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.