Critical adsorption of polyelectrolytes onto highly oppositely charged surfaces: Effects of charge renormalization

The critical adsorption conditions of polyelectrolytes (PEs) onto planar, cylindrical, and spherical surfaces were obtained by solving the Edwards equation using the Wentzel-Kramers-Brillouin (WKB) method. It demonstrated to provide a suitable analytical approach for all three geometries, in conformity with some experimental results for weakly charged micelles. However, our Monte Carlo simulations implementing approximate solutions of the nonlinear Poisson-Boltzmann equation for highly charged surfaces indicated recently the emergence of a limiting value of ionic strength due to a nonlinear dependence of the electrostatic (ES) potential on the surface-charge density σ. Beyond this limiting ionic strength, the PE adsorption no longer occurs, shifting the standard paradigm. In this work, we employ the concept of a renormalized charge and use the WKB method to study the effects of this nonlinearity on the critical adsorption conditions, density profile, and adsorbed layer of PE segments, all in comparison with the results of the linear Debye-Hückel (DH) approach. Charge renormalization makes it possible to use the known WKB solutions in the DH regime also for surfaces with high σ, introducing a saturation effect observed in the nonlinear case. The larger ES screening affects the density profile and the adsorbed layer of PEs, promoting a more dispersed distribution of PEs at higher surface-charge densities. Our analytical results for the critical adsorption curve reproduce the limiting ionic strength for high σ and also recover the DH regime at low σ.