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

A universal description is presented for weak adsorption of flexible polyelectrolyte chains onto oppositely charged planar and curved surfaces. It is based on the WKB (Wentzel-Kramers-Brillouin) quantum mechanical method for the Green function equation in the ground state dominance limit. The approach provides a unified picture for the scaling behavior of the critical characteristics of polyelectrolyte adsorption and the thickness of the adsorbed polymer layer formed adjacent to the interface. We find, particularly at low-salt conditions, that curved convex surfaces necessitate much larger surface charge densities to trigger polyelectrolyte adsorption, as compared to a planar interface in the same solution. In addition, we demonstrate that the different surface geometries yield very distinct scaling laws for the critical surface charge density required to initiate chain adsorption. Namely, in the low-salt limit, the surface charge density scales cubical with the inverse Debye screening length for a plane, quadratic for an adsorbing cylinder, and linear for a sphere. As the radius of surface curvature grows, the parameter of critical chain adsorption onto a rod and a sphere turns asymptotically into that of a planar interface. The transition occurs when the radius of surface curvature becomes comparable to the Debye screening length. The general scaling trends derived appear to be consistent with the complex-formation experiments of polyelectrolyte chains with oppositely charged spherical and cylindrical micelles. Finally, the WKB results are compared with the existing theories of polyelectrolyte adsorption and future perspectives are outlined.