Adsorption of Polymer Solutions onto a Flat Surface

Abstract

We present a theoretical description of polymer adsorption from solution which is based on a mean field approximation but which goes beyond the standard ground state dominance approximation. The properties of the adsorbed polymer chains are described by two coupled order parameters. This allows a description of the chains in terms of tails and loops. When the bulk solution is dilute, the adsorbed polymer layer has a double layer structure with an inner layer dominated by loops and an outer layer dominated by tails. Explicit asymptotic forms are found for the monomer concentration profile and for the crossover distance between the loops and tail regions. The precise concentration profile is obtained by a numerical solution of two coupled differential equations. One of the surprising results is that the total polymer adsorbed amount has a nonmonotonic variation with molecular weight and decreases for large values of the molecular weight. The concentration profiles are also determined when the bulk solution is semidilute or concentrated. At any bulk concentration, the monomer concentration has a nonmonotonic variation with the distance to the adsorbing wall and shows a minimum at a finite distance. This depletion effect can be significant in the vicinity of the crossover between dilute and semidilute solutions. All the results are in agreement with the existing numerical solutions of the complete mean field theory of polymer adsorption. Excluded volume correlations are taken into account by constructing scaling laws for polymers in a good solvent both in dilute and in semidilute solutions.

Theoretical Study of Comb Polymers Adsorption on Solid Surfaces

“…These partition functions are discussed in Appendix C. The expressions (19) for the loops and tails contributions to the total monomer volume fraction for a triblock copolymer of N ∼ N B monomers are the same as the one found for the adsorption of a linear polymer chain of N B monomers. For the side-chains monomer volume fraction Φ TB sc (z), one finds (see Fig.5):…”

“…(18), (19) and (20)), one can calculate the correction to the surface coverage (of backbone monomers) due to the side-chains:…”

“…Our analysis is based on the idea of describing the combs as linear chains having 'triblock copolymers' as renormalized monomers (see is a solution of the so-called Edwards equation [17,19]:…”

Polymer Adsorption on Curved Surfaces: Finite Chain Length Corrections

“…In order to account for the finiteness of the polymer chain length, a second order parameter, ϕ(z), was introduced [20] connected to the description of chain ends. To understand better the physical origin of this term, consider a polymer chain with at least one segment touching the surface.…”

“…The profiles of the two order parameters, ψ(z) and ϕ(z), are determined by the following set of Edwards-like equations [20]:…”