Statistical properties of spikes in single particle ICP-MS time scans

Abstract

Single particle inductively coupled plasma-mass spectrometry (sp-ICP-MS) is based on the detection of spikes in a time-resolved signal. Close to zero for very dilute dispersions, the probability for a given spike to be generated by strictly more than one nanoparticle increases with the flux rate of particles entering the plasma. This work is devoted to the statistical properties of individual spikes. In particular, the average number of nanoparticles giving rise to a single spike is calculated, a very good approximation of the probability mass function ruling the number of nanoparticles in individual spikes is derived and a tight upper bound for the average duration of spikes is obtained. The confrontation of these theoretical predictions with Monte Carlo simulations and experimental data obtained with gold nanoparticle dispersions is very satisfactory. A few possible applications of these findings are also discussed, regarding data processing and the determination of the average size of nanoparticles, whatever the particle number concentration of the dispersion is.