# Three-phase coexistence with sequence partitioning in symmetric random block copolymers - Condensed Matter > Soft Condensed Matter

Three-phase coexistence with sequence partitioning in symmetric random block copolymers - Condensed Matter > Soft Condensed Matter - Download this document for free, or read online. Document in PDF available to download.

Abstract: We inquire about the possible coexistence of macroscopic and microstructuredphases in random Q-block copolymers built of incompatible monomer types A and Bwith equal average concentrations. In our microscopic model, one blockcomprises M identical monomers. The block-type sequence distribution isMarkovian and characterized by the correlation \lambda. Upon increasing theincompatibility \chi\ by decreasing temperature in the disordered state, theknown ordered phases form: for \lambda\ > \lambda c, two coexisting macroscopicA- and B-rich phases, for \lambda\ < \lambda c, a microstructured lamellarphase with wave number k\lambda. In addition, we find a fourth region in the\lambda-\chi\ plane where these three phases coexist, with different,non-Markovian sequence distributions fractionation. Fractionation is revealedby our analytically derived multiphase free energy, which explicitly accountsfor the exchange of individual sequences between the coexisting phases. Thethree-phase region is reached, either, from the macroscopic phases, via a thirdlamellar phase that is rich in alternating sequences, or, starting from thelamellar state, via two additional homogeneous, homopolymer-enriched phases.These incipient phases emerge with zero volume fraction. The four regions ofthe phase diagram meet in a multicritical point \lambda c, \chi c, at whichA-B segregation vanishes. The analytical method, which for the lamellar phaseassumes weak segregation, thus proves reliable particularly in the vicinity of\lambda c, \chi c. For random triblock copolymers, Q=3, we find the characterof this point and the critical exponents to change substantially with thenumber M of monomers per block. The results for Q=3 in the continuous-chainlimit M -> \infty are compared to numerical self-consistent field theorySCFT, which is accurate at larger segregation.

Author: ** Alice von der Heydt, Marcus MÃ¼ller, Annette Zippelius**

Source: https://arxiv.org/