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

Abstract

A free-space density functional theory for polymer adsorption: Influence of packing effect on conformations of polymer J. Chem. Phys. 134, 044713 (2011); 10.1063/1.3533796Self-consistent field theory of polymer-ionic molecule complexation Erratum: "Density depletion profile and solvation free energy of a colloidal particle in a polymer solution" [J.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.

Adsorption of charged and neutral polymer chains on silica surfaces: The role of electrostatics, volume exclusion, and hydrogen bonding

“…where G(r,r ,N ) is a two-point Green's function that is proportional to the statistical weight of a polymer chain of length N with ends at positions r and r [28,29]. When applied to polymer chains, G is often referred to as chain propagator or chain order parameter [28,30,31].…”

“…(1) implicitly assumes that the polymer chains obey random walk statistics [28,31,33,34]. The general solution to the above equation can be written as a series of eigenfunctions [29]. For very long polymer chains the contribution of the ground-state eigenfunction dominates all other terms and the solution can be limited to the ground-state term.…”

“…In previous work on adsorption of neutral polymer chains and polyelectrolytes where the size of the polymer chains and the ions was not explicitly taken into account, the adsorption potential was assumed to be an infinitely sharp function at the surface [28][29][30]. Our choice of the adsorption potential in Eq.…”

Polymer Adsorption on Curved Surfaces: Finite Chain Length Corrections

“…One may show [27] that the next term in the expansion of the surface tension in eq 2.40 goes as ≃ −0.1540 ε 3/2 .…”

Self-Consistent Field Theory for the Distal Ordering of Adsorbed Polymer: Comparison with the Scheutjens−Fleer Model

“…Recently, a self-consistent field formalism was derived for weakly adsorbed polymers, valid for any chain length [21]. One notable difference from the classical ground state dominance result of de Gennes [1] is the distal ordering of the polymers; the finite chain length gives rise to oscillations on the scale of the radius of gyration away from the surface.…”