Explanation for the unusual phase behavior of polystyrene-b-poly(n-alkyl methacrylate) diblock copolymers: Specific interactions

The observed variation in the nature of the order-disorder transition (lowe r vs upper temperature phase diagram) with the length of the n-alkyl side g roup in polystyrene-b-poly(n-alkyl methacrylate) diblock copolymers [PS-b-P (nAMA)] by Mayes, Russell, and their co-workers (Macromolecules 1998, 31, 8 509) is explained using a simple version of the lattice cluster theory that distinguishes between specific interactions of different united atom group s and that determines the temperature-independent portion of the effective Flory interaction parameter chi solely from the monomer molecular structure s without employing adjustable parameters. The presence of this temperature independent part of chi provides the entropic driving force for the lower disorder-order transition in systems with negative enthalpic chi. The only adjustable parameters of the theory are three independent combinations of t he specific interaction energies. The theory is developed for arbitrary mon omer structures of the two block components (or alternatively for two homop olymer blend species) and is extended to describe A-b-CxD1-x diblock copoly mers in which one block is a random copolymer. The calculated disorder-orde r transition temperatures accord reasonably with experimental data, and the utility of the theory is illustrated further by presenting predictions of how the phase behavior of the PS-b-P(nAMA(x)-co-n'AMA(1-x)) systems changes with n and n' and with the random copolymer composition x.