Thermodynamics of Polymer-Clay Nanocomposites Revisited: Compressible Self-Consistent Field Theory Modeling of Melt-Intercalated Organoclays

We formulate a ``compressible'' version of lattice self-consistent field theory (SCFT) to describe thermodynamic behavior of organically modified clays in polymer melt. The melt consists of the homopolymer matrix and a fraction of end-functionalized ``active'' chains, each chain having a single ``sticker'' end-group with strong affinity to the clay surface. We calculate the phase map for this system as function of the melt composition and the strength of the ``sticker'' adhesion to the clay. It is shown that within the compressible SCFT model, intercalated morphologies are favored in a significantly broader parameter range than was expected based on the incompressible SCFT analysis. We provide a qualitative analysis of this result and discuss implications for the physics of nanocomposites in general.