# Bjerrum Pairs in Ionic Solutions: a Poisson-Boltzmann Approach

## TL;DR

This paper models the formation of Bjerrum pairs in ionic solutions using the nonlinear Poisson-Boltzmann equation, revealing their impact on dielectric properties, screening length, and surface interactions at higher concentrations.

## Contribution

It introduces a Poisson-Boltzmann framework to analyze Bjerrum pair formation and its effects on electrolyte properties, providing new insights into ion association phenomena.

## Key findings

- Bjerrum pairs reduce dielectric decrement with increasing ionic concentration.
- Pairs influence the Debye screening length and surface-force interactions.
- They decrease bulk ionic concentration and enhance attraction between charged surfaces.

## Abstract

Ionic solutions are often regarded as fully dissociated ions dispersed in a polar solvent. While this picture holds for dilute solutions, at higher ionic concentrations, oppositely charged ions can associate into dimers, referred to as Bjerrum pairs. We consider the formation of such pairs within the nonlinear Poisson-Boltzmann framework, and investigate their effects on bulk and interfacial properties of electrolytes. Our findings show that pairs can reduce the magnitude of the dielectric decrement of ionic solutions as the ionic concentration increases. We describe the effect of pairs on the Debye screening length, and relate our results to recent surface-force experiments. Furthermore, we show that Bjerrum pairs reduce the ionic concentration in bulk electrolyte and at the proximity of charged surfaces, while they enhance the attraction between oppositely charged surfaces.