Improved First-Principles Model of Differential Mobility Using Higher Order Two-Temperature Theory

Differential mobility spectrometry is a separation technique that may be applied to a variety of analytes ranging from small molecule drugs to peptides and proteins. Although rudimentary theoretical models of differential mobility exist, these models are often only applied to small molecules and atomic ions without considering the effects of dynamic microsolvation. Here, we advance our theoretical description of differential ion mobility in pure N₂ and microsolvating environments by incorporating higher order corrections to two-temperature theory (2TT) and a pseudoequilibrium approach to describe ion-neutral interactions. When comparing theoretical predictions to experimentally measured dispersion plots of over 300 different compounds, we find that higher order corrections to 2TT reduce errors by roughly a factor of 2 when compared to first order. Model predictions are accurate especially for pure N₂ environments (mean absolute error of 4 V at SV = 4000 V). For strongly clustering environments, accurate thermochemical corrections for ion-solvent clustering are likely required to reliably predict differential ion mobility behavior. Within our model, general trends associated with clustering strength, solvent vapor concentration, and background gas temperature are well reproduced, and fine structure visible in some dispersion plots is captured. These results provide insight into the dynamic ion-solvent clustering process that underpins the phenomenon of differential ion mobility.