Necklace globule and counterion condensation

We have developed a necklace model of polyelectrolyte chain in which the necklace structure appears as a result of the counterion condensation on the polyelectrolyte backbone. This necklace structure optimizes the correlation-induced attraction of the condensed counterions and charged monomers and electrostatic repulsion between uncompensated charges. The new feature of this necklace globule is that it can be formed even in good solvent conditions for the polymer backbone. By using the scaling analysis, we have calculated the diagram of state of polyelectrolyte chain as a function of the solvent quality for the polymer backbone and value of the Bjerrum length. To test the predictions of a scaling model, we have performed molecular dynamics simulations of polyelectrolyte chains with the degrees of polymerizations N = 124-304 and fraction of charged monomers f= 1/3 in good, theta, and poor solvent conditions for the polymer backbone. We have identified the range of parameters in which the necklace globule is formed due to correlation-induced attractive interactions in the good solvent conditions for the polymer backbone. The results of the molecular dynamics simulations are in qualitative agreement with the predictions of a scaling model.