Inflation of the screening length induced by Bjerrum pairs

Within a modified Poisson-Boltzmann theory we study the effect of Bjerrum pairs on the typical length scale $1/\bar{\kappa}$ 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 $1/\kappa\propto 1/\sqrt{\rho_\mathrm{s}}$, with $\rho_\mathrm{s}$ the free ion density. At high densities of Bjerrum pairs, however, we find $1/\bar{\kappa}\propto \sqrt{\rho_\mathrm{s}}$ which is significantly larger than $1/\kappa$ 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.