Larry A. Viehland

Gaseous lon mobility in electric fields of arbitrary strength

Abstract The first rigorous kinetic theory of ion mobility in neutral gases, valid for electric fields of arbitrary strength without restriction on the ion-neutral mass ratio or interaction potential, is presented. The theory is based on the use of a set of basis functions in which the ions are allowed to have a temperature different from that of the neutral gas. The convergence of a series of approximations for the mobility is good, and the resulting expressions are not expansions in powers of the field strength. In lowerst approximation, the equation for the mobility is nearly the same as that obtained from an approximate free-flight theory, except for the appearance of an effective temperature in the diffusion, or momentum-transfer, collision integral. This difference is the crucial point that allows experimental measurements of ion mobility as a function of field strength to be used to obtain information on ion-neutral potentials. Data on K+ ions in He, Ne, and Ar are analyzed as an example; the range of effective temperatures is approximately 100 to 20,000°K. At high effective temperatures the results agree with similar information obtained from the scattering of ion beams in gas targets.

Gaseous ion mobility and diffusion in electric fields of arbitrary strength

Abstract In a previous paper we presented the first kinetic theory of gaseous ion mobility which is valid for electric fields of arbitrary strength and for arbitrary ion-neutral interaction potentials and mass ratios. In this paper we extend this theory to gaseous ion diffusion and systematize it so as to greatly decrease the effort involved in computing high approximations to the transport coefficients. Analytical results in low approximation are discussed, as are scaling rules for ion mobilities and diffusion coefficients. An extensive study of the convergence of the successive approximations of this theory is given for model systems, from which it is concluded that the theory is accurate, particularly in third and higher approximation, when applied to ion mobility and mean kinetic energy. When applied to diffusion, the theory is less successful in some circumstances, but it is still the best general theory currently available.

Statistical–mechanical theory of gaseous ion–molecule reactions in an electrostatic field

A theory is developed for gas‐phase swarm measurements of ion–molecule reactions in electrostatic fields of arbitrary strength. The theory allows measurements of reaction rate coefficients made at low temperatures and strong electric fields to be converted directly to equivalent thermal rate coefficients at elevated temperatures inaccessible by direct methods. It is not necessary to calculate the ion velocity distribution function explicitly, or to unfold the reaction cross section from the rate data. In first approximation the measured rate coefficient is equal to the thermal rate coefficient at an effective temperature calculated directly from the measured ion drift velocity. Higher approximations are obtained from more detailed analysis of the dependence of the rate coefficient and drift velocity on electric field strength. Comparison is made with experimental data reported in an accompanying paper by Albritton et al. In another accompanying paper, Lin and Bardsley compare the present theory with their...

Three-temperature theory of gaseous ion transport

Abstract A three-temperature kinetic theory of gaseous ion transport through neutral atomic gases, valid for electric fields of arbitrary strength without restriction on the ion—atom mass ratio or interaction potential, is presented. The theory is based on the use of a set of basis functions in which the ions are allowed to have different temperatures parallel and perpendicular to the field, neither of which is necessarily equal to the gas temperature, and for which the ion velocity distribution function is displaced from the origin. Although the theory is more difficult to use than is the two-temperature theory of Viehland and Mason and of Burnett, it has the important advantage of yielding accurate results in low orders of approximation to quantities that are intrinsically anisotropic, notably ion diffusion coefficients.

Statistical–mechanical theory of membrane transport for multicomponent systems: Passive transport through open membranes

Equations for transport through membranes are derived from basic principles of statistical mechanics, with the classical–mechanical Liouville equation as the starting point. General fluid‐dynamic equations are first obtained, following the methods of Bearman and Kirkwood and of Snell, Aranow, and Spangler; a quasicontinuum or coarse‐graining assumption then allows these equations to be inverted to a Stefan–Maxwell form in which the diffusion and thermal diffusion coefficients can be given an experimental interpretation. The remaining assumptions pertain specifically to membranes. The membrane is taken as one component of the mixture, held fixed in space, and the structure of the membrane is assumed to lead only to a geometrical space‐filling role. Finally, the assumption of nonseparative viscous flow allows the transport equations to be decoupled from the details of membrane structure. The results have the same final form as those obtained earlier by heuristic generalization of gas transport equations. Co...

Direct determination of ion-neutral molecule interaction potentials from gaseous ion mobility measurements*

In the last fifteen years it has become possible to make measurements of the mobility of trace amounts of ions through a neutral gas with an accuracy of 1–2% over a wide range of E/N, the ratio of electric field strength to the neutral gas number density. Only recently, however, has theory developed sufficiently to permit attempts to obtain accurate information about ion-neutral potentials from analysis of such measurements. We present a scheme that allows the theoretical expressions to be inverted, so that the direct determination of ion-neutral potentials from gaseous ion mobility measurements becomes feasible with good accuracy (5% or better) over a wide range of separation distances. The accuracy of the inversion scheme is tested using simulated data for Li+ in He.

Effect of spin polarization on the thermal conductivity of polyatomic gases

Expressions are developed for the thermal conductivity and Eucken factor of a polyatomic gas which include the effects of spin polarization (molecular angular momentum) in terms of experimentally accessible quantities. Comparisons are made of calculations based on these equations with results for the loaded sphere and spherocylinder models, and for nitrogen. Although the effect of spin polarization is small, it is greater than the uncertainty in present experimental thermal conductivity measurements. The numerical importance of spin polarization appears to be greater than the effect of equating the diffusion coefficient for internal energy to the self‐diffusion coefficient.

Tests of alkali ion-inert gas interaction potentials by gaseous ion mobility experiments

Gaseous ion mobilities are mainly dependent on ion–neutral collision energies in the range 0.03–1 eV and, using a recently developed kinetic theory method, can be directly related to ion–neutral interaction potentials. In this paper, experimental mobilities are used to test recent theoretical calculations based on the electron–gas model of the interaction potentials for the twelve combinations of Li+, Na+, K+, and Rb+ with He, Ne, and Ar. The model potentials are quite good, but some systematic discrepancies with experimental mobilities exist. These discrepancies are analyzed in terms of the relation between the mobility and the ion–atom potential.

The Li+–He interaction potential

New measurements of the mobility of Li+ ions in He gas at 300°K are reported for a wide range of E/N, the ratio of the electric field strength to the gas number density. These data are used in conjunction with kinetic theory to test various Li+–He interaction potentials over a wide range of separation distance. It is shown that the ab initio potential of Hariharan and Staemmler gives mobility values in excellent agreement with experiment at low and moderate E/N, but that significant discrepancies exist at high E/N. The mobility data are also directly inverted to give the Li+–He interaction potential. This directly determined potential is in excellent agreement with the ab initio at intermediate and long range, but differs significantly in the short‐range region. In the latter region, however, it is in agreement with the potential obtained by analysis of beam‐scattering experiments.

Mean energy distribution of gaseous ions in electrostatic fields

Expressions for the distribution of ion energy among thermal, drift and random field components are given in terms of the ion drift velocity and the field derivative of the ion mobility. Comparison with available Monte Carlo calculations indicates that the expressions are accurate to high field strengths, without restrictions on the ion-neutron mass ratio or force law.