Electrovariable Devices

Electriﬁed Liquid-Liquid Interfaces
From Theory to Applications

Monica Marinescu
Imperial College London

September 14, 2010
The University of Iowa

Debye screening
1 Q
Φ(r) =
4πε0 r

Debye screening
1 Q
Φ(r) =
4πε0 εr

Debye screening
1 Q
Φ(r) =
4πε0 εr

Potential proﬁle Φ(r)

Structure of screening layer λD

Debye screening
1 Q
Φ(r) =
4πε0 εr

Potential proﬁle Φ(r)

Structure of screening layer λD

2 1
Poisson Φ(r) = − ρ(r)
ε0 ε
1 −qi Φ(r)/kb T
Boltzmann ci (r) = e
Zi

Debye screening
1 Q
Φ(r) =
4πε0 εr

1 Q e−r/λD
Potential proﬁle Φ(r) =
4πε0 εr r
ε0 εkB T
Structure of screening layer λD = 2
n i qi

2 1
Poisson Φ(r) = − ρ(r)
ε0 ε
1 −qi Φ(r)/kb T
Boltzmann ci (r) = e
Zi

Debye screening
examples

• Pure water pH = 7 ⇒ c[H + ],[OH − ] = 10−7 M ⇒ λD ∼ 1 µm
(cf. r = 1 ˚ )
¯ A

Debye screening
examples

• Pure water pH = 7 ⇒ c[H + ],[OH − ] = 10−7 M ⇒ λD ∼ 1 µm
(cf. r = 1 ˚ )
¯ A
• 1 teaspoon NaCl in 1l water ⇒ c[N a+ ],[Cl− ] = 10−1 M
⇒ λD ∼ 1 nm (cf. r = 2.5 nm)
¯

Interfaces: Electrolyte/non-conducting liquid

Interfaces: Electrolyte/non-conducting liquid

Gouy(1910), Chapman(1913)

Cdl = 0 r
λD cosh φ2
dl

∂ρ zeΦ
C= ∂Φ , φ= kB T

electric double layer, diﬀuse
layer (dl)

Electrolyte/electrode interface

−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−

Stern(1924)
diﬀuse layer (dl) + inner layer (il)
1 1 1
= + −−
C Cdl Cil −−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−

Stern(1924)
diﬀuse layer (dl) + inner layer (il)
1 1 1
= + −−
C Cdl Cil −−
−−
−−
−−
Mott, Watts-Tobin(1961) −−
−−
−−
˜
Cil = K∞ 1 + χ0 sech2 ∆φil /φ −−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−

Plan

• Electrolytes and interfaces

• Electrowetting - 1 conducting liquid

• Electrowetting - 2 conducting liquids

• Nanoparticles at interfaces

Electrowetting

The area of a liquid/ﬂuid interface changes as a result of an
applied electric ﬁeld.

Electrowetting


G. Lippmann(1875)
−
Electrocapillarity: electrostatic charge
modiﬁes capillary forces
∂γ
∂Φ = −Q
A

+

Electrowetting


G. Lippmann(1875)
−
∂γ
∂Φ = −Q
A
A. Frumkin(1930)
Chemical reactions at electrode surface, Hg
electrode
+

Electrowetting


G. Lippmann(1875)
∂γ
∂Φ = −Q
A
A. Frumkin(1930)
+ +
electrode

+++++

Electrowetting


G. Lippmann(1875)
∂γ
∂Φ = −Q
A
A. Frumkin(1930)
+ +
electrode
B. Berge(1993)
+++++
Polymer coating for applications - ewod

ewod
electrowetting on dielectric

ewod

− +
− +
−
− +
− +
−
−− −− +
+
+
+
+
+
+
+
+
+

+
+
+
+
+
+
+
+
+
− − −− +
− +
−
− +
− +
−
− +

ewod

+ + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + +

ewod

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

ewod
theory

α

γsw − γso
Young-Laplace cos α0 =
γwo

ewod
theory

− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −

α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +

γsw − γso
γwo

ewod
theory

− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −

α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +

γsw − γso
γwo

C
Berge cos α = cos α0 + V2
2γwo

ewod
challenges

• Practical
• Electric ﬁeld divergence ⇒ dielectric coating ⇒ large
operation voltages (20 V) (CD Cdl )

ewod
challenges

• Practical
• Theoretical - not thoroughly developed

ewod
challenges

• Practical
• Theoretical - not thoroughly developed
• Electric ﬁeld divergence ⇒ full analytical solution does not
exist
• Contact angle saturation
• No satisfactory model of dynamics

