Mechanical behaviour of nano composite aerogels T. Woignier 1,2,*, J Primera 3, A. Hafidi Alaoui 4, S Calas-Etienne 5 1
UMR Eco&sols , IRD-PRAM, 97200 , Le Lamentin, Martinique, France
2
CNRS - UM 2, Place E. Bataillon, 34095 Montpellier Cedex 5, France.
3
Departamento de fisica, FEC, LUZ. Maracaibo, Venezuela.
4 5
Faculté des Sciences et Techniques de Tanger, B.P. 416, Tanger, Marocco
, Laboratoire Charles Coulomb-UM2, Place E. Bataillon, 34095 Montpellier Cedex. *
[email protected]
Abstract In order to improve the mechanical properties of silica aerogels, we propose the synthesis of nano composite aerogels. Silica particles (20-100nm) are added in the monomer solution, just before gelling and supercritical drying. The silica particles addition increases the mechanical properties, but also affects the aggregation process, the aerogel structure and the pore sizes. We discuss the different parameters which infer in the mechanical behaviour of silica aerogel such as: brittle behaviour, load bearing fraction of solid (pore volume), internal stresses (shrinkage) , size and distribution of flaws, subcritical flaws propagation (chemical susceptibility). With silica particles addition, the mechanical properties rapidly increase, stiffening and strengthening the structure by a factor 4-8. Moreover, the mechanical strength distribution and the Weibull modulus characterizing the statistical nature of flaws size in brittle materials show a more homogeneous strength distribution. The composite structure is made of two imbricate networks, the polymeric silica and the particles silica networks. Ultra Small Angle X-ray Scattering experiments show that besides the fractal network usually built up by the organosiloxane, the silica particles is forming another fractal structure at a higher scale. The fractal structure could be related to the low Weibull parameter characteristic of a large flaws size distribution, pores being the critical flaws.
Key words : aerogels, composites , mechanical properties, Weibull modulus, fractal.
1) Introduction Aerogels have drawn increasing interest in different fields from their use in fundamental physics research to their application as specific materials. Silica aerogels are fascinating materials because of their peculiar physical properties, such as very low sound velocity [1], large specific surface area [2], low thermal conductivity [3], and fractal structure [4,5]. The current applications of aerogels include their use as catalysts [8], insulators [3], cosmic dust and space debris captors [9] and glass precursors [7,10]. These peculiar features are essentially due to the very large pore volume, which can be easily tailored from 0% to 99.5%. This pore volume is controlled by the sol-gel synthesis conditions [6] or sintering [7]. Aerogels are generally described as fractal network [4,5,11,12] in the length scale between 1 to 100 nm. This fractal structure is the result of the aggregation of small particles (1-2 nm) and depends on chemical reaction conditions [5-12]. The aerogel network can be described as an assembly of aggregates (~ 100 nm). The aggregates can be fractal (Df~ 2-2.4) and the porosity is totally open and spans over the range of the meso and macroporosity. However, the counterpart of this very large pore volume and tenuous structure is poor mechanical properties. The mechanical strength, toughness and elastic modulus of silica gels and aerogel are 103 lower than the data measured on dense silica [13-18], with the consequence that aerogels tend to crack when they are subjected to stresses. In the literature, aerogels are generally described as elastic and brittle materials like glasses but authors only characterize the classical mechanical features like rupture strength and/or elastic modulus. The theory of linear elastic fracture [19,20] could be applied on gels and aerogels [21]. Consequently, in previous works, we have shown that the brittle behavior of silica aerogels is the result of several kinds of features [17, 22-27]. 1) The large porosity results in a poor "load bearing fraction of solid" which leads to poor elastic modulus and rupture strength. 2) The flaws responsible of the catastrophic failure could be related to the pore size distribution. The macropores link into a macroscopic flaw and rupture occurs when the size of the flaws becomes critical in the sense of the linear elastic fracture mechanics of brittle materials [27]. 3) In silica aerogel, the Weibull modulus characterizing the statistical nature of flaws is low indicating a large flaws size distribution. Because of the fractal structure and associated large pores size distribution we can suppose that the Weibull modulus and the pore size distribution could be related [23-25].
