Transmission electron microscopy based direct mathematical quantifiers for dispersion in nanocomposites

A rigorous mathematical foundation and a procedure for quantifying three-dimensional exfoliation and dispersion of clay particles in polymer-clay nanocomposites from their two-dimensional transmission electron microscopy micrographs have been developed. Two independent parameters, exfoliation number and interparticle distance, have been proposed. The exfoliation number gives the percentage of exfoliation achieved, whereas the interparticle distance is a measure of spatial separation between particles. The quantitative description of the nanocomposite microstructure would enable the establishment of synthesis/processing-structure-property linkages in nanocomposites and provide a benchmark for other indirect characterization techniques, such as x-ray diffraction, rheology, etc.