Classical aspects of the reduced collision cross section for elastic scattering in ion mobility spectrometry

A classical theory for the collision cross section associated with elastic scattering in ion mobility spectrometry is developed. The collision cross section is found to be equal to a hard-sphere collision cross section evaluated at the turning radius plus a potential scattering term inversely proportional to the effective temperature. The results of the theory are compared to current theories by fitting reduced collision cross sections for both small-ion and large-ion mobility data using a molecular modeled hard-sphere collision cross section as reference. The turning point radius is found to be 0.7 of the hard-sphere collision radius and the interaction potential evaluated at the turning point varies inversely as the square of the turning radius. Taken in combination, classical theory provides an incomplete description of the scattering event.