part of the binodal curve) or ACN-H2O (for the right part of the binodal curve) were prepared, and the third component (H2O or TEOS, respectively) was added to the solution drop by drop under constant stirring. Experiments were conducted as fast as possible. Isobaric, isothermal data (binodal curve) could be obtained by this method. Chemicals ACN (99.9%) and TEOS (98%) were provided by Fluka and Merck, respectively. CO2 was given with 99.995% purity (Messer-Griesheim). Deionized H2O was used for all experiments. Calculations: PC-SAFT EOS The SAFT framework was developed by Chapman et al. in 1988,18 and it served as a starting point for numerous applications and further developments. Two SAFT derivatives, which have gained particular interest in research and industry, are the modified SAFT EOS introduced by Huang and Radosz19,20 and, more recently, the PC-SAFT EOS.9,21-23 The PC-SAFT EOS was applied to the calculation of liquid-liquid, vapor-liquid, and solid-liquid equilibria of nonassociating and associating components9 from low molecular mass up to polymers and copolymers.9,23 The reduced residual Helmholtz energy of a system is given in terms of the ideal gas contribution, the hardchain term (hc), the dispersive part (disp), and the contribution due to association (assoc) according to
ares ) ahc + adisp + aassoc
(2)
where the residual property (res) is the actual property minus the ideal gas contribution of that property:
ares(T,V,N) ) a(T,V,N) - aideal(T,V,N)
(3)
Five pure-component parameters have to be given: (1) the segment number m, (2) the segment diameter σ, (3) the segment energy parameter /k, (4) the association energy AiBj/k, and (5) the effective association volume κAiBj. The parameters are identified by fitting them simultaneously to vapor pressures and liquid densities. When mixtures are considered, the van der Waals one-fluid mixing rule is applied.9 Different species of segments are treated with the Barthelot-Lorentz combining rules
1 σij ) (σi + σj) 2
(4)
ij ) xij(1 - kij)
(5)
where kij is a factor that corrects segment-segment interactions of unlike chains.
Ind. Eng. Chem. Res., Vol. 43, No. 15, 2004 4459
Figure 1. Experimental data and calculation of the VLE for the binary system TEOS-CO2: P-T plot.
Figure 2. Experimental data and calculations of the VLE for the binary system TEOS-ACN.
Table 2. P-T-x Data of the Binary System TEOS-CO2
Table 3. P-x Data for the Binary System TEOS-ACN at 329.15 K
xTEOS [mol/mol] 0.838
0.736
0.623
0.555
T [K]
P [MPa]
293.3 303.1 313.2 323.2 333.2 343.1 293.4 303.1 312.9 323.1 333.4 343.3 293.1 303.2 313.1 323.0 333.0 343.2 293.1 303.1 313.1 323.3 332.9 342.9
0.76 0.89 1.03 1.18 1.32 1.46 1.25 1.46 1.68 1.92 2.16 2.38 1.79 2.16 2.5 2.84 3.22 3.59 2.16 2.59 3.04 3.49 3.95 4.37
xTEOS [mol/mol] 0.452
0.321
0.240
0.106
T [K]
P [MPa]
P [kPa]
xACN
P [kPa]
xACN
294.7 303.2 313.1 323.1 333.1 342.8 294.2 303.4 313.1 322.9 332.9 342.9 294.1 303.1 313.1 323.0 333.1 343.2 293.7 303.3 313.1 323.3 332.9
3.01 3.44 4.05 4.65 5.25 5.81 3.67 4.30 5.12 5.88 6.75 7.50 4.22 5.01 6.0 7.04 8.08 9.09 5.03 6.13 7.39 8.8 10.2
10.2715 13.215 22.087 23.348 32.395 36.0845
0.099 0.145 0.297 0.341 0.608 0.717
35.944 38.0765 39.743 41.528 41.099 42.898
0.734 0.784 0.824 0.862 0.873 1
Combination rules for the association parameters are not needed in this work because only H2O is considered to have associating sites. Results and Discussion Experimental Data. 1. VLE: TEOS-CO2. To validate the bubble-point measurements, the VLE of the binary mixture ACN-CO2 (xACN ) 0.610) was measured in the temperature range 293-373 K and compared with the data of Reighard et al.14 Good agreement with the literature14 was achieved; the deviation did not exceed 5% for all data points. Eight TEOS-CO2 compositions were studied over the entire range of concentration at 293, 303, 313, 323, 333, and 343 K. The experimental results are summarized in Table 2 and presented graphically as P-T (Figure 1) diagrams. No liquid-liquid-vapor region could be observed in this system at any experimental conditions studied here. Although no vapor-liquid critical loci were measured, the absence of the vapor-liquid-liquid equilibrium (VLLE) region allows one to suggest that this system belongs to type I according to the classification of Konynenburg and Scott.24 2. VLE: TEOS-ACN. The apparatus was validated by measuring the vapor pressure of pure ACN at 300-
