Adsorption of a polyelectrolyte chain to a charged surface

The criteria for the adsorption of a polyelectrolyte chain in a salt solution on a uniformly charged planar membrane are derived using mean field arguments. Explicit formulas are obtained to describe the adsorption characteristics for varying surface charge density, charge on the polymer, Debye screening length κ−1, chain length L, and temperature T. The adsorption can be tuned using any one of these parameters. When T is the tuning variable, for example, the chain is adsorbed at T<Tc, where Tc is proportional to κ−3L−1 and κ−11/5L−1/5 in the weak and strong Coulombic screening limits, respectively. The thickness of the adsorbed layer is derived to vary linearly with κ−1 ln(Tc /T) for T<Tc.