Electron thermalization distance distribution

FIGURE 8.4 Electron thermalization distance distribution in n-hexane at 290K starting from an initial separation 23A. See text for details. Reproduced from Rassolov (1991). 

In all liquids, the free-ion yield increases with the external electric field E. An important feature of the Onsager (1938) theory is that the slope-to-intercept ratio (S/I) of the linear increase of free-ion yield with the field at small values of E is given by e3/2efeB2T2, where is the dielectric constant of the medium, T is its absolute temperature, and e is the magnitude of electronic charge. Remarkably S/I is independent of the electron thermalization distance distribution or other features of electron dynamics in fact, it is free of adjustable parameters. The theoretical value of S/I can be calculated accurately with a known value of the dielectric constant it has been well verified experimentally in a number of liquids, some at different temperatures (Hummel and Allen, 1967 Dodelet et al, 1972 Terlecki and Fiutak, 1972). 

We have derived the escape probability for a pair of charges initially separated by a given distance for various cases. However, in real systems, the electron thermalization distance is distributed. If we denote the distribution of thermalization distances by /(r), the total averaged escape probability, (ptot, can be calculated from... 

This equation shows that at low electric fields, the escape probability is a linear function of F, and the slope-to-intercept ratio of this dependence is given by erJlk T. It is worth noting that this ratio is independent of /-q. Therefore plots of (p F)l(p 0) vs. 7 may be used to test the applicability of the presented theory to describe real systems, even if the distribution of electron thermalization distances is unknown. 

In a nonattaching gas electron, thermalization occurs via vibrational, rotational, and elastic collisions. In attaching media, competitive scavenging occurs, sometimes accompanied by attachment-detachment equilibrium. In the gas phase, thermalization time is more significant than thermalization distance because of relatively large travel distances, thermalized electrons can be assumed to be homogeneously distributed. The experiments we review can be classified into four categories (1) microwave methods, (2) use of probes, (3) transient conductivity, and (4) recombination luminescence. Further microwave methods can be subdivided into four types (1) cross modulation, (2) resonance frequency shift, (3) absorption, and (4) cavity technique for collision frequency. 

With an increase of E beyond a certain value specific to the liquid, the free-ion yield increases sublinearly with the field, eventually showing a saturation trend at very high fields (see Mathieu et al.,1967). Freeman and Dodelet (1973) have shown that a fixed electron-ion initial separation underestimates the free-ion yield at high fields, and that a distribution of thermalization distance must be used to explain the entire dependence of Pesc on E. Therefore, the theoretical problem of the variation of free-ion yield with external field is inextricably mixed with that of the initial distribution of electron-cation separation. 

As would be expected, these results indicate that the thermalization distances and spatial distribution of the hydrated electron are key parameters in modelling the radiation chemistry of water. Although the stochastic approach is the more logical one to adopt, its present status does not appear to outweigh the advantages of using the simpler deterministic model to represent the essential features of water radiolysis over a wide range of conditions. 

Fig. 3. Escape probability predicated by On-sager theory for isotropic initial distribution of electron-hole pairs. T = 296 K static permittivity of e = 3 thermalization distance of r0 [11, P 248]...

The tunneling mechanism only applies at low temperatures when the electrons and hole are immobile. The luminescence and LESR decay more rapidly above about 50 K. Hong, Noolandi and Street (1981) solved the complicated time-dependent diflfusion equation for geminate recombination when there is a distribution of thermalization distances and temperature-dependent multiple hopping of carriers. The asymptotic solution for the liuninescence intensity is... 

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