Investigation of structural frustration in symmetric diblock copolymers confined in polar discs through cell dynamic simulation

Abstract

Nanotechnology has opened new avenues for advanced research in various fields of soft materials. Materials scientists, chemists, physicists, and computational mathematicians have begun to take a keen interest in soft materials due to their potential applications in nanopatterning, membrane separation, drug delivery, nanolithography, advanced storage media, and nanorobotics. The unique properties of soft materials, particularly self-assembly, have made them useful in fields ranging from nanotechnology to biomedicine. The discovery of new morphologies in the diblock copolymer system in curved geometries is a challenging problem for mathematicians and theoretical scientists. Structural frustration under the effects of confinement in the system helps predict new structures. This mathematical study evaluates the effects of confinement and curvature on symmetric diblock copolymer melt using a cell dynamic simulation model. New patterns in lamella morphologies are predicted. The Laplacian involved in the cell dynamic simulation model is approximated by generating a 17-point stencil discretized to a polar grid by the finite difference method. Codes are programmed in FORTRAN to run the simulation, and IBM open DX is used to visualize the results. Comparison of computational results with existing studies validates this study and identifies defects and new patterns.