Effect of nonzero chain diameter on “DNA” condensation

We present a simple model to investigate the effect of chain diameter on multivalent-counterion-induced attractions between two charged chains. In our minimal model, the chains are rigid rods of diameter D with a uniform charge density on the surface, and the counterions are point ions. As a function of the separation between two rods, we find a repulsive barrier in the free energy whose height increases with D. We have also explored the effect of counterion valency Z on the interaction. For parameters characteristic of DNA, we find that a minimum valency of Z=3 is required to produce condensation. We also find that the shape of the potential is fairly insensitive to Z for Z>~3. These results are consistent with experimental observations of DNA condensation.