Polyelectrolyte Knot Delocalization Induced by Counterion Condensation

Knots on ring polymers tend to be tight. For knots on charged polymers (polyelectrolytes), electrostatic repulsion among the monomers is considered to enhance the persistence length and further localize the knots. However, the effects of counterion condensation on knots behavior are not clear. Here we use molecular dynamics simulations to systematically study the effect of counterion condensation on the knot behavior under different electrostatic strength and solvent quality conditions, with the focus on the knot sizes. We show that generally counterion condensation \emph{delocalizes} the knots in systems with strong electrostatic strength. At small to intermediate electrostatic strength, the knot size and overall chain size and can be positive correlated or negative correlated, as a result of the interplay between electrostatic correlation and solvent quality.