Adsorption of water soluble ionic/hydrophobic diblock copolymer on a hydrophobic surface

We consider the adsorption of a A-B diblock copolymer on a planar hydrophobic surface in aqueous solution. The hydrophobic anchor (A) block is envisioned to avoid water and adsorbs on the solid-liquid interface in a collapsed state. The buoy block (B) is a polyelectrolyte which expands in solution and forms a brush whose structure depends strongly on the ionic strength of the solution. The minimization of the grand canonical free energy of the system gives access to the surface density (σ), the thickness of the collapsed layer (L_A) and the thickness of the external polyelectrolyte layer (L_B). These three parameters L_B, L_A and σ are functions of the molecular weight of the anchored block (N_A), the molecular weight of the buoy block (N_B), the charge of the polymer (Z) and the ionic strength of the aqueous solution (∅_s).