Field theoretic approach for block polymer melts: SCFT and FTS

This perspective addresses the development of polymer field theory for predicting the equilibrium phase behavior of block polymer melts. The approach is tailored to the high-molecular-weight limit, where universality reduces all systems to the standard Gaussian chain model, an incompressible melt of elastic threads interacting by contact forces. Using mathematical identities, this particle-based version of the model is converted to an equivalent field-based version that depends on fields rather than particle coordinates. The statistical mechanics of the field-based model is typically solved using the saddle-point approximation of self-consistent field theory (SCFT), which equates to mean field theory, but it can also be evaluated using field theoretic simulations (FTS). While SCFT has matured into one of the most successful theories in soft condensed matter, FTS are still in its infancy. The two main obstacles of FTS are the high computational cost and the occurrence of an ultraviolet divergence, but fortunately there has been recent groundbreaking progress on both fronts. As such, FTS are now well poised to become the method of choice for predicting fluctuation corrections to mean field theory.

Target-Directed Design of Phase Transition Path for Complex Structures of Rod-Coil Block Copolymers

We apply the string method to the self-consistent mean-field theory framework of the rod-coil block copolymer system to calculate the minimum energy pathways in the rearrangement transitions of lamellae and cylinders with different orientations under certain epitaxial growth relationship. Metastable phases appearing in the reordering transition pathway tend to form the structure at low χN side of the order-order transition boundary compared with the initial phase. In particular, for complex network, metastable phases, such as single gyroid and perforated lamellae, need to select a rearrangement transition between lamellae or cylinders near the order-disorder transition boundary with the same epitaxial growth relationship but different orientations. It is confirmed that this strategy for obtaining complex metastable phases by rational design of rearrangement transition between specific phases in the phase diagram can be applied to a wide range of χN as well as the coil-coil block copolymer system. We further investigate the rearrangement transition behavior combining with the analysis of contribution from the free energy, entropy, degree of mixing between different blocks, and the average orientation degree of rods during the phase transitions. Based on this mechanism, we have developed a target-directed design strategy for constructing self-assembled metastable structures of rod-coil block copolymers.