Towards pulse-overlapped single particle ICP-MS: a forward approach relying on a combination of theory, numerics and experiments
Résumé
The time-resolved signal measured when a dilute nanoparticle dispersion is analysed by ICP-MS in single particle mode (sp-ICP-MS) displays a succession of peaks. When the particle number concentration ρ of the dispersion is sufficiently low, each peak is associated with a single nanoparticle (i.e., is a particle event) with a probability close to one. However, when ρ increases, some particle events may overlap and give rise to composite peaks, resulting from the superposition of two or more particle events. This overlapping phenomenon causes a counting bias, i.e. a discrepancy between the number of particles entering the plasma of the instrument and the number of detectable peaks in the measured time signal. After showing that there is a one-to-one correspondence between the times at which particle events appear in an experimental time signal and the discontinuity points of a one-dimensional, homogeneous Poisson process, we build on this theoretical foundation to compute analytically this bias. The highly nonlinear relationship obtained depends on the flux λ of nanoparticles entering the plasma, the average duration of a particle event and the integration time of the measurement. We also present some results regarding the statistical properties of the peaks. In particular, we calculate the average number of nanoparticles giving rise to a peak, the probability law of the number of nanoparticles per peak and the average duration of a peak. Monte Carlo simulations and sp-ICP-MS measurements performed with gold nanoparticle dispersions are in excellent agreement with the theory, over three orders of magnitude in λ. Finally, we show how to obtain the average nanoparticle mass of a potentially multimodal dispersion, even in the case of particle events pileup in the sp-ICP-MS signal, and we study the impact of overlapping on the effective particle size distribution measured by sp-ICP-MS. This work consolidates the theoretical basis of sp-ICP-MS and is a first step towards the analysis of real samples by pulse-overlapped sp-ICP-MS. Such an approach could indeed be useful to streamline the experimental workflow, or for unstable or specific samples for which dilution is not an option.