Table 4. P-x Data for the Binary System TEOS-ACN at 314.9 K P [kPa]
xACN
P [kPa]
xACN
7.294 14.254 17.526 20.833
0.1271 0.3472 0.5032 0.7044
22.624 23.61 24.9
0.7921 0.8561 1
325 K. A good agreement with the literature data25 is achieved. The highest relative deviation is 1.2%. The VLE of the binary system TEOS-ACN was studied at 314.9 and 329.15 K. Tables 3 and 4 list the experimental P-x values, which are graphically presented in Figure 2. The vapor pressure of TEOS is extremely low, so this value could not be measured reliably with this method and was taken from the literature.26 No liquid-liquid-vapor region could be observed in this system at any experimental conditions studied here, although it cannot be excluded that it appears at lower temperatures. However, the similar binary systems TEOS-methanol and TEOS-ethanol were reported in the literature in a wide range of temperatures,27 and no liquid-liquid immiscibility was found. 3. LLE: H2O-ACN-TEOS. The LLE of the ternary system H2O-ACN-TEOS was measured at ambient pressure and 293.15 K. The experimentally obtained binodal curve can be found in Figure 3 and Table 5. The system shows a wide miscibility gap. TEOS and H2O are practically immiscible, so that a rather high concentration of ACN is needed to get a homogeneous mixture. A similar phase behavior was observed for the ternary systems TEOS-H2O-ethanol and TEOS-H2Omethanol.28 Generally, if systems containing TEOS and H2O are studied, the hydrolysis of TEOS must be taken into account. The reaction between TEOS and H2O without any catalyst is rather slow; the gel formation at 293 K takes place within several hours.2 In contrast, the formation of oligomers can take place within minutes. During the measurements of the ternary system, rather large concentrations of ACN were used in order to slow the reaction. Under these conditions according to the literature,28 the influence of the hydrolysis can
4460 Ind. Eng. Chem. Res., Vol. 43, No. 15, 2004
donors. A large dipole moment and the fact that ACN is not capable of self-association lead to the presumption that dipole-dipole interactions have to be taken into account. One way to do so is the incorporation of a term for dipole-dipole interactions derived from molecular simulations. Saager and co-workers30,31 give an expression of the Helmholtz energy f dipole caused by dipoledipole interactions. They have chosen a two-center Lennard-Jones molecule with varying-point dipoles (2CLJ) to determine the change in the free energy with temperature, density, and dipole moment, according to
f dipole kT
28
)
∑ i)1
ci
( )() T
ni/2
1.15T0
F
F0
mi/2
[ ( )]
(µ*2)ki/4 exp -oi
F
2
F0
(6)
Figure 3. LLE of TEOS-ACN-H2O at T ) 293.15 K and P ) 1.013 bar. Comparison of experimental data to calculations. Table 5. Experimental Data of LLE of the Ternary System H2O-TEOS-ACN at 293 K xTEOS
xH2O
xACN
xTEOS
xH2O
xACN
0.15 0.09 0.0003 0.0016 0.02 0.03 0.05 0.01 0 0.36
0.18 0.24 0.899 0.798 0.49 0.4 0.3 0.59 0.71 0.07
0.67 0.67 0.10 0.2 0.49 0.57 0.65 0.4 0.29 0.57
0.75 0.17 0.36 0.25 0.75 0.88 0.68 0.44 0.48 0.62 0.65
0.04 0.17 0.08 0.13 0.02 0.02 0.03 0.07 0.07 0.05 0.04
0.21 0.66 0.56 0.62 0.23 0.1 0.29 0.49 0.45 0.33 0.31
Table 6. Antoine Parameters for TEOS {log P [bar] ) A - B [K]/(T [K] + C [K])} component
A
B [K]
C [K]
TEOS
6.333 32
3323.353
83.630
