Strong and fragile liquids in percolation approach to the glass transition

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 ⟨ r 2 ⟩ 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 T 1 at which the first infinite cluster of liquid-like particles appears. The second threshold T 2 corresponds to a point at which the last infinite cluster of solid-like particles disappears. In the 3D case T 1 ⩽ T g ⩽ T 2 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 ⟨ r 2 ⟩ and, respectively, of the elastic constants is broader in the former case than in the latter one. Comparison with neutron experimental data on ⟨ r 2 ⟩ shows that numerically T 1 is close to the Vogel-Fulcher-Tammann temperature T 0 and T 2 is close to the critical temperature T c defined within mode coupling theory.