Modulus of aerogels

Measuring permeability and modulus of aerogels using dynamic pressurisation in an autoclave... 

Fig. 4 Bulk modulus of the aerogel as function of pressure as determined from the fits.

Figure 2 Young modulus and modulus of rupture of silica aerogels as a function of the aerogel bulk density. (From Woignier and Phalippou [2].)...

Figure 5 Scaling of the elastic modulus cii of aerogels versus density p. Materials Si02 (triangles) sintered Si02 (dots) carbon (diamonds) MF (circles) RF (squares). Open symbols denote evacuated aerogels filled symbols denote aerogels in air.

All applications of aerogels make use of their high porosity, which is responsible for the low index of refraction, the small Young s modulus, the low acoustic impedance, the low thermal conductivity, and the excellent accessibility of the inner surface. In addition, in some applications the high optical transparency is of importance. 

The Y value of the as-prepared aerogels was found to be 9.6 x 10 and 2.6 x 10 times smaller than those of Iron and Indium, respectively. The Y values of these aerogels are closer to those of rubber when compared with the metals mentioned above. It is only 2.6 X 10 times smaller than the Y value of rubber which is quite rarely observed in case of silica aerogels. This improvement in elastic modulus of superhydrophobic flexible aerogels with those of native silica aerogels is roughly two orders of magnitude. 

Though the MTMS -derived aerogels are very flexible and elastic, it does not take much force to compress them. For example, Rao [28] reports a Young s modulus of only 0.03-0.06 MPa for the flexible MTMS-derived aerogels ranging in density from 0.04 to 0.1 g/cm. Kanamori [29] does not report Young s modulus, but stress-strain curves indicate that stresses of less than 1 MPa are sufficient to compress samples with bulk densities around 0.2 g/cra to 25% strain. 

Figure 20.20. SAXS intensity as a function of the modulus of scattering vector q for a light sono-aerogel. The small circle lines are the htting of the mass fractal approach to the experimental data at low- and medium- region. Reprinted from [67] with permission.

The elastic modulus of dense sono-aerogel is several orders of magnitude higher than for classic ones (Chap. 22). Table 20.9 summarizes results obtained for the bulk modulus and apparent density. 

Standard stress-strain curves for both aerogels under uniaxial compression show a first linear region up to 4% strain making it possible to estimate an elastic modulus of 72.4 MPa for S20Ca20, which is close to the low range for cancellous human bone (50-500 MPa). The strain to rupture occurred at 17% and the corresponding stress was 9 MPa. 

Depending on the average pore size, the modulus of compression, and the type of aerogel under investigation, the compression of the sample can be in part or totally irreversible. In particular, sUica-based aerogels without organic surface modification are irreversibly deformed. 

Most published literature analyzed the elastic modulus of silica aerogels by drawing inspiration from the cellular solids models. For example, Ashby and Gibson (1997) describe the open cellular foam model compressive modulus to follow power law dependence on the relative density as shown in Eq. (5.1) where C and /i are geometric constants that depend on the topological features and microstructure undergoing cell wall bending as the dominant deformation. 

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