Charge-Fluctuation Forces between Rodlike Polyelectrolytes: Pairwise Summability Reexamined

We formulate low-frequency charge-fluctuation forces between charged cylinders, parallel or skewed, in salt solution. At high-salt concentrations, forces are exponentially screened. In low-salt solutions, dipolar fluctuation energies go as $R^{-5\mathrm{}}$ or $R^{-4\mathrm{}}$; monopolar energies vary as $R^{-1\mathrm{}}$ or $\ln R$, where $R$ is the minimal separation between cylinder axes. The most important result is not the derivation of long-sought pair potentials but rather the demonstration that pairwise summability of rod-rod ion-fluctuation forces is easily violated under low-salt conditions.