Electrowetting with ities
interface between two immiscible electrolyte solutions

α


− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −

α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +


− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −

• 2 back-to-back diﬀuse layers (in series)

α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +


− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −

• ⇒ E ∼ 107 V/cm
α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +


− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −

• ⇒ E ∼ 107 V/cm
α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +

• No energy divergences occur ⇒ no dielectric coating needed
⇒ ultra-low operation voltages
• The droplet bulk is electroneutral ⇒ a comprehensive
mathematical model can be derived

equilibrium theory

∆G = [γde − γse + εde − εse ] Ade + [γds + εds ] Ads + Vd ∆p
¯ ¯ ¯

− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −

α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +

C. Monroe, M. Urbakh, A. Kornyshev. J. Electrochem. Soc., 156(2009)

equilibrium theory

¯ ¯ ¯

− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −

> (ds): 2 x Cdl in series
> (de), (se): Cdl , Cil in series α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +

> spherical, macroscopic droplet


equilibrium theory

¯ ¯ ¯

− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −

+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +


Minimisation G(α) ⇒ α(V)


equilibrium theory

¯ ¯ ¯

− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −

+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +


→ large contact angle variation Φ < 1 V


equilibrium theory

¯ ¯ ¯

− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −

+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +


→ eﬀect of α0


equilibrium theory

¯ ¯ ¯

− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −

+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +


→ eﬀect of α0 ,c


experiment

A. Kucernak(2010)
> non-ideal electrode ⇒ hysteresis
> new pulsing technique

A. Kornyshev, A. Kucernak, M. Marinescu, C. Monroe, A. Sleightholme, M. Urbakh. J. Phys. Chem. C, in print

experiment

A. Kucernak(2010)

• eliminate hysteresis
• strong α(V) dependence
• stick-slip motion, step size


experiment

A. Kucernak(2010)

• eliminate hysteresis
• strong α(V) dependence
electric pulsing ←→ eﬀect of
• stick-slip motion, step size
roughness?


theory of pulsing R(t)

¨
Ff + Fd = mR

M. Marinescu, M. Urbakh, T. Barnea, A. Kucernak, A. Kornyshev. J. Phys. Chem. C, submitted


Ff + Fd = mR¨
¨ ˙ ˙
mR + η R = k(Re − R) − F0 sign(R)



Ff + Fd = mR¨
¨ ˙ ˙

k(V ) = ∂ 2 G/∂R2
Re (V )



Ff + Fd = mR¨
¨ ˙ ˙

k(V ) = ∂ 2 G/∂R2
Re (V )

→ qualitative success



Ff + Fd = mR¨
¨ ˙ ˙

k(V ) = ∂ 2 G/∂R2
Re (V )

→ need better system characterisation



Ff + Fd = mR¨
¨ ˙ ˙

k(V ) = ∂ 2 G/∂R2
Re (V )

→ need better system characterisation
F0 F0
→ F0 ⇒ Re − k , Re + k metastable


remarks

• Theoretical description the dynamics of electrowetting
• Ultra-low electrowetting with ities is real

remarks


• Pulsing technique
− tool for facilitating electrowetting
− a new electroanalytical method for wetting dynamics

remarks


• Pulsing technique
− tool for facilitating electrowetting
− a new electroanalytical method for wetting dynamics

• Current focus on minimising F0 (A. Kucernak, N. Cousens)

Functionalised ities

−− +
−− +
+
−− +
−− +
+
−− +
+
−− +
−− +
+
−− +
−− +
+
−− +
+
−− +
−− +
+
−− +
−− +
+
−− +
+
−− +
−− +
+
−− +
−− +
+
−− +
+
−− +
−− +
−− +
+
−− +
+


Use optical properties of monolayer (plasmon
−− +
+
resonance)
−− +
−−
−− +
+
+
mirror
−− +
+
−− +
−− +
+
−− +
−− +
+
−− +
+
−− +
−− +
+
−− +
−− +
+
−− +
+
−− +
−− +
+
−− +
−− +
+
−− +
+
−− +
−− +
−− +
+
−− +
+


