A graph theoretical approach to fluctuating networks in glass-forming liquids: A molecular dynamics study with applications of the pebble game algorithm

Abstract

The network structures fluctuating in space and time are studied in glass-forming liquids of silica (SiO2) and silicate (Mg2SiO4), by carrying out molecular dynamics (MD) simulations and then applying the graph theoretical algorithm of a "pebble game". The pebble game algorithm was developed in Thorpe and coworkers' studies on the percolation of rigidity to form amorphous solids and, although its exactness is proved only in two dimensions, it has been demonstrated to apply to three-dimensional networks. In liquid silica and silicates, the network connections are extended with amounts of network-forming Si, O atoms, and infinitely-percolating clusters emerge over an extensive range of compositions. The search along a network for free "pebbles", attached virtually to the constituent atoms to represent their degrees of freedom of motions, shows that one infinitely-percolating cluster contains some rigid clusters. These rigid clusters in liquid states fluctuate in space and time because of the alteration of connections at high temperatures, in contrast to those solidified below glass transition temperatures, and these fluctuations are responsible for the slow structural relaxations. The pebble game analyses thus give insights into the internal structures in infinitely-spanning networks, beyond surveys by the conventional theory of percolation, and reveal the behaviors of rigid clusters playing the dominant role in the slow structural relaxations in glass-forming liquids. We discuss these results especially by taking focus on varieties in network structures, such as the composition-dependent degrees of connectivity and structural transformation under high pressures.