(164g) A Novel Self-Consistent Field Theory Formalism for Sequence-Defined Copolymers

Self-consistent field theory (SCFT) has proven itself a powerful tool in investigating equilibrium phases of polymer melts. In particular, the theory’s ability to predict phases for multiblock copolymers using Flory-Huggins interaction parameters has enabled the design of material properties based on the phase separation of each block. However, a key limitation of the current formalism is the need to explicitly account for all distinct block-block interactions. While this poses little challenge for simple di- and triblock copolymers, more complicated systems such as gradient copolymers quickly become difficult to model. To overcome this challenge, we have derived a novel SCFT formalism which takes as input a continuous function encoding the block or monomer sequence of the polymer. This eliminates the need to reformulate the model whenever any changes to the sequence of blocks are made; instead, changes to copolymer sequence are captured in the input function while the mathematical form of the SCFT model remains invariant. Through choice of interaction model, it also substantially reduces the number of interactions that must be modeled for systems with a large degree of monomers where the number of binary interaction parameters goes as the square of the number of monomers.

With this formalism, we are able to investigate the self-assembly of multiblock copolymer melts containing a large number of binary interaction parameters, which precluded them to efficient modeling using previous SCFT methods. Beyond modeling multiblock copolymers, this new formalism enables all possible sequences for a given design space of monomers to be encoded as a set of interaction functions rather than as a permutation of the monomer set. The dimensionality of the problem can therefore be limited to just the number of specified functions no matter how many monomers are included in the design space. This low dimensional description coupled with our new SCFT formalism makes it possible to simulate complex sequence-defined polymers which were previously inaccessible to modeling; this technique should enable the discovery of new copolymer designs that help to realize the full potential of sequence-controlled polymerization.