Aerogels density

Table 2. Effect Analysis for Dried Aerogel Density...

In the figs 5 a/b the dielectric permittivity at zero frequency ( aat) and at very high frequencies ( ) are shown as a function of density for the RF-aerogel density series with R/C-raUoofSOOand 1500, respectively. 

Above about 0.5 GHz, Brillouin scattering provides an elegant technique of measuring phonon mean free paths (which are inversely proportional to the sound attenuation coefficient) by evaluating the width of the Brillouin lines [53]. However, as a result of finite spectrometer resolution and contrast, this method is limited to aerogel densities above 180 kg/m. ... 

Higher density aerogels have elastic moduli well above 10 MPa, but for lower densities elastic moduli become small enough to allow the atmospheric air pressure to become noticeable. The gas inside the aerogel pores influences both the total (dynamic) modulus and, at very low aerogel densities, the total density of the system. According to a simple model (Kelvin-Voigt model), the sound velocity becomes... 

The index 0 indicates properties of the evacuated aerogel, k is an effective adiabatic exponent for the system gas-skeleton. For most aerogels it is very close to unity. Only at extremely low aerogel densities does it become both larger and pressure dependent [65]. In Fig. 6, the variation in Ci with gas pressure is depicted for air and SFe for p = 5 kg/m3 aerogel. 

A linear variation of the aerogel density of cellulose concentration should be observed on simple theoretical grounds. If Pa denotes the density of the aerogel and Wc is the salt hydrate melt weight fraction having a density then for small concentration, Wc << 1, the aerogel density should obey the relation. 

Figure 18.6. Structural model of chitosan-silica aerogel density 0.27 g/cm, 10% chitosan.

Figure 23.6. Total thermal conductivity of a resorcinol-formaldehyde aerogel (density = 330 kg m , porosity = 0.78, average pore size 0.6 pm) as a function of argon gas pressure at 21°C. The solid line is the calculated thermal conductivity according to (23.10) without taking a coupling effect into account.

Figure 23.12. Effective total thermal conductivity of resorcinol-formaldehyde aerogels with different R/C ratios as a function of aerogel density at room temperature [24, 37].

Figure 23.17. Effective total thermal conductivity of a carbon aerogel (density p = 225 kg m , size of primary particles 100-150 nm, average pore size 570 nm, pyrolysis temperature 1,800 0) under different atmospheres and the corresponding sohd (red line) and radiative (green line) thermal conductivity as well as the sum of both (black line) as a function of temperature [44].

Figure 32.3. The nanometer-scale filaments composing a silica aerogel network can be seen in this scanning electron microscope image. The aerogel density is 13 mg/cc.

Figure 32.11. Silica aerogel (density of 20 mg/cc) opacified with graphite was cut and attached to the walls. The aerogel is seen as the bluish-gray materials under the gold Kapton.

Figure 32.15. Thermal conductivity of siUca aerogel opacified with Ti02 powder in varying concentrations. The aerogel density was 50 mg/cc.

Figure 5-1. Backscattering Brillouin spectra for six silica aerogel densities (in kg/m ).The relative intensities, not adjusted for sample turbidity, are otherwise significant. IW is the full instrumental width at half-height. The central portion of the spectra, affected by the elastic line, was removedfor clarity. (Reprinted figure with permission from [E. Courtens etaL, Phys. Rev. Lett. 58, 128 (1987)]. Copyright (1987) by the American Physical Society.)...

Finally the specific surface area can be calculated using the bulk aerogel density and the value of W deduced from relation (5-6). 

---