Quantification of layered silicate dispersion in polymer nanocomposites

The dispersion of layered silicates strongly influences the performance of polymer/clay nanocomposites, making the ability to assess clay dispersion quantitatively essential to any effective product quality control effort. However, a quantitative description of dispersion that can be related directly to product performance remains a challenge. Here, we propose a methodology for quantifying clay dispersion, based on describing particle length distribution data obtained from transmission electron microscopy (TEM) micrographs with a gamma probability distribution model, γ(α,β), where the parameter α, (which represents the mean number of platelets per particle), and β, (which represents the mean “effective platelet length”), are shown to be related to the degree of dispersion. Published data sets on a wide variety of polymer nanocomposites are then used to establish an explicit quantitative relationship between these parameters and the extent of dispersion. Specifically, we found that dispersion characteristics are captured effectively by a characteristic dispersion parameter, δ, defined along dispersion contours represented by the empirical relation δ = α + 0.05β, where δ < 5 for exfoliated composites, 5 < δ < 6.5 for less exfoliated composites with stacks containing several layers, and δ > 6.5 for intercalated composites. The proposed method is validated experimentally by using it to quantify the dispersion of polymer nanocomposites produced in our laboratory.