−− +
+
resonance)
−− +
−−
−− +
+
+
mirror
−− +
+
−− +
−− +
+
−− +
−− +
−−
−−
+
+
+
+ Reversible localization of nanoparticles with
+
−−
−−
−−
+
+
+ applied voltages ∼ 1 V
+
−− +
−− +
+
+
tunability
−− +
−− +
−− +
+
−− +
+
−− +
−− +
−− +
+
−− +
+


−− +
+
resonance)
−− +
−−
−− +
+
+
mirror
−− +
+
−− +
−− +
+
−− +
−− +
−−
−−
+
+
+
+ Reversible localization of nanoparticles with
+
−−
−−
−−
+
+
+ applied voltages ∼ 1 V
+
−− +
−− +
+
+
tunability
−− +
−− +
−− +
+
−− +
+
−−
−−
−−
+
+
+
+
Magnetic and optic properties of material
−− +
+
functionality
• optical switches, faraday rotators, SERS in
chemical and biological analysis, what else?

reversible localisation

−− +
−− +
+
− +
−−−
+
+
−− +
+
− +
−− +

Wtot (x) = Wcap (x)+Wsolv (x)+Wext (x)+Wline (x) −−
−−
−−
−
−
+
+
+
+
+
+
+
−− +
−− +
+
−−−
+
+
−− +
+
− +
−−− +
+
−− +
−− +
+
−− +
+
− +
−− +
−− +
+
−−− +
+


−− +
−− +
+
− +
−−−
+
+
−− +
+
− +
−− +

−−
−−
−
−
+
+
+
+
+
+
+
−− +
−− +
+
−−−
+
+
−− +
+
− +
−−− +
+
−− +
−− +

> Interfacial energy ⇒ γow , α0
+
−− +
+
− +
−− +
−− +
+
−−− +
+


−− +
−− +
+
− +
−−−
+
+
−− +
+
− +
−− +

−−
−−
−
−
+
+
+
+
+
+
+
−− +
−− +
+
−−−
+
+
−− +
+
− +
−−− +
+
−− +
−− +

+
−− +
+
− +
−− +
−− +
+
−−− +
+

> Re-solvation energy ⇒ dl prop, zn
(co , cw , εo , εw , T )


−− +
−− +
+
− +
−−−
+
+
−− +
+
− +
−− +

−−
−−
−
−
+
+
+
+
+
+
+
−− +
−− +
+
−−−
+
+
−− +
+
− +
−−− +
+
−− +
−− +

+
−− +
+
− +
−− +
−− +
+
−−− +
+

(co , cw , εo , εw , T )
> Energy in electric ﬁeld ⇒ dl prop, zn , V


−− +
−− +
+
− +
−−−
+
+
−− +
+
− +
−− +

−−
−−
−
−
+
+
+
+
+
+
+
−− +
−− +
+
−−−
+
+
−− +
+
− +
−−− +
+
−− +
−− +

+
−− +
+
− +
−− +
−− +
+
−−− +
+

(co , cw , εo , εw , T )
> Line tension eﬀects ⇒ µ


−− +
−− +
+
− +
−−−
+
+
−− +
+
− +
−− +

−−
−−
−
−
+
+
+
+
+
+
+
−− +
−− +
+
−−−
+
+
−− +
+
− +
−−− +
+
−− +
−− +

+
−− +
+
− +
−− +
−− +
+
−−− +
+

(co , cw , εo , εw , T )
> Line tension eﬀects ⇒ µ

H. Girault(2010)
Reversibility obtained experimentally (in print)

remarks

Theory for coverage, reﬂection/transmission - awaits
experimental proof

Theory of Faraday rotation - in work

Magnetic properties (spin, ferroﬂuids) - planned

Beyond ities:
Functionalise electrolyte/electrode interface(E-Ink)

Who is who in ities
theory

Who is who in ities
experiment

Fundamental constants

Name Value Units Expression
ε0 8.854 · 10−12 F/m
kB 1.381 · 1023 J/K
8.617 · 10−5 eV/K
e 1.602 · 10−19 C
NA 6.022 · 1023 1/mol
F 9.648 · 104 C/mol NA e
R 8.314 J/(mol K) kB NA
LB 7 · 10−10 ( ) m e2 /(4πε0 εkB T )
kB T @RT 4.11 · 10−21 J
0.026 eV

( ) for ε = 80, water @ RT

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