- Email: [email protected]
Plastic behaviour of aerogels under isostatic pressure
IOURNA L OF
ELSEVIER
Journal of Non-Crystalline Solids 186 (1995) 321-327
Plastic behaviour of aerogels under isostatic pressure L. Duffours, T. Woignier *, J. Phalippou Laboratoire de Sciences des Matdriaux Vitreux, Universitd de Montpellier 11, Place Eugene Bataillon, 34095 Montpellier, France
Abstract The bulk modulus of a set of aerogels was measured as a function of applied pressure by means of a Hg porosimeter. With increasing pressure, the aerogels, which are known to be elastic, display irreversible shrinkage corresponding to plastic behaviour. The magnitude of the plastic shrinkage and the value of the bulk modulus depend strongly on the volume fraction of solid in the aerogel. The plastic behaviour is related to the condensation reaction between silanols. Both plastic shrinkage and bulk modulus are clearly increased when the aerogel has undergone an oxidation treatment which induces the formation of silanols at the expense of organic groups. As a consequence of this plastic shrinkage, it is possible to densify and stiffen the aerogel at room temperature. The connectivity of the aerogel is strongly increased by the densification under isostatic pressure and the power laws describing the elastic constant evolution as a function of the bulk density lead to values of the power exponent different to those found in the literature. Fatigue effect due to cycling runs of pressurization and also delayed elasticity have been observed for the stiffer aerogels.
1. Introduction Aerogels are generally described as purely elastic materials [1-4]; their mechanical behaviour is identical to those of glasses and ceramics which display a brittle failure [3,5]. The main difference compared with silica glass is the order of magnitude of the elastic constants and the mechanical strength which is 10 4 times lower. Elastic and mechanical features have been measured by beam bending or diametral compression which characterizes the materials in tension. Some papers also relate uniaxial compression experiments [6]. Recently it has been proposed to characterize the compressibility of the aerogels and to measure their bulk moduli by means of mercury porosimetry [7,8].
" Corresponding author. Tel: + 33 67 52 59 03. Telefax: + 33 67 14 34 98. E-mail: [email protected].
In these experiments, because Hg does not penetrate the pore volume, the aerogel undergoes isostatic compression. Owing to the large compliance of the material, it deforms easily under the isostatic stress and the measurement of the volumetric strain at a given pressure allows calculation of the bulk modulus, K. However, in these studies and in a previous one [9], it is observed that, above a certain pressure (depending on the aerogel), a permanent deformation appears which would suggest that the material displays plastic behaviour. After this densification, the compressibility of the aerogel should change. The pressure necessary to irreversibly shrink the aerogel and the amplitude of the shrinkage should strongly depend on the bulk density of the aerogel. In this paper, we focus our study on the plastic behaviour of a set of aerogels having different bulk densities, under isostatic pressures. The effect of pressure on aerogel densification and on compressibility of the densified material is
0022-3093/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0022-3093(95)00059-3
322
L. Duffours et al. /Journal of Non-Crystalline Solids 186 (1995) 321-327
measured. We assume that the magnitude of shrinkage is related to the number of siloxane bonds created by condensation of silanols. To check this assumption, the effect of the oxidation treatment which transforms the organic groups of the esterified aerogels by silanol was also investigated.
2. Experimental Silica gels used in this study were made from tetramethoxysilane (TMOS, Fluka Chemical, grade assay 98%, cat No. 87682) hydrolyzed under basic conditions (10 -2 M NH4OH). The molar ratio of the hydrolyzing solution to TMOS was equal to 4. Ethanol (R.P. Normapur Analytical Reagent, 99.85%) was used as the solvent at various volumetric ratios TMOS/ethanol. When the TMOS constitutes y vol.% of the total solution, gels are designated as By. Five volumetric TMOS concentrations have been prepared and are designated as B46, B40, B33, B26 and B18. The TMOS - ethanol solution was stirred and poured into cylindrical tubes with diameter equal to 6 mm and aged one week at room temperature. The alcogels were transformed into aerogels by supercritical drying according to a procedure previously reported [10]. The conditions of the supercritical drying were 305°C and 13 MPa. The oxidation
treatment is made on as prepared aerogel by a heat treatment in air at 350°C for 15 h. The samples are labelled By OX, where By is defined as above and OX represents the oxidative heat treatment in air. Isostatic compression experiments were done using a Hg porosimeter (Carlo Erba porosimeter 2000) on outgassed monolithic aerogels. Hg pressure can be varied from 0.1 to 200 MPa. The aerogel was compressed to a chosen maximum pressure value. The sample was then depressurized at the smallest possible rate down to atmospheric pressure. Sometimes an amount of Hg must be added to reach again the starting level of mercury which was previously measured on the capillary tube of the sample container. The Hg volume added corresponds to the pore volume lost during the irreversible shrinkage.
