Partial localization, two-state model

In Section 3.11.2 we discussed the phenomenological model of electron transport in the conduction band of tetramethylsilane modulated by trapping by biphenyl. Such a model can be generalized for the electron transport in low mobility hydrocarbons, as, for instance, n-hexane. Localized electrons have been detected by their optical absorption. The traps in hydrocarbons are assumed to be structural voids which upon occupation by an electron increase further in depth. The electrons are only partially localized in these traps (Schiller et al., 1973). By thermal activation they 

Here Xp denotes the mobility in the conduction band. P is the trapping probability. Implicitly it is assumed that the filled electron trap is immobile. In a liquid, the filled trap migrates with the mobility of an ion. With these assumptions, the drift mobility of an electron can be written as 

Tp is the time in the quasifree state, while denotes the time the electron is localized. As long as ppXp p, x, the second term of the r.h.s. of Equation 22 can be neglected, and the effective mobility becomes 

The residence time in a trap is a function of temperature, such that 

With the assumption that T, /Tp 1, it follows from Equation 23 for the temperature dependence of the electron mobility that 

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