Self-consistent field theory simulations of polymers on arbitrary domains

Journal Article · Thu Dec 15 04:00:00 EST 2016 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2016.09.021· OSTI ID:22622223

Ouaknin, Gaddiel ^[1]; Laachi, Nabil; Delaney, Kris ^[2]; Fredrickson, Glenn H. ^[2]; Gibou, Frederic ^[1]

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1. Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106-5070 (United States)
2. Materials Research Laboratory, University of California, Santa Barbara, CA 93106-5080 (United States)

We introduce a framework for simulating the mesoscale self-assembly of block copolymers in arbitrary confined geometries subject to Neumann boundary conditions. We employ a hybrid finite difference/volume approach to discretize the mean-field equations on an irregular domain represented implicitly by a level-set function. The numerical treatment of the Neumann boundary conditions is sharp, i.e. it avoids an artificial smearing in the irregular domain boundary. This strategy enables the study of self-assembly in confined domains and enables the computation of physically meaningful quantities at the domain interface. In addition, we employ adaptive grids encoded with Quad-/Oc-trees in parallel to automatically refine the grid where the statistical fields vary rapidly as well as at the boundary of the confined domain. This approach results in a significant reduction in the number of degrees of freedom and makes the simulations in arbitrary domains using effective boundary conditions computationally efficient in terms of both speed and memory requirement. Finally, in the case of regular periodic domains, where pseudo-spectral approaches are superior to finite differences in terms of CPU time and accuracy, we use the adaptive strategy to store chain propagators, reducing the memory footprint without loss of accuracy in computed physical observables.

• OSTI ID: 22622223
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 327; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ACCURACY
BOUNDARY CONDITIONS
CALCULATION METHODS
COMPUTERIZED SIMULATION
COPOLYMERS
DEGREES OF FREEDOM
FIELD EQUATIONS
FIELD THEORIES
FOKKER-PLANCK EQUATION
GRIDS
INTERFACES
LOSSES
MEAN-FIELD THEORY
PERIODICITY
SELF-CONSISTENT FIELD
VELOCITY