A study of time dependence of ortho-positronium annihilation in a poly(butadiene) at different temperatures: a meaning of I3 parameter

Positron annihilation measurements as a function of temperature and time have been carried out on a poly(butadiene). The measurements were performed at several temperature points from 14 to 225 K. The measurement time was several hours to four days. The analysis of data shows the following features:

(i) the value of τ₃ does not depend on the rate of cooling or time,

(ii) the value of I₃ depends on the rate of cooling and the history of thermal treatment,

(iii) the dependence of I₃ on time can be described by Debye function. But the rise in I₃ is observed at very low temperatures,

(iv) the I₃ decays to value of I₃ observed during very slow cooling.

Article Outline

1. Introduction

2. Experiments

3. Results

4. Discussion

5. Conclusions

6. Uncited Reference

Acknowledgements

References

1. Introduction

If a glass is formed by rapid cooling of a super-cooled liquid to a temperature below the glass–liquid transition temperature, T_g, its properties will not be static, but will relax toward values characteristic of the corresponding “equilibrium” supercooled liquid as extrapolated from above to below T_g. This process named as structural relaxation or “physical aging” is of great practical importance because of its relevance to the designing and engineering of amorphous materials with desired properties. The relaxation property and transport phenomena of disordered polymers can be explained within the free-volume concept (Ferry, 1980). However, an unsettled problem is a way of quantifying the free-volume properties, such as the free-volume fraction, the average and the distribution of the free-volume size. In the last decade, the positron annihilation lifetime spectroscopy (PALS) technique has been recognised as a useful method to detect atomic scale free-volume holes of polymers ( Schrader and Jean, 1988). This technique involves using a positron source, mostly ²²Na, to emit positrons into the sample. But these positrons and the accompanying gamma–quanta have sufficient energy (average positron energy 200 keV, gamma 890 keV) to induce radiation effects, and the positron probe can thus affect the sample being investigated during PALS experiments.The basic assumption of positron annihilation lifetime spectroscopy (PALS) data interpretation in terms of the free-volume concept is the proportionality of the intensity of long-lived ortho-positronium (o-Ps) component, I₃, to the concentration of free-volume holes (Kobayashi et al., 1989). However, there are different findings regarding the influence of external factors on the “true” intrinsic value of I₃. Its variation with the measurement time is regarded as a manifestation of the relaxation of free-volume fraction. On the other hand, the decrease in I₃ with PALS measurement time is related to the activity of the positron source and the chemical processes in the positron spur, e.g., formation of free radicals. There are PALS measurements on semi-crystalline samples (Suzuki et al., 1996), observing the I₃ increase with elapsed time when the temperature of the sample is below T_g.All these reports indicate that the o-Ps formation in polymers is more complicated and the basic assumption of PALS interpretation may be questionable.In this work, PALS results will be presented on the amorphous cis–trans-1,4-poly(butadiene), cis–trans-1,4-PBD, in a wide temperature range from 14 to 350 K. The aim of this paper is the study of the influence of temperature, time and sample history on the intensity I₃, life time of o-Ps, τ₃, as well as the S-parameter from Doppler broadening measurements.

2. Experiments

The PALS experiments were conducted using a conventional fast–fast coincidence system having a time resolution of ca. 320 ps (FWHM). Cis–trans-1,4-PBD has a molecular weight of M_w = 2 × 10⁴, the glass transition temperature T_g = 178 K (Zorn et al., 1995). The isomer composition was 41% cis, 52% trans and 7% vinyl form. This isomer composition was chosen to avoid a crystallisation process on the PBD sample (Zorn et al., 1995).The positron source, consisting of 2 MBq ²²N a sealed between two 3.5 μm Ni foils, was sandwiched between polymer discs, each of about 3 mm thick and with a diameter of 10 mm. At a chosen temperature, each spectrum was accumulated for 1 h, resulting in a total number of counts of about 1.14 mil. At least, two such spectra were recorded at each temperature point.The ²²Na source–sample assembly was mounted on a closed cycle helium gas refrigerator. The assembly was kept in a rotary pump vacuum of about 4 Pa. Automatic temperature regulation was used during all the measurements and the temperature was controlled within ±1 K. Several different temperature scans on the specimens were performed. The first sequence (heating) was the following: I₃, τ₃ were first evaluated at room temperature of 300 K immediately after the source installation. Then, fast cooling to the temperature of 40 K at a rate 4 K/min was performed and the temperature increased in steps of 10 K. The second sequence (cooling) started at 300 K, then the temperature decreased to 14 K in steps of 10 K.For the PALS measurement as a function of time, the PBD was annealed in the chamber at 300 K for several hours, then cooled to the measurement temperature and the measurement began immediately.The positron life-time spectra were measured as a function of the elapsed time at 14 different temperature points below and above T_g.The PALS data were also accumulated during heating of the samples to 300 K and cooling of PBD to chosen temperature below 300 K. The total irradiation time of 1080 h was divided between PALS and calibration (Bi) measurements. To clearly describe the thermal history of the experiment, the time dependence of I₃ and τ₃ is shown in Fig. 1 and Fig. 2, respectively. The values of I₃ and τ₃ at room temperature were the same despite the long irradiation time and complicated thermal history. This indicates that a possible irradiation damage does not influence the annihilation observables.