Shape and size of non-spherical silver nanoparticles: implications for calculating nanoparticle number concentrations

The international drive to measure accurate number concentrations of nanoparticles is impeded by the typically heterogeneous populations of non-spherical nanoparticles. The irregular shape and size of 50 nm silver nanoparticles is studied using Electron Tomography. It is evidenced that even for highly symmetrical particles the volume can be over 20% less than that of the circumscribed sphere; more irregularly shaped particles can have volumes of over 45% less. On this basis, criteria are provided to determine the particle sphericity from 2D projections obtained from Electron Microscopy, including an empirical method for particle volume estimation. The results allow the visualisation of irregularly shaped particles, revealing the presence of previously unseen voids in the nanoparticle structure. Comparison of tomographic data with other commonly used particle-sizing methods exposes the limitations of these methods in studying nanoparticle populations that exhibit heterogeneity.