Self-consistent field theory simulations of polymers on arbitrary domains

JOURNAL OF COMPUTATIONAL PHYSICS

卷:327

Article

Ouaknin, Gaddiel¹  Laachi, Nabil³  Delaney, Kris³  Fredrickson, Glenn H.^3,4,5  Gibou, Frederic^1,2 

[1] Univ Calif Santa Barbara, Dept Mech Engn, Santa Barbara, CA 93106 USA

[2] Univ Calif Santa Barbara, Dept Comp Sci, Santa Barbara, CA 93106 USA

[3] Univ Calif Santa Barbara, Mat Res Lab, Santa Barbara, CA 93106 USA

[4] Univ Calif Santa Barbara, Dept Chem Engn, Santa Barbara, CA 93106 USA

[5] Univ Calif Santa Barbara, Dept Mat, Santa Barbara, CA 93106 USA

关键词: SCFT;    Neumann boundary conditions;    Sharp boundary conditions;    Quad-/Oc-tree;    Parallel computing;    Fokker-Planck;    Level set;   

DOI  :  10.1016/j.jcp.2016.09.021

来源: Elsevier

【 摘 要 】

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 pseudospectral 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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free