Free-Ion Yield on External Field

Jay-Gerin et al. (1993) also found an empirical correlation between G. and the most probable thermalization length b as follows  

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). 

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. 

At this stage, it should be recalled that although the S/I ratio has been derived in the Onsager model for a geminate pair, there is extensive Monte Carlo simulation work to extend the same value for multiple-ion-pair cases and, therefore, to the entire track as well (see Sect. 9.3). Hence, the comparison of the experimental value of S/l with the theoretical value of Onsager is meaningful. For example, Hummel and Allen (1967) measure S/I = 6.0 x 10-5 cm/V in n-hexane at 298 K, whereas the theoretical value is 5.81 x 10-5 cm/V. 

Onsager s (1938) formula for the probability of escaping geminate-ion recombination in the presence of an external field E may be written as 

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