G. Dlubek

Do the CONTIN or the MELT programs accurately reveal the o-Ps lifetime distribution in polymers? Analysis of experimental lifetime spectra of amorphous polymers

Abstract High quality positron lifetime spectra (total count of 70 million) were taken for polycarbonate (PC) and polystyrene (PS Hoechst). The spectra were analysed employing the routines CONTIN and MELT which both assume continuous lifetime distributions, as well as the discrete-term analysis routine LIFSPECFIT. The lifetime distributions consist of three peaks, of these, the long-lived one, corresponding to the o-Ps lifetime distribution, splits for low regularization into two sub peaks. No way was found to decide whether these sub peaks, or the smoothed o-Ps lifetime distribution obtained for higher regularization, were due to two (discrete) close neighbour lifetimes, or came from a single, broad o-Ps lifetime distribution. Assuming discrete lifetimes, values of approximately 1700 ps and 2350 ps were estimated for PS (1750 and 2400 ps for PC). Assuming a single but broad o-Ps lifetime distribution, the mass centre τ 3 of that in PS was estimated to 1985 ps (2020 ps in PC). The same analysis was carried out with distributions from simulated lifetime spectra for comparison with experimental data. From this comparison the full width at half maximum (FWHM) of the o-Ps lifetime distribution was estimated to 800–950 ps for both PS and PC. The o-Ps lifetime results may be attributed to two different Ps states or, alternatively, to hole size distributions ranging approximately from r =0.24–0.32 nm ( v =0.06–0.14 nm 3 ). Furthermore, short comments on how to estimate a reliable width for the o-Ps lifetime distribution and on the handling and resolving power of CONTIN and MELT are given.

Does the MELT Program Accurately Reveal the Lifetime Distribution in Polymers

In previous studies we have investigated artefacts which appear in analysed parameters of positron lifetime spectra containing distributed o-Ps lifetimes. Recently, we discovered also that the disagreements between the experimental positronium lifetime parameters and theoretical expectations, I 1 /I 3 > I p-Ps /I o-Ps = 1/3 and τ 1 > τ p-Ps , may be well understood by assuming a distribution of e + lifetimes in addition to an o-Ps lifetime distribution. In this paper we give further experimental evidence for these deviations by taking positron lifetime spectra of high statistical accuracy for various amorphous polymers. Furthermore, a systematic study of the influence of the widths of the e + and o-Ps lifetime distributions on the analysed lifetime parameters will be presented. The analysis of computer-generated spectra showed that all of the analysed lifetimes τ 1 , τ 2 and τ 3 increase artificially with increasing width of the e + and o-Ps lifetime distributions. The intensity I 1 increases also, while I 2 and 13 decrease. The deviations of I 1 /I 3 and τ 1 from the theoretical expectations are mainly controlled by the width of the e + lifetime distribution. Suggestions for suitable constraints in the discrete-term analysis in order to get reliable lifetime parameters are also made.

The local free volume in metallocene-catalysed poly(α-olefin)s: a positron lifetime study

Abstract Positron lifetime measurements are reported for linear poly(α-olefin)s from polypropylene to poly-1-eicosene polymerised using zirconocene catalyst. For comparison a low density polyethylene was also studied. Four lifetimes are resolved, the longest of them (τ4) is attributed to o-Ps annihilation from free-volume holes in the amorphous phase and is used to estimate the mean volume of these holes. It is observed that the hole size increases with increasing separation between the measuring temperature (T=300 K ) and the glass transition temperature Tg, estimated with differential scanning calorimetry. Among the poly(α-olefin)s the average hole volume is the largest in poly-1-dodecene (0.205xa0nm3, T g =166 K ) and the lowest in polypropylene (0.117xa0nm3, T g =262 K ). A method for estimation of the glass transition temperature Tg from the experimental hold volumes is proposed. From comparison of amorphous and crystalline densities the fractional free volume was calculated. From this the number of holes was estimated to be 0.5–0.9xa0nm−3. The effect of exposure of the polymers to positron radiation from the source on the o-Ps annihilation parameters was also studied. While lower poly(α-olefin)s show a more or less pronounced exponential decrease of the o-Ps intensity I4 as a function of time, a slight increase is observed in higher poly(α-olefin)s. Possible reasons for this behaviour are discussed.

Studies of the positron lifetime and Doppler-broadened annihilation radiation of polypropylene-polystyrene alloys

Abstract Positron annihilation lifetime spectroscopy and Doppler-broadened annihilation radiation (DBAR) experiments were performed on polypropylene–polystyrene (PP–PS) alloys (0–100% styrene) prepared by in situ polymerisation of styrene in a PP host matrix. The mean size of free-volume holes estimated from the ortho -positronium lifetime τ 3 shows a continuous decrease from 0.119xa0nm 3 in PP to 0.095xa0nm 3 in PS. The intensity of the o -Ps component, I 3 , the average positron lifetime τ av , the curve-shape parameter S and the peak height H of the DBAR spectra increase linearly with the styrene concentration. This is attributed to a linear superposition of the Ps yields of PP and PS in the PP–PS alloys. The DBAR spectra were fitted by a sum of three Gaussians, the narrowest of them is attributed to self-annihilation of para -positronium confined within holes. After its subtraction, a ‘broad component’ is obtained which represents the momentum distribution of electrons bound to molecules. Its normalised peak height does not show any change with the composition which reflects the fact that both constituents of the PP–PS alloys contain only hydrogen and carbon atoms in their chemical units. Immersing of PP into styrene liquid leads to a very pronounced increases in the lifetime parameters which is attributed to the plasticisation of PP.