Modeling the Phase Behavior of Polymer−Clay Composites

To model the phase behavior of polymer−clay composites, we develop a free energy expression for a mixture of polymers and solid, thin disks. The free energy expression is adopted from the Onsager model for the equilibrium behavior of rigid rods. Thus, our theory takes into account the possible nematic ordering of the disks within the polymer matrix. By minimizing this free energy and calculating the chemical potentials, we construct phase diagrams for the polymer−disk mixtures. The findings provide guidelines for tailoring the polymer molecular weight and the volume fraction of the different components to fabricate thermodynamically stable mixtures with the desired morphology.