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 $\lambda$. Upon increasing the incompatibility $\chi$ (by decreasing temperature) in the disordered state, the known ordered phases form: for $\lambda >{\lambda }_c$, two coexisting macroscopic $A$- and $B$-rich phases, for $\lambda <{\lambda }_c$, a microstructured (lamellar) phase 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 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 $({\lambda }_c,{\chi }_c)$, 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 $({\lambda }_c,{\chi }_c)$. 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 $M\to \infty$ are compared to numerical self-consistent field theory (SCFT), which is accurate at larger segregation.

• Received 24 August 2010

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