Phase behaviour in binary mixtures of diblock copolymers as analysed by the random phase approximation calculations

Abstract

Binary mixtures of diblock copolymers are interesting materials for controlling the size and the morphology of the microdomains in novel ways. We report here simulation results for the phase behaviour in binary mixtures of the diblock copolymers. The random phase approximation calculations were conducted for the binary mixtures of diblock copolymers, α: (A-B) 1 and β: (A-B) 2 to discuss stability of the homogeneous (α + β) mixture. The parameter values used for the simulations are that total degree of polymerization, N(= N α = N β ), is 1000, the radius of gyration, R g(= R g,α = R g,β), is l0nm, and the segmental volume, v A = v B = 100 cm 3 mol −1 for monodisperse and polydisperse samples ( 1.0 ≤ MW Mn ≤ 1.5 ). The fraction of A in α(f A α) and that in β(f A β) are varied in such a way to satisfy f A α + f A β = 1. As a result, it is predicted that the homogeneous mixture undergoes microphase separation as the segregation increases, for f A α larger than a particular value (f A α, crit) which is dependent on the values of M w M n . On the other hand, for f A α > f A α, crit the macroscopic phase separation between α and β is expected to occur prior to the microphase separation. It is also found that the wavelength of the dominant concentration fluctuation in the homogeneous mixture increases gradually as f A α approaches f A α, crit from the upper side of f A α. At f A α = f A α, crit, the wavelength diverges, indicating the macrophase separation. These results give some implications to the unit size of the microdomains formed upon the disorder-to-order transitions (ODT) for f A α > f A α, crit. Namely, the unit size might be larger than those of the component pure diblocks. The phase diagram of the ODT for the binary mixtures are found to depend on the compositions of α and β, i.e. the values of f A α and f A β. The phase boundary between the homogeneous (disordered) state and the microphase separated state for the binary mixture is found to be different from the one for the pure block copolymer. The result shows that the miscibility (disordered state) is suppressed in the binary mixture.