Technical note: Simplified approaches to estimate the output of particle mass analyzers paired with unipolar chargers

Particle mass analyzers (PMAs) classify particles by their mass-to-charge ratio. PMAs are often paired with bipolar chargers, which produce charge distributions that consist of positively-, negatively, and neutrally-charged particles, which greatly limits the transmission efficiency of PMAs and allows small, uncharged particles to be classified erroneously. These limitations provide an opportunity for unipolar chargers, which impart several charges per particle. However, the PMA setpoint (mass-to-charge ratio) loses physical meaning when the average number of charges per particle mass is unknown. The average charge of the PMA classified particles can be inferred from downstream size distribution measurements or by running detailed models. However, downstream measurements are often practically infeasible and detailed models require knowledge of the unclassified aerosol size and density. These challenges motivate a need for simplified approaches. Using simulations, we show that the unipolar charger-PMA average charge can be estimated to within +/- 20% for a reasonable range of parameters for typical aerosol scenarios. The most significant uncertainties behind the simplified approach are related to particle morphology (e.g., fractal versus spheroidal particles). Our simplified approach relies on the derivation of an empirical power-law relationship between the particle average charge and particle diameter, which is consistent with several previous experimental studies and existing models. The approaches described in this work improve the capabilities of unipolar charger-PMA systems to classify a known average mass (rather than a known mass-to-charge ratio) which is valuable for characterizing and calibrating the response of optical and mass instruments.