3. Results Fig. 1 shows the typical curves which are obtained on the different samples between 0.1 MPa and 1.8 MPa. A V / V corresponds to the volumetric shrinkage in percent. On the aerogel elaborated with 18% TMOS concentration, the sample volume shrinks with pressure but when the pressure is released the sample dilates partially and the volume after depressurization is lower than the initial one.
3O
30" 25" 20'
~--. 75" '~ 10'
0,2
0,4
(],6
0,8
1,0
P(MPa)
1,2
1,4
1,6
o
1,8
0.2 04 0.6 08 t.0 12 ].4 1.6 18 P(MPa)
25
25 20-
-
,~10-
5~
.
8 P (MPa)
1131,12 o
P(MPa)
Fig. 1. A V / V versus P for different aerogels(18, 33, 40 and 46% TMOSconcentration)in the pressure range 0.1-1.8 MPa.
L. Duffours et al. / Journal of Non-Crystalline Solids 186 (1995) 321-327
323
80-
60,
70-
50'
60"
40'
5o40-
30
~
20
3020"
10
100
0
2'0
4',0
dr 0
80
I 0,0 I 2,0 ] ;.0 ~6¢0
0
30.
5,0
0
P OvfPa)
10,0 15,0 P (MPa)
20,0
25,0
50
2015. 10" 5"
{3
/
(&I-1.8MPa)
o12 o14 o% ~
1% ;.2 1'4 ;.6 is
}i F u
{0.1-5.8MPa) . 10
. 20
P (MPa)
.
.
30 P (MPa)
4.0
5,0
Fig. 2. ,~V/V versus P for different cycles of pressurization (sample with 46% TMOS concentration).
Identical behaviour is observed for the material with 26% (not shown) and 33% T M O S but with a lower permanent deformation. For the material with 40% T M O S concentration, this shrinkage is poor and for the material with 46% sample, in this pressure range the behaviour is different. W h e n the pressure is decreased to 0.1 MPa, the sample dilates to the initial volume. However, Fig. 2 shows that irreversible shrinkage is observed if the material with 46% T M O S sample is compressed at 14.6 MPa. In the literature some authors interpret these curves in terms of the pore size distribution. This is wrong because the mercury does not penetrate the pore volume [11-13]. However, these curves give us different types of information. Because the mercury cannot penetrate the pores, the pressure increase induces an isostatic pressure on the aerogel and, in the absence of irreversible deformation, the volumetric strain is due to its compressibility. Thus, the slope of the curve at low pressure is related to the elastic bulk modulus K ( P ) (the inverse of the compressibility):
mercury, at the beginning of the pressurization experiment, the samples are at a pressure equal to 0.1 MPa and the volume is lower than the initial volume, without mercury. Taking this effect into account, it is possible to calculate the evolution of K ( P ) . Fig. 3 shows the curve of K ( P ) as a function of P for different aerogels. In the case of the 40 and 26% T M O S concentration samples, we can see that K ( P ) is constant or decreases over a range of P which is dependent on the type of material. Then for higher pressure K ( P ) increases. The slight decrease of K ( P ) between 0.1 and 0.9 MPa has already been observed and has been at-
~,'
=E
, -~"
____
0
I
0.4
K(P)
= - V(P)dP/dV,
where V ( P ) is the volume of the sample at the pressure, P . It must be noted that, due to the fact that the aerogel is out-gassed before the addition of
.~7-. ~ ' ~
i
,,(Mp.)
i
B 26 B18 i
1.2
J 1.6
Fig. 3. K(P) versus P for the different aerogels (18, 26, 40 and 46% TMOS concentration) in the pressure range 0.1-1.8 MPa. The arrows correspond to the position of the point of inflexion of the curves.
L. Duffours et aL /Journal of Non-Crystalline Solids 186 (1995) 321-327
324 100o 0
evolution of K 0 as a function of the bulk density for different aerogels after pressurization.
