Monte Carlo Simulation of Electron Thermalization Distribution in Liquid Hydrocarbons:  Effects of Inverse Collisions and of an External Electric Field

Abstract

A Monte Carlo simulation has been developed for electron thermalization in a liquid hydrocarbon taking n-hexane as a paradigm. For the first time, both the effect of the geminate cation and that of an external electric field have been included in the predicted electron thermalization distance distribution (ETDD). Also for the first time, both energy losing (direct) and energy gaining (inverse) collisions of the epithermal electron are included in a manner that ensures the equality of their rates, averaged over the Maxwellian distribution, in the long-time limit. Parametric values have been rationalized from the experimental data. Comparison with a free-ion yield experiment in n-hexane at 300 K indicates that about one-third of total epithermal collisions involve the energy exchange of quanta related to intermolecular motion. These energy exchange collisions partition between energy losing to energy gaining processes approximately as 3:2 in the initial stage of thermalization. The important features of the ETDD are displacement from the origin and an exponential tail for which rationalization has been provided. Distortion of the ETDD by an external field does not affect the free-ion yield in the first order; in the second order, an effect quadratic in the field may be seen.

Processes and time-scales of energy loss of low-energy electrons (<5 eV) in liquid water

“…Principal contributors for energy degradation are intramolecular vibrational excitation and dielectric interaction in stage A and H-bond vibrational excitations, stretching and bending, in stage B, combined with rotational excitation. In our earlier work with liquid n-hexane [3,4], the cross-sections of these low-energy interactions were adjusted to the free-ion yield at RT through the thermalization length and then the result was extended to higher temperatures. In the present work, for the first time, we have derived the cross-sections directly from various experiments and then calculated the respective time scales.…”

“…Subvibrational interactions that ultimately thermalize the electron have been described in liquid n-hexane, assuming intermolecular vibration of a quantum ∼0.01 eV [3,4]. Qualitatively the idea was borrowed from that part of the Raman spectrum in the liquid for which there is no correspondence in the gas phase.…”

“…Eventually, the electron energy falls below the molecular vibrational level which it cannot excite effectively, but it is still very hot. Such electrons, called subvibrational, play an important role in thermalization as seen in the analysis of freeion yield in liquid hydrocarbons [3,4]. Taking a cue from Raman scattering process in the liquid, electron-induced cross-section was linked with a thermalization distance distribution, and the result was compared with experiment on the free-ion yield.…”

States of the electron in hydrocarbon liquids

“…This is also true for Rassolov and Mozumder (2001) which considers proper thermalization using both energy loss and gain of low-energy electrons through detailed balancing. Since the electron is a light quantum mechanical entity in the free or quasi-free state, these procedures ignore the inherent spreading of the wave packet without scattering, although spreading due to collisions (elastic and inelastic) are properly taken into account.…”

“…Nevertheless, there are important gaps in our understanding of how lowenergy electrons thermalize and the exact nature of the stabilized trapped state. For example, theories of electron thermalization still use a classical Monte Carlo procedure for the transport part, although more recently detailed balancing of energy loss and gain has been incorporated (Rassolov and Mozumder, 2001). For the electron-ion geminate escape probability, several improvements on the Onsager (1938) theory have been proposed and evaluated, including the use of a fractal diffusion model (Mozumder, 1990) and numerical calculation (Tachiya, 1988).…”