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

TL;DR

This paper introduces a finite element method for self-consistent field theory calculations of multiblock polymers, overcoming spectral approach limitations and enabling accurate modeling of complex geometries and nanoscale confinement effects.

Contribution

It develops a scalable finite element formulation for SCFT, addressing implementation challenges and demonstrating high accuracy and efficiency for complex geometries.

Findings

Achieves spatial and temporal convergence in simulations.

Scales efficiently up to 2048 cores.

Shows confinement effects in complex geometries.

Abstract

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.