A finite element approach to self-consistent field theory calculations of multiblock polymers
Date
Authors
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Authors
Research Projects
Organizational Units
The Department of Electrical and Computer Engineering (ECpE) contains two focuses. The focus on Electrical Engineering teaches students in the fields of control systems, electromagnetics and non-destructive evaluation, microelectronics, electric power & energy systems, and the like. The Computer Engineering focus teaches in the fields of software systems, embedded systems, networking, information security, computer architecture, etc.
History
The Department of Electrical Engineering was formed in 1909 from the division of the Department of Physics and Electrical Engineering. In 1985 its name changed to Department of Electrical Engineering and Computer Engineering. In 1995 it became the Department of Electrical and Computer Engineering.
Dates of Existence
1909-present
Historical Names
- Department of Electrical Engineering (1909-1985)
- Department of Electrical Engineering and Computer Engineering (1985-1995)
Related Units
- College of Engineering (parent college)
- Department of Physics and Electrical Engineering (predecessor)
Journal Issue
Is Version Of
Versions
Series
Department
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.
Comments
This is a manuscript of an article is published as Ackerman, David M., Kris Delaney, Glenn H. Fredrickson, and Baskar Ganapathysubramanian. "A finite element approach to self-consistent field theory calculations of multiblock polymers." Journal of Computational Physics 331 (2017): 280-296. DOI:10.1016/j.jcp.2016.11.020. Posted with permission.