be neglected. Because the reaction rate increases rapidly with temperature,2 no measurements at higher temperature were done. Calculations of Phase Equilibria Pure Components. 1. TEOS. TEOS is a nonpolar substance. Hence, three pure-component parameters have to be identified: the segment number, the segment size, and the segment energy. Vapor pressure data are published by Solana and Moles26 and liquid density data by Yokoyama et al.29 Solana and Moles provide data in a temperature range from 285.25 to 446.35 K.26 These data scatter particularly in the low-temperature region. Therefore, Antoine parameters have been fitted to the data, and moreover calculated vapor pressures were used for the parameter identification. The Antoine parameters are given in Table 6. Average deviations of 1.87% in the densities and 8.14% in the vapor pressures were yielded. Compared to the experimental data, the deviation is 16.2%. This is close to the deviation (12.2%) that is attained when the two-parameter vapor pressure equation suggested by Solana and Moles is taken. For highly accurate data, the vapor pressure deviation usually takes on values of around 2%.21-23 However, this cannot be achieved here because the data base is not sufficiently accurate. 2. ACN. ACN is a very polar substance. The nitrogen atom exhibits a free pair of electrons, which might cause hydrogen bonds in solvents, which then act as proton
where µ*2 is the reduced dipole moment, with µ*2 ) µ2/ σ3, and and σ are the parameters of the molecular model (2CLJ) used by Saager and co-workers. The 5 × 28 coefficients of eq 6 can be found in work by Saager et al.30 This expression has to be adapted to the concept of chains within the PC-SAFT EOS. It is assumed that of segments within the chain a certain number mdipole i interact via dipolar forces with the strength µ*2. mdipole i and µ*2 are parameters that have to be fitted along with the three pure-component parameters of nonpolar components. An application to mixtures is possible in the same way as that described above, when unlike segments are combined as follows:
1 ) (mdipole + mdipole ) mdipole ij j 2 i
(7)
/2 µ/ij2 ) xµ/2 i µj
(8)
This approach is tested against the common procedure of describing multipolar components. There exist two suggestions to take multipolar or dipolar interactions into account: 1. Identification of five parameters, namely, segment number, segment size, segment energy, association energy, and association volume. Although ACN is not self-associating, the dipolar moment induces a molecular orientation that is similar to the one observed in associating substances.32 Furthermore, in a mixture with H2O or alcohol, ACN may cross-associate. The cross-association of components that do not self-associate is described by Wolbach and Sandler.33 2. Identification of three parameters, namely, segment number, segment size, and segment energy. Here the segment energy holds information on polar and nonpolar interactions. Usually this goes along with a large value of the binary interaction parameter kij. Systems containing CO2 were successfully described through that procedure.9 Table 7 gives the results of the three different fitting strategies. The average deviation of vapor pressure and liquid density show that pure ACN is best described with the dipole-dipole term by Saager and Fischer. However, this parameter set is not used for further calculations, because, first, the Saager-Fischer term results in difficulties when used in a mixture and, second, the fitted reduced dipole moment µ*2 ) 23.95 D2/(J Å3) is much larger than the value that was covered by the simulation data used by Saager and Fischer. The five-parameter set also leads to good results, but the
Ind. Eng. Chem. Res., Vol. 43, No. 15, 2004 4461 Table 7. Pure-Component Parameters Used with the PC-SAFT Equation AAD % component
Mi [g/mol]
mi
σi [Å]
i/k [K]
ACN ACN ACN TEOS CO2 H2O
41.05 41.05 41.05 208.33 44.01 18.015
1.6092 3.7034 2.2661 3.5452 2.0729 1.0656
3.6162 2.5587 3.3587 4.4134 2.7852 3.0007
190.21 150.76 313.04 274.54 169.21 366.51
κAiBi
AiBi/k
[K]
3.8618
1468.37
0.034868
2500.7
µ [D]
mdipole
psat
r
ref
5.4531
1.2380
0.41 0.26 1.35 8.14 2.78 1.88
0.89 3.11 12.08 1.87 2.73 6.83
3 3
Table 8. Binary Interaction Parameters kij binary system ACN-H2O ACN-CO2 ACN-TEOS TEOS-CO2 TEOS-H2O H2O-CO2 a
kija -0.0122b 0.04 0.02 0.15 -0.05 0.0
ref (exptl data) 10 12 this work this work this work 8 and 13
kij ) kji, nonzero for i * j. b AACNBH2O ) 1700 K, κAACNBH2O ) 0.03.
