**Title:** Model-free test of local density mean-field behavior in electric double layers

**Presenter:** Brian Giera

**Authors:** Brian Giera, Neil Henson, Edward Kober, Todd Squires, and M. Scott Shell

**Affiliation:** UC Santa Barbara

**Abstract:** Electric double layers (EDLs) form at all interfaces between charged surfaces (including electrodes, colloids, proteins, and cell membranes) and electrolytes or ionic liquids.
EDL structure governs the differential capacitance, electrokinetic flow, surface conductivity, capacitive desalination, and rational design of supercapacitors, for example. The standard
starting point to modeling EDLs are “local density approximations” (LDAs) that assume uncorrelated, bulk-like ion interactions to predict the spatial ion density profiles. LDAs are ubiquitous
in many fields, e.g., models of ionic liquids, ion distributions near liquid-liquid interfaces, and electrochemical cells, because they are simple yet physically insightful. Despite their
widespread use, numerous computations and experiments measure deviations from LDAs in a variety of electrochemical systems.

We present a general and powerful formalism to identify and elucidate LDA behavior in EDLs that follows from a remarkably simple observation: in any LDA, an ion does not know where the interface is located. Without assumptions, our approach enables one to analyze planar EDLs and determine directly from contact value expressions whether any LDA can possibly succeed, without considering any specific LDA models. If an LDA will work, measured profiles of the free charge density for many different electrolyte systems will collapse onto a single, master curve as a function of an intrinsic, derivable similarity variable. Where measured EDL profiles do not collapse, the test reveals the boundaries of LDA feasibility space, beyond which more sophisticated treatments capable of addressing correlation effects are needed.

We demonstrate this model-free test using extensive molecular dynamics simulations of EDLs with detailed ions and interactions in which LDAs are by no means guaranteed to work. Our model-free approach is broadly applicable to any planar EDL system and will be valuable in assessing potential LDA behavior in more general electrolytes, e.g. where solvation effects, emergent electrostatic correlations, and/or discrete interfacial charges play an important role.

Keywords: Molecular dynamics, Poisson-Boltzmann, electric double layer, mean-field, local density approximation