Number of spikes in single particle ICP-MS time scans: from the very dilute to the highly concentrated range

Abstract

The particle number concentration (PNC) of dilute nanoparticle dispersions can be determined by single particle inductively coupled plasma-mass spectrometry (sp-ICP-MS). Virtually equal to zero for very dilute dispersions, the difference between the number of nanoparticles having entered the plasma of the instrument and the number of detectable spikes in the time scan increases in a strongly nonlinear fashion with the PNC. This counting bias, which was unquantified yet, is due to particle event coincidences in the time scan and precludes at first sight the possibility to get meaningful information about the PNC of even moderately concentrated dispersions. In this article, we show that the counting bias is related to a stochastic process that models the spike occurrences in the time scan. This stochastic theory turns out to be amenable to analytical methods and yields universal predictions. We confirm their validity through Monte Carlo simulations and experiments with gold nanoparticle dispersions, for the full spectrum of PNC values we tested.