A lattice-statistical model for ternary polymer mixtures: exact phase diagrams

We consider a model for ternary polymer mixtures with bi- and tri-functional monomers and solvent molecules embedded on a honeycomb lattice. We first show that the grand partition function of the model polymer mixture is equivalent to the partition function of an eight-vertex model on the same lattice. This equivalence transforms the model into an Ising model in a non-zero external magnetic field. Using the known results for the Ising model, an exact analysis of the phase diagrams for the phase separation transition in the ternary system is carried out. Particularly, we determine the exact two-phase coexistence surface in the temperature-composition space and study the connectivity properties of the model. It is noteworthy that the theory incorporates cyclicity (polymer rings) as well as excluded volume effects.