Figure 4. P-F plot of the VLE of ACN. Comparison of different fitting strategies.
values of the parameters seem unusual in comparison to components that truly exhibit self-association. The value of the association volume is 100 times higher than usual, the segment energy and the segment size are fairly low, and the segment number is relatively high.9,21,22 This observation, in particular the relatively high association volume parameter, can be attributed to the long-range nature of dipolar interactions compared to the short range of associative interactions. Therefore, this set will not be used in further calculations. The authors decided rather to use the threeparameter set because the description of the purecomponent properties is still considered satisfactory and difficulties in mixtures are avoided. Figure 4 compares experimental VLE data of ACN to calculation results from the PC-SAFT EOS in a P-F plot. When compared to the results from the SAFT EOS, for which a threeparameter set was published by Byun et al.,15 the threeparameter set identified here overestimates the critical point significantly, whereas vapor pressure34 and liquid densities at lower temperatures are better described. The low-temperature region is more important in this work than the area at the critical point of the mixture. Binary Systems 1. ACN-H2O. As pointed out above, ACN exhibits strong long-range interactions. It does not self-associate. However, in a mixture with H2O, ACN molecules can cross-associate with H2O molecules. Following the idea of Wolbach and Sandler,33 one association site A is assigned to the molecular model of ACN. H2O is characterized with two association sites A and B according to Gross.9 H2O now is able to associate via association site B with site A of ACN. The crossassociation parameters AACNBH2O and κAACNBH2O cannot be calculated with the usual combination rules because ACN is characterized by only three pure-component parameters here. The cross-association parameters and
Figure 5. VLE of ACN-H2O at P ) 1.013 bar. Comparison of experimental data10 to calculations.
Figure 6. VLE of ACN-CO2 at different temperatures. Comparison of experimental data12 to calculations.
the binary interaction parameter kij are fitted simultaneously to binary LLE data.11 To reduce the number of adjustable parameters, the association volume κAACNBH2O is set to 0.03, which was suggested by Tumakaka.35 The parameters are listed in Table 8. The energy of crossassociation AACNBH2O/k was determined to be 1700 K. The comparison of experimental VLE data10 and the calculated data is presented in Figure 5. 2. ACN-CO2 and H2O-CO2. VLE data for both of the systems were available in the literature. A constant value of kACN,CO2 ) 0.04 describes the published ACNCO2 data by Reighard et al.14 at best (Figure 6). Binary data for the system H2O-CO2 can be found in many publications. The data published by Wiebe and Gaddy12
4462 Ind. Eng. Chem. Res., Vol. 43, No. 15, 2004
and Wiebe13 have been chosen because they correspond to the process conditions aimed at here. A kH2O,CO2 ) 0.0 was identified for the system H2O-CO2. The value of kij is independent of the temperature for both systems. 3. ACN-TEOS and TEOS-CO2. A constant value of kACN,TEOS ) 0.02 was identified to represent the data of the binary system ACN-TEOS (Figure 2). In the TEOS-CO2 (Figure 1) system, the kij value is much higher than those in all other systems. Its value was fitted to kTEOS,CO2 ) 0.15. This is still in accordance with other binary systems containing CO2 (see refs 9, 21, and 22). CO2 is a molecule that interacts as a quadrupolar substance. This type of interaction is not considered explicitly in the EOS, and the quadrupolar contribution is artificially covered by the dispersion term. This results in a large kij. As in the systems considered before, kij is independent of the temperature. 4. TEOS-H2O. The binary interaction parameter has been identified by fitting it to ternary data of the system TEOS-ACN-H2O. Results are described there.
Figure 7. Bubble-point data of the system ACN-H2O-CO2. Comparison of experimental data36 with calculations.