B46
~, B 4 0 ~. ~
0
500
B26
13 B 18
A
0
0 o o
o
==
o
2 0
~
o
O
o.2
0
4. Discussion
0
~ oo Oi0
P
/ ~/cm3 )
r
i
O.8
0.e
Fig. 4. K a versus the bulk density for the different aerogels after compaction.
tributed either to the known anomaly of silica [14] or a knee bending effect [15]. Recently Scherer and Smith [7] proposed that the minimum is related to compressive stresses which act on the sample during the last stages of any drying process. The increase of K(P) is due to two kinds of mechanism. First of all, owing to the compaction, solid parts which were not connected in the aerogel are then in contact and these new contacts increase the stiffness of the sample. The second effect is the consequence of the first mechanism. When solid parts are in contact, the formation of siloxane bonds is possible and the connectivity of the network will be increased. In that case, after depressurization, a part of the volumetric shrinkage is irreversible and the value of K at 0.1 MPa ( K 0) is enhanced. In the highest pressure range, the material is no longer elastic and behaves plastically. The links between clusters are broken which allows restructuring of the material. The pressure range corresponding to the plastic deformation is at pressure above the point of inflexion of the curves. For the material with 46% TMOS concentration, this point is not observable because the aerogel does not exhibit permanent deformation. For the two lightest aerogels with 18 and 33% TMOS concentration, the minimum is not observable but it could be present in the pressure range lower than 0.1 MPa. These two materials present an important increase of the values of K in the P range 0.1-0.94 MPa, which suggests that the mechanisms previously presented to explain the stiffening are faster when the gel is less dense. If several cycles of pressurization are applied with increasing pressure, the aerogel densities and stiffens progressively with each cycle. Fig. 4 shows the
The most likely explanation for the observed irreversible shrinkage is the formation of siloxane bonds when the sample is strained and, therefore, the compacted volume is partially frozen. The formation of new siloxane bonds is necessarly due to the condensation reaction between silanols. However, owing to the esterification reaction during the supercritical drying, the aerogel structure contains a large amount of organic species which are hydrophobic and limit the OH content [10]. The organic species can be replaced by OH groups after oxidation. To check our assumption that the irreversible shrinkage is the consequence of condensation between silanols, we have tested the effect of the oxidation treatment on the behaviour of the material under pressure. Two types of aerogel, 18 and 46% TMOS concentration, have been investigated. Fig. 5 shows the curve obtained by porosimetry on the two oxidized materials. A comparison between the two curves related to the 18% TMOS 50" 40=
" 2o =
IOo P (MPa)
2O 15-
10-
50 0,5
] ,0
1,5
2.0
2,6
P (MPa)
Fig. 5. A V / V versus P for the aerogels (18 and 46% TMOS concentration) oxidized.
325
L. Duffours et al. /Journal of Non-Crystalline Solids 186 (1995) 321-327
o
o~
o
eo
o
Lx B46 as prepared 300
z~
A
0
0 B46 oxidized
z~
o 0
0
A
0
o
&
g,
0
&
~E 200 0
0
o
0
i a°
O&
/x I]46 as prepared
0
0 0
100 0
0 B46 oxidized 0 i
i
t
,
40
100 p (MPa)
00.2
0.5
0.9 p (g/c"
3 )
Fig. 6. Effect of the oxidation treatmenton A V / V versus P for the sample with 46% TMOS concentration.
Fig. 7. Effect of the oxidation treatment on K0 as a function of the bulk density.
concentration materials (Figs. 1 and 5) leads to several comments. First of all, the expected effect is clearly observed. After heat treatment and under a pressure of 0.7 MPa, the irreversible shrinkage is more than twice those measured on the as-prepared material. Second, the shape of the curve is different when the aerogel has been oxidized. In the first part of the curve, the curvature is positive while for the non-oxidized sample the curvature is always negative. This effect is also observed for the material with 26% TMOS concentration (see Fig. 5). In a pressure range where the as-prepared aerogel does
not present an irreversible shrinkage, the oxidized aerogel loses 15% of its original volume. In Fig. 5, the negative curvature of A V / V versus P related to the as-prepared aerogels means that the volumetric strain is self-retarding. Because of the volumetric strain, the clusters get closer but the solid part with the organic species does not form siloxane bonds and opposes a further strain. On the other hand, the large amount of SiOH in the oxidized samples favours the formation of S i - O - S i and induces a more important shrinkage. However, by increasing the number of S i - O - S i bonds, the mate-
P
P
>
P Fig. 8. Schematic illustrationof structural change during pressurizationfor the as-prepared and oxidized aerogels. For the as-prepared sample, the pressure induces the cleavage of siloxane bonds. In the case of the oxidized aerogel, the condensation of silanols forms new siloxane bonds.
