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 (q) and (qn) 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.

The Influence of Deformation and Chemical Composition on Elementary Free Volumes in Glassy Polymers

“…In contrast to the assumption of Ps formation after the concurrent localization of e+ and e - [6], we assumed [1] the existence of nonlocalized Ps and Ps trapping by EFV. In this case, the long-lived component intensity I 3 (I4 ) is dependent only on the Ps trapping rate and annihilation rate in the trap, but not on the e+ trapping rate.…”

Light-cured dimethacrylate dental restorative composites under a prism of annihilating positrons

“…[14][15][16][17][18][19][20][21] Under such analysis (arranged as constraint-free decomposition [14][15][16][17][18][19][20] or partially-constrained decomposition fixing the shortest τ 1 lifetime 14,15,21 ), the 3 rd component with a long-lived lifetime τ 3 is ascribed to o-Ps annihilation in free-volume holes (voids), the 2 nd component with an intermediate lifetime τ 2 is due to free positron annihilation in interfacial free volumes or other defect states mainly in a solid phase, and the 1 st component with the shortest lifetime τ 1 is attributed to p-Ps self-annihilation conjugated with reduced e + annihilation from defect-free bulk state. [4][5][6] The lifetime-fixing fitting is preferred to overcome inadequacy in the resolving of the shortest component due to mixing different annihilation events (especially, when I 1 intensity occurs to be substantially greater than I 3 ).…”

“…[4][5][6] The lifetime-fixing fitting is preferred to overcome inadequacy in the resolving of the shortest component due to mixing different annihilation events (especially, when I 1 intensity occurs to be substantially greater than I 3 ). 14,15 In such a case, the fixing τ 1 to the value of p-Ps lifetime improves the reliability of the finite-term analysis, not affecting the o-Ps lifetime. 14 Nevertheless, unconstrained x3-decomposition has some, albeit limited, physical rel- evance allowing the most stable fitting.…”

“…This task can be solved due to multicomponent fitting of PAL spectra with 3 or 4 negative exponentials under unconstrained (free fitting components) or constrained (most often for some fixed fitting parameters, such as shortest positron lifetime maintained close to 0.125 ns) [14][15][16] decomposition procedures, and normalized component intensities (I = 3.4): (2) Positron annihilation lifetime spectra treatment algorithms…”

“…In case of stronger input from Ps decaying in the x3-term decomposed PAL spectrum (as for many nanocomposites 5,9,[14][15][16][17][18][19][20][21] ), the e + -trapping can be defined in terms of a simple trapping model assuming 2 additive inputs arise from trapped e + and decayed o-Ps states. 22 This model with 2 additive e + -trapping defects with κ d1 and κ d2 annihilation rates defined as …”