Unconditionally Stable Algorithm for Copolymer and Copolymer-Solvent Systems

In the time evolution simulation of a copolymer system towards its equilibrium configuration, it is common to use the Otha-Kawasaki approach for free energy and time evolution by means of a Cahn-Hilliard diffusion equation. The conventional numerical resolution is to use the cell dynamics simulation method (CDS). Although this method gives an adequate response, it is limited since it needs very small time steps to present both appropriate resolution and stability. Recently, unconditionally stable methods have been used in gradient systems that provide adequate resolution and stability with a greater time step in solving Cahn-Hilliard equations. In this paper, we develop and implement unconditionally stable algorithms for copolymer-solvent systems and for the resolution of the time evolution of block copolymer systems under the Otha-Kawasaki functional.