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, T-g, 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, N-h', is calculated using different methods; this varies between 0.54 and 0.86 x 10(21) g(-1). It is found that the extrapolated free volume becomes zero at a temperature T-0' that is smaller than the Vogel temperature T-0' of the a-relaxation. The a-relaxation frequencies can be fitted by the free volume theory of Cohen and Turnbull, but only when the free volume V-f is replaced by (V-f-Delta V) where Delta V(= E-f(T-0 - T-0'), E-f is the thermal expansivity of V Delta varies between 0.060 and 0.027 +/- 0.003 cm(3)/g, decreasing with side-chain length, apart from poly(n-hexyl methacrylate) where Delta V increases to 0.043 +/- 0.003 cm(3)/g. One possible interpretation of this is that the alpha-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. (c) 2006 Elsevier Ltd. All rights reserved.