Fluctuation theory of diblock copolymer/homopolymer blends and its effects on the Lifshitz point

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Abstract
We have considered the stability of lamellar, cylindrical, and spherical morphologies of a ternary melt system of A homopolymers, B homopolymers, and AB diblock copolymers in the weak segregation limit. We have extended the mean field analysis by including composition fluctuations in a one-loop self-consistent approximation. We find rich binary and ternary phase diagrams with multiphase equilibria which are highly sensitive to parameter variations. The order–disorder transition points (χN) ODT are shifted upward relative to the mean field theory (MFT) transition points and all second order MFT microphase separation transitions are changed to first order. Composition fluctuations modify the MFT microphase separation and macrophase separations differently. As a consequence, the MFT Lifshitz critical point is destroyed. This implies that observation of the scattering function by itelf does not suffice to infer the existence of Lifshitz critical points. We demonstrate this in a quantitative comparison between our results and experiments.