Self-consistent Field Theory of Inhomogeneous Polymeric Systems

Using a binary polymer blend as a model system, we provide a detailed derivation of the self-consistent field theory (SCFT) of inhomogeneous polymeric systems in canonical and grand-canonical ensembles. Starting from a particle-based description of the polymers, the partition function of the system is transformed to a field-theoretical description. Evaluating the partition function using a saddle-point approximation leads to a set of SCFT equations and a SCFT free energy functional of the system. The SCFT free energy functional can be used to describe the phases and phase transitions of inhomogeneous polymeric systems such as polymer blends and block copolymer melts.