Ternary Systems The calculations for the ternary mixtures are performed at conditions of interest for the gel-sol process, namely, a system pressure of 20 bar and a temperature of 293 K. The PC-SAFT EOS was shown to be robust toward such extrapolations in temperature using constant kij parameters.9,21-23 Furthermore, it will be discussed how temperature and pressure changes affect the phase equilibrium. This is to find out more suitable conditions for the gelation process in the presence of CO2. 1. TEOS-ACN-H2O. As mentioned earlier, this system was investigated to identify the binary interaction parameter kTEOS,H2O. Because all of the other binary interaction parameters are known at this point, the binary interaction parameter of the system TEOS-H2O is determined by fitting it to the ternary system TEOSH2O-ACN. This usually is questionable because ternary phase equilibrium calculations are less sensitive to one binary parameter out of three. However, it was observed here that kTEOS,H2O has an enormous effect on the ternary system. In Figure 3, the experimental data along the liquid-liquid binodal curve are compared with the results of the calculations. Although the critical point of the mixture is overestimated, a value of kTEOS,H2O ) -0.05 was found to fit the data in the desired region, the region of lower ACN fractions, best. Experimental data in the region of lower ACN concentrations have been weighted more than data at higher ACN concentrations. Our intention was to meet the width of the binary (TEOS-H2O) miscibility gap. The interaction parameter then was verified by calculating the ternary system ACN-H2O-CO2. It was found that kTEOS,H2O ) -0.05 provides the best agreement with experimental data (Figure 7) and it demonstrates that the identified parameter is meaningful and transferable. The extrapolation to a pressure of 100 bar does not narrow the immiscibility gap. The binary LLE of the system TEOS-H2O was calculated using the identified binary interaction parameter and answers the question of how the mutual solubility of TEOS and H2O changes with temperature. The solubility of H2O in TEOS decreases from xH2O(293.15 K) ) 0.014 to xH2O(343.15 K) ) 0.08. The solubility of TEOS in H2O is nearly independent of the temperature and remains constant
Figure 8. Calculated VLLE of TEOS-CO2-H2O at T ) 293.15 K and P ) 20 bar (L1, H2O-rich liquid phase; L2, TEOS-rich liquid phase; V, vapor phase).
at about 10-5 mole fractions in the considered temperature interval. 2. TEOS-ACN-CO2. Two of the corresponding binary systems, TEOS-CO2 and ACN-CO2, form a VLE at 20 bar and 293.15 K. The vapor phase in the ternary system consists of nearly pure CO2; the liquid phase is a mixture of ACN, TEOS, and CO2. 3. TEOS-CO2-H2O. All three corresponding binary systems are immiscible at 20 bar and 293.15 K. The ternary system shows a wide vapor-liquid-liquid miscibility gap (V + L1 + L2); see Figure 8. It is surrounded by vapor-liquid and liquid-liquid areas (L1 + L2, V + L2, V + L1). When the pressure is increased, the L1L2/VL1L2 boundary shifts to higher CO2 concentrations. The vapor phase disappears when the critical point of the mixture is exceeded. The phase boundary of the L2 and L1L2 region is fairly invariant to the pressure, as calculations at 293.15 K and 100 bar show. The ternary calculations show that the reaction between TEOS and H2O cannot be carried out in pure CO2. Looking at Figure 8, it can be seen that no homogeneous region is crossed when pure CO2 is added to a mixture of H2O and TEOS; the usual molar ratio of H2O/TEOS is 4. Neither a higher temperature nor a higher pressure would lead to a homogeneous mixture. Therefore, the solvent ACN cannot be replaced by CO2 completely. This is in accordance to the experimental investigations of Loy et al.8 Figure 3 implies that a fairly large amount (more than 70 mol %) of ACN has to be added to a binary mixture of TEOS and H2O to achieve a homogeneous solution. 4. ACN-H2O-CO2. Experimental data at constant mole fractions have been published by Lee et al.36 These boiling points were used to verify the binary interaction
Ind. Eng. Chem. Res., Vol. 43, No. 15, 2004 4463
Figure 9. Phase equilibrium of the quaternary system TEOSH2O-CO2-ACN at T ) 293 K and P ) 20 bar: calculation results.
