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#### Three-phase coexsistence with sequences partitioning in symmetric random block copolymers

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##### Citation

von der Heydt, A., Müller, M., & Zippelius, A. (2011). Three-phase coexsistence
with sequences partitioning in symmetric random block copolymers.* Physical Review E,* *83*: 051131. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/21728514.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0029-11A9-7

##### Abstract

We inquire into the possible coexistence of macroscopic and microstructured phases in random Q-block copolymers built of incompatible monomer types A and B with equal average concentrations. In our microscopic model, one block comprises M identical monomers. The block-type sequence distribution is Markovian and characterized by the correlation λ. Upon increasing the incompatibility χ (by decreasing temperature) in the disordered state, the known ordered phases form: for λ>λ(c), two coexisting macroscopic A- and B-rich phases, for λ<λ(c), a microstructured (lamellar) phase with wave number k(λ). In addition, we find a fourth region in the λ-χ plane where these three phases coexist, with different, non-Markovian sequence distributions (fractionation). Fractionation is revealed by our analytically derived multiphase free energy, which explicitly accounts for the exchange of individual sequences between the coexisting phases. 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. These incipient phases emerge with zero volume fraction. The four regions of the phase diagram meet in a multicritical point (λ(c),χ(c)), at which A-B segregation vanishes. The analytical method, which for the lamellar phase assumes weak segregation, thus proves reliable particularly in the vicinity of (λ(c),χ(c)). For random triblock copolymers, Q=3, we find the character of this point and the critical exponents to change substantially with the number M of monomers per block. The results for Q=3 in the continuous-chain limit M→∞ are compared to numerical self-consistent field theory (SCFT), which is accurate at larger segregation.