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Abstract 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.
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This content will become publicly available on June 21, 2026
Improved algorithm for identifying partial saddle-points in polymer field theoretic simulations
Field-theoretic simulations that rely on a partial saddle-point approximation have become powerful tools for studying complex polymer materials. The computational cost of such simulations depends critically upon the efficiency of the iterative algorithm used to identify a partial saddle-point field configuration during each step of a stochastic simulation. We introduce a new algorithm for this purpose that relies on a physically motivated approximation in which the linear response of the density to a small change in a pressure-like field is approximated by the response of a hypothetical homogeneous system. The computational cost of the resulting algorithm is significantly less than that of the commonly used Anderson mixing algorithm.
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- Award ID(s):
- 2103627
- PAR ID:
- 10629284
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 162
- Issue:
- 23
- ISSN:
- 0021-9606
- Page Range / eLocation ID:
- 234901
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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