Two-order-parameter model of the liquid-glass transition. III. Universal patterns of relaxations in glass-forming liquids

In the preceding companion papers (paper I and 11), we propose a possible origin of the slow dynamics associated with the liquid-glass transition in the light of our two-order-parameter model of liquids. Our model suggests that there exist two levels of dynamic structural heterogeneity, namely, 'locally favored structures and their clusters' and 'metastable solid-like islands'. On the basis of this picture, we consider how all the dynamic modes associated with a glass transition, covering from the boson peak to the structural relaxation (alpha) mode, can be explained within the same model. We assign the boson peak to (quasi-) localized vibrational modes characteristic of locally favored structures and their clusters and the ultrafast mode to their overdamped states. We assign the fast beta mode to the restricted 'translational' motion, while the slow P mode to the restricted 'rotational' (librational) motion characteristic of molecules in metastable islands, which exist only below T*(m). The a mode is associated with dynamics of creation and annihilation of metastable islands below T*(m). The appearance and disappearance of the modes as a function of the temperature are discussed, focusing on the behavior of locally favored structures and metastable solid-like islands. (c) 2005 Elsevier B.V. All rights reserved.