Nonlinear screening of charged macromolecules.

We present several aspects of the screening of charged macromolecules in an electrolyte. After a review of the basic mean field approach, based on the linear Debye-Hückel theory, we consider the case of highly charged macromolecules, where the linear approximation breaks down and the system is described by the full nonlinear Poisson-Boltzmann equation. Some analytical results for this nonlinear equation give some interesting insight on physical phenomena like the charge renormalization and the Manning counterion condensation.