Algebraic Test of Material Conservation in Mean Field Theory of Polymers and the Use of Finite Volume Method

Abstract

The self-consistent field theory (SCFT) is one of the most successful theories explaining statistical behavior of polymers, and it has been especially powerful in predicting the nanostructures created by heterogeneous polymers. For the purpose of checking material conservation of various numerical methods used in SCFT, we develop an algebraic test using matrix and bra-ket notation, which traces the Hermiticity of the product of the volume and evolution operators. The algebraic test reveals that the popular pseudo-spectral method in the Cartesian grid conserves material perfectly. The story is more complicated for the real space SCFT methods but the use of finite volume method (FVM) is recommended in general. With the combination of FVM and alternating direction implicit method, accurate SCFT tools are developed and using them, calculations are performed for systems with irregular geometries.