Strong and fragile liquids in percolation approach to the glass transition

¹ IA& E, Russian Academy of Sciences - Novosibirsk, 630090, Russia
² Physikalische Institut, Universität Bayreuth - 95440 Bayreuth, Germany

Received: 15 January 1996
Accepted: 17 June 1996

Abstract

Liquid- and solid-like particles in a glass are defined via the Lindemann criterion of melting. Due to structure inhomogeneity the amplitude of the mean-square thermal atomic displacements varies spatially. This situation defines a percolation problem for liquid- and solid-like clusters. There are two percolation thresholds: the first corresponds to the temperature T₁ at which the first infinite cluster of liquid-like particles appears. The second threshold T₂ corresponds to a point at which the last infinite cluster of solid-like particles disappears. In the 3D case holds. We argue that this interval is relatively broader in strong glass-formers in comparison with fragile ones; this means that the spatial distribution of and, respectively, of the elastic constants is broader in the former case than in the latter one. Comparison with neutron experimental data on shows that numerically T₁ is close to the Vogel-Fulcher-Tammann temperature T₀ and T₂ is close to the critical temperature T_c defined within mode coupling theory.