Polymer adsorption in finite range surface potentials: Planar and spherical adsorbing surfaces

Abstract

We analytically solve the problem of the reversible adsorption of Gaussian polymers onto the planar and spherical surfaces in the presence of the square well attractive potential. By making use of the obtained exact solution of the Edwards equation, we calculate the end density and surface excess of the polymers at the planar and spherical substrates. We derive the exact equation that determines the surface bound states that give rise to the dominant contributions to the polymer surface excess. In the case of the spherical substrate, the exact expression for the polymer surface excess is obtained in the remarkably simple form of a quadratic function of the radius of the substrate. Using the calculated polymer surface excesses, we obtain the adsorption-desorption diagrams of the polymers adsorbed onto the spherical and planar surface in terms of the introduced “effectiveness” of the adsorption potential. By performing the analogous calculation based of the standard boundary condition approach, we demonstrate that this method overlooks the effect of the spatial interplay between the depletion and adsorption forces acting on the adsorbed polymers. Based on the comparison with the obtained exact solutions, we propose a modification of the boundary condition for the spherical substrate that preserves, in particular, the correct “protein” limit.