Ortho-positronium lifetime

Positron annihilation spectroscopy (PAS) was first applied to investigate [Fe(phen)2(NCS)2] [77]. The most important chemical information provided by the technique relates to the ortho-positronium lifetime as determined by the electron density in the medium. It has been demonstrated that PAS can be used to detect changes in electron density accompanying ST or a thermally induced lattice deformation, which could actually trigger a ST [78]. 

Hasbach, P., Hilkert, G., Klempt, E. and Werth, G. (1987). Experimental determination of the ortho-positronium lifetime in vacuum. II Nuovo Cimento A 97 419-425. 

The specific feature of short pulses of slow positrons could be used to make a new determination of the Ortho-Positronium lifetime. 

The positron lifetime hovers around 0.5 ns ( ). All other lifetimes are due to positronium. The para-positronium (o) with nominally 0.125 ns and the smallest ortho positronium lifetime (A) of about 3.6 ns originate the cages inherent to MSSQ. This result agrees well with measurements on thick samples published earlier by Li et al. [23] The remaining three larger lifetimes originate from positronium in small (B) and large (7) closed pores and pores, connect to channels which link to the surface (Q open porosity). 

Kluin, J.E., Yu, Z., Vleeshouwers, S., McGervey, J.D., Jamieson, A.M., Simha, R., Sommer, K. (1993) Ortho-positronium lifetime studies of free volume in polycarbonates of different structures Influence of hole size distributions . Macromolecules. 26, 1853. 

Schmidt, M., Maurer, F.H.J. (2000) Ortho-positronium lifetime and intensity in pressure-densified amorphous polymers . Radiation Physics and Chemistry. 58, 535. 

Fig.l Ortho-positronium lifetime r=l/(Apu+ t) as a function of the void radius a-cylindrical void (infinitely long), lowest state b- spherical void, lowest state c- cylindrical void, first excited state d- spherical void, first excited state. The penetration parameter AR is assumed 0.166 nm. 

Despite all simplifications the model of particle in the rectangular potential well, extended to include the population of excited le els. describes quite well the dependence of ortho-positronium lifetime on the pore radius. In this model the o-Ps lifetime is ruled entirely by geometrical factors, however, maybe the chemical composition of the medium should be taken into account. The lifetime vs. average radius dependence is particularly steep below 5 nm. and in this range the positron annihilation method can be useful for determination of average pore radii. The specific surface determines the distribution of o-Ps between small voids in the bulk and pores. 

Fig. 29.2 PALS analysis of an unaged epoxy thin film on an Au substrate. Average ortho-positronium lifetime Vps is illustrated with respect to the average positron implantation depth.

An /q.ps reduction is sometimes interpreted in terms of a reduction of the density of free-volume voids in a polymer [10, 20]. However, the influence of the free volume on Iq-ps should be less pronounced than on the ortho-positronium lifetime ro-Ps, which depends directly on the average free-volume void size [Ij. We will see later that Tq-ps varies much less than lo.ps during aging. Therefore, the T.ps reduction should not be interpreted in terms of a free-volume change. 

Jasifiska, B., Koziol, A. E., andGoworek, T., Ortho-positronium lifetimes in nonspherical voids, J. Radioanal. Nucl. Chem., 210, 617-623 (1996). 

Cao, H., G. H. Dai, J.-P. Yuan, and Y. C. Jean. 1997. Reliability of ortho-positronium lifetime distribution analysis in polymers by using CONTIN program. Materials Science Forum 255-257 238-242. 

Fig. 2. Ortho-positronium lifetimes (a) and intensities (b) for as synthesized MCM-41 as a function of increasing temperature in vaeuum. Large size symbols correspond to the parameters obtained after cooling the sample, n denotes the lifetime spectrum component.

Ortho-positronium lifetimes and intensities for MCM-41 silica with filled pores against pressure are shown in Fig.3. Three ortho-positronium componoits are presoit in the obtained PALS spectra at the beginning of experiment when the sample is under normal external pressure. Short lifetimes (T3 = 2.2 ns and xa = 3.5 ns) correspond to the spherical empty spaces of the radii 0.31 nm and 0.40 run. Existence of such fi volumes is possible inside or in die neighbourhood of the micella. 

Positron annihilation lifetime spectroscopy (PALS) provides a method for studying changes in free volume and defect concentration in polymers and other materials [1,2]. A positron can either annihilate as a free positron with an electron in the material or capture an electron from the material and form a bound state, called a positronium atom. Pnra-positroniums (p-Ps), in which the spins of the positron and the electron are anti-parallel, have a mean lifetime of 0.125 ns. Ortho-positroniums (o-Ps), in which the spins of the two particles are parallel, have a mean lifteime of 142 ns in vacuum. In polymers find other condensed matter, the lifetime of o-Ps is shortened to 1-5 ns because of pick-off of the positron by electrons of antiparallel spin in the surrounding medium. 

