Free volume in poly(n-alkyl methacrylate)s from positron lifetime and PVT experiments and its relation to the structural relaxation

Free volume data from positron annihilation lifetime spectroscopy (PALS) experiments are combined with a Simha–Somcynsky (S–S) equation of state analysis of pressure–volume–temperature (PVT) data to model free volume contributions to structural mobility in a series of poly(n-alkyl methacrylate)s. From the PALS data the glass transition temperature, Tg, decreases (from 382 to 224 ± 5 K) and a given mean free volume is observed at lower temperatures as the side-chain length increases (going from methyl- to hexyl-). This is evidence of an internal plasticization whereby the side-chains reduce effective packing of molecules. By comparing PALS and PVT data, the hole number per mass unit, Nh′, is calculated using different methods; this varies between 0.54 and 0.86 × 1021 g−1. It is found that the extrapolated free volume becomes zero at a temperature T0′ that is smaller than the Vogel temperature T0 of the α-relaxation. The α-relaxation frequencies can be fitted by the free volume theory of Cohen and Turnbull, but only when the free volume Vf is replaced by (Vf − ΔV) where ΔV( = Ef(T0 − T0′), Ef is the thermal expansivity of Vf) varies between 0.060 and 0.027 ± 0.003 cm3/g, decreasing with side-chain length, apart from poly(n-hexyl methacrylate) where ΔV increases to 0.043 ± 0.003 cm3/g. One possible interpretation of this is that the α-relaxation only occurs when, due to statistical reasons, a group of m or more unoccupied S–S cells are located adjacent to one another. m is found to vary between 8 and 2 for poly(methyl methacrylate) and poly(n-butyl methacrylate), respectively. We found that no specific feature in the free volume expansion was consistently in coincidence with the dynamic crossover.