Critical adsorption and charge reversal in polyelectrolyte solutions: Analytical mean-field theory

An analytical linearized mean-field theory is presented to describe the adsorption behavior of polyelectrolytes near charged colloidal surfaces with additional short-ranged non-electrostatic interactions. The coupling between the polyelectrolyte segment density and electrostatic potential is explicitly accounted for in a self-consistent manner. This coupling gives rise to highly non-linear behavior, such as oscillations of the electrostatic potential. We derive analytical expressions for the critical surface charge density σ_c, after which adsorption takes place, and recover the well-known σ c ∼ n s 3 / 2 scaling regime, where n_s is the salt concentration. In addition, the theory yields a new n s 1 scaling regime if the surface is hard and a unified n s 1 scaling regime if the surface also possesses some short-ranged attraction with the polyelectrolyte. Furthermore, we derive an analytical expression to describe the critical polyelectrolyte concentration φ_c to achieve complete charge reversal, which is found to scale as φ_c ∼ σ²/(f²c²), where c is related to the magnitude of short-ranged interactions and f is the average charge per monomer of the polyelectrolyte. It is observed that within our theory, complete charge reversal can only take place if the short-ranged interactions are sufficiently strong to completely compensate for the entropy loss of adsorption.