Supramolecular diblock copolymers: A field-theoretic model and mean-field solution

We consider a supramolecular diblock copolymer melt in which two homopolymers of different species can reversibly bond at terminal binding sites to form a diblock copolymer. The grand canonical ensemble is particularly convenient for formulating field-theoretic models of supramolecular assembly because the chemical equilibrium of bonding reactions impose constraints on the chemical potentials of the polymer species. Unlike the analogous model for a three component blend of A and B homopolymers with an irreversibly bonded AB diblock copolymer, both chi N and N appear as independent parameters, where chi is the Flory interaction parameter and N is the length of the diblock copolymer. In addition, an extra parameter characterizes the free energy of forming a bond. Analytic methods and numerical self-consistent field theory are used to calculate the phase diagram in the mean-field approximation. For symmetric systems with equal volume fractions and chain lengths of the two homopolymers, we predict re-entrant behavior upon cooling in narrow parameter ranges for both disordered and lamellar phases. In the case of the lamellar phase, we find re-entrant behavior in which the intermediate phase is either disordered or macrophase separated. We explain this behavior as a competition between the bonding equilibrium, the chemical incompatibility of the two species and the translational entropy loss upon forming a diblock copolymer.