Charge Fluctuation Forces Between Stiff Polyelectrolytes in Salt Solution: Pairwise Summability Re-examined

TL;DR

This paper examines charge-fluctuation forces between stiff polyelectrolytes in salt solutions, highlighting how screening and salt concentration affect force behavior and questioning the applicability of pairwise summation in low-salt conditions.

Contribution

It re-examines the pairwise summability of charge-fluctuation forces between polyelectrolytes, emphasizing limitations in low-salt environments and clarifying the conditions under which derived expressions are valid.

Findings

Forces are exponentially screened at high salt concentrations.

Dipolar energies decay as R^{-5} or R^{-4} in low-salt solutions.

Pairwise summability can be violated in low-salt conditions.

Abstract

We formulate low-frequency charge-fluctuation forces between charged cylinders - parallel or skewed - in salt solution: forces from dipolar van der Waals fluctuations and those from the correlated monopolar fluctuations of mobile ions. At high salt concentrations forces are exponentially screened. In low-salt solutions dipolar energies go as $R^{-5}$ or $R^{-4}$; monopolar energies vary as $R^{-1}$ or $\ln{R}$, where $R$ is the minimal separation between cylinders. However, pairwise summability of rod-rod forces is easily violated in low-salt conditions. Perhaps the most important result is not the derivation of pair potentials but rather the demonstration that some of these expressions may not be used for the very problems that originally motivated their derivation.