A thermodynamic model for the O\(_2^-\) mobility in Ne gas in broad density and temperature ranges

Abstract

We report new measurements of the mobility \(\mu\) of O$_{2}^{-}$ ions in supercritical neon in the range $45\,\mathrm{K}\le T\le 334\,\mathrm{K}$ for number density $N\ge 0.5\,$nm$^{-3}.$ We rationalize the experimental data of all isotherms with the Stokes-Cunningham formula by computing the ion hydrodynamic radius as a function of \(T \) and \(N\) with the thermodynamic free volume model developed for the ion mobility in superfluid He. The model parameters are determined by re-analyzing published data for $T=45\,$K for \(N\) up to $N\approx 1.65N_{c} $ ($N_{c}\approx 14.4\,$nm$^{-3}$ is the critical number density), which roughly span four orders of magnitude of the Knudsen number $(0.1\le \mathrm{K}_{n}\le 1000)$, covering the transition from the kinetic- to the hydrodynamic transport regime. These parameters provide an excellent description of the dependence of \(\mu\) on \(N\) for all higher isotherms and yield a strict test of the model validity, thereby bridging the gap between the kinetic- and the hydrodynamic transport regimes.