STUDY OF POLYELECTROLYTES ADSORPTION ONTO HIGHLY CHARGED SURFACES

The interaction between polyelectrolytes and oppositely charged surfaces is a central topic in the Statistical Physics of Macromolecules and its study provides the fundamentals for understanding interactions involving proteins. It has been observed that varying the solution pH and ionic strength can lead to abrupt variations in measurable quantities sensitive to adsorption, such as turbidity, demonstrating behavior similar to a phase transition. In other studies using the Debye-Hückel approximation, the critical adsorption conditions onto flat, cylindrical, and spherical surfaces were obtained by solving the Edwards equation using the WKB method, leading to a suitable approach for all three geometries in conformity with experimental results using low-charged micelles. However, recent Monte Carlo simulations using approximate solutions of the non-linear Poisson-Boltzmann equation in highly charged surfaces indicated the emergence of a limiting value of ionic strength due to the non-linear dependence of the potential on the surface charge, beyond which adsorption does not occur. In this work, we employed the concept of renormalized charge and the WKB method to study the effects of this non-linearity on the critical adsorption conditions, density profile, and adsorbed layer of the polyelectrolyte segments in comparison with the Debye-Hückel approach. The renormalized charge makes it possible to use the known solutions obtained with the WKB method in the Debye regime for surfaces with high charge density, introducing a saturation effect observed in the non-linear case. The results obtained for the critical curve reproduce the limiting ionic strength for high charge densities with good agreement between the curves and recover the Debye-Hückel regime for low charges. The larger electrostatic screening also affects the density profile and adsorbed layer, promoting a dispersed distribution for higher values of surface charge.