Fundamentals of ion mobility in the free molecular regime. Interlacing the past, present and future of ion mobility calculations

While existing ion mobility calculators are capable of feats as impressive as calculating collision cross sections (CCS) within a few per cent and within a very reasonable time, the simplifications assumed in their estimations precludes them from being more precise, potentially overreaching with respect to the interpretation of existing calculations. With ion mobility instrumentation progressively reaching resolutions of several hundreds to thousands (accuracy in the range of ∼0.1%), a more accurate theoretical description of gas-phase ion mobility becomes necessary to correctly interpret experimental state-of-the-art separations. This manuscript entails an effort to consolidate the most relevant theoretical work pertaining to ion mobility within the ‘free molecular’ regime, describing in detail the rationale for approximations up to the two-temperature theory, using both a momentum transfer approach as well as the solution to the moments of the Boltzmann equation for the ion. With knowledge of the existing deficiencies in the numerical methods, the manuscript provides a series of necessary additions in order to better simulate some of the separations observed experimentally due to second-order effects, namely, high field effects, dipole alignment, angular velocities and moments of inertia, potential interactions and inelastic collisions among others.