Positronium can exist in the two spin states, S = 0, 1. The singlet state (5 = 0), in which the electron and positron spins are antiparallel, is termed para-positronium (para-Ps), whereas the triplet state (5 = 1) is termed ortho-positronium (ortho-Ps). The spin state has a significant influence on the energy level structure of the positronium, and also on its lifetime against self-annihilation. 

Experiments on these two gases, reported by Griffith and Heyland (1978), showed that a fast component, with a density-dependent decay rate, was present in the lifetime spectra, and this was tentatively linked to the dearth of long-lived ortho-positronium. Furthermore, it was found for mixtures of krypton with helium that the maximum value of F, which was observed at a concentration of around 0.01% of krypton, was in excess of the sum of the individual F-values for the two gases when pure. 

Fig. 6.5. Examples of positron lifetime spectra for (a) argon and (b) xenon gases. The argon data are for a density of 6.3 amagat at 297 K. The channel width is 1.92 ns. In (a), (i) shows the raw data, (ii) shows the signal with background removed, (iii) shows the free-positron component and (iv) shows the fitted ortho-positronium component. In (b), the spectrum for xenon is for room temperature and 9.64 amagat and has a channel width of 0.109 ns. The inset shows the fast components as extracted and discussed by Wright et al. (1985).

Kakimoto et al. (1987) attributed component I to the conversion of ortho-positronium, with initial kinetic energy below Ea, to para-positronium by elastic exchange collisions. The momentum is smaller than that of component II since the lower energy ortho-positronium has a sufficiently long lifetime to undergo appreciable slowing down. Analysis of the spectra yielded an elastic conversion cross section of 1.5 x 10 19 cm2, in accord with other measurements (Klobuchar and Karol, 1980 Kiefl, 1982). 

One of the first studies of PsCl was that of Tao (1965), who used a lifetime experiment (subsection 1.3.1) in this experiment positronium was formed in argon or N2 gases to which small quantities of CI2 vapour had been added. The intensity of the long-lived ortho-positronium component was found to decrease as the CI2 concentration was increased,... 

The 2 dominant components are due to the annihilation of positrons in the sample MSSQ material independent of pores ( 0.5 ns) para-positronium (-0.1 ns). Ortho-positronium annihilations in the MSSQ cage structure occur with a -4 ns lifetime. Lifetimes of 10 ns and greater are due to positronium in pores and tend to increase with increasing porogen load. Open porosity is associated with a lifetime of -100 ns (80% case, dashed line). 

Figure 7.21 Intensities corresponding to the lifetimes shown in figure 7.20. The intensities associated with positrons and positronium annihilation in the MSSQ matrix are shown in the bottom panel and the positronium annihilations (ortho positronium) from pores and open porosity in the top panel. The line-and-star in the bottom panel indicates 1/3 of the sum of all ortho positronium annihilations. Statistical errors are shown or smaller than the symbols. See text.

Positrons emitted for a radioactive source (such as 22Na) into a polymeric matrix become thermalized and may annihilate with electrons or form positronium (Ps) (a bound state of an electron and positron). The detailed mechanism and models for the formation of positronium in molecular media can be found in Chapters 4 and 5 of this book. The para-positronium (p-Ps), where the positron and electron have opposite spin, decays quickly via self-annihilation. The long-lived ortho positronium (o-Ps), where the positron and electron have parallel spin, undergo so called pick-off annihilation during collisions with molecules. The o-Ps formed in the matrix is localized in the free volume holes within the polymer. Evidence for the localization of o-Ps in the free volume holes has been found from temperature, pressure, and crystallinity-dependent properties [12-14]. In a vacuum o-Ps has a lifetime of 142.1 ns. In the polymer matrix this lifetime is reduced to between 2 - 4 ns by the so-called pick-off annihilation with electrons from the surrounding molecule. The observed lifetime of the o-Ps (zj) depends on the reciprocal of the integral of the positron (p+(rj) and electron (p.(r)) densities at the region where the annihilation takes place ... 

For R > 8 nm the lifetime approached its. .vacuum" value (140 ns), however, with R increase certain changes of the spectrum still occurred. Ortho-positronium locates not only in the pores but also in small voids in the amorphous structure of the bulk medium. The lifetime of o-Ps in these voids (1.3 ns in Vycor. up to 2.5 ns in polymers) is by two orders of the magnitude shorter than in the pores. These small free volumes always appear at a high concentration and effectively trap the positronium only those of Ps atoms which were formed close to the surface, or on it. had the chance to outdiffuse there. One can expect that the fraction of Ps annihilating in pores will rise with the specific surface. A series of Vycor glasses with specific surfaces from 17 to 190 m"/g was studied. It was found that the intensity ratio of the 140 ns component to the sum of intensities 1.3 and 140 ns k = 1, / (F + 1 ,) increased systematically from 9% at the smallest surface to 90% at the largest one. I he dependence of k on specific pore surface area observed in our experiments seems to follow well the equation given by Brandt and Paulin [13] and modified by Venkateswaran [14]. 

---