Numerical Simulation Of A Finite Element Method Of The Self-consistent Field Theory On General Curved Surfaces

Block copolymers are an important class of soft matter material,which can self-assemble into a variety of nanoscale ordered structure.The self-consistent field theory(SCFT)model has been proven to be a powerful tool for studying the selfassembly behavior of block copolymers.At present,many numerical methods have been developed to solve SCFT model in 2D and 3D space.However,most of these focus on the bulk systems,and only few work on the confined systems,especially the numerical algorithm for the SCFT model on general curved surfaces needs further study.In this work,based on the surface linear finite element method with strict mathematical theory and precision guarantee,a diblock copolymer system is taken as an example to develop an effective numerical method for solving the selfconsistent field theory of block copolymers on general curved surfaces.The method also includes an algorithm for adaptively adjusting the surface size,which can automatically optimize the surface size according to the ordered phase structure to obtain more accurate structure and energy.Numerical results illustrate the efficiency of the proposed method.More significantly,the proposed numerical framework can be applied to study the phase behaviors of block copolymers on general surfaces accurately.