Adsorption of a polyampholyte chain

We discuss the adsorption of a single polyampholyte chain on a planar solid surface carrying $\sigma$ charges per unit area. We consider the two cases where the interaction between the monomers and the surface is short range (strongly screened) and long range (unscreened). For short range interactions we use the replica trick and a Hartree approximation to show that the chain adsorbs even if it has the same net charge as the surface if the interaction potential is larger than a critical value $V_{\rm c} = {\rm Log}\, f/g$ where $f$ and $g$ are the fraction of monomers having respectively the same charge as the surface and the opposite charge. For long range interactions the adsorption is monitored by the electric field gradient existing in the vicinity of the surface. It occurs if the charge density of the surface is large enough $\sigma a\ell_{\rm B}>(f - g)/(f + g)^{1/2}$ where $a$ is the monomer size and $\ell\rm _B$ the so-called Bjerrum length