Journal of Non-Crystalline Solids 333 (2004) 68–73 www.elsevier.com/locate/jnoncrysol
Nanostructural damage associated with isostatic compression of silica aerogels L. Perin, A. Faivre *, S. Calas-Etienne, T. Woignier Laboratoire des Verres, Universite de Montpellier II – Place E. Bataillon, UMR 5587, 34095 Montpellier cedex 5, France Received 1 May 2002; received in revised form 4 February 2003
Abstract Isostatic compression of silica aerogels is known to allow densification of these highly porous materials. However, at the onset of compression, hydrophobic and consequently slightly reacting aerogels, exhibit a decrease in bulk modulus. This unusual behavior is associated with damage occurring at low pressures which recovers with further density increase. Damage development and healing are analyzed measuring elastic modulus and, for the first time, internal friction as a function of compression. It is proposed that the origin of damage and healing could be associated with the rupture of tenuous links between clusters of dense silica particles at low density levels, and with the creation of new links between the resulting arms and reacting species that are revealed at cluster interface under higher pressure. 2003 Elsevier B.V. All rights reserved. PACS: 62.20.)x; 62.20.Fe; 62.40.+i; 61.43.G
1. Introduction The mechanical properties of aerogels, which are porous materials, have been investigated under different stress conditions, and unusual behaviors have been observed. Unusual mechanical behavior has been observed when aerogels are uniaxially compressed: the sound velocity decreases upon external uniaxial stressing and recovers its initial value when the aerogel is unloaded. This phenomenon was initially observed in silica aerogels [1], but analogous behavior was also evidenced in carbon aerogels [2]. This behavior was consequently assumed to be associated with the specific porous texture of aerogels and not to the specific chemical nature of silica that is known to be an Ôanomalous’ glass. The Ôknee model’ [1] was proposed to account for this unusual mechanical behavior. The porous aerogel network is considered as a bar-like structure, where the most tenuous legs can Ôknee-bend’ under the application of uniaxial stress. In this configuration, the restoring forces *
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01. E-mail address:
[email protected] (A. Faivre). 0022-3093/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2003.09.046
become weaker with decreasing angle between the legs, leading to a weaker mechanical behavior. Compression of aerogels under isostatic conditions has also been investigated. Isostatic compression is reversible under a certain pressure level. Above this level, it leads to an irreversible volume shrinkage of the sample. The limiting pressure level between reversible and irreversible compression obviously depends on the aerogel nature. Under adequate conditions, aerogels can consequently be densified at room temperature [3–6]. Because of their very low mean pore size, mercury penetration is avoided in these porous materials and Hg porosimeter can be used to densify aerogels under isostatic conditions [3–6]. The texture evolution under high isostatic pressure has been reported for a series of aerogels [6]. It was shown that the size of the largest pores remaining after compression is proportional to the power – 1/4 of the pressure. It was consequently proposed that shrinkage is induced by a buckling phenomenon of tenuous solid parts of the gel located in the vicinity of largest pores [7]. Such a power law can also be deduced analyzing the cell’s strain induced by an external stress, when the aerogel porous texture is modeled by a network of cubic cells.
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Unexpected mechanical behavior has been observed in the first steps of irreversible isostatic compression (relatively low pressure levels). The bulk modulus:
internal friction using dynamic mechanical measurements.
dP ð1Þ dV which can be determined in the elastic range of aerogels compression, measuring the volume V evolution as a function of pressure P [4], decreases at the onset of densification. This decrease is followed by a more classical increase of K with densification. The amplitude of the K minimum depends on the initial bulk density, on the structure and on the chemical nature of aerogels surface [5]. It has been shown to be especially pronounced in Ôas prepared’ aerogels (just removed from supercritical drying autoclave). ÔAs prepared’ aerogels are hydrophobic materials. They contain organic groups remaining from the esterification reaction occurring in the autoclave. An oxidation treatment can be performed around 350 C in order to remove those organic groups, and consequently increase the number of –OH groups. It has been shown that this oxidation treatment leads to a greater densification of aerogels samples under isostatic pressure. The bulk modulus minimum has been observed to be less pronounced and/or maybe shifted towards smaller pressure values [5]. It is consequently easier to analyze the unexpected rigidity minimum in Ôas prepared’ aerogels than in oxidized ones. The Ôknee model’, as well as the model proposed by Pirard cannot directly take into account these differences between Ôas prepared’ and oxidized aerogels at low pressure levels. But the mechanism proposed by Pirard is expected to account well for the behavior under higher external pressure levels. In this paper, we try to go deeper in the analysis and interpretation of the physical mechanisms involved in the first steps of densification under isostatic compression, and especially to understand the minimum of bulk modulus that is clearly observed in Ôas prepared’ aerogel samples. A set of base catalyzed aerogels samples has been synthesized and densified under various pressures in an Hg porosimeter. These samples have dimensions allowing to evaluate both their elastic modulus and
