Multiphase coexistence with sequence fractionation in random block copolymers

Abstract

Random binary block copolymers emerge from linking permanently and at random prepolymer blocks of two different chemical species A and B. The competitive interplay of conformational entropy, connectivity within one polymer, temperature-dependent incompatibility between A and B, and incompressibility gives rise to a complex phase behavior with a variety of possible morphologies of A- and B-rich domains. For random Q-block copolymers, this work addresses theoretically the conjectured coexistence of macroscopic phase separation and a structured phase of microscopic A- and B-rich domains. Sequence fractionation according to the copolymers' internal A-B structure promotes the coexistence of phases with different morphologies in equilibrium, as is revealed by a theory with explicit account for the exchange of individual sequences. In our semi-microscopic model, one block comprises M identical segments. The Markovian block-type sequence distribution is characterized by the type correlation λ of adjacent blocks and the global A content. Our focus is on block copolymer distributions with A-B exchange symmetry, for which phase transitions from the disordered state are continuous within mean-field theory. Upon increasing the incompatibility χ (by decreasing temperature) in the disordered state, we observe the formation of the known global, ordered phases: for λ > λc, two coexisting macroscopic A- and B-rich phases, and for λ < λc, a microstructured (lamellar) phase with nonzero wave number. In addition, we encounter a fourth region in the λ-χ plane where these three phases coexist with different, for Q≥ 3 non-Markovian, sequence distributions. The three-phase region is reached, either from the macroscopic phases via a third lamellar phase that is rich in alternating sequences, or starting from the lamellar state, via two additional homogeneous, homopolymer-enriched phases; in both cases, the incipient phases have zero volume fraction. The four regions of the phase diagram meet at a multicritical point (λc,χc), at which A-B segregation vanishes. Since our analytical method assumes weak segregation for the lamellar phase, it proves reliable particularly in the vicinity of (λc,χc). For random triblock copolymers, we find that both the character of this point and the critical exponent of the segregation amplitude change substantially with the number M of segments per block: The lamellar wave number vanishes continuously on approach to (λc,χc) only for M<7.