Universal scaling between structural relaxation and caged dynamics in glass-forming systems: Free volume and time scales

It is shown that the Debye-Waller factor (DW), a measure of the cage dynamics, is contributed by free-volume in o-terphenyl (OTP) and glycerol. An elementary ansatz provides an alternative way to get the reduced DW from Positron Annihilation Lifetime Spectroscopy (PALS). The ansatz supports the scaling of the slow relaxation with the fast caged dynamics over about ten decades in relaxation times in OTP and glycerol. Both PALS and neutron scattering experiments show that, in order to evidence the scaling, the observation times must be shorter than the time scales of the relaxation processes.