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 separation of open and closed porosity samples is presented. The methods range from observing count rates to measuring the longest lifetime of positronium. In either open or closed porosity, it is useful to know the level of how interconnected pores are. Porosity not only lowers the dielectric value, it also opens the door for impurity intmsion. This is addressed next. Finally the holy grail of porosimetry is addressed the determination of pore size distributions with the positronium lifetime technique. 

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). 

For subnanometer free volumes, the Tao-Eldrup model [33] is conventionally used to relate positron lifetime to free-volume size. For nanometer pores as studied here, Gidley s model [23, 24] was used to relate the positron lifetimes to pore sizes. The 47-ns lifetime for the F88 copolymer-generated porous film yields a diameter pore size of 3.7 nm if the pores are assumed to be a closed sphere, while the 54-ns lifetime for the PI03 copolymer-generated film corresponds to a diameter pore size of 4.3 nm. It is pointed out that future work is needed to relate positronium lifetimes and pore sizes, especially for uncapped films, since positronium lifetimes of those samples include contributions from both closed and open pores. 

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.3. The theoretical dependence of positronium lifetime on pore radius for - RP-2 -RP 8 - RP-18. Full points - LiChrosorbs RP, open points - LiChrosorbs RP after burning off Triangle - lifetime and pore radius for amorphous silica gel Si-100. The size of symbols is longer than experimental error.

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, 4.16. Positronium lifetime dependence on pore diameter. Solid line is the theoretical relation found from the Schrddinger equation for spherical pores [118]. 

Positronium lifetime spectroscopy is particularly well suited for stud)hng defects in crystals and structural fluctuations in amorphous materials and can give an estimate of free volumes in condensed matter [116]. It is a useful technique to estimate the free volume of polymeric membranes [117]. In a study on silica gels, the decay lifetime has been found (Fig. 4.16) to be proportional to the pore diameters (measured by N2 adsorption) between 30 and 100 A [118]. Information on pore size distribution and surface area may also be obtained by means of calibration curves. 

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. 

Ito, K., Li, H., Saito, Y, Yamamoto, T, Nishihara, Y, Ujihira, Y, and Nomura, K., Free-volume study of ethylene-vinyl alcohol copolymer evaluated through positronium lifetime measurement, J. Radioanal. Nucl. Chem., 255, 437-441 (2003). 

Jean, Y. C., and Shi, H., Positronium lifetime in an ellipsoidal free-volume hole of polymers,... 

Dlubek, G., Supej, M., Bondarenko, V., Pionteck, J., Pompe, G., Krause-Rehberg, R., and Emri, I., Orf/zo-positronium lifetime distribution analyzed with Melt and LT and free volume in poly(e-caprolactone) during glass transition, melting, and crystallization, J. Polym. Sci. B, 41, 3077-3088 (2003b). 

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

In the course of the positronium lifetime measurements, radioactive isotopes of positron decay serve as sources, e.g., sodium-22, copper-64. At the moment of the emission of the positron from this source a y-photon is also released. (In the case of, e.g., sodium-22 its energy is 1.28 MeV.) This y-photon serves as the start signal in the coincidence equipment used. The y-photon produced by the 2y-annihilation process to be studied (0.51 MeV) is the stop signal. The magnitude of the time measured between the start and stop signals (the positronium lifetime) is in the range 10 —10 s. To get a lifetime curve of adequate statistics, the apparatus repeats the time measurement about 10 — 10 times. For the details of the experimental technique see, e.g., refs. [De 53, Fe 56, Go 71a]. 

As discussed in the previous section, all the possible interactions of o-Ps decrease its lifetime. The degree of this lifetime decrease is another parameter that can be related to physical and chemical properties of a system. The connection is quite obvious in the case of chemical reactions and ortho-para conversion. In the case of pick-off annihilation, the effects of the substance on positronium lifetime are expressed indirectly through the overlap integral in 0 Eq. (27.7). Any change in t/ v (e.g., changes of electron orbits) or in the overlap integral (e.g., free-volume changes) is reflected in the lifetime of o-Ps. 

The evaluation of positron lifetime spectra is usually performed by commercial computer codes. POSITRONFIT and RESOLUTION programs (Kirkegaard et al. 1981) work on the basis of Eqs. (27.14) and (O 27.15) supplying the lifetimes and relative intensities of the assumed states as final results. Positronium lifetime distributions are obtained applying the CONTIN (Gregory and Zhu 1990) algorithm or the MELT (Shukla et al. 1993) code for lifetime spectra. 

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. 

The PALS spectra were collected using a standard fast-slow lifetime spectrometer. The air was evacuated from the measurements chamber to p 0.3 Pa in order to avoid oxygen influence on o-Ps lifetime. Positronium lifetime measurements (PALS method) are based on the relation between ortho-positronium (o-Ps) lifetime and the size of fi volume, in which o-Ps is trapped. PALS spectra were processed as described in Ref. [10]. 

Fig. 1. Positronium lifetime dependence on the spherical free volume radius given by the Tao-Eldnq> model.

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. 

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