On the collapse of weakly charged polyelectrolytes

The behaviour of weakly charged polyelectrolytes in a poor salt-free solution is considered, using the notion of blobs. It is shown that in a very dilute solution, where different polyions do not overlap, a transition of the coil-globule type takes place, upon making poorer the thermodynamic quality of the solvent. This transition occurs in each blob separately. In the region of higher concentrations (the polyions overlap strongly, but the volume fraction occupied by the blobs in the solution is small) an additional effect is predicted: avalanche-type counter-ion condensation. This effect is due to the fact that the polyelectrolyte conformation varies self-consistently, together with the variation of the number of condensed counter ions.