(19a) Theory of Overscreening at Charged Surfaces

The electrical double layer underlies the electrochemical properties of charged interfaces in colloidal dispersions, electrochemical energy storage devices, desalination membranes, and biological media. Even so, the layered structuring of ionic charges and polar solvent molecules in the electrical double layer is not captured by common classical continuum theories that assume dilute point ionic charges in a constant dielectric constant medium. In particular, the phenomenon of overscreening, corresponding to alternating layers of positive and negative screening charge, is central to the interfacial structure of concentrated electrolytes and ionic liquids, as well as for the local interfacial dielectric properties of polar liquids such as water.

Here, we report a continuum weighted-density theoretical approach that can mathematically capture the overscreening phenomenon in polar liquids, concentrated electrolytes, and ionic liquids. The theory reproduces the oscillatory charge ordering of ionic liquids at interfaces, as well as the interfacial dielectric properties of polar liquids, both consistent with reported molecular dynamics simulations. We highlight the implications for capacitance at charged interfaces and oscillatory surface forces for a nanoconfined fluid between two charged surfaces. For dilute electrolytes, the local solvent structuring leads to molecular oscillations that decay over a nanometric hydration length. In the opposite limit of highly concentrated electrolytes and ionic liquids, decaying oscillations of alternating ionic charge emerge from the theory. We present simple analytical formulas for the charge screening length, the hydration length, and density decay lengths in the limit of low and high ionic concentrations that depend on the molecular properties of the solvent and ions. The continuum theory successfully describes the main qualitative features of layered interfacial structures at charged interfaces and may be useful to interpret surface force apparatus and electrochemical measurements.