Positron lifetime studies of free volume hole size distribution in glassy polycarbonate and polystyrene

Abstract

Positron lifetime spectroscopy has been applied to estimate the free volume hole size distribution in polycarbonate (PC) and in polystyrene (PS) at room temperature. The hole radius density distributions are determined from the ortho-positronium lifetime distributions obtained via a Laplace inversion of the measured positron lifetime spectra. The hole volume density distributions and the number density distributions of holes are estimated from the hole radius density distributions. All of the distributions may be well approximated by single Gaussians. The hole radius and the hole number density distributions have centres 〈rf〉 and 〈vfn〉 at 0.29 nm and 0.1 nm3 in PC, and 0.28 nm and 0.09 nm3 in PS. The FWHM of the corresponding distributions are 0.042 nm and 0.040 nm3 (PC), and 0.039 nm and 0.34 nm3 (PS), respectively. Both, the shape and the width of the distributions correlate well with the free volume theory of Bueche. The possible influence of different effects, such as a nonspherical shape of holes and a scanning of several holes by positronium before annihilation, on the mean hole size and the hole size distribution as detected by the positron lifetime method is finally discussed.