Characterization of size, anisotropy, and density heterogeneity of nanoparticles by sedimentation velocity

A critical problem in materials science is the accurate characterization of the size dependent properties of colloidal inorganic nanocrystals. Due to the intrinsic polydispersity present during synthesis, dispersions of such materials exhibit simultaneous heterogeneity in density ρ, molar mass M, and particle diameter d. The density increments ∂ρ/∂d and ∂ρ/∂M of these nanoparticles, if known, can then provide important information about crystal growth and particle size distributions. For most classes of nanocrystals, a mixture of surfactants is added during synthesis to control their shape, size, and optical properties. However, it remains a challenge to accurately determine the amount of passivating ligand bound to the particle surface post synthesis. The presence of the ligand shell hampers an accurate determination of the nanocrystal diameter. Using CdSe and PbS semiconductor nanocrystals, and the ultrastable silver nanoparticle (M₄Ag ₄₄(p-MBA)₃₀), as model systems, we describe a Custom Grid method implemented in UltraScan-III for the characterization of nanoparticles and macromolecules using sedimentation velocity analytical ultracentrifugation. We show that multiple parametrizations are possible, and that the Custom Grid method can be generalized to provide high resolution composition information for mixtures of solutes that are heterogeneous in two out of three parameters. For such cases, our method can simultaneously resolve arbitrary two-dimensional distributions of hydrodynamic parameters when a third property can be held constant. For example, this method extracts partial specific volume and molar mass from sedimentation velocity data for cases where the anisotropy can be held constant, or provides anisotropy and partial specific volume if the molar mass is known.