Determination of 2D Particle Size Distributions in Plasmonic Nanoparticle Colloids via Analytical Ultracentrifugation: Application to Gold Bipyramids.

Multidimensional particle properties determine the product properties in numerous advanced applications. Accurate and statistically meaningful measurements of complex particles and their multidimensional distributions are highly challenging but strongly needed. 2D particle size distributions of plasmonic nanoparticles of complex regular shape can be obtained from analytical ultracentrifugation experiments via the optical back coupling method. A workflow for the calculation of frictional properties of arbitrarily shaped nanoparticles was developed based on bead shell models and applied to gold bipyramids with a pentagonal cross-section. The obtained 2D particle length-diameter distributions and the reduced cumulative 1D length and diameter distributions were compared to transmission electron microscopy measurements. While we find very good agreement for most measurements, the obtained length and diameter distributions were shifted by a few nanometers for some samples. Transmission electron microscopy, energy-dispersive X-ray spectroscopy, electron tomography, and finite element modeling indicate that the shift originated from a slight mismatch between the assumed shape of the simulated perfect bipyramids and the real particle shape and composition due to the presence of silver in the particles. This study demonstrates the feasibility of the applied techniques for complex shape analysis of nanoparticle ensembles with unmatched particle count numbers.