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.

Rates of the colloid coagulation in the presence of irreversibly adsorbing and non‐adsorbing polymers

“…The excess (over the bulk) grand potential ΔΩ can be shown [12, 13] to be equivalent to the negative of the depletion potential V D . In the considered limit of long polymers N >>1, ΔΩ is given [9, 14] by a simple expression of the form Substituting ρ given by Eq 8 into Eq 9, one finds where ${\phi_{\rm{p}}} = {{4\pi \rho_b R_{\rm{G}}^3} \over {3N}}$ is the polymer volume fraction and the parameter v equals to 0.5. Note that the above value of the parameter v = 0.5 is inherited from the simple Gaussian gradient representation of the entopic part of the polymer free energy.…”

Analytic theory of the interactions between nanocolloids mediated by reversibly adsorbed polymers

“…(3) specific to the considered spherical geometry has been derived in Ref. [12] upon analyzing the solution of the Edwards equation given by…”

Polyelectrolyte adsorption onto oppositely charged interfaces: unified approach for plane, cylinder, and sphere

“…77,78 All these interesting and motivating features are, however, beyond the scope of this study. Their potential impact on the scaling characteristics of the PE critical adsorption transition and the thickness of the PE adsorbed layers in the three fundamental adsorption geometries is yet to be quantified in future theoretical studies.…”