First- and second-order phase 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 three-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≡εAA/εBB between monomers of the A species and of the B species a value different from 1. Using multiple histogram extrapolation and finite size scaling 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 and various asymmetries up to λ=5. At a critical potential difference Δμc unmixing occurs below a critical temperature Tc. It is found that the quantities Δμc/(1−λ)ε and 4kBTc/(3+λ)ε are both independent of the asymmetry, consistent with the prediction of the Flory theory. But the numerical values are overestimated by Flory theory by roughly a factor 1.5 for Δμc and 3.2 for Tc. For the first time a finite size scaling at first-order transitions and a way to distinguish first- and second-order transitions are presented for polymer mixtures.