Scaling between structural relaxation and caged dynamics in Ca_0.4K_0.6(NO₃)_1.4 and glycerol: free volume, time-scales and implications for pressure–energy correlations

Abstract

The scaling of slow structural relaxation with fast caged dynamics is seen in the molten salt Ca_0.4K_0.6(NO₃)_1.4 (CKN) over about 13 decades of the structural relaxation time. Glycerol scaling has been analysed in detail. In glycerol, the short-time mean-square displacement , a measure of the caged dynamics, is contributed by the free volume. It is seen that, in order to see the scaling, the observation time of the fast dynamics must be shorter than the time-scales of the relaxation processes. Systems with both negligible (like CKN, glycerol and network glassformers) and high (like van der Waals liquids and polymers) pressure–energy correlations exhibit scaling between the slow relaxation and the fast caged dynamics. According to the available experiments, an isomorph-invariant expression of the master curve of the scaled data is indistinguishable from a simpler non-invariant expression. Instead, the latter agrees better with the simulations on a wide class of model polymers.

Keywords:

• glass transition
• fast-dynamics
• relaxation

Acknowledgements

Discussions with J. Bartoš and K.L. Ngai are gratefully acknowledged.

Notes

Note

1. In a system with N particles and density ρ, two system states, say (r ₁, r ₂, … , r _N ) and , are isomorphic under the prescription that, if , then they have proportional configurational NVT Boltzmann factors 10.