Phase equilibria in copolymer/homopolymer ternary blends: Molecular weight effects

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Abstract
The phase behavior of ternary blends of an A–B random copolymer with two homopolymers (A and B) is investigated within the Flory–Huggins lattice theory. We restrict consideration to the formation of (isotropic) liquid phases. For compositionally symmetric systems in which the two homopolymers have equal molecular weights, two different topologies are found for the phase diagrams according to the length of the copolymer relative to the homopolymers. Namely, upon lowering the temperature, a three-liquid-phase region emerges either continuously via a tricritical point if the copolymer is long enough, or discontinuously otherwise. This change in phase behavior, an entropy of mixing effect, occurs when the copolymer length is a fraction 2/5 of the homopolymer molecular weight. The properties of the (symmetric) tricritical points are discussed, as well as the phase behavior of systems in which the copolymer is not symmetrical in composition and/or the two homopolymers differ in size. This Flory–Huggins approach should be valid for blends containing random copolymers, but also, at high enough temperatures, for blends that contain block copolymers, the temperature range of validity being broader for smaller block copolymers. The critical behavior of systems containing block copolymers is described by the simple Flory–Huggins theory over a range delineated by isotropic Lifshitz points. These Lifshitz points are located within the random phase approximation.