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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
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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
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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
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Finite sized ions Stern (1924) Bikerman (1942) Bazant, Kilic, Storey, Ajdari – ACIS 2009 Volume fraction
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All mean-field theories 1. Electrochemistry 2. Electrostatics 3. Flow Same “mean electric field” in all equations
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“Ginzburg-Landau” theory for ionic liquids
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“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
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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
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Is this crazy? Maybe not… Wavelength-dependent permittivity (Tosi 1986, molten salts) “Intermediate coupling” in one-component plasma (Santangelo 2006; Hatlo, Lue 2010 --- 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)
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RTIL double-layer structure charge density at V=1,10,100 kT/e
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This model vs. MD simulations Fedorov, Kornyshev 2009 Solid: this model, Open: MD
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RTIL differential capacitance This model MD Simulations (Fedorov & Kornyshev, 2008) No correlations, but includes size effects (Fedorov & Kornyshev, 2008)
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Correlated electrolytes high valence, high concentration 1M 2:1 salt Boda et al 2002 MC simulations -
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Comparison to DFT 2:1 salt This model No corr.
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Comparison to DFT 2:1 salt DFT of Gillespie et al, 2011 This model DFT No corr.
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Slip velocity 2:1 salt C=1M C=0.1M C=0.01M
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Comparison to experiment 2:1 salt Van der Heyden 2006 nanochannel experiments
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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
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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.
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Overscreening vs. crowding MZ Bazant, BD Storey, AA Kornyshev, Phys. Rev. Lett. (2011)
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Boundary conditions Electrostatic BC (no correlations) Neglect “bulk” correlations (finite size ions)
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Concentration profiles 2:1 salt, 1M, a=0.3 nm kT/e
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1 2 3 4 1 2 3 45 RTIL double-layer structure
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