Predicting ion mobility as a function of the electric field for small ions in light gases

High resolution mobility devices such as Field Asymmetric Waveform Ion Mobility Spectrometry (FAIMS) and Differential Mobility spectrometers (DMS) use strong electric fields to gas concentration ratios, E/N, to separate ions in the gas phase. While extremely successful, their empirical results show a non-linear, ion-dependent relation between mobility K and E/N that is difficult to characterize. The one-temperature theory Mason-Schamp equation, which is the most widely used ion mobility equation, unfortunately, cannot capture this behavior. When the two-temperature theory is used, it can be shown that the K-E/N behavior can be followed quite closely numerically by equating the effect of increasing the field to an increase in the ion temperature. This is attempted here for small ions in a Helium gas environment showing good agreement over the whole field range. To improve the numerical characterization, the Lennard-Jones (L-J) potentials may be optimized. This is attempted for Carbon, Hydrogen, Oxygen and Nitrogen at different degrees of theory up to the fourth approximation, which is assumed to be exact. The optimization of L-J improves the accuracy yielding errors of about 3% on average. The fact that a constant set of L-J potentials work for the whole range of E/N and for several molecules, also suggests that inelastic collisions can be circumvented in calculations for He. The peculiar K-E/N hump behaviors are studied, and whether mobility increases or decreases with E/N is shown to derive from a competition between relative kinetic energy and the interaction potentials.