Free ion yield

Hummel et al. (1966) have used radiations from 37Ar to determine the free-ion yield in n-hexane (see Sect. 9.3.1), but no molecular product has yet been measured with this radiation, which is highly desirable in view of its mono-energetic (2400 eV) character. Mozumder (1971) has developed a diffusion theory for ion recombination for (initially) multiple ion-pair cases, which can be applied to 3H and 37Ar radiations. According to this theory, the track is cylindrically symmetric to start with. As neutralization proceeds, the track... 

In liquefied rare gases (LRG) the ejected electron has a long thermalization distance, because the subexcitation electrons can only be thermalized by elastic collisions, a very inefficient process predicated by the small mass ratio of the electron to that of the rare gas atom. Thus, even at a minimum of LET (for a -1-MeV electron), the thermalization distance exceeds the interionization distance on the track, determined by the LET and the W value, by an order of magnitude or more (Mozumder, 1995). Therefore, isolated spurs are never seen in LRG, and even at the minimum LET the track model is better described with a cylindrical symmetry. This matter is of great consequence to the theoretical understanding of free-ion yields in LRG (see Sect. 9.6). 

Scavenging experiments in hydrocarbon liquids (Rzad et al, 1970 Kimura and Fueki, 1970) tend to give low observed ionization yield, although the primary yield may be greater. The situation is similar for free-ion yield measurement under a relatively large external field. Both processes require large extrapolations to obtain the W value. 

Mozumder and Magee, 1967), the success of the geminate pair model in kinetics (Warman et al., 1969 Rzad et al, 1970) and in free-ion yield determination (Hummel and Allen, 1966 Freeman, 1963a, b) has been rationalized on the basis that in multi-ion pair spurs all but the final e-ion pair would quickly neutralize due to intense internal coulombic interaction. Therefore, emphasis is laid in this section on the geminate pair with two caveats ... 

Rzad et al.( 1970) compared the consequences of the lifetime distribution obtained by ILT method (Eq. 7.27) with the experiment of Thomas et al. (1968) for the decay of biphenylide ion (10-800 ns) after a 10-ns pulse-irradiation of 0.1 M biphenyl solution of cyclohexane. It was necessary to correct for the finite pulse width also, a factor rwas introduced to account for the increase of lifetime on converting the electron to a negative ion. Taking r = 17 and Gfi = 0.12 in consistence with free-ion yield measurement, they obtained rather good agreement between calculated and experimental results. The agreement actually depends on A /r, rather than separately on A or r. 

The eigenvalue method was extended by Abell and Funabashi (1973) to investigate the effect of the initial distribution. This only required an integration over that distribution. However, the authors also used the effect of an external field on the free-ion yield as a further probe of the initial distribution. The... 

MC simulation for multiple ion-pair case is straightforward in principle. A recombination, if necessary with a given probability, is assumed to have taken place when an e-ion pair is within the reaction radius. Simulation is continued until either only one pair is left or the uncombined pairs are so far apart from each other that they may be considered as isolated. At that point, isolated pair equations are used to give the ultimate kinetics and free-ion yield. 

Green and Pimblott (1991) criticize the truncated distributions of Mozumder (1971) and of Dodelet and Freeman (1975) used to calculate the free-ion yield in a multiple ion-pair case. In place of the truncated distribution used by the earlier authors, Green and Pimblott introduce the marginal distribution for all ordered pairs, which is statistically the correct one (see Sect. 9.3 for a description of this distribution). 

In hydrocarbon liquids other than n-hexane, the procedure for obtaining the thermalization distance distribution could conceivably be the same. However, in practice, a detailed theoretical analysis is rarely done. Instead, the free-ion yield extrapolated to zero external field (see Chapter 9) is fitted to a one-parameter distribution function weighted with the Onsager escape probability, and the mean thermalization length (r ) is extracted therefrom (see Mozumder, 1974 ... 

Dodelet and Freeman, 1975 Jay-Gerin et ah, 1993). The main outcome from such analysis is that the free-ion yield, and therefore by implication the (r(h) value, increases with electron mobility, which in turn increases with the sphericity of the molecule. The heuristic conclusion is that the probability of inter-molecular energy losses decreases with the sphericity of the molecule, since there is no discernible difference between the various hydrocarbons for electronic or intramolecular vibrational energy losses. The (rth) values depend somewhat on the assumed form of distribution and, of course, on the liquid itself. At room temperature, these values range from -25 A for a truncated power-law distribution in n-hexane to -250 A for an exponential distribution in neopentane. 

It has been shown by Mozumder and Tachiya (1975) that, within the context of the diffusion model, the probability of generation of free ions is independent of postthermal electron scavenging, both in the absence and presence of an external field. Thus, the experimental finding—that the free-ion yield is reduced in neopentane (NP) by the addition of electron attaching solutes SF6,... 

Lekner, 1967 Lekner and Cohen, 1967). From the experimental viewpoint, LRGs are excellent materials for the operation of ionization chambers, scintillation counters, and proportional counters on account of their high density, high electron mobility, and large free-ion yield (Kubota et al., 1978 Doke, 1981). Since the probability of free-ion formation is intimately related to the thermalization distance in any model (see Chapter 9), at least a qualitative understanding of electron thermalization process is necessary in the LRG. 

Taking Ay = 15 nm, . = 5 eV, and other values as before, the b value for LAr is evaluated as 1400 nm, which is much larger than 133 nm, obtained by fitting the free-ion yield to the Onsager formula (vide supra). Similar calculations for LKr and LXe give b values of the gaussian thermalization distribution... 

Dependence of Free-Ion Yield on Molecular Structure and Mobility... 

Measured free-ion yields depend strongly on molecular structure and the LET of radiation. Gfl increases with molecular sphericity (vide infra) and decreases sharply with the LET. Unless otherwise specified, the free-ion yield in this chapter will refer to near-minimum ionizing low-LET radiations, such as y-rays or X-rays or electrons of a few MeV energy. Many experiments have been performed... 

Effective thermalization length, the b value for origin-centered gaussian distribution (see text) only when G[( < 0.2 is a truncated power law distribution used by Freeman and his associates. For the free-ion yield in kcal/mole. 

In a later report, Schmidt and Allen (1970) extended their measurement to 38 pure liquids and mixtures at room temperature and to 5 liquids as a function of temperature. The free-ion yields are arranged by the alkanes and their isomeric and cyclic counterparts, which show considerable differences in the results. Thus, the free-ion yield in neopentane (NP) is about seven times that in n-pentane. Some of the results are shown in Table 9.1. In mixtures of NP with CC1, or CS, the observed decrease of Gf with the additive concentration has been interpreted by Mozumder and Tachiya (1975) as due to epithermal electron scavenging (vide infra). 

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