Two-order-parameter model of the liquid–glass transition. II. Structural relaxation and dynamic heterogeneity

We propose that there exist two key temperatures relevant to glass transition: (i) a transition from the ordinary-liquid to the frustrated metastable-liquid (the Griffiths-phase-like) state at Tm∗, which is characterized by the appearance of metastable high-density solid-like islands and the resulting appearance of the cooperative nature of α relaxation, and (ii) another transition into the spin-glass-like state and the resulting divergence of the α relaxation time at T0. Tm∗ is a density-ordering (melting) point of the corresponding hypothetical pure system that is free from disorder effects. Below Tm∗, a system has a complex free-energy landscape characteristic of the frustrated metastable-liquid state; metastable solid-like islands with different densities coexist and fluctuate dynamically. In our model, the α   mode is associated with dynamics of creation and annihilation of metastable islands below Tm∗. The metastable solid-like islands are the origin of dynamic heterogeneity. We propose a modified Vogel–Fulcher law, which can phenomenologically describe the Arrhenius/Vogel–Fulcher crossover induced by a transition from the ordinary-liquid to the frustrated metastable-liquid state around Tm∗. We also argue that the hidden crystalline ordering in metastable islands may cause the change in the structure factor of a supercooled liquid below Tm∗, which is more enhanced upon cooling.