Inflation of the screening length induced by Bjerrum pairs

Abstract

Within a modified Poisson–Boltzmann theory we study the effect of Bjerrum pairs on the typical length scale 1/¯κ over which electric fields are screened in electrolyte solutions, taking into account a simple association–dissociation equilibrium between free ions and Bjerrum pairs. At low densities of Bjerrum pairs, this length scale is well approximated by the Debye length 1/κ ∝ 1/ √ ρs, with ρs the free-ion density. At high densities of Bjerrum pairs, however, we find 1/¯κ ∝ √ ρs, which is significantly larger than 1/κ due to the enhanced effective permittivity of the electrolyte, caused by the polarization of Bjerrum pairs. We argue that this mechanism may explain the recently observed anomalously large colloid-free zones between an oil-dispersed colloidal crystal and a colloidal monolayer at the oil–water interface.