326
L. Duffours et al. /Journal of Non-Crystalline Solids 186 (1995) 321-327
rial becomes stiffer and the curvature is negative again. Fig. 6 shows the effect of the oxidation treatment on the volumetric shrinkage of the aerogel with 46% TMOS concentration for increasing values of the pressure. The oxidation favours the magnitude of the volumetric shrinkage at low pressure but for higher pressures the difference is low. The volumetric shrinkage induces densification of the material after each run of pressurization. To confirm the formation of siloxane bonds and thus the increase of connectivity of the solid network, we have measured the value of K 0 for different compressed materials and compared the changes of K 0 as a function of the bulk density (Fig. 7). This figure clearly shows that even at a given bulk density (identical volumetric shrinkage) the values of K 0 of the oxidized sample are ten times higher than those of the as-prepared sample. In the case of the as-prepared sample, the densification is due to the action of the pressure which forces the clusters to interpenetrate but only a few siloxane bonds are created and the increase in K 0 is slight. It must be noted that, in the low-pressure range where we do not observe a large irreversible shrinkage, the value of K o slowly decreases. This result can be interpreted by the cleavage of S i - O - S i bonds under stress which is not compensated by the formation of new bonds. This effect is analogous to a fatigue phenomenon and it would be interesting to measure the Young's modulus to confirm this loss in connectivity. In the case of oxidized material, the cleavage of S i - O - S i bonds related to the restructuring of the clusters is largely compensated by the condensation of silanols (Fig. 8). Other comments can be drawn from this study. First, it is noted that the depressurization cycle for the two curves of Fig. 2 (0.1-1.8 MPa and 0.1-5.8 MPa) presents a hysteresis compared with the pressurization cycle. This effect of delayed elasticity is probably due to the entanglement of the clusters under pressure. When the pressure is released, the disentanglement is not instantaneous because of friction effects of the solid parts in contact. The second comment concerns the evolution of the elastic constant as a function of the bulk density. It has been proposed in the literature by different authors that the elastic constant of aerogels scales
with bulk density, p, as G or E ot p'~, where G and E are the shear and Young's modulus respectively and a is the exponent of the power law. Experimental studies [17,6,16] have shown that for silica aerogel the exponent is in the range 2.9-3.8. Taking into account that the Poisson's ratio, u, is nearly constant for the silica aerogels (~-0.2) [18], the power-law evolution should also apply to the bulk modulus, K. These results have been obtained from sets of aerogels for which the bulk density evolution is due to different dilution of the gelifying solutions. In the present work, different bulk densities can be obtained by the pressure effect. The log-log plot of Fig. 4 shows that the value of a is strongly dependent on the way the bulk density varies (concentration of alkoxide, effect of pressure with or without oxidation treatment). The value of ce varies from 2.3 to 5.9. Obviously, the elastic constants depend on the volumetric fraction of the solid but also on the connectivity of the solid network at the scale of the cluster and the parameters which could modify this connectivity intercluster, such as isostatic pressure, will change the exponent, a.
5. Conclusion
The silica aerogels show unusual plastic behavior under isostatic pressure. This plastic deformation induces a restructuring of the solid network which densities and stiffens. Preliminary small-angle X-ray scattering data confirm the restructuring of the clusters which shorten under pressure. The replacement of the organic species by silanols amplifies the densification and the stiffening of the aerogels which shows clearly that the condensation reactions of silanol are responsible for the irreversible shrinkage by freezing the strained network.
References [1] M. Gronauer, A. Kadur and J. Fricke, Aerogels, Proceedings in Physics, Vol. 6, ed. J. Fricke (Springer, Berlin, 1986) p. 167. [2] R. Calemczuk, A.M. De Goer, B. Scale, R. Maynard, A. Zarembovitch, Europhys. Lett. 3 (1987) 1205. [3] T. Woignier and J. Phalippou, J. Non-Cryst. Solids 93 (1987) 17.
L. Duffours et al. /Journal of Non-Crystalline Solids 186 (1995) 321-327 [4] T. Woignier and J. Phalippou, Rev. Phys. Appl. 24 (4) (1989) 157. [5] L. Duffours, F. Pernot, A. Alaoui, T. Woignier and J. Phalippou, J. Sol-Gel Sci. Technol. 2 (1994) 211. [6] R.W. Pekala, L.W. Hrubesh, T.M. Tillotson, C.T. Alviso, J.F. Poco and J.D. Lemay, in: Mechanical Properties of Porous and Cellular Materials, ed. K. Sieradzki, D.J. Green and L.J. Gibson (Materials Research Society, Pittsburgh, PA, 1991) p. 197. [7] G.W. Scherer and D.M. Smith, submitted to J. Sol-Gel Sci. Tcchnol. [8] L. Duffours, T. Woignier and J. Phalippou, submitted to J. Non-Cryst. Solids. [9] R. Pirard, S. Blacher, F. Brouers and J.P. Pirard, submitted to J. Mater. Res. 10] J. Phalippou, T. Woignier and M. Prassas, J. Mater. Sci. 25 (1990) 3111.
