  Mixture quality plays a crucial role in the physical properties of
multi-component immiscible polymer mixtures including nanocomposites and
polymer blends. Such complex mixtures are often characterized by hierarchical
internal structures, which have not been accounted for by conventional mixture
quantifications. We propose a way to characterize the mixture quality of
complex mixtures with hierarchical structures. Starting from a concentration
field, which can be typically obtained from TEM/SEM images, the distribution of
the coarsegrained concentration is analyzed to obtain the scale-dependent
inhomogeneity of a mixture. The hierarchical nature of a mixture is
characterized by multiple characteristic scales of the scale-dependent
inhomogeneity. We demonstrate how the proposed method works to characterize
sizes and distributions in different dispersions. This method is generally
applicable to various complex mixtures.
