Determination of the particle size distribution of 5–100-nm nanoparticles with the analytical ultracentrifuge: consideration and correction of diffusion effects

Small nanoparticles in the diameter range 5–100 nm are used in large quantities for very different applications. A precise determination of the important physical quantities which are responsible for the application properties such as diameter, particle size distribution, density, and (specific) surface area is therefore essential. Analytical ultracentrifugation is one of the best methods for the characterization of such nanoparticles as they are fractionated in the analytical ultracentrifuge cell during sedimentation. This paper presents the theoretical foundations for the determination of the physical quantities of nanoparticles with special consideration of the diffusion effect with respect to the particle size distribution measurements in the analytical ultracentrifuge. Besides several extrapolation procedures a new method for the correction of the sedimentation coefficient and its distribution is presented. Several examples demonstrate that the suggested diffusion-broadening correction procedures work. The procedure which gives the best values depends on the particular nano-particle.