Quantitative evaluation of mixing using a refined Shannon entropy

Abstract A method to quantify the dispersion level of fillers in a polymer composite using optical microscopy and image processing is demonstrated. Optical microscope images of a graphene suspension were taken throughout an ultrasonication procedure. A mixing index was calculated for each image using a modified Shannon entropy analysis, demonstrating that the index can be used to optimize procedures for dispersing fillers in polymers. The flexibility of the Shannon entropy index is achieved through two user-defined variables based on physically meaningful features, allowing the analysis to be applicable to a wide range of filler size distributions. Calculating a mixing index allows for characterization beyond the typical categories of ‘highly’ and ‘poorly’ dispersed systems. An index can be calculated at various stages of composite processing allowing for robust statistical analysis of the dispersion level, using only a small sample volume. The adoption of this method would lead to quantitative characterization of dispersion level in polymer composites, deepening the understanding of how processing impacts composite properties, and aiding in the design of new composite materials.