Simulation of first- and second-order transitions in asymmetric polymer mixtures

The critical properties of dense asymmetric binary polymer mixtures are studied by grand canonical simulations within the framework of the 3-dimensional bond fluctuation lattice model. The monomers interact with each other via a potential ranging over the entire first peak of the pair distribution. An asymmetry is realized by giving the ratio of interactions λ = ∈_AA/∈_BB between monomers of the A-species and of the B-species a value different from 1. Using multiple histogram extrapolation techniques for the data analysis, the two phase region, which is a line of first-order transitions driven by the chemical potential difference, and the critical point are determined for a mixture of chains with 32 monomers each. At a critical potential difference Δμ_c unmixing occurs below a critical temperature T_c. It is found that Δμ_c is proportional to the asymmetry (1 - λ) and that the quantity 4k_BT_c/(3 + λ)∈ is independent of the asymmetry, consistent with the prediction of the Flory theory.