Lattice theory of a multicomponent mixture of monodisperse polymers of fixed architectures

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Abstract
We present a lattice theory for a multicomponent mixture of p distinct polymeric species, each of a prescribed architecture but without any cycles and s monomeric species along with a solvent species, the latter playing the role of a reference species whose amount is controlled not by any activity but by the sum rule of fixed amount of material. The theory is an extension of our previous work on a binary mixture of polymers in bulk or a general mixture next to a surface. The model allows for nearest-neighbor interactions between unlike species. The chemical bondings are allowed to be between monomers (of the same species) that are nearest-neighbor. The resulting theory is obtained by solving the model on a Bethe lattice. The theory has a very simple structure and supersedes random mixing approximation to which it reduces in a special limit, the random mixing approximation limit, see text. We study the behavior of a ternary system numerically and compare it with that of a binary system. We also compare the predictions of our theory with simulations and find them to be consistent. However, our theoretical predictions are inconsistent with the conventional Flory–Huggins theory. Thus, our theory is superior to the Flory–Huggins theory.