A Methodology for Quantitatively Characterizing the Dispersion of Nanostructures in Polymers and Composites

We seek to provide a metric for quantifying the degree of dispersion of nanostructures, such as carbon nanotubes in polymeric and other matrices, motivated by the technological importance of nanostructure-based composites. Our proposed measure of dispersion uses a quadrat-based sampling algorithm and a metric d(P| | Q), to correlate randomness to the dispersion. This allows a quantitative comparison of the given distribution (say, P) to a preferred distribution or pattern (say, Q). We provide examples from our own studies and those from the literature on the application of the metric.