Self-consistent field theory simulations of polymers on arbitrary domains

• Published in: Journal of computational physics Vol. 327; pp. 168 - 185
• Main Authors: Ouaknin, Gaddiel, Laachi, Nabil, Delaney, Kris, Fredrickson, Glenn H., Gibou, Frederic
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 15.12.2016; Elsevier Science Ltd
• Subjects: ACCURACY; Block copolymers; BOUNDARY CONDITIONS; Boundary layers; CALCULATION METHODS; Coding; Computational physics; Computer memory; Computer simulation; COMPUTERIZED SIMULATION; CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; COPOLYMERS; DEGREES OF FREEDOM; FIELD EQUATIONS; FIELD THEORIES; Field theory; FOKKER-PLANCK EQUATION; Fokker–Planck; Galling; GRIDS; INTERFACES; Level set; LOSSES; MEAN-FIELD THEORY; Memory; Neumann boundary conditions; Parallel computing; PERIODICITY; Quad-/Oc-tree; SCFT; Self-assembly; SELF-CONSISTENT FIELD; Sharp boundary conditions; Simulation; Studies; VELOCITY; Parallel computing; Level set; Sharp boundary conditions; Fokker–Planck; Quad-/Oc-tree; Neumann boundary conditions; SCFT
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2016.09.021

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.