A Particle Size-Shape-Dependent Three-Phase Two-Step Mori-Tanaka Method for Studying the Interphase of Polymer/Clay Nanocomposites

The enhancement of polymers by nano fillers can improve their mechanical properties beyond those achieved in macro, meso and micro composites with the same volume fraction, particle morphology and particle aspect ratio. The basic enhancement mechanism is analogous to traditional composite mechanics and can be partly explained by classical composite theories. However, the much higher enhancement efficiency of fillers at the nano scale, i.e. the particle size effects, can not be explained by classical composite mechanics theories alone. The interphase is a main structural feature of nano composites within which a significant surface-to-volume ratio is achieved, and it plays a crucial role in understanding the size effects and enhancement mechanisms of nanocomposites. In this investigation, a semi-empirical method of determining the interphase thickness and elastic properties is developed by a combination of finite element simulation, thermodynamic formulation and experimental calibration and applied to LBL (layer by layer) polyurethane-clay nanocomposites studied by Podsiadlo, et al. [1, 2] and Li, et al. [3]. Based on this study, the classical two-phase Mori-Tanaka model is extended into three-phases by introducing the interphase through a two-step procedure using the concept of an effective matrix. It is shown that this two-step Mori-Tanaka method can predict the brittle to ductile transition in terms of interphase overlap. Most importantly, this approach overcomes a serious drawback of the classic Mori-Tanaka model: size-independency. Particle size effects as well as shape effects and their interactions can be studied as applications of this method.