Counterion-mediated, non-pairwise-additive attractions in bundles of like-charged rods

Stiff polyelectrolyte chains, such as DNA, can attract each other in solution even though they have the same sign of charge. The attractions are mediated by multivalent counterions, which lead to an effective interaction at the two-chain level that is attractive at short range and repulsive at long range. However, the effective interchain interactions are not pairwise additive. We present a formulation that allows theoretical treatment of the many-chain problem without assuming pairwise additivity. We show that a bundle of chains held together by counterion-mediated attractions can be described in terms of a bulk and surface free energy, and discuss the temperature dependence of the attraction.