A three-state model for counterions in a dilute solution of weakly chargedpolyelectrolytes

In this paper we consider the influence of counterion distribution on the b ehavior of polyelectrolyte systems. We propose the unified model to describ e and to compare the swelling and collapse properties of single polyelectro lyte chains in dilute solutions, microgel particles of various molecular ma sses, and las a limiting case) macroscopic gels. A novel feature of the new approach is that we distinguish three possible states of counterions: free counterions inside and outside the polymer macromolecule and a bound state of counterions forming ion pairs with corresponding ions of polymer chains . The latter possibility becomes progressively important when macromolecule s or gels shrink. In this case the formation of a supercollapsed state is p ossible, when all counterions are trapped and form ion pairs. On the other hand, the fact that counterion scan float in the outer solution affects ess entially the conformation of polyelectrolyte chains in dilute solutions of good quality where practically all counter ions can escape the spae inside polymer coils and the repulsion between uncompensated charges plays an impo rtant role in the chain behaviour.