327
[11] F.J. Broecker, W. Heckmann, F. Fisher, M. Mielke, J. Shroeder and A. Stange, in: Aerogels, Proceedings in Physics, Vol. 6, ed. J. Fricke (Springer, Berlin, 1986) p. 160. [12] J. Zarzycki and T. Woignier, in: Aerogels, Proceedings in Physics Vol. 6, ed. J. Fricke (Springer, Berlin, 1986) p. 42. [13] J. lura, H. Hishikura, M. Kamikatano and T. Kawagushi, J. Non-Cryst. Solids, 100 (1988) 241. [14] P. Xhonneux, E. Courtens, J. Pelous and R. Vacher, Europhys. Lett. 10 (1989) 733. [15] J. Gross, R. Goswin, R. Gerlach and J. Fricke, Rev. Phys. Appl. 24 (4) (1989) C4-185. [16] T. Woignier, J. Phalippou and R. Vacher, J. Mater. Res. 4 (1989) 688. [17] J. Gross and J. Fricke, J. Non-Cryst. Solids 145 (1992) 217. [18] J. Gross, G. Reichenauer and J. Fricke, J. Phys. D21 (1988) 1441.
ELSEVIER
Journal of Non-Crystalline Solids 186 (1995) 321-327
Plastic behaviour of aerogels under isostatic pressure L. Duffours, T. Woignier *, J. Phalippou Laboratoire de Sciences des Matdriaux Vitreux, Universitd de Montpellier 11, Place Eugene Bataillon, 34095 Montpellier, France
Abstract The bulk modulus of a set of aerogels was measured as a function of applied pressure by means of a Hg porosimeter. With increasing pressure, the aerogels, which are known to be elastic, display irreversible shrinkage corresponding to plastic behaviour. The magnitude of the plastic shrinkage and the value of the bulk modulus depend strongly on the volume fraction of solid in the aerogel. The plastic behaviour is related to the condensation reaction between silanols. Both plastic shrinkage and bulk modulus are clearly increased when the aerogel has undergone an oxidation treatment which induces the formation of silanols at the expense of organic groups. As a consequence of this plastic shrinkage, it is possible to densify and stiffen the aerogel at room temperature. The connectivity of the aerogel is strongly increased by the densification under isostatic pressure and the power laws describing the elastic constant evolution as a function of the bulk density lead to values of the power exponent different to those found in the literature. Fatigue effect due to cycling runs of pressurization and also delayed elasticity have been observed for the stiffer aerogels.
1. Introduction Aerogels are generally described as purely elastic materials [1-4]; their mechanical behaviour is identical to those of glasses and ceramics which display a brittle failure [3,5]. The main difference compared with silica glass is the order of magnitude of the elastic constants and the mechanical strength which is 10 4 times lower. Elastic and mechanical features have been measured by beam bending or diametral compression which characterizes the materials in tension. Some papers also relate uniaxial compression experiments [6]. Recently it has been proposed to characterize the compressibility of the aerogels and to measure their bulk moduli by means of mercury porosimetry [7,8].
" Corresponding author. Tel: + 33 67 52 59 03. Telefax: + 33 67 14 34 98. E-mail: [email protected].
In these experiments, because Hg does not penetrate the pore volume, the aerogel undergoes isostatic compression. Owing to the large compliance of the material, it deforms easily under the isostatic stress and the measurement of the volumetric strain at a given pressure allows calculation of the bulk modulus, K. However, in these studies and in a previous one [9], it is observed that, above a certain pressure (depending on the aerogel), a permanent deformation appears which would suggest that the material displays plastic behaviour. After this densification, the compressibility of the aerogel should change. The pressure necessary to irreversibly shrink the aerogel and the amplitude of the shrinkage should strongly depend on the bulk density of the aerogel. In this paper, we focus our study on the plastic behaviour of a set of aerogels having different bulk densities, under isostatic pressures. The effect of pressure on aerogel densification and on compressibility of the densified material is
0022-3093/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0022-3093(95)00059-3
322
L. Duffours et al. /Journal of Non-Crystalline Solids 186 (1995) 321-327
measured. We assume that the magnitude of shrinkage is related to the number of siloxane bonds created by condensation of silanols. To check this assumption, the effect of the oxidation treatment which transforms the organic groups of the esterified aerogels by silanol was also investigated.
