Investigation of Theoretical Models for the Elastic Stiffness of Nanoparticle-Modified Polymer Composites

Mathematical models are investigated and suggested for the calculation of the elastic stiffness of polymer nanocomposites. Particular emphasis is placed on the effect on the elastic stiffness from agglomerates and the particle interphase properties. The multiphase Mori-Tanaka model and an interphase model are considered as two relevant models. These models only include and require the designation of a few system independent parameters with a clear physical meaning. Extensions of the models are also presented. The model calculations are compared to results from other models, as well as experimental data for different nanocomposites. For nanocomposites with spherical particles and with fiber-like particles, the suggested models are found to be the most flexible ones and are applicable to estimate the stiffness increase of nanocomposites for both low and high particle volume fractions. The suggested theoretical models can hence be considered as a general multiscale “model toolbox” for analysis of various nanocomposites.