Beyond Poisson-Boltzmann : strong correlations and extreme confinement in ionic fluids

Abstract

Understanding the electrostatic interactions of ions in the bulk and near electrified surfaces has been a fundamental question in physics for over a century since the "Poisson-Boltzmann" theory was first introduced. In this thesis, we study the bulk properties of ionic fluids in two important cases where the "Poisson-Boltzmann" theory fails: extreme confinement and strong ion-ion interactions. We first ask how ions behave when confined to a long and narrow tube. Recent advances in nanofabrication technology enabled us to make precise measurements in extremely narrow nanopores and revealed critical gaps in our understanding. A striking result of constraining ions to reside along a line is the exponentially long screening length that easily exceeds the macroscopic length of the pore, leading to electronetrality breakdown. Remarkably, this result has not been reported before, despite its fundamental consequences for ion transport and electrokinetic phenomena.

We build a general theoretical framework for electroneutrality breakdown in nanopores and show how it provides an elegant interpretation for the peculiar scaling observed in experimental measurements of ionic conductance in carbon nanotubes. Strong ion-ion correlations arise when the electrostatic interaction between neighboring ions is comparable to or greater than their thermal energy. This is most pronounced in ionic liquids, highly concentrated solvent-free electrolytes. While generally the Poisson-Boltzmann theory predicts monotonically decaying correlation function, ionic liquids have strong charge ordering and long-ranged charge oscillations. In this work, we show that the charges in ionic liquids are forming the optimal structure that minimizes the electrostatic energy, in the presence of strong positional distorter. We develop an approximated minimization scheme based on the Goemans-Williamson Max-Cut algorithm, adapted for a fully-connected graph with Coulombic interactions.

We demonstrate how the persistent layering structure exists due to partial ordering, which is maximized in ionic solids but gradually disappears with added solvent. Eventually, by adding solvent molecules or increasing the temperature, the system departs from its ground state and a mean-field description is more suitable. Finally, we study the regime of intermediate ionic strength using a non-local permittivity operator, which captures two important effects: ion-ion correlations and solvent structure. Our approach is phenomenological and introduces a small number of fitting parameters. We study the activity coefficients of bulk electrolytes in a wide range of ionic solutions and find that our models capture well the experimental data.