4) The last parameter characteristic of the mechanical and brittle behaviour of silica aerogels is the sub critical flaw propagation. This feature describes how monolithic aerogels samples can cracks several months later without apparent stresses [22]. This behavior is the result of internal stresses (consecutive to syneresis and shrinkage during supercritical drying) and to the water (or alcohol) action at the tip of the flaw [24-26]. Sub critical flaw propagation is well known in brittle materials like glass [28-30] and could induces delayed rupture. The sub critical flaw size propagation is characterized by the n factor called "chemical susceptibility"; n has been measured in silica aerogels [24,25] and seems to be related to the OH content [25] (and thus to the materials specific surface area). It is clear that these peculiar features: poor load bearing fraction of solid, small Weibull modulus and high susceptibility to sub critical flaw propagation are important drawbacks to aerogels applications. They confirm that aerogels are brittle materials with poor mechanical resistance but also they describes that the rupture is poorly predictable (small m value) and the statistical occurrence of rupture could also change with time and chemical environment (n value). The aim of this study is to propose new kind of silica aerogels presenting improved mechanical properties in terms of mechanical resistance and rigidity but also in terms of the control of the flaw size and strength distribution. In composites technology, the inclusion of particles or fibers in the material improves the mechanical properties. In this work we will adjust the mechanical properties of aerogels by the addition of silica particles (20-100nm) in the monomer solution, just before gelation. We will show that this addition will improve the mechanical properties, affect the aggregation process and change the structural features. We will follow the evolution of the textural features (bulk density, specific surface area) and characterize the structural features (fractal dimension and aggregates size) versus the silica particles addition. We will also measure the mean mechanical properties (elastic modulus and rupture strength) and statistical failure features (strength distribution and Weibull modulus) for a set of nano composite aerogels versus the silica particles addition. Finally we will discuss the effect of structural features on the whole mechanical behavior. 2) Experimental Synthesis The "composite aerogels" are prepared as follows. Silicon tetraethoxide (TEOS) is hydrolyzed with water (15 moles of water per moles of TEOS) and silica particles (Aerosil), with size in the range 20-100nm, were added to the hydrolyzed solution of TEOS under
stirring. The pH of the sol was then adjusted to 4.5 which lead to gelation in a few minutes in such a way to avoid particles segregation. The silica particles weight percentage (reported to the total silica weight) ranges between 0 and 70 %. After gelation, the gels were transformed into aerogels by supercritical drying at 305°C and 13 MPa in an autoclave [31-33]. Structural and textural analysis Since shrinkage was observed to be isotropic within experimental accuracy, it was determined simply by measuring the length of the bar of gel with a cathetometer. The bulk density is calculated from the weight and the dimensions of the sample. Specific surface area (S) is measured by nitrogen adsorption-desorption experiments (BET analysis). USAXS spectra have been obtained from the Bonse–Hart optics on line ID2 at ESRF, the European Synchrotron Radiation Facilities. We systematically measured the background spectrum (without the samples) and this signal was subtracted from the original one and the resulting signal was plotted versus the scattering vector in log – log scales. Experiments were done at a wavelength of 1Å. The lateral area of the sample probed by X-ray was approximately of a few nanometers. The smallest scattering wave vector for which relevant data were measured was about 1.10-4 Å-1. For clarity the curves are shifted and the intensity is plotted in arbitrary units. Mechanical analysis To characterize the mechanical properties, the elastic modulus E, of the set of samples is calculated from indentation experiments. Using a Berkovitch indentor, the force required to indent the sample is monitored as a function of the penetration depth. The Young modulus of the sample Es is obtained using the unloading part of the indentation curve [34,35] : The rupture modulus (σ) was measured by a three point bending technique using an Instron testing machine previously described [16,24]. Five experiments at least are done on each sample. For some samples, more than 40 measurements have been done and the mean value is calculated using Weibull statistic. For brittle materials, the broad scattering of the mechanical strength values, is attributed to statistical nature of flaws. The sample strength distribution is usually analysed using Weibull’s statistical analysis [23,26,36]. For samples of identical dimensions, for which the effective volume is assumed constant, the failure probability is given by the relationship [37]:
