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

Abstract

a b s t r a c tThe various processes responsible for the energy degradation and eventual thermalization of low-energy subexcitation electrons (<5 eV) in liquid water are completely delineated for the first time, while previous work assumed the formation of thermalized electrons in the 10 −11 -10 −12 s for liquid water at room temperature. Chief among these are intramolecular vibrational and rotational excitation, dielectric interaction and excitation of intermolecular vibration through H-bond stretching and bending. Crosssections for these processes are taken from experiments or derived theoretically. Individual time scales are obtained for subexcitational and subvibrational regimes in water at room and higher temperature.

Ab initio spur size calculation in liquid water at room temperature

“…In the sub-excitation stage, excitation of intramolecular vibration is the main mechanism, augmented by dielectric loss [7]. In water at room temperature this stage persists for ~2.89×10 -13 s [1]. In the sub-vibrational stage, excitation of H-bond vibrations, stretching and bending, is the dominant mechanism while rotational excitation makes a minor contribution.…”

“…In the sub-vibrational stage, excitation of H-bond vibrations, stretching and bending, is the dominant mechanism while rotational excitation makes a minor contribution. In room temperature water, this stage persists for ~0.83×10 -13 s [1]. The thermalization time is the time invested in the two stages which work out to be ~3.72×10 -13 s at room temperature.…”

“…Time to get to 0.2 eV (t 1 ) has already been computed in the first paragraph under subexcitation stage to be t 1 ≡ 2.46×10 -13 s. Energy loss rate in the sub-vibrational regime depends on energy E. It is given by -dE/dt = k eff E -1/2 , with k eff = 1.584k s = 4.76×10 11 (eV) 3/2 s -1 [1]. Here k s refers to the contribution due to excitation of H-bond stretching only and k eff is that due to excitation of both stretching and bending of H-bonds.…”

“…Considering that the electron remains untrapped at energy 0.2 eV, and eliminating t in the sub-vibrational regime by writing E = 0.2 -(dE/dt) sub •t, where (dE/dt) sub is considered constant, the above equation for P(E) is easily derived satisfying the boundary condition P(E) = 1 at E = 0.2 eV. The rate of energy loss, (dE/dt) sub , actually depends on energy, but for the present purpose we take an average value 0.91×10 12 eVs -1 [1]. Substituting in the above equation, we get P(E) = exp[-13.6×(0.2-E)].The probability, so calculated, for the electron to remain untrapped at a given energy is shown in Fig.…”

“…In an earlier publication [1], we considered the processes for thermalization of low-energy electrons in liquid water and thereby determined the time scales (~10 -13 s) for it. Important among these processes are intramolecular vibrational and rotational excitation, and dielectric interaction in the sub-excitation stage and intermolecular vibrational excitation through H-bond stretching and bending in the sub-vibrational stage.…”