Fractal analysis as a complimentary technique for characterizing nanoparticle size distributions

Fractal analysis of nanoparticles can provide extra information about primary particle size distributions as well as their associations in various media. Fractal dimension and lacunarity of nanoparticles were determined using two-dimensional images and particle size distributions, from either electron microscopy or dynamic light scattering measurements. Metal oxide nanoparticles, both commercial products and in-lab synthesized, were analyzed to determine fractal dimension and lacunarity coefficients. The box counting method appears to be the most robust of the methods evaluated. For aggregated nanoparticles synthesized in the vapor phase, the fractal dimensions appear to reflect aggregate growth mechanisms. For unaggregated nanoparticles that have agglomerated, fractal dimensions appear to reflect differences in surface chemistries. For the aggregated nanoparticle materials in this study, both fractal coefficients (fractal dimension and lacunarity) can provide information about powder morphology, which could be useful for quality control. For nanoparticles that agglomerate, lacunarity may be useful for defining the stability of these colloidal systems in toxicological, environmental or drug delivery applications.