σ m P(σ ) = 1 − exp − = Pj . σo The cumulative failure probability, Pj has been calculated using the estimator [38]:
Pj =
j − 0.5 , where j is the order of the sample and N is the total number of samples. N
The Weibull's modulus, m, is a shape factor which characterizes the breadth of the strength distribution. σo is a scale parameter characterizing the mean rupture strength. 3) Results For a better understanding of the mechanical features evolution with the silica particles addition, it is important to first characterize the modification of textural and structural features like pore volume, specific surface area and fractal structures. 3-1) Textural characterization It is obvious that the poor mechanical properties of aerogels are due to the large pore volume, which characterizes these materials. Consequently, the increase of the bulk density (decrease of the pore volume) will generally improve the mechanical properties. It should be possible to adjust the apparent density by the addition of silica powder if the sample volume is not changed. It has been explained in the introduction, that some monolithic aerogels can cracks several months later [22] because of a sub critical flaw propagation. This behavior is the result of internal stresses and progressive rupture of siloxane bonds by the action of water at the tip of the flaws [22,24,25]. Generally internal stresses are the results of the shrinkage occurring during the supercritical drying [26]. Because capillary forces are avoided during supercritical drying, theoretically the shrinkage during the gel-aerogel transformation should be close to 0 and the aerogel porous volume should be identical to that of the starting gel. However, previous studies [39] have shown that a volume shrinkage occurs which can be as high as 60 volume %. This shrinkage during supercritical drying can be explained if we consider that the heating treatments accelerate the condensation reactions. The structure of gels is expected to consist of relatively flexible chains whose surface is covered by SiOH groups and shrinkage results from condensation between neighboring groups. When two branches come into contact, condensation reactions of silanol groups take place increasing the connectivity. This process would impose stress on the gel network and explain the shrinkage. Thus, to control
the bulk density and to favour the synthesis of aerogels without internal stresses it is necessary to minimize this shrinkage. The figure 1 shows that the addition of silica particles decreases the volume shrinkage. The addition of silica particles hinders the syneresis effect because the large silica particles are stiffer than the polymeric network and oppose to a restructuring. So, large silica additions (higher than 50%) limit the shrinkage, allow a better control of the sample volume and should decrease the internal stresses. From these results we can make the assumptions that the aerogel structure certainly will be affected by the addition of silica particles. The figure 2 shows the density evolution versus particles addition. Data in figure 2 are the results of the mass increase (addition of silica particles) and volume decrease (shrinkage). In the range 0 to 30% of particles added, the increase of bulk density is not clearly observed. The mass increase (due to particles addition) is related to a smaller shrinkage and the net result is a quite constant bulk density. For higher aerosil content, the shrinkage tends to 0 and the mass addition increases the bulk density. Previous studies [11,17] have shown that the mechanical properties of aerogels generally scale with the density with an exponent close to 3-4. So, we can expect a large increase of the E and σ in the range 30-70%. The figure 3 shows the evolution of the specific surface area with the increase of the silica particles addition. Two conclusions can be drawn from these data : Specific surface area is almost constant in the range 0 to 30% of added silica particles. It means that the microporosity and mesoporosity are not strongly affected; high specific surface area is generally the signature of pores having small size. For higher silica addition, the specific surface area decreases rapidly, indicating a change in the mean pore size and certainly an important structural modification. The monomers condense on the silica particles surface. So, the polymeric network formation is hindered and the developed surface is reduced. 3-2) Structural characterization To understand the mechanism responsible for the changes in mechanical properties (E, σ, m, and σ0), new structural data obtained by USAXS experiments could be helpful. USAXS experiments generally give information on three main features of the aerogel structure: the mean size of the aggregates ( ξ) which are connected to form the network, the mean size of the primary particles (a) which stick together to build the aggregate and the fractal dimension Df which expresses the aggregates compactness. So, to have a better description of the porous
