Attraction of like-charged macroions in the strong-coupling limit

TL;DR

This paper uses strong-coupling theory to analyze how like-charged macroions attract each other under different curvature conditions, revealing a universal unbinding transition for rods and a discontinuous transition for spheres.

Contribution

It applies the strong-coupling theory to curved macroions, introducing the Manning parameter to study curvature effects on electrostatic attraction and unbinding transitions.

Findings

Large Manning parameter leads to strong attraction and bound states.

Small Manning parameter results in macroion unbinding as volume increases.

Unbinding transition is continuous for rods and discontinuous for spheres.

Abstract

Like-charged macroions attract each other as a result of strong electrostatic correlations in the presence of multivalent counterions or at low temperatures. We investigate the effective electrostatic interaction between i) two like-charged rods and ii) two like-charged spheres using the recently introduced strong-coupling theory, which becomes asymptotically exact in the limit of large coupling parameter (i.e. for large counterion valency, low temperature, or high surface charge density on macroions). Since we deal with curved surfaces, an additional parameter, referred to as Manning parameter, is introduced, which measures the ratio between the radius of curvature of macroions to the Gouy-Chapman length and controls the counterion-condensation process that directly affects the effective interactions. For sufficiently large Manning parameters (weakly-curved surfaces), we find a strong long-ranged attraction between two macroions that form a closely-packed bound state with small surface-to-surface separation of the order of the counterion diameter in agreement with recent simulations. For small Manning parameters (highly-curved surfaces), on the other hand, the equilibrium separation increases and the macroions unbind from each other as the confinement volume increases to infinity. This occurs via a continuous universal unbinding transition for two charged rods at a threshold Manning parameter of 2/3, while the transition is discontinuous for spheres because of a pronounced potential barrier at intermediate distances.