Expanded theory for the resolving power of a linear ion mobility spectrometer

Abstract

An expanded theory for the resolving power of a linear ion mobility spectrometer (IMS) is derived. By definition, the resolving power is directly proportional to the total drift time for the ion through the drift tube divided by the full-width-at-half-height (FWHH) of the observed ion mobility peak. Two approaches to theoretically estimating these two parameters are possible, depending on the operating parameters of the IMS cell. The drift time is given by the first moment of the IMS response. If the electric fields (assumed uniform) are equal in both the shutter/aperture and aperture/collector region, the FWHH is given by a difference in error functions. If the electric fields (again assumed uniform) are not equal, the FWHH is given by the second central moment of the IMS response and can only be known to within a multiplicative factor. The effectiveness of these two approaches is demonstrated using IMS data from the published literature. The additional peak broadening often observed in a linear IMS has several possible sources. One depends on the construction of the cell and the parallelism (or lack thereof) that might exist between the aperture grid and ion collector. Another depends on electric fields used to bias the cell. If the electric field in the aperture/collector region is less than in the shutter/aperture region, peak broadening occurs. Induction effects in the aperture/collector region not only shorten drift times, but also create diffusion-like broadening of the peak. Shortening the distance between the aperture grid and ion collector, or using a higher electric field in that region, minimizes induction effects. Drift time calibration requires adjustments for induction effects.