structure, we used these scattering techniques to characterize the fractal features of the composite aerogels. We have described the microstructure of composite aerogels by two imbricate network: the polymeric network and the aerosil particles network. Results concerning polymeric "classic" aerogel already published in the literature show that the structure of these aerogel is fractal in the range 1-100 nm, with a fractal dimension close to 2.3. This high fractal dimension has been interpreted as the signature of a cluster-cluster aggregation process followed by a possible restructuring. The important syneresis effect and associated shrinkage observed on such aerogels is likely responsible for the restructuring and Df increase [4,5,12,39,40]. Preliminary results for composite aerogels show that for high aerosil concentration, the fractal structure disappears giving place to a structure more homogeneous, with a narrow pore size distribution [31-33]. In this study, our results confirm previous data [33]. The figure 4 shows the evolution of scattered intensity I(q) versus q for a "classical" polymeric aerogel and for a composite aerogel with 5% of silica particles. For the classical polymeric aerogel, we observe the usual structure in the q ranges 2.10-2-7.10-2 Å-1. The polymeric aerogel network can be described as an assembly of aggregates (~ 50-100 nm) which are the result of the aggregation of small particles (1-2 nm). However, the domain of low q ranges (10-4-10-3 Å-1) shows the increasing intensity for decreasing q values which can be associated to macropores with a typical length higher than 102 nm. With only 5 % of silica particles addition, besides the polymeric structure (q ranges: 2.10-27.10-2 Å-1), we observed a fractal structure between 10-3 and 10-4 Å-1 (length scales in the range of 100-1000 nm) which can be attributed to the structure issued from the aggregation of the silica particles). The fractal dimension is close to 1.6, in agreement with the DLCA model [40]. The fractal range is broad, ∼ 2 orders of magnitude. Figure 5 shows that the fractal range decreases with the silica particles addition and for the highest concentrations (30-65%), the fractal range is no longer observed. The description of this material in terms of fractals is meaningless. From curves 5 to 30%, it seems that the polymeric structure associated to TEOS gelation progressively disappears. During the TEOS gelation, the aerosil particles covered with hydroxyl groups could be suitable sites to the condensation of the TEOS. Therefore, the polymeric network will grow at the surface of the aerosil particles. For low aerosil content the gel forms as usually observed giving rise to the
classical aerogel structure previously described [4,5,12]. For low aerosil content the aggregation mechanism of the organosiloxane is preserved, but for high soot content a large part of the TEOS is consumed and the polymeric clusters cannot grow. Moreover the presence of a large number of aerosil particles should limit the possible extent of the polymeric network. Consequently, the aggregation process of the TEOS is strongly perturbed by a high particles addition in the solution. 3-3) Mechanical characterization The silica particles addition increases the bulk density and therefore should change the mechanical properties. The data in Figures 6 and 7 show the evolution of the mechanical properties (σ and E) of the composite aerogels as a function of the silica particles content. Mechanical properties show a clear different behaviour in the range 0-30 % compared to the range 30-70 %. We have seen that the structure is made of two imbricate networks, the polymeric and the silica particles networks and the mechanical properties of the composite depends on the relative influence of the two structures. The mechanical features are quite constant between 0 and 30 %. These nano composite aerogels show a mechanical behavior analogous to that of the polymeric classical aerogel which proves that the polymeric network is still present. This result is the direct consequence of the non evolution of the bulk density (Figure 2). For concentrations higher than 30 %, the mechanical properties rapidly increase and silica particles stiffen and strengthen the structure by a factor respectively of 4 and 8 in figures 6 and 7. The addition of silica particles increases the bulk density and consequently the load bearing fraction of solid. We note that the large increases of σ and E agree with previous studies showing that the mechanical properties of aerogels generally scale with the density and with exponent close to 3-4 [11,17]. As explained in introduction, the characterization of σ and E is not enough to have a true description of the whole mechanical behaviour. For brittle materials like glasses and aerogels the broad scattering of the mechanical strength values is attributed to the statistical nature of flaws and the sample strength distribution could be analyzed using the Weibull’s statistics. On figures 8 and 9 are reported the experimental cumulated failure probability distribution function using the Weibull’s statistical analysis. We can see the large scattering in the data due to the statistical nature of the mechanical strengths.
