Prediction of the overall moduli of layered silicate-reinforced nanocomposites—part II: analyses

In this part of the two-part paper, the basic theory and formulas presented in Part I are applied to various montmorillonite silicate-reinforced polymeric nanocomposites. Considering the microstructural characteristics of composites containing intercalated silicate stacks, a hierarchical model is also proposed in this part to predict the overall moduli of these composites. Theoretical predictions are compared with experimental data for isotropic composites. It is found that for the chosen elastic constants of montmorillonite silicate, all the experimental results fall within the Hashin-Shtrikman bounds for two-phase isotropic composite materials, as does the theoretical prediction of the hierarchical model. The theoretical predictions for the intercalated and exfoliated nanocomposites are close to the experimental data for the considered cases. This paper also points to the need for further examinations of the so-called constrained region that has been widely mentioned in the literature. A simple model for calculating the overall moduli of composites containing constrained regions around the reinforcements is proposed. This simple model shows that the thickness of platelet-like inhomogeneities plays a very important role in stiffening composites containing constrained regions.