On the Kinetic Theory of Simple Dense Fluids. XI. Experimental and Theoretical Studies of Positive Ion Mobility in Liquid Ar, Kr, and Xe

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Abstract
We report in this paper measurements of the mobility of positive ions in liquid Ar, Kr, and Xe at various temperatures and pressures, and an extension of the theory of Rice and Allnatt to the description of ionic motion. It is found that (a) The magnitude, the pressure dependence, and the temperature dependence of the positive ion mobility in liquid Ar, Kr, and Xe can be quantitatively accounted for by an extension of the theory of Rice and Allnatt [S. A. Rice and A. R. Allnatt, J. Chem. Phys. 34, 2144 (1961)]. As in our previous studies of self-diffusion in these same liquids [J. Naghizadeh and S. A. Rice, J. Chem. Phys. 36, 2709 (1962)], it is found that negative contributions to the momentum autocorrelation function are of dominant importance. (b) Modification of the simple Nernst—Einstein relationship between the charge mobility and the self-diffusion constant of the parent atom by inclusion of the effects of polarization leads to quantitative agreement between theory and experiment. (c) The effect of the long-range Coulomb potential is to increase the local density about the ion and thereby to increase the frictional forces arising from the short range interaction potential. The rate of dissipation of energy directly by the long-range Coulomb potential is small compared to the rate of energy dissipation by the short range potential. (d) The agreement between experiment and theory is very satisfactory if the positive ion is Ar2+, Kr2+, or Xe2+ and it is suggested that this is the ionic species present. Agreement is much poorer if a different ionic species (say Ar+) is postulated. (e) If the ions are regarded as probes to alter and study the liquid structure it can be deduced that the current theory of liquids seriously miscalculates the change in the equilibrium pair correlation as a function of temperature and pressure. We believe the error to arise from either a premature truncation of a slowly convergent series used in the solution to an integral equation or, at worst, that the assumed series expansion is invalid [T. L. Hill, Statistical Mechanics (McGraw-Hill Book Company, Inc., New York, 1956)].