  This chapter deals with charged polymers (polyelectrolytes) in solution and
at surfaces. The behavior of polyelectrolytes is markedly different from that
of neutral polymers. In bulk solutions, i.e. disregarding the surface effect,
there are two unique features to charged polymers: first, due to the presence
of long-ranged electrostatic repulsion between charged monomers, the polymer
conformations are much more extended, giving rise to a very small overlap
concentration and high solution viscosity. Second, the presence of a large
number of counter-ions increases the osmotic pressure of polyelectrolyte
solutions, making such polymers water soluble as is of great importance to many
applications. At surfaces, the same interplay between monomer-monomer repulsion
and counter-ion degrees of freedom leads to a number of special properties. In
particular, the adsorption behavior depends on both the concentration of
polymers and added salt in the bulk. We first describe the adsorption behavior
of single polyelectrolyte molecules, and discuss the necessary conditions to
obtain an adsorbed layer and characterize its width. Depending on the stiffness
of the polyelectrolyte, the layer can be flat and compressed or coiled and
extended. We then proceed and discuss the adsorption of polyelectrolytes from
semi-dilute solutions. Mean-field theory profiles of polyelectrolyte adsorption
are calculated as function of surface charge density (or surface potential),
the amount of salt in the system and the charge fraction on the chains. The
phenomenon of charge inversion is reviewed and its relevance to the formation
of multilayers is explained. The review ends with a short overview of the
behavior of grafted polyelectrolytes.
