Free-volume dynamics in glasses and supercooled liquids

A free-volume theory is developed based on the defect diffusion model (DDM). In addition, positronium annihilation lifetime spectroscopy (PALS) ortho-positronium free-volume and intensity data are presented for poly(propylene glycol) with a molecular weight of 4000 (PPG 4000) in both the glassy and liquid states and dielectric relaxation and electrical conductivity data are reported for PPG 4000 in the liquid state. The DDM is used to interpret all of the data for PPG 4000 and previously reported PALS and dielectric relaxation data for glycerol. It is shown that while the PPG 4000 data exhibit a preference for the three-halves power law, the data for glycerol favor the first power (standard Vogel-Fulcher-Tammann) law. Good agreement between the DDM and the experimental results is found for all of the electrical data and the PALS free-volume data. While reasonable agreement is also found for the PALS intensity data for PPG 4000, a discrepancy exists between the experimental PALS intensity data and theory for glycerol. For the electrical conductivity for PPG 4000, a transition is observed at the same temperature (about 1.4T(g) where T-g is the glass transition temperature) where the PALS free volume changes from steeply rising with temperature to approximately independent of temperature. The same behavior is observed at about 1.5T(g) for previously reported dielectric relaxation and PALS data for glycerol. Model parameters are presented that show the dominance of mobile single defects above (1.4-1.5)T-g and the dominance of immobile clustered single defects below T-g. Finally, a coherent picture of glasses and glass-forming liquids is presented based on the theory and results of the experiments.