Correcting for a density distribution: particle size analysis of core-shell nanocomposite particles using disk centrifuge photosedimentometry

Many types of colloidal particles possess a core-shell morphology. In this Article, we show that, if the core and shell densities differ, this morphology leads to an inherent density distribution for particles of finite polydispersity. If the shell is denser than the core, this density distribution implies an artificial narrowing of the particle size distribution as determined by disk centrifuge photosedimentometry (DCP). In the specific case of polystyrene/silica nanocomposite particles, which consist of a polystyrene core coated with a monolayer shell of silica nanoparticles, we demonstrate that the particle density distribution can be determined by analytical ultracentrifugation and introduce a mathematical method to account for this density distribution by reanalyzing the raw DCP data. Using the mean silica packing density calculated from small-angle X-ray scattering, the real particle density can be calculated for each data point. The corrected DCP particle size distribution is both broader and more consistent with particle size distributions reported for the same polystyrene/silica nanocomposite sample using other sizing techniques, such as electron microscopy, laser light diffraction, and dynamic light scattering. Artifactual narrowing of the size distribution is also likely to occur for many other polymer/inorganic nanocomposite particles comprising a low-density core of variable dimensions coated with a high-density shell of constant thickness, or for core-shell latexes where the shell is continuous rather than particulate in nature.