Generation of fractal structures by negative pressure rupturing of SiO₂ glass

Recently there have been several studies of the dynamics of fractal structures utilizing SiO₂ in low-density gel and 'smoke' forms ^(1,2). It is found that over a range of densities, down to a twentieth of the density of silica glass, mechanically stable structures can be formed whose characteristics satisfy the criteria of fractal structures and whose range of self-similarity increases with decreasing density. In this work we test the possibility of producing the fractal low-density silica aggregates by catastrophically rupturing a condensed amorphous silica phase utilizing the methods of molecular dynamics computer simulation. The isotropic expansion causes bond angle opening without rupture up to a tensile limit of -70 kbar. Beyond this point (instability or spinodal) the structure ruptures in a very specific way, viz., by developing a self similar void structure which can be well described by a fractal dimension changing linearly with density. The structure maintains the preferred bond distances and coordination numbers, but permits the density to change by formation of internal surface at a minimum cost in energy. Down to a threshold density, the resulting structures span the simulation box and form a continuous network by sharing oxygens between the basic SiO₄ tetrahedra but gradually lose connectivity in higher dimensions. An analysis of the density correlation functions shows the structures to have fractal dimensions. The bond stretching vibrations and the density of states are monitored over a range of densities. The simulated density of states is interpreted by reference to theoretical studies of fracton dynamics ^(1,2) in aggregates near the percolation threshold and compared with data obtained from neutron and light scattering on the experimental low-density amorphous silicas ⁽¹⁾ of the aerogel type.