Counterion distribution around the strongly stretched polyelectrolyte chains: from single molecules to hydrogels

Using all-atom molecular dynamics simulations of a polyacrylic acid chain in explicit water as a model system, we calculated the counterion distribution and condensation profiles around the stretched (weak) polyelectrolyte chains. The condensation under deformation is highly non-monotonic. Ionic condensation around the chain increases as the chain is stretched strongly up until its contour length. This increase reaches a maximum and decreases as the chain is stretched beyond its counter length. A Manning-type condensation behavior can explain the latter case. However, in moderate stretching, condensation changes with solvent distribution around the chain. If chains are crosslinked by their ends to form a polyelectrolyte hydrogel, this unexpected stretch-dependent phenomenon leads to a deformation-dependent counterion condensation in the polyelectrolyte hydrogel. Our results suggest that counterion condensation around polyelectrolytes can exhibit a rich behavior of electrostatic response under deformation.