Positron lifetime measurements were then performed in these SSNTD at room temperature (about 25˚C) as a function of the gamma doses using a standard lifetime spectrometer, details of which are described elsewhere [24]. The principle of operation for the positron annihilation lifetime (PAL) spectrometer is to allow γ-γ coincidence measurements, positron emission should be accompanied by an appropriate start signal from a nuclear de-excitation like the 1.28 MeV photon in the case of the ²²Na isotope. The 511 keV annihilation photon provides the stop signal. The PAL spectrometer consists of conventional fast-fast coincidence system with start and stop detectors, each of them made by coupling a fast (plastic) scintillator to a photomultiplier. The timing pulses are obtained by differential constant-fraction discrimination. The time delays between the start and stop signals are converted into amplitude pulses the heights of which are stored into a multichannel analyzer. Using ²²Na, which is commercially available as an aqueous solution of ²²NaCl, as a positron source. The source was prepared by evaporating a few drops of aqueous solution, about 15 μCi, of ²²NaCl on a thin kapton foil of 12 μm thicknesses and an area of 10 × 10 mm². After drying, ²²NaCl spots were covered with another similar foil and properly sealed together with epoxy glue to avoid any leakage. Positrons emitted from the source had sufficient energy (E_max = 544 keV) to penetrate a certain depth of the sample. The source absorption by the kapton foil was about 7% and contributed to the medium lifetime components. This absorption was separated in the analysis of the lifetime spectra. The time resolution (full-width at half-maximum, FWHM) of the lifetime spectrometer was around 260 picoseconds (ps), as determined by the RESOLUTION computer code [25]. Each positron lifetime spectrum contains 10⁶ counts which is sufficient to be analyzed with the computer program LT 9.0 in its distribution mode. The program gave three positron lifetimes as the best variance of fit.From a semiempirical model [26], o-Ps is assumed to be localized in an infinite high potential well with the radius r_h + dr where r_h is the hole radius and dr = 1.66 A˚ [15,20] describes the penetration of the Ps wave function into the hole walls. In this model the (mean) o-Ps lifetime is used to calculate the mean radius of the holes (assumed spherical) by means of the equation

where l_po is the pick-off annihilation rate of o-Ps inside the holes. The mean hole volume follows then from Since the holes show a size and a shape distribution, a more reasonable way is to calculate the mean hole volume as mass centre of the hole volume distribution. LT9.0 assumes the annihilation rate distribution of the third annihilation channel to be log normal functions. Therefore the lifetime spectrum is expressed by the Laplace transformation of the functions where

and

where is the standard deviation of the distribution.

By determining the distribution of the o-Ps annihilation rates and using Equation (1), the hole radius probability distribution can be calculated [27,28] as:

where is the free volume holes fraction with radii between and. The volume fraction of free volume holes with volume between and

can be given by while the fraction of holes with volume between and could be given by.

The resulting o-Ps annihilation data will be correlated with the thermogravimetric analysis (TGA) of the PM- 355 samples. The analysis was carried out by TGA thermogram using a DuPont thermal analysis apparatus with temperature rate of 5˚C/min and temperature range from 20˚C to 500˚C.

The Conventional morphology observations of the PM- 355 samples were carried out by transmission electron microscopy (TEM) using JEOL JSM-1200 microscope operated at an acceleration voltage of 90 kV.

The outline of this research is exposing the PM-355 polymeric solid state nuclear track detector to low gamma radiation doses and investigate the changes induced by gamma irradiation on the microscopic structure of the PM-355 by using PAL, TGA, and TEM techniques.

All of the PAL spectra of the non-irradiated and irradiated PM-355 were analyzed assuming three discrete exponential components and the source correction due to annihilation in the source and source supporting Kapton [29]. Each lifetime corresponds to the average annihilation rate of a positron in a different state. The shortest lifetime component (τ₁ = 0.12 - 0.15 ns, with intensity I₁ = 24% - 43%) is related to the self-annihilation of p-Ps, atoms, while the intermediate one (τ₂ = 0.364 - 0.417 ns and I₂ = 39% - 56%) to annihilation of free positrons in the polymer matrix. τ₂ is usually associated with the annihilation of positrons with valence or core electrons of the constituent atoms .The longest-lived component (τ₃ = 2.071 - 2.328 ns and I₃ = 12.2% - 29.2%) is associated with annihilation of o-Ps in the intermolecular spaces of polymer structure via the pick-off annihilation [30]. Taking τ₃ as a measure of the free volume hole size and I₃ as a number of free volume holes, the lifetime of o-Ps and its intensity for the non-irradiated sample have been deduced to be τ₃ = 2.156 ± 0.026 ns and I₃ = 29.2% ± 1.2%.

The positrons have a tendency to localize in comparatively more ordered regions, while Ps atoms tend to be localized in the disordered parts of a polymer matrix, and in semi-crystalline polymers Ps is localized in the amorphous regions and crystalline-amorphous interface [30].

Figure 1 shows the second lifetime τ₂ and its relative intensity I₂ of PM-355 samples as a function of gamma dose. The middle positron lifetime τ₂ can be connected with positron annihilation on structurally intrinsic free volume traps, such as extended vacancy-like clusters [31]. The unirradiated sample had a τ₂ of about 402 ps, so the vacancies in the sample are called vacancy clusters [32]. It is obvious from the figure that defect lifetime τ₂ decreases after gamma irradiation. However, the relative intensity I₂ increases with increasing irradiation dose. This implies that the concentration of vacancy clusters increased after irradiation [33]. During irradiation, both vacancies and interstitials are generated. The interstitials migrate to the vacancy clusters and diminish the size of vacancy clusters, so the defect lifetime τ₂ decreases after gamma irradiation. More supersaturated vacancies are generated with increasing irradiation dose, the vacancies migrate and agglomerate, so the concentration of vacancy cluster decreased with increasing dose from 4 kGy up to 9 kGy.