2. Experimental procedure
K ¼ V
A series of nine silica gels were synthesized from tetramethoxysilane (TMOS) hydrolyzed under basic conditions (NH4 OH 4 · 102 M). The molar ratio of the hydrolyzing solution to TMOS was 4. Ethanol was used as solvent and the percent volume ratio TMOS/Vt (where Vt is the whole volume of solution) was 46%. This series of gels was transformed into aerogels by supercritical drying at 305 C and 13 MPa [8]. The nine obtained monolithic aerogels (cylinders with a 5.8 mm diameter and a 30 mm height) were then outgassed (at about 1 mm Hg). The initial bulk density of these uncompacted samples was determined measuring their weight and volume. It was found to be the same for all samples, at least in the precision of our measurements: 0.217 ± 0.005 g/cm3 . Eight of the nine samples were then densified under isostatic compression using a porosimeter. Mercury pressure can be varied from 0.1 to 200 MPa. The aerogels were compressed to a given pressure, ranging between 0.1 and 14 MPa, at a rate of 1 MPa/min and were immediately depressurized to atmospheric pressure at 0.2 MPa/min. After depressurization, the irreversible volume shrinkage was measured from the change in mercury level using a cathetometer. Density of compacted samples was then deduced from this measurement, with a precision of 3%. Results are reported in Table 1. The bulk modulus K of each of these densified and raw aerogels has been measured using the same porosimeter. The bulk modulus K (Eq. (1)) can indeed be determined from the slope of the isostatic compression curve (DV =V as a function of applied pressure P ). The slope has to be measured in the elastic range, where the pressure level is far from the pressure that compacts the sample (about 5–10% of the maximum pressure value) and where the volume shrinkage DV is fully reversible [4–7]. Results are also reported in Table 1.
Table 1 Different applied and measured characteristics for the uncompressed (1) and compressed (2)–(9) aerogel samples: maximum pressure P applied using the Hg porosimeter, and resulting relative volume shrinkage (DV =V ) and density, bulk modulus K, apparent Young’s storage M 0 and loss M 00 moduli measured on the compacted samples Samples
1
2
3
4
5
6
7
8
9
P (MPa) DV =V0 (%) Density (g/cm3 ) K (MPa) M 0 (1 Hz) (MPa) M 00 (1 Hz) (MPa)
0.1 0 0.217 8.0 16.7 0.18
2 1.36 0.220 6.9 4.5 0.22
4 2.69 0.223 5.8 12.8 0.33
5 4.40 0.227 5.6 11.6 0.77
6 6.06 0.231 5.5 12 0.34
8 10.33 0.242 5.9 15.3 0.15
10 14.90 0.255 6.9 16.9 0.36
12 19.63 0.270 7.8 17 0.4
14 25.94 0.293 – – –
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The dynamic mechanical measurements were performed using a dynamic mechanical analyzer. The internal friction tan d corresponding to the ratio between the loss M 00 and the storage M 0 moduli, as well as M 0 and M 00 , were determined using a standard three points bending configuration. The aerogel samples were cut from the nine previous described compressed cylinders to have a length of 20 mm. The sample compressed under 14 MPa unfortunately broke during the DMA measurement. To perform experiments, a static force (100 mN) was used to hold the sample in place, while a dynamic force (80 mN) corresponding to the amplitude of the oscillating load, were applied. The deflection resulting from these static and dynamic forces was usually around 20 lm and always lower than 40 lm. The samples were perturbed at a fixed frequency (between 0.1 and 10 Hz) at room temperature.
3. Results Fig. 1 exhibits the evolution of bulk density for the series of nine Ôas prepared’ base catalyzed aerogels samples that have been irreversibly compressed in Hg porosimeter, as a function of the applied compression pressure level. As observed, density continuously increases as isostatic compression level increases. It is indeed possible to increase the aerogel density by a factor 1.4 using a quite low pressure level (14 MPa) at room temperature, and this, without inducing any macroscopic crack. After compression, the aerogel remains monolithic. The obtained bulk modulus is reported as a function of applied pressure in Fig. 2. While the sample density continuously increases with the applied pressure level, the bulk modulus evolution exhibits a minimum for aerogels compressed under around 6 MPa. A decrease of about 30% is observed and pressures higher than 12 MPa are required to reach again bulk modulus of the uncompressed aerogel. The minimum of bulk modulus is obtained for an aerogel having a density of about 0.23 g/cm3 .
Fig. 1. Bulk density of the compressed aerogels as a function of applied pressure.
Fig. 2. Evolution of bulk modulus K obtained from reversible isostatic compression and apparent Young’s modulus M 0 as measured by DMA at 1 Hz, both plotted as a function of applied pressure. Corresponding densities of the compressed samples are indicated on the upper axis.
