Lifshitz points in blends of AB and BC diblock copolymers

– We consider microand macro-phase separation in blends of AB and BC flexible diblock copolymers. We show that, depending on architecture, a number of phase diagram topologies are possible. Microphase separation or macrophase separation can occur, and there are a variety of possible Lifshitz points. Because of the rich parameter space, Lifshitz points of multiple order are possible. We demonstrate Lifshitz points of first and second order, and argue that, in principle, up to 5th-order Lifshitz points are possible. Introduction. – The phase behaviour of block copolymer melts is remarkably rich. In a blend of homopolymers only macrophase separation (with wave number q∗ = 0) occurs. Macrophase separation in a block copolymer melt is prevented by the chemical connectivity of the constituent blocks, which leads to microphase-separated structures with q∗ 6= 0, typically corresponding to structural periods L ' 10−100 nm [1, 2]. In a blend containing a block copolymer melt and one or more molten homopolymers, microphase separation of the block copolymer can compete with macrophase separation of the homopolymers at low temperatures [1]. In a binary blend of a block copolymer and a homopolymer, the homopolymer swells the microphase-separated structure formed by the copolymer, if the homopolymer chain length is less than or equal to that of the corresponding block [1, 3]. On the other hand, macrophase separation can occur for homopolymer chains longer than the corresponding block. In a ternary blend, block copolymer added to a blend of homopolymers acts as a compatibilizer to prevent macrophase separation or reduce the lengthscale associated with the macrophaseseparated structure [1,4]. A similar interplay between microand macro-phase separation has recently been explored experimentally for AB/AB diblock copolymer blends by Hashimoto () E-mail: [email protected] () E-mail: [email protected]