The observed variation in the nature of the order-disorder transition (lower vs upper temperature phase diagram) with the length of the n-alkyl side group in polystyrene-b-poly(n-alkyl methacrylate) diblock copolymers [PS-b-P(nAMA)] by Mayes, Russell, and their co-workers (Macromolecules 1998, 31, 8509) is explained using a simple version of the lattice cluster theory that distinguishes between specific interactions of different united atom groups and that determines the temperature-independent portion of the effective Flory interaction parameter chi solely from the monomer molecular structures 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 the specific interaction energies. The theory is developed for arbitrary monomer structures of the two block components (or alternatively for two homopolymer blend species) and is extended to describe A-b-CxD1-x diblock copolymers in which one block is a random copolymer. The calculated disorder-order 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.