From this data we have calculated the m and σ0 values, small m value being characteristic of a wide distribution of the strength. Figure 10 shows the results of the Weibull's analysis and as expected, for low silica concentrations, the m value is low close to 3 which corresponds to a broad strength and flaw size distributions. When the particles concentration is higher than 30% the m value is more than twice (~ 8). These results show that critical flaw sizes are clearly less dispersed for aerogels with higher aerosil concentration which corresponds to aerogels with a narrow pore size distribution. In the literature [31,32], it has been shown that the pore size distribution is controlled by the addition of aerosil. The large pore size distribution and the fractal structure of the composite aerogels having a particles concentration lower than 30 % evolves, with the concentration, towards a more homogeneous non fractal porous material with a narrow pore size distribution. These new results show the likely correlation between the pore size distribution and the flaw size distribution and comfort the idea that the failure would occur by progressive collapsing of a large number of pores [22,27].
4) Discussion The results concerning mechanical properties can be first explained by considering that the composite aerogel structure is the sum of the a network coming from the classical gelation of organosilane (polymeric gel) and a network issued from the silica particles. The polymeric network will grow at the surface of the silica particles. For low silica particles content the gel forms as usually observed giving rise to the polymeric structure previously described [4,5,12]. This structure is preserved in spite of the presence of the silica particles. It is supposed that the silica particles play the role of a seed for the polymeric cluster formation. On the other hand, the network of silica particles is formed when the polymeric aggregates surrounding the silica particles touch and link. When the aggregates link, the gel point is reached and the spatial arrangement of the particles is characterized by its fractal dimension. So, for concentration lower than 30%, the structure is made of the polymeric gel with micro and mesoporosity and a fractal structure of aerosil particles with a large distribution of macropores leading to a broad pore size distribution in the whole range 1-1000 nm. On the other hand, for higher concentration (30-70%), the polymeric structure is not observed and the fractal extent of the aerosil network narrows. Consequently the pore size distribution becomes more homogeneous. These structural considerations should explain the evolution of the m parameter. For low silica particles concentration, the low m value means a
large flaw size distribution and the clear increase of m for high aerosil content is the signature of the narrowing of the flaw size distribution. We have already proposed that the flaw responsible for the aerogel failure occurs by progressive breaking bonds, collapsing a large number of pores. The macropores link into a macroscopic flaw and catastrophic failure occurs when the size of the flaw becomes critical. Consequently the broad pore size distribution leads to a broad flaw size distribution and a small m value. On the opposite, the narrowing of the pore size distribution will homogenize the flaws and increase m. In the literature the role of the fractal structure on the aerogels elastic features (Young’s modulus, sound velocity, sound attenuation) has been largely discussed [11,17,41-43]. Different works have tried to relate the scaling exponents of elastic constant to the fractal dimensions [11,17]. High frequency measurements of elastic constant have shown that the "fracton theory" [41-43] is relevant in aerogels and have shown the influence of the fractal and spectral dimensions on the sound propagation, in these materials. Our results show that the fractal description of the aerogel structure could be important for another feature of mechanical behavior. The broad pore size distribution characterizing the fractal porous structure affects the statistical nature of the rupture strength. For this kind of mechanical features the fractal extent likely will control the m value. It is not clear if the fractal dimension plays a role on m but the weibull modulus depends simply on the pore size distribution whatever the features of the pore size distribution (issued of a fractal porous structure or not). The understanding of the aerogel mechanical behavior requires a complete description of σ , E but also m and n to be able to predict life time of aerogels in a given environment. Some aerogels having higher mechanical resistance and elastic modulus are finally broken because of internal stresses, low m value and high chemical susceptibility. In the case of composites aerogels, we have demonstrated that a large addition of silica particles will increase the bulk density and consequently improved σ and E. Firstly, it will narrow the pore size distribution and consequently reduce m. Secondly, it will decrease the shrinkage and consequently eliminate the internal stresses and finally, it will decrease the specific surface area and consequently we can expect a smaller influence of the OH content on chemical susceptibility and slow crack propagation. The understanding of the whole mechanical behavior suggests that the pores play the role of stress concentrators and large pore size distribution will lead to a broad dispersion of the rupture strength. It has been shown that the theory of linear elastic fracture could be
applied on gels and aerogels. In brittle materials the rupture strength is strongly dependant on the presence of flaws which act as stress concentrators and one relevant parameters is the toughness (which characterizes the ability of the material to resist to the flaw propagation). The knowledge of the rupture strength and toughness allows to calculate the critical flaw size ac [18,21,27,28]. Further works are in progress to measure the composite aerogels toughness but preliminary calculations using the toughness measured for aerogels with different bulk density [27] and the data of the σ value (figure 6) has allowed to estimate the critical flaw size ac of the composite aerogels set. The results show that the critical flaw size ac would be in the range 103-10 4 nm. This scale range is larger than the pore size, so the scale of critical crack extends on several pores. To satisfy this statement, it is necessary to consider that the flaws, which lead to failure is created during the test. Under load, the failure occurs by progressive breaking bonds following the minimum solid area and collapsing a large number of pores. The macropores link into a macroscopic flaw and catastrophic failure occurs when the size of the flaw becomes critical.
