Mechanical percolation in nanocomposites: Microstructure and micromechanics

Polymer nanocomposites can enable innovative designs of multifunctional materials. Metallic fillers in polymer matrices exhibit improved electrical properties at low volume fractions, often maintaining the low density, transparency and easy processing of polymers. Surprisingly, enhanced mechanical properties have also been observed at uncharacteristically low volume fractions in these nanocomposites. The majority of mathematical models used to describe this novel mechanical behavior are based on percolation models of microstructural connectivity. Changes in mechanical properties, however, are likely to be affected by complex microstructures, beyond simply connected, as well as by the micromechanical mechanisms associated with a composite material. Both microstructural and micromechanical mechanisms are thought to be significantly influenced by the presence and properties of an interface region, between particles and matrix, which functions as a third composite phase. In this work, the relative influence of the competing and compounding effects of the spatial position/distribution of the particles (microstructure) and of the composite constitution (micromechanics) are examined. The results show that models based solely on the inclusion of a third composite phase do not predict the experimentally observed mechanical response. This work continues with a study of the micromechanical effects of microstructure using a probabilistic and statistical characterization of the local strain fields associated with random microstructures. These continuous fields are not only more amenable to statistical characterization than the spatial ternary (matrix, particle and interface) fields that describe the microstructure, but offer a more direct, and potentially more visual, link between microstructure and mechanics. An apparent percolation threshold for a 2D material model is identified based on statistical characterization of the elastic moduli, distributions of local strains and spatial autocorrelation of local strain fields. The statistics of strain fields associated with microstructures producing minimum and maximum moduli are also compared.