Determination of an accurate size distribution of nanoparticles using particle tracking analysis corrected for the adverse effect of random Brownian motion

The particle tracking analysis (PTA) method has been widely used to determine the size of nanoparticles from their Brownian motion, using the Stokes–Einstein assumption. However, the size distribution obtained by PTA is broader than the true distribution because of the uncertainties in determining the diffusion coefficients, and a correction of such a broadening effect is essential to obtain reliable results. In order to transform the apparent broadened size distribution from the PTA method to the true size distribution, we begin by approximating the true size distribution as a gamma distribution determined by a shape parameter and a scale parameter, and then we perform a hybrid analysis based on the maximum likelihood estimation and Bayesian parameter inference that accounts for the uncertainties in determining the diffusion coefficients. To examine the accuracy of our analysis, we compared the size distributions of polystyrene-latex spherical nanoparticles obtained by this transformation process, dynamic light scattering, and asymmetric flow field-flow fractionation with multi-angle light scattering (AF4-MALS). The transformed size distribution resulting from applying our Brownian motion correction to apparent PTA data agrees well with that obtained from AF4-MALS, indicating the success of the correction in obtaining the true nanoparticle size distribution.