Roles of intermediate-range orders on the glass transition process: Fictive temperature, residual entropy, relaxation time and boson peak

Intermediate-range orders (IROs) have important roles on the glass transition process which is explained by their self-organization. We propose that a periodic Turing pattern, which is based on the reaction diffusion equation proposed by Turing, is constituted in a supercooled liquid and glass by IROs in a wide temperature range. The nonequilibrium structural state determines the fictive temperature and the residual entropy of a glass at the hypothetical equilibrium transition. There are two structural relaxation times in a glass with their own fictive temperatures, namely, Tf1 and Tf2, which are indicated by the configurational states of molecules inside and outside IROs, respectively (Tf1 < Tf2). Tf1 introduces a long relaxation time and Tf2 introduces a short relaxation time, where the equilibrium temperature T has vibrational contributions to both relaxation times. The boson peak is excited by the thermal phonons at the Ioffe-Regel limit due to the periodic Turing pattern. The glass transition is a purely kinetic phenomenon, so that the activity of slow configurational dynamics governs the structural relaxation to inhibit crystal nucleation and vitrify a supercooled liquid. The glass transition is a nano-emergence of IROs and a melted glass is a nanomaterial which is composed of a periodic nano-structure with IROs.