Collapse of polyelectrolyte macromolecules revisited

The simplest theory of the collapse transition of single polyelectrolyte chains in dilute solutions is reconsidered. A novel feature of the new treatment is that the counterions can either remain within the coil or float in the outer solution. It is shown that the latter possibility is realized in many cases; thus, for these situations, the electrostatic repulsion between the uncompensated charges plays an important role in the chain behavior. These uncompensated charges lead to a significant difference between the collapse behavior of single chains and macroscopic gels where electrostatic repulsion is normally negligible and the swelling is mainly due to the osmotic pressure of counterions kept inside the gel sample. In addition the intermediate case of microgel particles of different molecular masses is considered, and the role of counterion redistribution between polymer and solution is investigated.