13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- silica than the BKS potential. 3.2. Structural correlations of porous silica aerogel Using the method discussed in Section 2, percolated silica aerogel was simulated on a cubic system of 52,728 atoms, with densities ranging from 0.3 to 1g/cm3. Fractal dimensions are determined using the method proposed by Kieffer et al. [7], where the total radial distributions for each density are calculated, and power-law decays are superimposed on the peak structures to determine the fractal dimensions. These results are plotted in Fig. 4 below along with their error bars, as well as data from previous theoretical studies by Murillo et al. [9]. Figure 4. Decreasing fractal dimensions as density decreased The variation of the fractal dimension, df, with density agrees with those found in previous theoretical and experimental studies. Experimental silica aerogel fractal dimensions varies with processing conditions, where it is approximately 1.8 under basic processing conditions, and about 2.2 to 2.4 in both acidic and neutral conditions [22]. 3.3. Thermal conductivity of porous silica aerogel Fig. 5 shows the data obtained, from RNEMD, as a log-scale plot with their corresponding errorbars, and the power-law fit of the data. Figure 5. Log-scale plot of the power-law variation of thermal conductivity with density Thermal conductivity is found to decrease as density decreases, in a non-linear fashion. At the lowest density of 0.3g/cm3, the thermal conductivity also reaches its lowest value of 0.05 ± 0.003W/(m.K). The power-law exponent, α, of experimental bulk aerogel was found to be 1.6 in the density range of 0.3 to 1.0g/cm3 [4]. Our results show an α value of 1.61 in this density range, correlating very well with experimental results. Our model is also advantageous in that very low densities are achievable, much lower than 0.1g/cm3, without any adverse phenomena. A downside
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