The Structure of the Free Volume in Poly(styrene‐co‐acrylonitrile) from Positron Lifetime and Pressure Volume Temperature (PVT) Experiments

Abstract

Summary: The structure of the free volume and its temperature dependence between 25 and 190 °C of copolymers of styrene with acrylonitrile, SAN (0 to 50 mol‐% AN), is studied by pressure volume temperature (PVT) experiments and positron annihilation lifetime spectroscopy (PALS). In this second part of the work, PALS data are reported from which the temperature dependence of the mean size and size distribution of local free volumes (subnanometer size holes) is analysed. The mean hole volume, vh, varies in PS between 105 Å3 (27 °C) and 220 Å3 (190 °C), and shows a systematic decrease with increasing AN content, at Tg from 121 Å3 for PS to 102 (±2) Å3 for SAN50. The specific number of holes, $N_{\rm h} '$, estimated from a comparison of PVT and PALS results, is independent on the temperature and the composition of SAN, $N_{\rm h} '$ = (0.56 ± 0.02) × 1021 g−1 which corresponds to Nh(Tg) = $N_{\rm h} '$/V(Tg) = 0.59 nm−3 and 1/Nh(Tg) = 1.7 nm3 for the volume which contains one hole. The analysed size distributions of the holes above Tg follow the compressibility of the free volume as it is predicted by the theory of thermal volume fluctuation. Moreover, we showed that the bulk elasticity modulus follows mastercurves as a function of vh above and below Tg.Free volume hole radius distribution n(rh) in PS for three different temperatures.magnified imageFree volume hole radius distribution n(rh) in PS for three different temperatures.

A Comparison of Different Theoretical Models of Positron Lifetime Spectra for Polymers

“…Similar declination of σ 3 was observed also for an epoxy resin [11]. However, usually σ 3 at T k (or just below T k ) becomes a weakly increasing temperature function [7][8][9][10][12][13][14][15]. Values of τ 2 from 112 K up to T g seems to be constant (Fig.…”

“…Therefore a discrete-term analysis overestimates the values of τ 1 and I 1 . This approach was applied successfully in many works [7][8][9][10][11][12][13][14][15] to analysis of lifetime spectra for different polymeric and other molecular substances.…”

“…According to suggestion given in papers [5][6][7][8][9][10][11][12][13][14][15], we assumed that first component of s(t) is discrete. The rates for e + and o-Ps were assumed distributed and the distributions were described by α i (λ).…”

Free volume dependence of polymer viscosity

“…Previous analyses demonstrated that the predicted h=h(T) behavior at ambient pressure is correct (Yu et al 1994;Higuchi et al 1995;Srithawatpong et al 1999;Schmidt and Maurer 2000;Schmidt 2000;Olson et al 2002;Olson 2004;Dlubek et al 2004Dlubek et al , 2006Consolati et al 2005). Assuming that at T≈T g +2 0t o2 5°Ch=f PALS , superposed the two sets of data in full range of temperature.…”

“…Documented dependence of I 3 on other factors than free volume fraction (Schmidt 2000), distance form T g (Kisliuk et al 2000), and the void geometry (Consolati et al 2005) may be a reason for this variability. Another approach was proposed by Dlubek et al (1998Dlubek et al ( , 2004Dlubek et al ( -2006. The authors calculated free volume cell size from Eq.…”