The dynamic elastic properties of the compressed and uncompressed aerogels have been analyzed using dynamic three point bending technique. We adjust the dynamic and static load level in order to make such that we work in a fully reversible and elastic domain. The maximum stress applied to the sample (35 kPa) is much lower than the rupture strength measured by three point bending on the same type of basic aerogel (200 kPa) [9]. Moreover each measurement at constant room temperature under a given frequency has been performed for about an hour in order to make such that the sample does not evolve during the dynamic load. As shown on Fig. 2, a minimum of storage modulus M 0 as measured by dynamic mechanical three points bending at 1 Hz is also observed for a pressure level of 5 or 6 MPa corresponding to an aerogel density of 0.227 g/cm3 . Pure Young’s modulus E and bulk modulus K are related with each other by the following expression: E ¼ 3Kð1 2mÞ:
ð2Þ
We take a Poisson’s ratio m ¼ 0:17 for silica aerogels [10] and assume m to be independent of compaction. It has actually been shown that for a series of compressed aerogels, the bulk modulus K obtained by Hg porosimetry is the same than the one calculated from the sound velocity measured by ultrasonic technique using a constant Poisson’s ratio m of 0.17 [11]. Using m ¼ 0:17, the ratio between E and K should be 1.98 (see Fig. 2 and Table 1). Here the ratio between M 0 and K is about 2.3. This difference is explained by the fact that due to the brittleness of aerogels, three point bending measurements were performed on samples having a too large diameter to span ratio. M 0 and M 00 were consequently not exactly pure elastic Young’s moduli E0 and E00 . Nevertheless, the evolution of apparent modulus M 0 and M 00 as a function of density can be used for comparative purposes and the storage modulus M 0 appears to be very close to E values obtained using Eq. (2). The storage M 0 and loss M 00 moduli as measured by DMA at a fre-
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Fig. 3. Evolution of apparent Young’s storage modulus M 0 and loss modulus M 00 as measured by DMA at 1 Hz, plotted as a function of applied pressure. Corresponding densities of the compressed samples are indicated on the upper axis.
Fig. 4. Internal friction values obtained as a function of applied pressure, as measured by DMA for different frequencies. Corresponding densities of the compressed samples are indicated on the upper axis.
quency of 1 Hz are reported on Fig. 3 for the nine samples compressed under different isostatic pressure. It can be observed that the decrease of M 0 in the first steps of compression is associated with an increase of the apparent loss modulus M 00 . M 00 is maximum for the sample compressed under 5 MPa (having a density of 0.227 g/cm3 ). For further densification level, M 0 increases and M 00 decreases. The fact that, for low compression levels, mechanical losses increase in the aerogel when rigidity decreases can also be evidenced by internal friction. Fig. 4 exhibits internal friction measured for different frequencies (0.01, 0.1, 1 and 10 Hz). A very significant maximum can be observed, as for M 00 , corresponding to about the minimum of K and M 0 . No clear frequency dependence can be revealed from these measurements, at least in the error bars of the experiments. Same conclusions can be drawn for M 0 and M 00 frequency dependence.
4. Discussion When an aerogel is isostatically compressed above a threshold pressure value, an irreversible volume
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shrinkage happens. As previously observed, this densification effect under a given pressure both depends on the structural properties of the aerogel and on the chemical nature of its surface. Silica aerogels are usually considered to consist of primary dense particles that assemble to form clusters. These clusters are then connected to each other to create the solid network. It has already been shown that densification by sintering or by compression corresponds to very different textural evolutions [12,13]. The specific surface area decreases in aerogels densified by sintering, but remains unchanged in aerogels densified by compression. SAXS measurements indicate that the mean size of the solid primary particles does not evolve with compression. The correlation length which may be associated to the mean size of clusters decreases. Such features have been attributed to an interpenetration of clusters [13,14]. It can consequently be concluded that densification by compression results from the collapse of pores having the largest size. Such collapse allows chemical species located at the solid surface to become closer and react with each other, leading to an increase of the network connectivity. So considering aerogel as a micro-cellular foam in a first approach, elastic properties increase is expected when density increases [15]. However, at the onset of densification, a minimum of bulk modulus is observed in Ôas prepared’ aerogels (Fig. 2). This behavior is observed in samples synthesized either under base or acid catalysis. The difference between the catalysis conditions lies in the level of pressure at which this minimum happens and in the values of bulk modulus [4]. The pressure level and the K value are lower for base catalyzed aerogels than for acid ones. On the contrary, as it has already been explained that, if an oxidation heat treatment is performed on aerogels after synthesis, no clear minimum in the elastic properties has been detected when density increases. It has been shown that the difference between oxidized and Ôas prepared’ aerogels is directly related to the nature of the chemical groups which are located at the solid surface [5]. It has also been evidenced that the oxidation treatment only changes the chemical nature of the aerogel surface; its texture is almost not affected at least if the thermal treatment is performed below 300 C [16]. It is worth noticing that the surface of as prepared silica aerogels is covered with organic groups resulting from the esterification reaction taking place between silanols and alcohol inside the autoclave during supercritical drying. Esterification reaction is usually not complete because of the steric hindrance of CH3 or C2 H5 groups, and consequently some silanols remain unreacted. In highly macroscopically hydrophobic aerogels obtained by covering surface with trimethylsilyl (TMS) groups, it has been clearly demonstrated that silanols are located under the umbrellas of TMS or R groups [17,18]. So, while Si–OH
