Ion-neutral Collision Cross Section as a Function of the Static Dipole Polarizability and the Ionization Potential 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 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 number of ions of certain type reaching the detector (ion mobility counts) depend 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 potential of the ion is found. A semiempirical correction of the equation is carry out based on the alignment of the polarizability tensors with the electric field. The equations are 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 them very attractive for helping applications in different areas, such as the deconvolution of mobilograms of protomers, ion-molecule chemical kinetics, and others.
Ion-neutral Collision Cross Section as a Function of the Static Dipole Polarizability and the Ionization Potential of the Ion, Journal of Physical Chemistry A, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=935384
(Accessed September 25, 2023)