A Born-Green-Yvon integral equation treatment of compressible lattice mixtures

The statistical thermodynamics of compressible multicomponent lattice mixtures is developed using the Born–Green–Yvon (BGY) integral equation technique. Expressions for the internal energy, Helmholtz free energy, chemical potential and equation of state are derived, and the routes to the volume, Gibbs energy, and noncombinatorial entropy are discussed. We use these results to study the phase separation behavior of a theoretical polymer blend which exhibits both an upper and lower critical solution temperature, focusing primarily on the spinodal. The effects of changing the pressure, polymer chain length, lattice coordination number, and interaction energies are also investigated.