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.Comment: 39 pages, 19 figure
