Onsager-Manning-Oosawa condensation phenomenon and the effect of salt

TL;DR

This paper analytically investigates how salt influences the Onsager-Manning-Oosawa condensation phenomenon in charged polymers, providing explicit formulas for critical charge density, condensate thickness, and potential, highlighting salt's significant impact.

Contribution

It introduces analytical expressions for salt effects on condensation, extending previous no-salt models to include finite salt concentrations and asymmetric electrolytes.

Findings

Salt significantly alters the critical line charge density.

Explicit formulas for condensate thickness and electric potential are derived.

Finite salt effects are crucial for accurate modeling of the phenomenon.

Abstract

Making use of results pertaining to Painleve III type equations, we revisit the celebrated Onsager-Manning-Oosawa condensation phenomenon for charged stiff linear polymers, in the mean-field approximation with salt. We obtain analytically the associated critical line charge density, and show that it is severely affected by finite salt effects, whereas previous results focused on the no salt limit. In addition, we obtain explicit expressions for the condensate thickness and the electric potential. The case of asymmetric electrolytes is also briefly addressed.