A Phenomenological Model of Volumetric and Free Volume Hole Properties in Supercooled Liquids: Theortho-Terphenyl Case

Abstract

A phenomenological model linking the macroscopic volume from dilatometry with the microscopic free volume from positron annihilation lifetime spectroscopy is presented. The temperature dependences of both quantities enable to obtain the so-called initial temperature Ti at which dynamic free volume change sets in, the corresponding initial volume Vi, and subsequently, all free volume characteristics. Application of this model on the literature data of a typical low-molecular weight glass former, o-terphenyl, leads to the findings that (i) Ti ≅ TK the Kauzmann temperature and (ii) a packing fraction of the extrapolated equilibrium liquid at Ti is close to the closest regular packing of hard spheres. The published viscosity−temperature data over 12 decades of magnitude are correlated with the free volume hole fraction fh, as determined from the PALS results, via the WLF−Doolittle type equation. These findings indicate that the orthopositronium (o-Ps) is able to detect the part of the total free volume distribution which is relevant for the viscosity over the measured temperature interval from Tg up to ∼ 1.5Tg. In addition, the change of the free volume hole behavior above Tr = 1.25Tg, lying in the vicinity of the crossover temperature Tc from the idealized version of mode-coupling theory, is critically analyzed within a modified bubble concept (the equilibrium interaction of o-Ps with the soft matrix).