Electrokinetics of correlated electrolytes and ionic liquids

Martin Z. BazantDepartments of Chemical Engineering and Mathematics

Massachusetts Institute of Technology

Brian D. StoreyOlin College

Ionic liquids• Molten salts (T~1000oC)• 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.

BMIMwikipedia

ln ezckT iii

At equilibrium:

Chemical potential of dilute point ions:

0 1 2 3 4 50

0.5

1

1.5

2

2.5

3

X

C

0 1 2 3 4 510

-20

10-10

100

1010

1020

X

C

Applied voltage =.025 V Applied voltage =0.75 V

,kT

ez

ii

i

ecc

Would need ions to be 0.01 angstrom

Classical double layer theory

Finite sized ionsStern (1924) Bikerman (1942)

Bazant, Kilic, Storey, Ajdari – ACIS 2009

)1ln(ln kTezckT iii

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.” --- wikipedia

“Ginzburg-Landau” theory for ionic liquids

chemical free energy

mean electrostatic energy

self energy of E field

electrostatic correlations (new)Require

4th 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 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)

�̂�=𝜀(1+ℓ𝑐2 𝑘2)

�̂�=𝜀(1−ℓ𝑐2 𝛻2)

RTIL double-layer structure

charge density at V=1,10,100 kT/e

Set to ion size,

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)

µ

0 1 2 3 4 50

1

2

3

4

5

x/a

g(x)

Correlated electrolytes high valence, high concentration

1M 2:1 salt

Boda et al 2002 MC simulations

-

10-3

10-2

10-1

100

-1

-0.8

-0.6

-0.4

-0.2

0

C+ (Molar)

Q (

C/m

2 )

V= -1

V= -2

V= -4

V= -6

V= -8

Comparison to DFT2:1 salt

This model

No corr.

10-3

10-2

10-1

100

-1

-0.8

-0.6

-0.4

-0.2

0

C+ (Molar)

Q (

C/m

2 )

V= -1

V= -2

V= -4

V= -6

V= -8

Comparison to DFT2:1 salt

DFT of Gillespie et al, 2011

This model

DFT

No corr.

-20 -10 0 10 20

-2

-1

0

1

V

U/U

Hs

Slip velocity2:1 salt

C=1M

C=0.1M C=0.01M

Comparison to experiment2:1 salt

10-4

10-2

100

0

20

40

60

80pA

/bar

C (M)

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

-20 -10 0 10 200

5

10

15

V

C/C

DH

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 profiles2:1 salt, 1M, a=0.3 nm

0 2 4 60

2

4

6

8

c(x)

/c

V=1

0 2 4 60

20

40

60

80V=5

0 2 4 60

20

40

60

80

c(x)

/c

x/a

V=10

0 2 4 60

20

40

60

80c(

x)/c

x/a

V=20

kT/e kT/e

kT/e kT/e

1

2

3

4

1 2 3 4 5

RTIL double-layer structure