Counterion condensation and self-condensation of single polyelectrolytes

Systems of a charged flexible polyelectrolyte and associated counterions are studied by molecular dynamics simulations. As the strength of the electrostatic interaction is increased from zero, the mean square of the end-to-end distance, (R_e²), of the polyelectrolyte first increases and then decreases. The increase is caused by the repulsive electrostatic interaction between charged monomers of the polyelectrolyte. The screening of the repulsive interaction by counterions condensed onto the polyelectrolyte causes the decrease. Moreover, (R_e²) eventually becomes smaller than the value for the corresponding neutral chain, which signals the self-condensation of the polyelectrolyte. By determining the onset of the self-condensation of the polyelectrolyte using the condition (R_e²)/(R_g²) = 6, where (R _g²) denotes the mean square of the radius of gyration, we found that the self-condensation occurs when about 90% of the charge of the polyelectrolyte is neutralized by counterions. This observation agrees with the experimental results for DNA solutions.