Temperature effects on threshold counterion concentration to induce aggregation of fd virus

We seek to elucidate the dominant mechanism of attractive interaction between like-charged biopolymers by measuring the temperature dependence of the critical divalent counterion concentration (Cc) for the aggregation of fd viruses. A decrease in either temperature or the dieletric constant alone causes a decrease in Cc, providing evidence for the Wigner crystal model. Surprisingly, the effects of these two parameters can be combined so that Cc is expressed as a function of a single parameter: the Bjerrum length. Cc decreases exponentially as the Bjerrum length increases, suggesting that an energetic balance between the entropic effect of counterions and the counterion mediated attractive interaction gives rise to the onset of bundle formation.