A three-dimensional finite element methodology for addressing heterogeneous polymer systems with simulations based on self-consistent field theory

Abstract

We present a finite element code, which was developed to perform simulations based on self-consistent field theory considering three-dimensional domains of arbitrary geometry. The aim is to address systems comprising polymer melts in contact with solid surfaces and study their interfacial properties. The code solves the Edwards diffusion equation for both matrix and grafted (to the solid surface) chains by applying the appropriate initial and boundary conditions. Our approach for inserting the grafted chains does not require any smearing across the tangential directions to the solid substrate. Convergence is achieved by means of a simple mixing iterative scheme with respect to the self-consistent field. Bonded interactions along the polymer chain are described by the continuous Gaussian chain model. Considering a compressible polymer melt, the nonbonded interactions amongst polymer segments are calculated via Helfand's equation. All simulations are performed in the grand canonical ensemble.