Positron mobility

Fig. 6.13. Superimposed zero field and pulsed field (81 V cm-1 peak amplitude) positron lifetime spectra. The pulsed field spectrum has been decomposed into heated components (broken line) and unheated components (crosses) to illustrate how the electric field splits up the positron ensemble. This is also illustrated by the inset, which shows, schematically, the energy distribution p(E,t) of the positron ensemble in the two-threshold model (see text). Reprinted from Physical Review Letters 56, Tawel and Canter, Observation of a positron mobility threshold in gaseous helium, 2322-2325, copyright 1986 by the American Physical Society.

Table 6.4. Values of density-normalized positron mobility (in cm2 V 1 s 1 amagat) for various molecular gases at T = 297 K. Uncertainties are around 10%-15%...

Azbel, M.Ya. and Platzman, P.M. (1981). Evidence for a positron mobility edge in gaseous helium. Solid State Cornmun. 39 679-681. 

Canter, K.F., Fishbein, M., Fox, R.A., Gyasi, K. and Steinman, J.F. (1980). Is there a positron mobility edge in gaseous helium Solid State Commun. 34 773-776. 

Charlton, M. (1985b). A determination of positron mobilities in low-density gases. J. Phys. B At. Mol. Phys. 18 L667-L671. 

Farazdel, A. (1986). Confirmation of the positron mobility edge in gaseous helium by Monte Carlo simulation. Phys. Rev. Lett. 57 2664-2666. 

It is interesting to compare the properties of positive electrons, positrons, with the properties of electrons in nonpolar liquids. Values of the mobility of positrons, )x +, are now available for a few liquids. Early measurements for in -hexane ranged from 8.5 to 100 cm /Vs [181,182]. In a recent study, the Doppler shift in energy of the 511-keV annihilation gamma ray in an electric field was utilized to measure the drift velocity. This method led to fi+ = 53 cm /Vs in -hexane and 69 cm /Vs in 2,2,4-trimethylpentane [183]. Interestingly, these values are comparable to the mobilities of quasi-free electrons in nonpolar liquids. 

In this section we review the results from positron annihilation experiments, predominantly those performed using the lifetime and positron trap techniques described in section 6.2. Comparisons are made with theory where possible. The discussion includes positron thermalization phenomena and equilibrium annihilation rates, and the associated values of (Zeff), over a wide range of gas densities and temperatures. Some studies of positron behaviour in gases under the influence of applied electric fields are also summarized, though the extraction of drift parameters (e.g. mobilities) is treated separately in section 6.4. Positronium formation fractions in dense media were described in section 4.8. 

When an electric field was applied across the chamber some positrons annihilated prematurely, following field-induced drift to one of the electrodes. In this case the free-positron component of the lifetime spectrum was field dependent the maximum drift time, rmd, was given by the end-point of the lifetime spectrum and was due to thermalized positrons which had traversed the entire drift length l. The drift speed was then v+ = 1/rmd and the mobility could be found from... 

Features of PEPT of particular benefit to engineering studies include the fact that the actual particles of interest may be used as tracers, rather than dissimilar materials of unknown behaviour, and that y-rays are sufficiently penetrating that location is unimpaired by the presence of metal walls, for example. In recent developments, the minimum size of particles which can be tracked has been reduced to approximately 60 pm. It is now possible to track multiple particles, to determine particle rotation and to track motion within real industrial equipment by use of a mobile modular positron camera. These developments are described later. 

Theoretical arguments are twofold. On one hand, one may expect that e+ also gets solvated over a time comparable with r . Mobility of solvated particles drastically drops and they simply do not have enough time to meet each other during the free-positron lifetime ( 0.5 ns). Really, corresponding diffusion displacement of e+ is smaller than e+ thermalization... 

On the other hand, it is clear that the solvated state of the positron is very different from that of the electron. Because of spin-exchange repulsion, an excess electron, being solvated, forms a small void and preferentially resides inside it. On the contrary, the positron is not involved in spin exchange and prefers to reside in the bulk of a liquid because of the prevalence of polarization interaction. e+ may be trapped by positive density fluctuations (aggregation of molecules) [12]. However, density of a liquid state is too high to permit clustering around e+. Therefore e+ solvation may be suppressed and this may explain the very high experimental values of e+ mobility [28]. 

Further developments in this field would probably be forthcoming with more precise studies of the energetics of Ps formation, and measurements of the work functions for e+ and Ps using low-energy positron beams. Better understanding may come from studies of Ps formation at different temperatures and external electric fields (determination of e+ mobility, investigation of the positron-blob interaction, e+ thermalization parameters and its spatial distribution). 

The energetic positron slows down on its track to it s implantation depth, it ionizes the sample and leaves a spur of free electrons behind [27, 28]. The number of electrons at the terminal of the spur and their mobility determine the formation likelihood for positronium. The cross section for positronium formation becomes constant independent of incident energy. The second path to positronium formation is the 0re process [29]. When the potential energy needed to ionize an electron from a molecule is less than the binding... 

Haidar, B., Singru, R.M., Maurya, K.K., Chandra, S. (1996) Temperature dependence of positron-annihilation lifetime, free volume, conductivity, ionic mobility, and number of charge carries in a polymer electrolyte polyethylene oxide complexed with NH4CIO4 . Phys. Rev. B. 54, 7143. 

The main conclusion of the calculations summarized here is that the packing efficiency (as determined by the shape of the chain contour and the mobility of chain segments) is an extremely important physical factor in determining the permeability. This conclusion is also supported by positron annihilation studies of the microstructure of polymers in... 

Olson, B. G., Lin, J., Nazarenko, S., and Jamieson, A. M., Positron annihilation lifetime spectroscopy of poly(ethylene terephthalate) contributions from rigid and mobile amorphous fractions. Macromolecules, 36, 7618-7623 (2003). 

Dlubek, G., Sen Gupta, A., Pionteck, J., Hapier, R., Krause-Rehberg, R., Kaspar, H., and Lochhaas, K. H., Glass transition and free volume in the mobile (MAF) and rigid (RAF) amorphous fractions of semicrystaUine PTFF a positron lifetime and PVT study. Polymer, 46, 6075-6089 (2005d). 

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