An electrical double layer is an interface between a charged surface and a salt solution, and understanding its structure is crucial to explain numerous phenomena associated with electrochemistry, biophysics, and colloidal science. The classical mean-field Poisson-Boltzmann (PB) theory for electrical double layers is physically intuitive and numerically soluble; however, it only works for monovalent salts, low surface charges, and low salt concentrations. The reason is that it does not account for three essential factors: spatial ion-ion correlations, dielectric variation, and excluded volumes of ions and solvent. In this talk, I will present a new theory titled "Modified Gaussian Renormalized Fluctuation Theory” to account for these missing factors. This theory is a multiscale approach as the final continuum level equations are derived rigorously from molecular level force and density operators using rigorous statistical mechanics. The theory is self-consistent in the sense that it does not use any phenomenological parameters or unphysical approximations.We will present the application of this theory in the context of two unsolved problems: vapor-liquid coexistence in ionic fluids and reversal in the sign of ionic current in charged nanochannels. In the case of vapor-liquid coexistence, our theory can predict both the bulk phase coexistence curve and interfacial tension between the two phases with quantitative accuracy. For the second problem, our theoretical predictions of ionic current as a function of multivalent salt concentration are also in quantitative agreement with experimental measurements. Our work is the first in the literature to solve these two problems. Finally, since our theory is derived using a field-theoretical approach, it is straightforward to incorporate into other field-theoretical formulations, such as self-consistent field theory for polymers or Poisson-Nernst-Planck equation for electrokinetic flows.
