Ion-Neutral Collision Cross Section as a Function of the Static Dipole Polarizability and the Ionization Energy of the Ion

Ion mobility spectrometry is becoming more and more popular as a fast, efficient, and sensitive tool for the separation and identification of ionized molecules in the gas phase. An ion traveling through a drift tube at atmospheric pressure under the influence of an electric field collides with the buffer gas molecules. The mobility of the ion depends inversely on the ion-neutral collision cross section. In the simplest hard-sphere approximation, the collision cross section is the area of the conventional geometric cross section. However, deviations are expected because of the physical interactions between the colliding species. More than a century ago, Langevin described a model for the interaction between a point-charge ion and a polarizable atom (molecule). Since then, the model has been modified many times to include better approximations of the interaction potential, usually preserving the point-charge nature of the ion. Although more advanced approaches allow for considering polarizable ions with dissimilar sizes and shapes, still explicit analytical dependencies on the properties of the ion remain elusive. In this work, an extended version of the Langevin model is proposed and solved using algebraic perturbation theory. A simple analytical expression of the collision cross section depending explicitly on both the static dipole polarizability and the ionization energy of the ion is found. The equation is validated using ion mobility data. Surprisingly, even low-level calculations of the polarizability tensors produce results that are consistent with the experimental observations. This fact makes the equation very attractive for helping applications in different areas, such as the deconvolution of mobilograms of protomers, ion-molecule chemical kinetics, and others.

Automated summary

Ion mobility spectrometry is a popular tool for separating and identifying ionized molecules in the gas phase. The mobility of the ion depends on its collision cross section with the buffer gas molecules. A modified Langevin model is proposed and solved using algebraic perturbation theory, providing an analytical expression for the collision cross section that depends on the ion's dipole polarizability and ionization energy. The equation has been validated using ion mobility data and shows promise for various applications in different areas.