Annealed and Quenched Polyelectrolytes

We study theoretically the behaviour of two types of polyelectrolytes in a poor solvent. If the number of charges and their position along the chain is quenched, the collapse is well described by a blob model introduced by Khokhlov. Weak polyacids or polybases have however an annealed structure where the charges are “mobile” along the chain. We show that these polymers undergo a discontinuous charge instability between a small-charge globular state and a high-charge extended state. This could explain several titration and viscometric data. At higher concentration, the electrostatic interaction is more screened for annealed than for quenched polyelectrolytes.