Plate-height model of ion mobility-mass spectrometry: Part 2-Peak-to-peak resolution and peak capacity

In a previous work, we explored zone broadening and the achievable plate numbers in linear drift tube ion mobility-mass spectrometry through developing a plate-height model [1]. On the basis of these findings, the present theoretical study extends the model by exploring peak-to-peak resolution and peak capacity in ion mobility separations. The first part provides a critical overview of chromatography-influenced resolution equations, including refinement of existing formulae. Furthermore, we present exact resolution equations for drift tube ion mobility spectrometry based on first principles. Upon implementing simple modifications, these exact formulae could be readily extended to traveling wave ion mobility separations and to cases when ion mobility spectrometry is coupled to mass spectrometry. The second part focuses on peak capacity. The well-known assumptions of constant plate number and constant peak width form the basis of existing approximate solutions. To overcome their limitations, an exact peak capacity equation is derived for drift tube ion mobility spectrometry. This exact solution is rooted in a suitable physical model of peak broadening, accounting for the finite injection pulse and subsequent diffusional spreading. By borrowing concepts from the theoretical toolbox of chromatography, we believe that the present study will help in integrating ion mobility spectrometry into the unified language of separation science.