2. Experimental Silica gels used in this study were made from tetramethoxysilane (TMOS, Fluka Chemical, grade assay 98%, cat No. 87682) hydrolyzed under basic conditions (10 -2 M NH4OH). The molar ratio of the hydrolyzing solution to TMOS was equal to 4. Ethanol (R.P. Normapur Analytical Reagent, 99.85%) was used as the solvent at various volumetric ratios TMOS/ethanol. When the TMOS constitutes y vol.% of the total solution, gels are designated as By. Five volumetric TMOS concentrations have been prepared and are designated as B46, B40, B33, B26 and B18. The TMOS - ethanol solution was stirred and poured into cylindrical tubes with diameter equal to 6 mm and aged one week at room temperature. The alcogels were transformed into aerogels by supercritical drying according to a procedure previously reported [10]. The conditions of the supercritical drying were 305°C and 13 MPa. The oxidation
treatment is made on as prepared aerogel by a heat treatment in air at 350°C for 15 h. The samples are labelled By OX, where By is defined as above and OX represents the oxidative heat treatment in air. Isostatic compression experiments were done using a Hg porosimeter (Carlo Erba porosimeter 2000) on outgassed monolithic aerogels. Hg pressure can be varied from 0.1 to 200 MPa. The aerogel was compressed to a chosen maximum pressure value. The sample was then depressurized at the smallest possible rate down to atmospheric pressure. Sometimes an amount of Hg must be added to reach again the starting level of mercury which was previously measured on the capillary tube of the sample container. The Hg volume added corresponds to the pore volume lost during the irreversible shrinkage.
3. Results Fig. 1 shows the typical curves which are obtained on the different samples between 0.1 MPa and 1.8 MPa. A V / V corresponds to the volumetric shrinkage in percent. On the aerogel elaborated with 18% TMOS concentration, the sample volume shrinks with pressure but when the pressure is released the sample dilates partially and the volume after depressurization is lower than the initial one.
3O
30" 25" 20'
~--. 75" '~ 10'
0,2
0,4
(],6
0,8
1,0
P(MPa)
1,2
1,4
1,6
o
1,8
0.2 04 0.6 08 t.0 12 ].4 1.6 18 P(MPa)
25
25 20-
-
,~10-
5~
.
8 P (MPa)
1131,12 o
P(MPa)
Fig. 1. A V / V versus P for different aerogels(18, 33, 40 and 46% TMOSconcentration)in the pressure range 0.1-1.8 MPa.
L. Duffours et al. / Journal of Non-Crystalline Solids 186 (1995) 321-327
323
80-
60,
70-
50'
60"
40'
5o40-
30
~
20
3020"
10
100
0
2'0
4',0
dr 0
80
I 0,0 I 2,0 ] ;.0 ~6¢0
0
30.
5,0
0
P OvfPa)
10,0 15,0 P (MPa)
20,0
25,0
50
2015. 10" 5"
{3
/
(&I-1.8MPa)
o12 o14 o% ~
1% ;.2 1'4 ;.6 is
}i F u
{0.1-5.8MPa) . 10
. 20
P (MPa)
.
.
30 P (MPa)
4.0
5,0
Fig. 2. ,~V/V versus P for different cycles of pressurization (sample with 46% TMOS concentration).
Identical behaviour is observed for the material with 26% (not shown) and 33% T M O S but with a lower permanent deformation. For the material with 40% T M O S concentration, this shrinkage is poor and for the material with 46% sample, in this pressure range the behaviour is different. W h e n the pressure is decreased to 0.1 MPa, the sample dilates to the initial volume. However, Fig. 2 shows that irreversible shrinkage is observed if the material with 46% T M O S sample is compressed at 14.6 MPa. In the literature some authors interpret these curves in terms of the pore size distribution. This is wrong because the mercury does not penetrate the pore volume [11-13]. However, these curves give us different types of information. Because the mercury cannot penetrate the pores, the pressure increase induces an isostatic pressure on the aerogel and, in the absence of irreversible deformation, the volumetric strain is due to its compressibility. Thus, the slope of the curve at low pressure is related to the elastic bulk modulus K ( P ) (the inverse of the compressibility):
mercury, at the beginning of the pressurization experiment, the samples are at a pressure equal to 0.1 MPa and the volume is lower than the initial volume, without mercury. Taking this effect into account, it is possible to calculate the evolution of K ( P ) . Fig. 3 shows the curve of K ( P ) as a function of P for different aerogels. In the case of the 40 and 26% T M O S concentration samples, we can see that K ( P ) is constant or decreases over a range of P which is dependent on the type of material. Then for higher pressure K ( P ) increases. The slight decrease of K ( P ) between 0.1 and 0.9 MPa has already been observed and has been at-
~,'
=E
, -~"
____
0
I
0.4
K(P)
= - V(P)dP/dV,
where V ( P ) is the volume of the sample at the pressure, P . It must be noted that, due to the fact that the aerogel is out-gassed before the addition of
.~7-. ~ ' ~
i
,,(Mp.)
