End Adsorption of Polymer Brushes

We study the adsorption of a polymer brush on a solid plate parallel to the plate where the chains are grafted in the limit where only the free-end monomers of the grafted chains adsorb. In the vicinity of the adsorbing plate, there exists a dead zone where no free chain ends are found; the monomer concentration is constant in this region and parabolic close to the grafting plate. In the absence of external force, the equilibrium distance between the two plates is smaller than the natural brush size. The fraction of chains forming bridges increases linearly with the adsorption energy at small adsorption energy and reaches one for a finite adsorption energy. The effect of an external force is also briefly discussed.