Fluctuation approach for the estimation of the dynamic heterogeneity in glass-forming liquids from the dispersion in o-Ps lifetimes: Free volume fluctuations in polymers

Positron annihilation lifetime spectra are analyzed with respect to the mean, τ3, and mean dispersion, σ3, of ortho-positronium lifetimes using the new routine LifeTime, version 9.0, which assumes a log-Gaussian distribution of annihilation rates λ = 1/τ. From these data the size distribution of subnanometer local free volumes (holes) characterized by their mean, 〈vh〉, and mean dispersion, σh=〈δvh2〉1/2, is derived. Pressure–volume–temperature experiments are analyzed employing the Simha–Somcynsky equation of state in order to obtain the fractional, h, and the specific, Vf = hV, hole free volume and its expansivity and compressibility. From comparison of Vf with 〈vh〉 the specific number of holes Nh′ is estimated. It is assumed that the hole size dispersion mirrors directly the fluctuation in the free volume as long as the relaxation time of structural motion is larger than the ortho-positronium lifetime of a few nanoseconds. The mean fluctuation in the fractional and specific free volume is calculated. Starting from a fluctuation approach the mean size of the smallest subvolume 〈VSV〉 representative for structural relaxations is estimated. This volume is assumed to be closely related to the volume of a cooperatively rearranging region and to mirror the dynamic heterogeneity. Limits of this interpretation and specific features of PALS are discussed. The variation of the subvolume with temperature and pressure is analyzed. A different behavior of 〈vh〉 and σh is interpreted in terms of Donth’s theory of dynamic glass transition heterogeneity.