i
B 26 B18 i
1.2
J 1.6
Fig. 3. K(P) versus P for the different aerogels (18, 26, 40 and 46% TMOS concentration) in the pressure range 0.1-1.8 MPa. The arrows correspond to the position of the point of inflexion of the curves.
L. Duffours et aL /Journal of Non-Crystalline Solids 186 (1995) 321-327
324 100o 0
evolution of K 0 as a function of the bulk density for different aerogels after pressurization.
B46
~, B 4 0 ~. ~
0
500
B26
13 B 18
A
0
0 o o
o
==
o
2 0
~
o
O
o.2
0
4. Discussion
0
~ oo Oi0
P
/ ~/cm3 )
r
i
O.8
0.e
Fig. 4. K a versus the bulk density for the different aerogels after compaction.
tributed either to the known anomaly of silica [14] or a knee bending effect [15]. Recently Scherer and Smith [7] proposed that the minimum is related to compressive stresses which act on the sample during the last stages of any drying process. The increase of K(P) is due to two kinds of mechanism. First of all, owing to the compaction, solid parts which were not connected in the aerogel are then in contact and these new contacts increase the stiffness of the sample. The second effect is the consequence of the first mechanism. When solid parts are in contact, the formation of siloxane bonds is possible and the connectivity of the network will be increased. In that case, after depressurization, a part of the volumetric shrinkage is irreversible and the value of K at 0.1 MPa ( K 0) is enhanced. In the highest pressure range, the material is no longer elastic and behaves plastically. The links between clusters are broken which allows restructuring of the material. The pressure range corresponding to the plastic deformation is at pressure above the point of inflexion of the curves. For the material with 46% TMOS concentration, this point is not observable because the aerogel does not exhibit permanent deformation. For the two lightest aerogels with 18 and 33% TMOS concentration, the minimum is not observable but it could be present in the pressure range lower than 0.1 MPa. These two materials present an important increase of the values of K in the P range 0.1-0.94 MPa, which suggests that the mechanisms previously presented to explain the stiffening are faster when the gel is less dense. If several cycles of pressurization are applied with increasing pressure, the aerogel densities and stiffens progressively with each cycle. Fig. 4 shows the
The most likely explanation for the observed irreversible shrinkage is the formation of siloxane bonds when the sample is strained and, therefore, the compacted volume is partially frozen. The formation of new siloxane bonds is necessarly due to the condensation reaction between silanols. However, owing to the esterification reaction during the supercritical drying, the aerogel structure contains a large amount of organic species which are hydrophobic and limit the OH content [10]. The organic species can be replaced by OH groups after oxidation. To check our assumption that the irreversible shrinkage is the consequence of condensation between silanols, we have tested the effect of the oxidation treatment on the behaviour of the material under pressure. Two types of aerogel, 18 and 46% TMOS concentration, have been investigated. Fig. 5 shows the curve obtained by porosimetry on the two oxidized materials. A comparison between the two curves related to the 18% TMOS 50" 40=
" 2o =
IOo P (MPa)
2O 15-
10-
50 0,5
] ,0
1,5
2.0
2,6
P (MPa)
Fig. 5. A V / V versus P for the aerogels (18 and 46% TMOS concentration) oxidized.
325
L. Duffours et al. /Journal of Non-Crystalline Solids 186 (1995) 321-327
o
o~
o
eo
o
Lx B46 as prepared 300
z~
A
0
0 B46 oxidized
z~
o 0
0
A
0
o
&
g,
0
&
~E 200 0
0
o
0
i a°
O&
/x I]46 as prepared
0
0 0
100 0
0 B46 oxidized 0 i
i
t
,
40
100 p (MPa)
00.2
0.5
0.9 p (g/c"
3 )
Fig. 6. Effect of the oxidation treatmenton A V / V versus P for the sample with 46% TMOS concentration.
