A finite element approach to self-consistent field theory calculations of multiblock polymers

Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of equations is based on using a spectral approach. While widely succe...

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Bibliographic Details
Published in:Journal of computational physics 2017-02, Vol.331, p.280-296
Main Authors: Ackerman, David M., Delaney, Kris, Fredrickson, Glenn H., Ganapathysubramanian, Baskar
Format: Article
Language:English
Subjects:
ACCURACY
Computational physics
CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
CONFINEMENT
CONVERGENCE
DESIGN
EFFICIENCY
EQUATIONS
EQUILIBRIUM
EXTRAPOLATION
FIELD THEORIES
Field theory
Finite element analysis
FINITE ELEMENT METHOD
Finite elements
High performance computing
Mathematical analysis
Mathematical models
Mathematical morphology
MICROSTRUCTURE
Modelling
Morphology
NANOSTRUCTURES
PERIODICITY
Polymer theory
POLYMERS
SELF-CONSISTENT FIELD
Self-consistent field theory
SIMULATION
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Summary:Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of equations is based on using a spectral approach. While widely successful, this approach has limitations especially in the context of current technologically relevant applications. These limitations include non-trivial approaches for modeling complex geometries, difficulties in extending to non-periodic domains, as well as non-trivial extensions for spatial adaptivity. As a viable alternative to spectral schemes, we develop a finite element formulation of the SCFT paradigm for calculating equilibrium polymer morphologies. We discuss the formulation and address implementation challenges that ensure accuracy and efficiency. We explore higher order chain contour steppers that are efficiently implemented with Richardson Extrapolation. This approach is highly scalable and suitable for systems with arbitrary shapes. We show spatial and temporal convergence and illustrate scaling on up to 2048 cores. Finally, we illustrate confinement effects for selected complex geometries. This has implications for materials design for nanoscale applications where dimensions are such that equilibrium morphologies dramatically differ from the bulk phases.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2016.11.020