Phase separation in binary hard-core mixtures: An exact result

We prove the existence of a first-order, entropy-driven demixing transition in a simple lattice model for a hard-core mixture. The existence of this transition follows from the fact that this lattice model can be mapped onto an Ising model with nearest-neighbor interactions for which the phase behavior is known. The same mapping leads to a very simple interpretation of the entropic contribution of the solvent to the interaction parameter {χ} in the Flory-Huggins theory of polymer solutions.