Measuring absolute nanoparticle number concentrations from particle count time series

Single-particle microscopy is important for characterization of nanoparticulate matter for which accurate concentration measurements are crucial. We introduce a method for estimating absolute number concentrations in nanoparticle dispersions based on a fluctuating time series of particle counts, known as a Smoluchowski process. Thus, unambiguous tracking of particles is not required and identification of single particles is sufficient. However, the diffusion coefficient of the particles must be estimated separately. The proposed method does not require precalibration of the detection region volume, as this can be estimated directly from the observations. We evaluate the method in a simulation study and on experimental data from a series of dilutions of 0.2- and 0.5-μm polymer nanospheres in water, obtaining very good agreement with reference values.