Universal scaling between structural relaxation and vibrational dynamics in glass-forming liquids and polymers

If liquids, polymers, bio-materials, metals and molten salts can avoid crystallization during cooling or compression, they freeze into a microscopically disordered solid-like state, a glass 1 , 2 . On approaching the glass transition, particles become trapped in transient cages—in which they rattle on picosecond timescales—formed by their nearest neighbours; the particles spend increasing amounts of time in their cages as the average escape time, or structural relaxation time τ α , increases from a few picoseconds to thousands of seconds through the transition. Owing to the huge difference between relaxation and vibrational timescales, theoretical 3 , 4 , 5 , 6 , 7 , 8 , 9 studies addressing the underlying rattling process have challenged our understanding of the structural relaxation. Numerical 10 , 11 , 12 , 13 and experimental studies on liquids 14 and glasses 8 , 15 , 16 , 17 , 18 , 19 support the theories, but not without controversies 20 (for a review see ref. 21 ). Here we show computer simulations that, when compared with experiments, reveal the universal correlation of the structural relaxation time (as well as the viscosity η ) and the rattling amplitude from glassy to low-viscosity states. According to the emerging picture the glass softens when the rattling amplitude exceeds a critical value, in agreement with the Lindemann criterion for the melting of crystalline solids 22 and the free-volume model 23 .