Dispersion quantification of inclusions in composites

Distribution of constituents within a composite material dictates important constitutive properties and is therefore of interest for all multiphase materials including nano-, micro-, and macro-composites. In the first part of this paper, previously proposed methods for quantifying dispersion are reviewed and their applications and possible shortcomings are discussed. In the second part, we propose a novel definition for dispersion based on the thermodynamic concept of work; dispersion is measured based on the amount of work required to translate inclusions so they form the state of maximum uniformity. The method quantifies dispersion with a single parameter. Although multiple parameter methods can provide more information about the spatial distribution of inclusions, the proposed method is particularly useful when comparing overall dispersion quality of different domains. As an example, the dispersion of carbon nanotubes in an Al coating is quantified to demonstrate the robustness and practicality of the novel dispersion quantification method.