parameters. Figure 7 shows that a good agreement over the temperature range can be achieved. Prediction of the LLE in the Reactive Quaternary System TEOS-H2O-CO2-ACN To simplify the discussion, the phase behavior of the system TEOS-H2O-CO2-ACN is presented in a quasiternary diagram (Figure 9). In this type of diagram, a constant ratio for two of the four components, ACN and TEOS, is chosen in one vertex of the diagram. The other two pure components, H2O and CO2, are located in the remaining two vertexes of the triangle. Like ternary diagrams, quasi-ternary diagrams apply for a fixed temperature and pressure. During the studies of the ternary systems, it was found that at 293.15 K and 20 bar about 70 mol % of ACN has to be added to a liquidliquid mixture of TEOS-H2O to achieve a single phase. On the other hand, the addition of CO2 to the same mixture of TEOS and H2O does not result in a homogeneous mixture. Therefore, a constant ratio of the two substances ACN and TEOS, ACN/TEOS ) 4, was chosen to discuss the phenomena in the quaternary system further. This ratio was chosen to ensure a homogeneous ACN-TEOS-H2O mixture. Figure 9 shows the calculated phase behavior of the system TEOS-H2O-CO2-ACN. For reasons of clarity, we do not show the complete phase diagram but limit the results to the LLE and VLE starting off at points 1 and 2. That is the interesting region, where conclusions about the demixing behavior when CO2 is added can be drawn. Starting from the liquid phase at the upper vertex (all compositions between ACN/TEOS ) 4 and point 2), a second liquid phase occurs when the H2O content exceeds a mole fraction between 5 and 7%. The composition of the first liquid phase is represented by the black solid line 1-C1. The occurring second liquid phase is represented by the black dashed line and does not lie in the triangular plane (it rather grows out of the plane and points toward the viewer). This second phase is here referred to as the shadow phase. Calculations show that the mole fraction of ACN in that shadow
phase decreases from 0.83 to 0.43, whereas the TEOS mole fraction changes from 0.07 to 0.01 (these values cannot be presented in the diagram). This shadow line ends at point S1 (liquid), which is in equilibrium with points C1 (liquid) and S2 (vapor). C1 is also the end point of the calculated cloud-point line (solid gray line) of the VLE that starts at point 2. The belonging shadow line of the vapor phase is located in the lower left vertex of the diagram and consists of nearly pure CO2. It ends at the three-phase shadow point S2. The ACN mole fraction in the vapor phase stays constant at about 5 × 10-3 and the TEOS mole fraction at 1 × 10-4. The liquid-phase area in the diagram (L) meets the requirement of a homogeneous mixture. That is the precondition for producing high-quality aerogels. Figure 9 implies that, if a homogeneous mixture containing TEOS, H2O, and ACN is considered (concentrations between ACN/TEOS ) 4 and point 1), the amount of CO2 that can be added so that no liquid-liquid demixing occurs is not limited. When pure CO2 is added, the concentrations of the quaternary mixture can be found on a straight line, which connects a given concentration of homogeneous ACN-TEOS-H2O and the CO2 corner. At concentrations above 40 mol % CO2, the formation of a vapor phase can be observed (VL). This does not affect the reaction in the liquid phase. It can be concluded that the only requirement is a minimum concentration of ACN, which provides a homogeneous mixture of TEOS-H2O-ACN. The addition of CO2 to this mixture then does not lead to a liquid-liquid demixing. This behavior cannot be experimentally proven because of the fast reaction process in the presence of CO2. However, in general it was observed that a system ACN-TEOS-H2O that was homogeneous does not demix after the addition of CO2. On the other hand, we never obtained a homogeneous system in the production process when we added CO2 to a inhomogeneous mixture of ACN-TEOS-H2O. Our calculations confirm exactly these practical experiences. Conclusions In this work calculations were carried out using the PC-SAFT EOS with the aim of optimizing the process parameters of the sol-gel process in the presence of CO2. Of particular interest