Pull-off of a polyelectrolyte chain from an oppositely charged surface

The conformation at equilibrium of a single polyelectrolyte molecule adsorbed electrostatically at an ideal planar charged surface with one of its ends constrained at a distance $z$ from the surface is investigated using different theoretical methods, and in particular a scaling theory. The force $F$ $\mathrm{}\left(z\right)\mathrm{}$ applied at the fixed end of the chain is calculated. Exact results are obtained for a Gaussian chain when all screening effects are negligible, and at high salt concentration, using a self-consistent field theory. When the salt concentration is large enough, the force profile $F\left(z\right)\mathrm{}$ reaches a plateau where the force is independent of chain length. When the electric field is screened by the counterions, a pseudoplateau is obtained, where the force increases logarithmically with $z.\mathrm{}$ The chain leaves the surface before it is fully extended, although the distance of detachment from the surface is proportional to the number of monomers $N.\mathrm{}$ The electrostatic interactions between the charged monomers of the polyelectrolyte chain can be taken into account using scaling arguments.