Free energy formalism for polymer adsorption: Self-consistent field theory for weak adsorption

Abstract

Polymer adsorption has been widely investigated in the context of self-consistent mean-field theories. As a further simplification, the “ground state dominance approximation” is often made, treating the polymer chains as infinitely long. For short polymers, or not so concentrated polymer solutions, corrections to ground state dominance may be important, however. In this work, we discuss analytical solutions to the full self-consistent field equations, valid for any chain length, in the limit of weak adsorption. We show how the resulting equations may be put into a free energy functional formalism, in analogy to the de Gennes–Lifshitz free energy for infinitely long polymer chains. Analytical expressions are derived for polymer density profiles, surface tension and the interaction potential between two planar, polymer-adsorbing surfaces. Particular attention is paid to the distal ordering of the polymer coils that shows up as oscillations in the polymer density profile and interaction potential at the scale of the polymer’s radius of gyration.