Electron thermalization distance

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). 

Here e is the electron charge, is the Boltzmann constant, and T is temperature. The value of rc in nonpolar liquids at room temperature may be as high as —30 nm, while in water it is only 0.7 nm. Because the electron thermalization distances are usually on the order of a few nanometers, the effect of the Coulomb attraction between the ionization products in water will be much weaker than that in, e.g., liquid hydrocarbons. This will result in much lower probabilities of geminate recombination in polar liquids compared to those in nonpolar ones. 

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. 

Gee, N. and Freeman, G. R., Electron mobilities, free ion yields, and electron thermalization distances in long-chain hydrocarbons, /. Chem. Phys., 86, 5716,1987. 

Jay-Gerin, J. R, Goulet, T., and Billard, L, On the correlation between electron mobility, free-ion yield, and electron thermalization distance in nonpolar dielectric liquids. Can. J. Chem., 71, 287, 1993. 

This article describes electron thermalization distances and then mobilities under diverse conditions. 

The fraction of ions produced in reaction (3) that become free ions is a function of the electron thermalization distance y, the relative permittivity 8 of the fluid, the temperature T, and the applied electric field strength E. We, therefore, write (for details see Freeman, 1987c) ... 

The correlation between values of thermal electron mobilities and secondary electron thermalization distances mentioned earlier is also observable in Fig. 3. Thus, the same two empirical factors that affect thermalization distances also affect mobilities ... 

Fig. 6. Correlations between thermal electron mobilities y and secondary electron thermalization distances b p in...

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