5) Conclusion The knowledge of the mechanical properties of gels and aerogels is clearly of interest for technological application but also for theoretical research. They are ideal material in the sense that the evolution of mechanical properties in relation to the structure can be experimentally studied over a very large range of porosity (0-99%). The composite aerogels show a structure clearly different from that usually described for classical aerogels. A fractal network of silica particles is embedded in a network of a polymeric gel. These two structures are identified because of their different length scale domains and different structural features. For high particle additions, fractality completely disappears and the elasto mechanical properties of the composite material are directly related to the particle content. To precise the whole mechanical behavior of the composite aerogel, the determination of the Weibull modulus m has allowed to show the narrower rupture strength distribution compared to polymeric aerogel. Understanding the whole fracture behaviour of the silica gels implies the study of the stress corrosion effect because mechanical fatigue will limit their technological applications if the materials are under stress. It is known that the strength and fatigue lifetime of vitreous silica decrease in humid environments [43,44]. Previous studies on aerogels have investigated the crack growth and the results revealed a stress corrosion phenomenon depending on the
atmosphere very close to that observed in dense silica glass. Complementary results on composite aerogels are needed but the lower specific surface area (and associated OH content) would suggest that the composite aerogels are certainly less sensible
to slow crack
propagation. Because of its enhanced mechanical features and its more homogeneous porous structure the composite aerogel has been successfully used as a porous and host matrix for nuclear wastes [32,44].
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Figure Caption Figure 1: Evolution of the volume shrinkage as a function of particles addition (weight%). Figure 2: Evolution of the density as a function of particles addition (weight%). Figure 3: Evolution of the specific surface area as a function of silica particles addition. Figure 4: Evolution of the scattered intensity I(q) versus q of a polymeric aerogel (0 weight% of silica particles (0%,O) and a composite aerogels ( 5% ■). Figure 5: Evolution of the scattered intensity I(q) versus q of composites aerogels as a function of the silica particles addition: from top to bottom: 5% ■, 15% O, 30% ▲; 50% ♦, 65% ▬). Figure 6: Evolution of the mechanical strength of the composite aerogels as a function of the silica particles addition. Figure 7: Evolution of the elastic modulus of the composite aerogels as a function of the silica particles addition. Figure 8: Experimental cumulated failure probability distribution function for different composite aerogels concentration of particle addition ( 0% ■, 10% X , 25% ●) Figure 9: Experimental cumulated failure probability distribution function for different composite aerogels concentration of particle addition ( 70% ■, 65% ∆ ; 50% ♦, 40% ▬) Figure 10: m and σ0 data as a function of the silica particles addition.
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1 0,9
σ (MPa)
0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 0
10
20
30
40
50
60
70
80
particulate silica addition (weight % )
Figure 6
100 90 80
E (MPa)
70 60 50 40 30 20 10 0 0
10
20
30
40
50
60
70
particulate silica content (weight %)
Figure 7
80
cumulated failure probability
1
0,8
0,6
0,4
0,2
0 0
0,1
0,2 0,3 Stress (MPa)
0,4
0,5
Figure 8
cumulated failure probability
1
0,8
0,6
0,4
0,2
0 0
0,2
0,4
0,6 Stress (MPa)
Figure 9
0,8
1
1,2
10
1,5
9
1,3 1,1
7 0,9
6 5
0,7
4
0,5
3 0,3 2 0,1
1 0
-0,1 0
10
20
30
40
50
60
silica particle content (weigth %)
Figure 10
70
80
σ0( MPa)
weibull modulus m
8
