Efficient Computation of Single-Chain Partition Functions in Field-Theoretic Simulations of Polymers With Nested Tree-Like Topologies

A general algorithm is introduced to compute single-chain partition functions in field-theoretic simulations of polymers with nested tree-like topologies, including self-consistent field theory simulations that invoke the mean-field approximation. The algorithm is an extension of a method used in a number of recent studies on the phase behavior of bottlebrush block copolymers. In those studies, the computational cost of computing single-chain partition functions is reduced by aggregating the statistical weight of degenerate side arms. By extending this method to chains with arbitrary degrees of branching, the computational cost is reduced to scale with the total length of unique segments in the chain instead of the total length/mass of the entire chain. The method is first validated on a model dendrimer system by comparing results to coarse-grained molecular dynamics simulations and also demonstrate its advantage over more conventional approaches to compute single-chain partition functions. The algorithm is subsequently used to analyze the phase behavior of a molecularly informed field-theoretic model of poly(butyl acrylate)-graft-poly(dodecyl acrylate) (pBA-graft-pDDA) copolymers in a dodecane solvent. The methodology can help advance field-theoretic investigations of branched polymers by leveraging degeneracy in the chain to reduce computational cost and avoid the need to develop architecture-specific algorithms.