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groups easily react together to form siloxane bonds, Si– OC2 H5 groups impede the polycondensation reaction to take place. Applying an external pressure, umbrellas can be strained or distorted: screened effect decreases allowing silanol groups to react with each other and polycondensation to happen. At low pressure values however, for which the esterified groups hinder silanol reaction in as prepared aerogels, densification is likely due to a different mechanism which indeed leads to a decrease in elastic properties. A very straight forward suggestion consists in relating this effect with a structure damage likely associated to the creation of textural defects in the solid network. According to this assumption, the modulus decrease could be originated from micro-cracks creation initiated by the applied external pressure. In the case of aerogels, the defects cannot really be seen as micro-cracks, but are related to rupture of chains connecting neighboring clusters. This assumption of damage occurring in the first steps of compression is supported by internal friction data. As shown in Fig. 4, internal friction is found to be maximum in aerogel compressed at a pressure corresponding to the minimum of bulk modulus. Quite similar results had already been observed using Brillouin technique on a few compressed aerogels [19]. Different works in literature have evidenced that cracks generation leads to a decrease of elastic modulus and an increase of internal friction [20–22]. It was also observed that during thermal heating of micro-cracked HfO2 , internal friction increases with cracks healing process [23]. Internal friction is assumed to arise from the tribological interaction of the asperities on opposite crack faces. According to these observations, the simultaneous occurrence of a decrease in elastic and bulk moduli and an increase in the internal friction indicates a mechanism leading to a network degradation. In the case of aerogel, the increase in internal friction at the first steps of compression can clearly be associated to rubbing and damping of free arms resulting from chains rupture. As we already said, pressure induces a collapse of the
largest pores. Consequently the solid chains of the network which define the pores become closer increasing internal friction. This collapse also leads to a small densification. At higher pressure levels, the free arms can connect to other species. The reacting groups are mainly silanol groups which can polycondense as much as the isostatic pressure induces deformation of Si–OR umbrellas. As soon as these created arms are again connected, they contribute at a much lower level to internal friction which consequently decreases. The clusters interpenetrate and contacts between neighboring arms increase in number, causing the observed increase of elastic modulus (Fig. 3). This mechanism acts as a healing phenomenon which firstly superimposes to that of free arms creation and then becomes predominant contributing to the enhancement of network reticulation and the reduction of internal friction (Fig. 4). A schematic representation of these phenomena is drawn in Fig. 5. As pressure increases, the length of chains that are broken will become shorter and reconnection will increase on a more and more local level.
5. Conclusion Both static and dynamic experiments indicate that the irreversible densification of hydrophobic aerogels using isostatic pressure induces first a decrease in the values of elastic moduli. Accordingly the internal friction increases. Such evolutions have been correlated to damage associated to the rupture of the tenuous links connecting clusters constituting the aerogel network. The longest arms, which define the largest pores, are most likely the first to break. Densification of aerogels under isostatic compression is indeed related to the collapse of these large pores, inducing a rearrangement of clusters. So, in the first steps of aerogel compression, internal friction increases and elastic and bulk moduli decrease. At higher applied pressure, previously broken arms become into contact with neighboring ones or remaining reacting species, leading to new links formation. As densification proceeds, enhancement of the network
Fig. 5. Schematic textural evolution of hydrophobic aerogels as a function of isostatic applied pressure.
L. Perin et al. / Journal of Non-Crystalline Solids 333 (2004) 68–73
connectivity happens, implying the further increase of elastic constants and decrease of the internal friction. If the above proposed assumptions are right, densified aerogels having the lowest elastic modulus should present a very low rupture modulus. It would consequently be interesting to analyze these properties as a function of compression. Although due to the statistical nature of rupture modulus, this analysis is not easy on a practical point of view. It would also be very interesting to get more information concerning the structure and texture evolution at quite large scales in the first steps of compression, to validate the proposed assumptions. Acknowledgements The authors wish to acknowledge very useful discussions with Professor Jean Phalippou.
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