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Effect of chain stiffness on ion distributions around a polyelectrolyte in multivalent salt solutions

Ion distributions in dilute polyelectrolyte solutions are studied by means of Langevin dynamics simulations. We show that the distributions depend on the conformation of a chain while the conformation is determined by the chain stiffness and the salt concentration. We observe that the monovalent counterions originally condensed on a chain can be replaced by the multivalent ones dissociated from the added salt due to strong electrostatic interaction. These newly condensed ions give an important impact on the chain structure. At low and at high salt concentrations, the conformation of a semiflexible chain is rodlike. The ion distributions show similarity to those for a rigid chain, but difference to those for a flexible chain whose conformation is a coil. In the mid-salt region, the flexible chain and the semiflexible chain collapse but the collapsed chain structures are, respectively, disordered and ordered structures. The ion distributions hence show different profiles for these three chain stiffness with the curves for the semiflexible chain lying between those for the flexible and the rigid chains. The number of the condensed multivalent counterions, as well as the effective chain charge, also shows similar behavior, demonstrating a direct connection with the chain morphology. Moreover, we find that the condensed multivalent counterions form triplets with two adjacent monomers and are localized on the chain axis at intermediate salt concentration when the chain stiffness is semiflexible or rigid. The microscopic information obtained here provides valuable insight to the phenomena of DNA condensation and is very useful for researchers to develop new models.