in this context was to find out which amount of CO2 can be added to the system TEOS-H2O-ACN so that no liquid-liquid demixing occurs. The pure-component parameters of the PC-SAFT EOS were determined for TEOS and ACN. Both substances were modeled without explicitly considering polar and associating interactions, thus using three pure-component parameters. The binary interaction parameters for five systems were determined by fitting binary phase equilibrium data. The VLE of the system TEOS-CO2 and ACN-TEOS were determined experimentally, the other data were taken from the literature. The binary pair of TEOS-H2O is chemically reactive. Therefore, the binary interaction parameter was fitted to ternary liquid-liquid data of the system ACN-H2O-TEOS, which was measured for this purpose. All four ternary phase diagrams were calculated at the conditions common for the investigated sol-gel process (T ) 293 K and P ) 20 bar) and compared to experimental data. Temperature and pressure changes were discussed. It was found that changes in the system
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pressure only affect the concentration of CO2 in the liquid phase. The response to temperature changes is also rather small. This can be attributed to the weak temperature dependence of the miscibility gap of the binary system TEOS-H2O. Finally, the behavior of the quaternary system TEOSH2O-ACN-CO2 was discussed. It is concluded that the addition of CO2 to a homogeneous solution of TEOSH2O-ACN never causes demixing of the liquid phase. For an effective sol-gel process, it is therefore sufficient to ensure that the initial mixture of TEOS-H2O-ACN is homogeneous. The amount of CO2 to be added to this mixture then can be chosen freely. Acknowledgment The authors are grateful to the Deutsche Forschungsgemeinschaft for supporting this work with Grant AR236/10-2. Stimulating discussions with W. G. Chapman and F. Tumakaka and the experimental assistance of Susanne Hoffmann and Gabi Vetter are gratefully acknowledged. Literature Cited (1) Fricke, J. Aerogels; Springer: Berlin, 1986. (2) Brinker, C. J.; Scherer, G. W. Sol-Gel Science: The Physics and Chemistry of Sol-Gel Processing; Academic Press: New York, 1990. (3) Rao, A. V.; Pajonk, G. M.; Parvathy, N. N. Effect of solvents and catalysts on monolithicity and properties of silica aerogels. J. Mater. Sci. 1994, 29, 1807. (4) Pajonk, G. M. Transparent silica aerogels. J. Non-Cryst. Solids 1998, 225, 307. (5) Stolarski, M.; Walendziewski, J.; Steininger, M.; Pnia, B. Synthesis and characteristic of silica aerogels. Appl. Catal. A 1999, 177, 139. (6) Smirnova I.; Arlt, W. Synthesis of silica aerogels: influence of the supercritical CO2 on the sol-gel process. J. Sol-Gel Sci. Technol. 2003, 28 (2), 175. (7) Tewari, P. H.; Hunt, A. J.; Lofftus, K. D. Ambient Temperature Supercritical Drying of Transparent Silica Aerogels. Mater. Lett. 1985, 3, 363. (8) Loy, D. A.; Russick, E. M.; Yamanaka, S. A.; Baugher, B. M. Direct formation of aerogels by sol-gel polymerizations of alkoxysilanes in supercritical carbon dioxide. Chem. Mater. 1997, 4, 749. (9) Gross, J. Entwicklung einer Zustandsgleichung fu¨r einfache, assoziierende und makromolekulare Stoffe. Dissertation, Technische Universita¨t Berlin, Berlin, 2001. (10) Acosta, J.; Arce, A.; Rodil, E.; Soto, A. A Thermodynamic Study on Binary and Ternary Mixtures of Acetonitrile, Water and Butyl Acetate. Fluid Phase Equilib. 2002, 203, 83. (11) Sazanov, V. P.; Shaw, D. G. IUPAC-NIST Solubility Data Series. 78. Acetonitrile Binary Systems. J. Phys. Chem. Ref. Data 2002, 31, 989. (12) Wiebe, R.; Gaddy, V. L. The Solubility of Carbon Dioxide in Water at Various Temperatures from 12 to 40 °C and at Pressures to 500 Atmospheres. Critical Phenomena. J. Am. Chem. Soc. 1940, 62, 815. (13) Wiebe, R. The Binary System Carbon-Dioxide-Water under Pressure. Chem. Rev. 1941, 29, 475. (14) Reighard, T. S.; Lee, S. T.; Olesik, S. V. Determination of Methanol/CO2 and Acetonitrile/CO2 Vapor-Liquid-Phase Equilibria Using a Variable-Volume View Cell. Fluid Phase Equilib. 1996, 123, 215.
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Received for review February 9, 2004 Revised manuscript received April 27, 2004 Accepted May 5, 2004 IE049893K
