Free volume factor in supercooled liquid dynamics

Abstract

The positronium ( o-Ps) annihilation lifetime parameters, i.e., the mean o-Ps lifetime, τ 3, and the relative o-Ps intensity, I 3, were measured for a series of molecular and structurally simple polymer glass formers over wide temperature ranges by means of positron annihilation lifetime spectroscopy (PALS). In addition to the most pronounced effect defining the PALS glass temperature, T g PALS, further two groups of the characteristic bend temperatures in the liquid state, one at T lq b1≅1.15–1.4 T g PALS and the other at T lq b2≅1.3–1.75 T g PALS were found. These characteristic temperatures were compared with certain crossover temperatures from both empirical ( T g, T m; T B, T A, T coll; T M) and theoretical ( T cr) analyses of the thermodynamic and numerous dynamic data and their coincidences were discussed. Decrease in I 3– T plots for glycerol and cis- trans-1,4-polybutadiene can be related to the fast motions on the nanosecond time scale as detected by neutron scattering or dielectric spectroscopy. The corresponding free volume hole characteristics, i.e., the mean free volume hole size, R h, and the free volume hole fraction, f h, were determined by using a quantum-mechanical model of o-Ps in spherical hole or a model of volumetric and free volume hole properties, respectively. Consequently, the role of the free volume hole fraction from the PALS data in the dynamics of some supercooled liquids was established by analyses of various expressions containing the free volume fraction such as the Doolittle-type equation or the Macedo–Litovitz ansatz.