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

<div><p>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 <i>d</i>(<i>P</i>| | <i>Q</i>), to correlate randomness to the dispersion. This allows a quantitative comparison of the given distribution (say, <i>P</i>) to a preferred distribution or pattern (say, <i>Q</i>). We provide examples from our own studies and those from the literature on the application of the metric.</p>