Comparing novel small-angle x-ray scattering approaches for absolute size and number concentration measurements of spherical SiOparticles to established methods.

Biomedical analytical applications, as well as the industrial production of high-quality nano- and sub-micrometre particles, require accurate methods to quantify the absolute number concentration of particles. In this context, small-angle x-ray scattering (SAXS) is a powerful tool to determine the particle size and concentration traceable to the Système international d'unités (SI). Therefore, absolute measurements of the scattering cross-section must be performed, which require precise knowledge of all experimental parameters, such as the electron density of solvent and particles, whereas the latter is often unknown. Within the present study, novel SAXS-based approaches to determine the size distribution, density and number concentrations of sub-micron spherical silica particles with narrow size distributions and mean diameters between 160 nm and 430 nm are presented. For the first-time traceable density and number concentration measurements of silica particles are presented and current challenges in SAXS measurements such as beam-smearing, poorly known electron densities and moderately polydisperse samples are addressed. In addition, and for comparison purpose, atomic force microscopy has been used for traceable measurements of the size distribution and single particle inductively coupled plasma mass spectrometry with the dynamic mass flow approach for the accurate quantification of the number concentrations of silica particles. The possibilities and limitations of the current approaches are critically discussed in this study.