Lattice mean-field method for stationary polymer diffusion

We present a method to study mean-field stationary diffusion (MFSD) in polymer systems. When gradients in chemical potentials vanish, our method reduces to the Scheutjens-Fleer self-consistent field (SF-SCF) method for inhomogeneous polymer systems in equilibrium. To illustrate the concept of our MFSD method, we studied stationary diffusion between two different bulk mixtures, containing, for simplicity, noninteracting homopolymers. Four alternatives for the diffusion equation are implemented. These alternatives are based on two different theories for polymer diffusion (the slow- and fast-mode theories) and on two different ways to evaluate the driving forces for diffusion, one of which is in the spirit of the SF-SCF method. The diffusion profiles are primarily determined by the diffusion theory and they are less sensitive to the evaluation of the driving forces. The numerical stationary state results are in excellent agreement with analytical results, in spite of a minor inconsistency at the system boundaries in the numerical method. Our extension of the equilibrium SF method might be useful for the study of fluxes, steady state profiles and chain conformations in membranes (e.g., during drug delivery), and for many other systems for which simulation techniques are too time consuming.