Steady-state analysis of polymeradsorption at and transport across an interface between two polymer phases

Abstract

We consider a mutually incompatible polymer mixture composed of two major components A_N and B_N and a third minority component C_N. The interactions, parameterized by short-range Flory–Huggins interaction parameters, are chosen such that C wets the A/B interface completely at three-phase coexistence. At sub-saturated conditions the adsorption of C remains necessarily microscopic. We study such a system in a stationary off-equilibrium state: due to imposed chemical–potential gradients, polymer A_N diffuses from the A-rich bulk phase through the interface to the A-poor bulk phase. Polymer B_N travels in the opposite direction. Symmetric conditions are selected for which the polymer C_N that accumulates at the A/B-interface has no net flux in the stationary state. This system is described by the Mean Field Stationary Diffusion (MFSD) model, an approach that solves the Scheutjens–Fleer self-consistent-field (SF-SCF) equations with the boundary condition that the chemical potentials in the two bulk phases are different (but constant) so that a stationary state can be described. When the chemical potentials in the two bulk phases are the same, MFSD reduces to the equilibrium SF-SCF results. From the MFSD method we obtain the stationary volume fraction profiles and segmental fluxes. By forcing the system further from three-phase coexistence, i.e. by imposing larger concentration gradients, the adsorption of C goes unexpectedly from a thin adsorption layer to a thick adsorption film. The susceptibility ∂J_A/∂Δφ_A of the flux of A (equal to minus the flux of B) with respect to the imposed concentration gradient changes abruptly at the transition in adsorption behaviour. Interestingly, upon variation of the concentration gradients, the fluxes of A and B are enhanced by the accumulation of C at the interface. This means that the adsorbed C-film does not behave as an inert barrier.