Field-theoretic methods for studying supramolecular self-assembly in multiblock copolymer melts are developed. The reversibility of noncovalent bonds in supramolecular assemblies allows for environmental control (temperature, pH, etc.) over reaction equilibrium. When chemically distinct polymers are linked, environmental and stoichiometric control over the bonding is used to select from a variety of phase behaviors including macrophase separation into homogeneous phases, microphase separation into ordered mesophases, coexistence of homogeneous phases and ordered mesophases, and coexistence of ordered mesophases that differ in composition and possibly structure.

The formalism for describing the gelation and macro- and microphase separation behavior of binary melts of A and B star-shaped polymers that reversibly bond to form copolymer networks is obtained by incorporating a graphical representation of polymers as trees into a grand canonical ensemble field-theoretic model of continuous Gaussian chains. The enumeration of clusters of different isomeric forms and compositions takes place via generating functions that are a system of nonlinear, transcendental, integral equations. The integral equations are turned into purely algebraic equations by making use of the random phase approximation (RPA). The macro- and microphase separation separation and gelation behavior is first investigated for heterogeneously bonded networks, and, later, the methodology is applied to calculate the melt phase behavior of polyester elastomers.

A new computational technique is developed to investigate the phase behavior of melts of multiple polymer species based on an intensive formulation of the Gibbs ensemble SCFT method. The intensive formulation allows constituent mesophases of macrophase separated systems to be represented by single representative unit cells. The compositions of coexisting phases in equilibrium are found by minimizing the intensive free energy of the overall system with respect to the compositions within each cell. The solutions are restricted to those where the mass conservation constraints and the volumetric constraints between coexisting phases are satisfied. The Gibb ensemble SCFT method is extended to supramolecular self-assembly by developing a canonical formalism for reversibly bonded multiblock copolymers.

The case of AB diblock copolymers that reversibly react at their B termini with monofunctional B homopolymers to produce longer ABB diblock copolymers is specifically addressed with the new methodology.