Rod-like polyelectrolyte adsorption onto charged surfaces in monovalent and divalent salt solutions

We analyze the adsorption of strongly charged polyelectrolytes onto weakly charged surfaces in divalent salt solutions. We include short-range attractions between the monomers and the surface and between condensed ions and monomers, as well correlations among the condensed ions. Our results are compared with the adsorption in monovalent salt solutions. Different surface charge densities (σ), and divalent (m) and monovalent (s) salt concentrations are considered. When the Wigner-Seitz cells diameter (2R) is larger than the length of the rod, the maximum amount of adsorption scales like n _max ∼ σ ^4/3 in both monovalent and divalent Solutions. For homogeneously charged surfaces, the maximum adsorption occurs at s* ∼ σ ² when s* > φ, where φ is the monomer concentration, the counterpart for divalent salt solution, m* roughly scales as σ ^2.2 when m* > φ. The effective surface charge density has a maximum absolute value at m' < m*. A discrete surface charge distribution and short-range attractions between monomers and surface charge groups can greatly enhance surface charge inversion especially for high salt concentration. The critical salt concentration for adsorption in divalent salt solution roughly scales as m _c ∼ bσ ^1.9, where b is the distance between two neighboring charged monomers.