Lattice cluster theory for copolymer blends: General theory in the incompressible system, long chain limit

The lattice cluster theory is developed for binary blends of two structured monomer copolymers in the simplifying limit of an incompressible system an d high molecular weights. The major advance in the present theory is the in clusion of nonrandom mixing effects that lead to a monomer sequence depende nce of the Helmholtz free energy without the introduction of new adjustable parameters beyond those present in descriptions of binary homopolymer blen ds formed from the constituent monomers. Equivalently, the sequence depende nt contributions are shown to emerge from a proper determination of the "su rface fractions" in individual copolymer chains. The general theory applies to blends of random copolymer, diblock copolymers, alternating copolymers, as well as of copolymers with kinetically controlled monomer sequences. Th e theory is illustrated for purely random copolymer blends of deuterated an d hydrogenated polybutadienes, where the computed phase boundaries depart q ualitatively from those predicted by random copolymer Flory-Huggins theory.