Modeling of Polymer Clay Nanocomposite for a Multiscale Approach
  The mechanical property enhancement of polymer reinforced with nano-thin clay platelets (of high aspect ratio) is associated with a high polymer-filler interfacial area per unit volume. The ideal case of fully separated (exfoliated) platelets is generally difficult to achieve in practice: a typical nanocomposite also contains multilayer stacks of intercalated platelets. Here we use numerical modelling to investigate how the platelet properties affect the overall mechanical properties. The configuration of platelets is modelled using a statistical interpretation of the Representative Volume Element (RVE) approach, in which an ensemble of "sample" heterogeneous material is generated (with periodic boundary conditions). A simple Monte Carlo algorithm is used to place non-intersecting platelets in the RVE according to a specified set of statistical distributions. The effective stiffness of the platelet-matrix system is determined by measuring the stress (using standard Finite Element analysis) produced as a result of applying a small deformation to the boundaries, and averaging over the entire statistical ensemble. In this work we determine the way in which the platelet properties (curvature, filling fraction, stiffness, aspect ratio) and the number of layers in the stack affect the overall stiffness enhancement of the nanocomposite. Thus, we bridge the gap between behaviour on the macroscopic scale with that on the scale of the nano-reinforcement, forming part of a multi-scale modelling framework. 
Paul E Spencer and John Sweeney