The Quasi-Ballistic Model of Electron Mobility in Liquid Hydrocarbons and Some of Its Consequences

Abstract

The two-state model of mobility is extended to include ballistic motion in the quasi-free state where a competition is seen between trapping and velocity randomization. The effective mobility is derived to be μ eff -1 = T -1 + F -1 , where T = (e/m)τ f 2 / (τ t + τ f ) is the ballistic mobility and F = μ qf τ f / (τ t + τ f ) is the usual trap-controlled mobility. Here μ qf is the mobility in the quasi-free state and τ t , τ f respectively are the lifetimes in the trapped and quasi-free states. For low-mobility hydrocarbon liquids the model consistently predicts effective mobility and activation energy of mobility in accordance with experiment, taking quasi-free mobility - 100 cm 2 v -1 s -1 and trap density ~10 19 cm -3 . Scavenging occurs in the quasi-free state but few reactions are found to be diffusion-controlled. Possible exceptions are low-mobility liquids (e.g. n-hexane) in which almost all reactions are diffusion-controlled except for biphenyl. Reaction with the same scavenger ranges from nearly diffusion-controlled to activation controlled in liquids of widely different mobility. Consideration of reversible equilibrium trapping and solute reaction leads to the conclusion that changes in all thermodynamic functions on trapping are negative. The negative entropy change on trapping from the quasi-free state may be interpretable by the Anderson model of localization. In terms of this model the quasi-free electron is seen to interact with a few hundred molecules in a hydrocarbon liquid of low mobility.