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Three-phase coexistence with sequence partitioning in symmetric random block copolymers

Alice von der Heydt1,*, Marcus Müller1, and Annette Zippelius1,2

  • 1Institut für Theoretische Physik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany
  • 2Max-Planck-Institut für Dynamik und Selbstorganisation, Bunsenstraße 10, D-37073 Göttingen, Germany

  • *heydt@theorie.physik.uni-goettingen.de
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Phys. Rev. E 83, 051131 – Published 31 May, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.051131

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>λc, two coexisting macroscopic A- and B-rich phases, for λ<λc, 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 (λc,χc), 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 (λc,χc). 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.

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      Phys. Rev. E 83, 051131– Published 31 May, 2011
      • Received 24 August 2010

      ©2011 American Physical Society

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