Fig. 7. Effect of the oxidation treatment on K0 as a function of the bulk density.
concentration materials (Figs. 1 and 5) leads to several comments. First of all, the expected effect is clearly observed. After heat treatment and under a pressure of 0.7 MPa, the irreversible shrinkage is more than twice those measured on the as-prepared material. Second, the shape of the curve is different when the aerogel has been oxidized. In the first part of the curve, the curvature is positive while for the non-oxidized sample the curvature is always negative. This effect is also observed for the material with 26% TMOS concentration (see Fig. 5). In a pressure range where the as-prepared aerogel does
not present an irreversible shrinkage, the oxidized aerogel loses 15% of its original volume. In Fig. 5, the negative curvature of A V / V versus P related to the as-prepared aerogels means that the volumetric strain is self-retarding. Because of the volumetric strain, the clusters get closer but the solid part with the organic species does not form siloxane bonds and opposes a further strain. On the other hand, the large amount of SiOH in the oxidized samples favours the formation of S i - O - S i and induces a more important shrinkage. However, by increasing the number of S i - O - S i bonds, the mate-
P
P
>
P Fig. 8. Schematic illustrationof structural change during pressurizationfor the as-prepared and oxidized aerogels. For the as-prepared sample, the pressure induces the cleavage of siloxane bonds. In the case of the oxidized aerogel, the condensation of silanols forms new siloxane bonds.
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L. Duffours et al. /Journal of Non-Crystalline Solids 186 (1995) 321-327
rial becomes stiffer and the curvature is negative again. Fig. 6 shows the effect of the oxidation treatment on the volumetric shrinkage of the aerogel with 46% TMOS concentration for increasing values of the pressure. The oxidation favours the magnitude of the volumetric shrinkage at low pressure but for higher pressures the difference is low. The volumetric shrinkage induces densification of the material after each run of pressurization. To confirm the formation of siloxane bonds and thus the increase of connectivity of the solid network, we have measured the value of K 0 for different compressed materials and compared the changes of K 0 as a function of the bulk density (Fig. 7). This figure clearly shows that even at a given bulk density (identical volumetric shrinkage) the values of K 0 of the oxidized sample are ten times higher than those of the as-prepared sample. In the case of the as-prepared sample, the densification is due to the action of the pressure which forces the clusters to interpenetrate but only a few siloxane bonds are created and the increase in K 0 is slight. It must be noted that, in the low-pressure range where we do not observe a large irreversible shrinkage, the value of K o slowly decreases. This result can be interpreted by the cleavage of S i - O - S i bonds under stress which is not compensated by the formation of new bonds. This effect is analogous to a fatigue phenomenon and it would be interesting to measure the Young's modulus to confirm this loss in connectivity. In the case of oxidized material, the cleavage of S i - O - S i bonds related to the restructuring of the clusters is largely compensated by the condensation of silanols (Fig. 8). Other comments can be drawn from this study. First, it is noted that the depressurization cycle for the two curves of Fig. 2 (0.1-1.8 MPa and 0.1-5.8 MPa) presents a hysteresis compared with the pressurization cycle. This effect of delayed elasticity is probably due to the entanglement of the clusters under pressure. When the pressure is released, the disentanglement is not instantaneous because of friction effects of the solid parts in contact. The second comment concerns the evolution of the elastic constant as a function of the bulk density. It has been proposed in the literature by different authors that the elastic constant of aerogels scales
with bulk density, p, as G or E ot p'~, where G and E are the shear and Young's modulus respectively and a is the exponent of the power law. Experimental studies [17,6,16] have shown that for silica aerogel the exponent is in the range 2.9-3.8. Taking into account that the Poisson's ratio, u, is nearly constant for the silica aerogels (~-0.2) [18], the power-law evolution should also apply to the bulk modulus, K. These results have been obtained from sets of aerogels for which the bulk density evolution is due to different dilution of the gelifying solutions. In the present work, different bulk densities can be obtained by the pressure effect. The log-log plot of Fig. 4 shows that the value of a is strongly dependent on the way the bulk density varies (concentration of alkoxide, effect of pressure with or without oxidation treatment). The value of ce varies from 2.3 to 5.9. Obviously, the elastic constants depend on the volumetric fraction of the solid but also on the connectivity of the solid network at the scale of the cluster and the parameters which could modify this connectivity intercluster, such as isostatic pressure, will change the exponent, a.
5. Conclusion
The silica aerogels show unusual plastic behavior under isostatic pressure. This plastic deformation induces a restructuring of the solid network which densities and stiffens. Preliminary small-angle X-ray scattering data confirm the restructuring of the clusters which shorten under pressure. The replacement of the organic species by silanols amplifies the densification and the stiffening of the aerogels which shows clearly that the condensation reactions of silanol are responsible for the irreversible shrinkage by freezing the strained network.
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