Electrokinetics of correlated electrolytes and ionic liquids Martin Z. Bazant Departments of Chemical Engineering and Mathematics Massachusetts Institute of Technology Brian D. Storey Olin College

Ionic liquids Molten salts (T~1000 o C) Room temperature IL Supercapacitors Batteries Actuators –Large ions (~1 nm) –No solvent. What is permittivity? –Ion-ion correlations ( ) –Ion size = 10 x Debye length –Capacitance data often interpreted through classic electrolyte model. BMIM wikipedia

At equilibrium: Chemical potential of dilute point ions: Applied voltage =.025 V Applied voltage =0.75 V Would need ions to be 0.01 angstrom Classical double layer theory

Finite sized ions Stern (1924) Bikerman (1942) Bazant, Kilic, Storey, Ajdari – ACIS 2009 Volume fraction

All mean-field theories 1. Electrochemistry 2. Electrostatics 3. Flow Same “mean electric field” in all equations

“Ginzburg-Landau” theory for ionic liquids

“In physics, Ginzburg–Landau theory, named after Vitaly Lazarevich Ginzburg and Lev Landau, is a mathematical theory used to model superconductivity. It does not purport to explain the microscopic mechanisms giving rise to superconductivity. Instead, it examines the macroscopic properties of a superconductor with the aid of general thermodynamic arguments.” --- wikipediaphysics Vitaly Lazarevich GinzburgLev Landausuperconductivitythermodynamic “Ginzburg-Landau” theory for ionic liquids

chemical free energy mean electrostatic energy self energy of E field electrostatic correlations (new) Require 4 th order modified Poisson-Boltzmann eqn “Ginzburg-Landau” theory for ionic liquids

Is this crazy? Maybe not… Wavelength-dependent permittivity (Tosi 1986, molten salts) “Intermediate coupling” in one-component plasma (Santangelo 2006; Hatlo, Lue statistical mechanics of point-like counterions near a wall) Nonlocal dielectric response (Kornyshev et al 1978, Hildebrandt et al 2004) Nonlocal ion-ion correlations (this work)

RTIL double-layer structure charge density at V=1,10,100 kT/e

This model vs. MD simulations Fedorov, Kornyshev 2009 Solid: this model, Open: MD

RTIL differential capacitance This model MD Simulations (Fedorov & Kornyshev, 2008) No correlations, but includes size effects (Fedorov & Kornyshev, 2008)

Correlated electrolytes high valence, high concentration 1M 2:1 salt Boda et al 2002 MC simulations -

Comparison to DFT 2:1 salt This model No corr.

Comparison to DFT 2:1 salt DFT of Gillespie et al, 2011 This model DFT No corr.

Slip velocity 2:1 salt C=1M C=0.1M C=0.01M

Comparison to experiment 2:1 salt Van der Heyden 2006 nanochannel experiments

Conclusions Electrostatic correlations lead to overscreening, which competes with crowding in ionic liquids and concentrated, multivalent electrolytes Correlations may explain reduced/reversed electro-osmotic flow at high concentration and enhanced capacitance of nanopores A simple continuum model is proposed

Capacitance 2:1 salt C=1M C=0.1M C=0.01M This model Size effects Included, no corr. Correlations might explain why mean field theories need large ions to fit exp.

Overscreening vs. crowding MZ Bazant, BD Storey, AA Kornyshev, Phys. Rev. Lett. (2011)

Boundary conditions Electrostatic BC (no correlations) Neglect “bulk” correlations (finite size ions)

Concentration profiles 2:1 salt, 1M, a=0.3 nm kT/e

RTIL double-layer structure