Self-Consistent Field Theory of Disordered Block-Copolymers

We derive the mean-field theory of disordered block-copolymers composed of two monomeric species, combining Edwards' functional method with the replica technique of disordered systems. In the absence of disorder we recover the canonical self-consistent field theory of inhomogeneous polymers. In the presence of sequence disorder the theory can be regarded as a comprehensive, novel self-consistent treatment of copolymer melts, unifying the weak- and strong-inhomogeneous regimes. In particular, we study the stability of the microphase separation transition in a melt of diblock-copolymers, composed of $N$ monomers and equal $A$- $B$-volume fraction, against the disruptive effect of disorder. We obtain a phase diagram in terms of the relevant parameters, namely the rescaled Flory-Huggins parameter $\chi N$ and disorder strength $p$.