Positron lifetime studies of free volume hole size distribution in amorphous and in semi-crystalline polymers

Abstract

Positron lifetime spectroscopy has been applied to estimate the free-volume hole size distribution in glassy polycarbonate (PC) and polystyrene (PS) as well as in plastically deformed and undeformed, semi-crystalline polyethylene (HDPE). The hole radius density distribution is determined from the ortho-positronium lifetime distribution which is obtained via a Laplace-inversion of the positron lifetime spectrum. The hole volume density distribution and the number density distribution of holes is estimated from the hole radius density distribution. In PC and in PS all of the distributions may be well approximated by a single Gaussian. The hole radius and the hole number density distributions have centres <r> and <v _n > at 0.29 nm and 0.1 nm³ in PC, and at 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. In PE the lifetime spectra consist of four components. The o-Ps lifetime distribution is bimodal and may be attributed to o-Ps annihilation in the crystalline and in the amorphous phase of the polymer. The corresponding hole size distributions show definite changes of their position and width following plastic deformation which we attribute to homogeneous crystal lattice dilatation and/or a local disorder in the crystals and to an increase in the eccentricity of holes in the amorphous phase.