13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- Murillo et al. [9] and obtaining aerogel densities in the range of 0.3 to 1.0g/cm3. The results are plotted and compared against experimental data [4]. The mechanical property, such as Young’s modulus is simulated by using same method. The Young’s modulus of aerogel with densities in the range of 0.3 to 1.0g/cm3 is presented also. 2. Simulation Methods The simulations are performed on the LAMMPS [12] software. The interaction potential used is the Tersoff potential [13], re-parameterized to model interactions between silicon and oxygen [14]. From comparison studies using the BKS potential and Tersoff potential, it is found that the Tersoff potential is more suitable for thermal conductivity studies. , while, the BKS potential augmented with a “24-6” Lennard Jones potential can prevent uncontrollable dynamics at very high temperatures [15]. Using the method by Murillo et al. [9], porous aerogel structures can be formed by expanding, heating and quenching, producing aerogels in the density range of 0.3 to 1.0g/cm3. RNEMD [6, 16-18] can be used to determine the thermal conductivity at each aerogel density, where energies are swapped once every 0.025ps, while the system is kept an average temperature of 300K. This amount of swapping ensures a rapid convergence of the simulated temperature gradient, and produced a linear response within the simulation cell. The system is allowed to equilibrate for a further 1.0ns till a fully linear response has been obtained, and finally, the temperature gradient is averaged over another 50ps. The total solid thermal conductivity can be found by averaging over 5 independent samples at each density. To investigate the Young’s modulus with the strain rate 0.0005ps-1 for 200ps, the tension tests are carried out on samples of different densities. 3. Results and Discussions 3.1. Thermal conductivity of dense amorphous silica The thermal conductivity of increasing lengths of amorphous silica is compared with experimental results to validate our MD scheme. These amorphous silica samples are generated by quenching β-cristobalite, from 5000K to 300K. Their thermal conductivities are determined, as shown in Fig. 1 with their error bars. Figure 1. Amorphous silica of various lengths and their thermal conductivities As the system length increases, so do the thermal conductivity, such that the BKS potential significantly overshoots the thermal conductivity of bulk amorphous silica, which lies between 1.37 – 1.4W/(m.K) [19]. The Tersoff potential plateaus at 1.10 ± 0.01W/(m.K) shows an almost linear dependence with increasing length scales. By extrapolating the results to an infinite length scale, thus representing bulk amorphous silica, the Tersoff potential can give a much better estimation of bulk thermal properties. The inverse of the thermal conductivities versus the inverse of the lengths
RkJQdWJsaXNoZXIy MjM0NDE=