Calculating phase diagrams of polymer-platelet mixtures using density functional theory: Implications for polymer/clay composites

We analyze the thermodynamics of disklike particles dispersed in a polymer matrix. Using the Somoza-Tarazona free energy functional for thin oblate ellipsoids of revolution in combination with the Flory-Huggins mixing free energy, we obtain a new expression that allows us to describe the complete (liquid, crystalline, and liquid crystalline) phase diagram for the mixture as a function of shape anisotropy k, polymer chain length N, and the disk-disk interaction parameter, q. It is shown that at large q and/or N positional ordering Plays an important role in determining the stability and morphology of such mixtures.