Charge density and bending rigidity of a rodlike polyelectrolyte: effects of multivalent counterions

We study line charge density and bending persistence length of a semiflexible polyelectrolyte rod typified by DNA in a z:1 electrolyte with or without pre-existing 1:1 salt. We use a wormlike chain model, where the effective Hamiltonian incorporates bending energy, as well as where the Coulomb interaction between charged segments is screened and mediated by the ions in the solution. By analytically evaluating the free energy associated with the contour undulation and charge density fluctuation affected by the adsorbed ions, we find renormalized mean line-charge-density and persistence length. Multivalent counterions bind to the polyelectrolyte more readily than monovalent counterions, due to electrostatic attraction dominant over the entropy. Also, our results show that at physiological conditions the electrostatic interaction gives no appreciable change on the persistence length from its bare value, against the implications of earlier studies. This is because the mean-field and charge fluctuation effects largely cancel each other in the rodlike conformation.