Development of novel plastic scintillators based on polyvinyltoluene for the hybrid j-pet/mr tomograph

8.2. Investigations with Positron Annihilation Lifetime Spectroscopy 
Positron Annihilation Lifetime Spectroscopy (PALS) is an extremely valuable 
technique of materials structure characterization. It is especially useful in polymers study, 
since in vast majority of them positronium is formed and trapped. Measurements of 
positronium mean lifetime enable estimation of free volumes sizes in the structure. 
Characteristic properties of materials based on polymers are dependent on their structure 
which is determined inter alia by unoccupied regions which has an access to segmental 
motions. Ratio and sizes of free volume in the polymer have an impact on the mechanical 
properties and ageing of the material. 
In this chapter structure of plastic scintillators will be described by determining 
temperatures of structural changes in the material. The most important is glass transition 
temperature (T
g
) of amorphous polymers. It indicates the point in which properties of 
polymer are changed from the rigid glassy solid to more flexible state [88].
At temperatures below T
g 
polymeric chains do not move around. After delivering thermal 
energy, motion is allowed. Macromolecules move around each other and amorphous rigid 
structure starts to be changed to the flexible one. It is connected with the change of heat 
capacity. Because of that T
g
can be determined by widely used methods of polymer 
structure characterization, e.g. Differential Scanning Calorimetry (DSC). However, it is 
also possible to determine temperatures of glass and other structural transition using PALS, 
basing on ortho-positronium mean lifetime and the intensity of its production. 
In this method, positron is emitted from the radioactive source and travels
a distance in the examined material, what is connected with the loose of its kinetic energy. 
When slowed down, positron can annihilate in two ways. The first one is free annihilation, 
with an electron encountered in the material. The second possible kind of positron 
annihilation is forming a meta-stable quantum mechanical state called positronium. It is
a hydrogen-like atom consisting of positron and electron.

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Depending on the positron and electron spin orientation, para- and ortho-
positronium can be formed. In para-positronium (p-Ps) spins are orientated antiparallel. 
Lifetime of p-Ps is equal to 0.125 ns. In ortho-positronium (o-Ps) spins are parallel and its 
lifetime is much longer, equal to 142 ns in vacuum. However in condensed matter the 
lifetime can decrease even to 1-5 ns, because positron from o-Ps annihilates with an 
electron from surroundings having an opposite spin. That leads to two gamma ray 
annihilation and it is called the pick-off annihilation [89].
PALS enables to detect pores with sizes from 0.1 nm to 100 nm. Free volumes in 
the matter are assumed as potential well, finite in depth, in which positronium atom 
annihilates [90] [91]. Formula (10) describes the relationship between o-Ps lifetime in the 
trap (τ
po
) and the radius of the free volume (R) approximated using Tao-Eldrup model with 
an infinite potential well: 
(10), 
with ΔR - empirical parameter corresponding to overlapping of o-Ps wave function with 
surroundings, for polymers equal to 0.166 nm [89].
In the large number of materials free volumes are not perfectly spherical and 
modification in the described model are necessary [92] [93]. However, in polymers free 
volumes are not perfectly defined and they can be interconnected, so Tao-Eldrup formula 
was applied in the original form. 
The structure of J-PET scintillators was studied by means of Positron Annihilation 
Lifetime Spectroscopy [94]. Measurements were conducted in laboratory of Institute of 
Physics, Maria Curie - Skłodowska University in Lublin with delay coincidence "fast - 
slow" spectrometer. The setup for such measurements was prepared as follows. The 
22
Na 
source of the activity of about 0.48 MBq was placed between two slices of plastic 
scintillators as shown in Fig. 25. Such "sandwich" was arranged in the chamber (Fig. 26).

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