Diffusion Distortions in a Differential Mobility Analyzer: The Shape of Apparent Mobility Spectrum

The effect of molecular and or small-scale turbulent diffusion in a differential mobility analyzer (DMA) is described in terms of apparent mobility spectrum. Without restricting generality, the normalized apparent spectrum, i.e., the apparent spectrum of unimobile particles with unity charge density is introduced. An approach based on the calculation of the probabilities of the random displacements of particles around their regular trajectories enables us to derive analytical expressions for the normalized apparent spectrum. A particular derivation is carried out for the case of a second-order DMA with one collecting electrode and variable electric field strength. Explicit analytical equations of various approximation degrees have been derived. The normalized apparent spectrum of the particular DMA shows a remarkable asymmetry; its mobility mode is shifted toward lower mobilities. The derived equations serve as a basis for the estimation of the spectral resolution of the DMA. The equations can also be used for a proper design of the DMA, reducing the effect of diffusion. Once the normalized apparent spectrum is known, a possibility appears to improve the resolution of the DMA by solving a relevant equation and eliminating the effect of diffusion in such a way.