The lifetime τ₃ associated with the pick-off process as a function of gamma irradiation doses exhibits an increase up to 2.328 ns with an inflection point at the gamma dose 4 kGy as shown in Figure 2. The observed decrease in τ₃ values with increasing dose may be attributed to a gradual formation of mobile charge carriers or

easily orientable dipolar molecules. It is presumed that these charge carriers or dipolar molecules were formed from structural modifications (chain scission) caused by irradiation [34]. The free volumes are estimated using Equation (1) and found to decrease from 128.35 to 103.26 ų.

Figure 2 shows the variations of the intensity of the o-Ps lifetime component I₃ for gamma irradiation processes. The variations of I₃ show a rapid decrease at the beginning up to 2 kGy. This decrease in I₃ at low doses reflects a decrease in the number of free volume holes seems to fit quite well with the interpretation based on the process of cross-linking of the detector molecules. At higher gamma doses the scission of the molecular chains increases [35]. With increasing dose a smooth decrease is attained up to 7 kGy followed by leveling off up to 9 kGy, which is familiar for γ-irradiated polymers [36]. This behavior may indicate that stability in the structure has been achieved.

It is well known that when radiation impinging a polymer matrix, it leaves a trail of damage along its track in the form of broken molecular chains and free radicals. This behavior is quite reminiscent of what is expected by recombination and promoting important chemical and structural changes in the matrix. The inhibiting effect of radiation induced free radicals in polymers has been conjectured in some occasions. This is to elucidate the decrease in I₃ with dose [37]. The cross-linking might take place due to the free radical recombination and the results indicated that the changes in the polymer properties depend on whether cross-linking or degradation dominates during the irradiation. An increase in crystallinity is effectively observed in the irradiation process where the decrease in I₃ with dose is thus attributed to this effect [15]. The variation of I₃ with dose established the trend observed for τ₃ where the decrease in I₃ could be persuaded by the change in the structural effect (i.e. an increase in the crystallinity degree with increasing dose).

The PM-355 has local molecular heterogeneity structure where the positron is annihilated therefore a continuous distribution of the inverse of the longest lifetime (τ₃) can be obtained by analyzing the PAL spectra with the LT program. LT allows both discrete and log normal distributed annihilation rates λ = 1/τ. From the distribution of the o-Ps annihilation rate, λ₃ = 1/τ₃, the mean size and the size distribution of free volume holes can be calculated. Figure 3(a) shows the detected positron annihilation lifetime distribution for non-irradiated and irradiated samples. For non-irradiated sample, the free volume size is distributed from 78.65 to 146.19 ų (Full width at

half maximum). Due to gamma-irradiation, the distribution shifts, Figure 3(b), to higher free volume size up to 5 kGy as a result of formation of new bonds or crosslinking which increase the o-Ps lifetime and after that the distribution shifts to lower free volume size up to 9 kGy. This is in agreement with the results obtained from the finite-term analysis.

To obtain a better understanding of the changes in thermal stability of PM-355 samples due to gamma irradiation TGA were performed in the temperature range from room temperature up to 500˚C, at a heating rate of 5˚C·min⁻¹. The TGA thermograms for non-irradiated and irradiated samples are shown in Figure 4. The values of onset temperature of decomposition T_o were calculated by using these TGA thermograms, and are given in Figure 5 as a function of the gamma dose. The figure shows that T_o increases until a maximum value at 4 kGy irradiated sample indicating an increase in thermal stability of the polymer samples due to the cross-linking process, followed by a decrease with increase in gamma dose due to degradation (i.e. preferentially chain scission). The interpretation of these results may be that, in the dose range 1 - 4 kGy, the free radicals formed due to scission are chemically active and can be used in some chemical reactions that lead to the cross-linking mechanism. With increasing the gamma dose scission dominates which is reflected in a decrease in T_o of the PM-355 samples.

The micrographs of non-irradiated PM-355 SSNTD displayed structure of a semicrystalline polymer. The crystalline regions appeared as white areas as shown in Figure 6(a). The white areas are randomly oriented and

separated by highly entangled polymer molecules, dark regions, which form the amorphous phase. At low doses (4 kGy), gamma irradiation generates different free radicals which causes radiolytic scission of molecular chains by cleavage of C-C and C-H bonds. These free radicals experience recombination (leading to crosslinking) [38]. In the proposed microstructure for this stage, the crystallinity is less than in the virgin samples which could be deduced from the ×15,000 image as an increase in the dark regions concentration (see Figure 6(b)). Our TGA and PAL results on gamma-irradiated PM-355 confirm the diminution in crystallinity at 4 kGy. According to our measurements of TEM micrographs, the irradiated PM- 355 sample with 9 kGy dose (Figure 6(c)) showed an increase in crystallite region thickness in comparison with the 4 kGy sample. Thus, the increase in the crystallinity produced by the irradiation dose of 9 kGy was confirmed by the decrease in the decomposition temperature T_o and the ortho-positronium lifetime t_o-Ps.