The document discusses electrified liquid-liquid interfaces from both a theoretical and applications perspective. It begins by covering concepts like Debye screening and the structure of electric double layers that form at electrolyte interfaces. It then discusses theories of electrowetting, where an applied electric field can change the shape of a liquid interface. Challenges with electrowetting on dielectric systems are noted due to high operating voltages. Interfaces between two immiscible electrolyte solutions are also discussed, which could enable ultra-low voltage electrowetting. Equilibrium theories of electrowetting at these types of interfaces are presented.

1. Electrified Liquid-Liquid Interfaces
From Theory to Applications
Monica Marinescu
Imperial College London
September 14, 2010
The University of Iowa

2. Is geeky the new cool?

3. Debye screening
1 Q
Φ(r) =
4πε0 r

4. Debye screening
1 Q
Φ(r) =
4πε0 εr

5. Debye screening
1 Q
Φ(r) =
4πε0 εr

6. Debye screening
1 Q
Φ(r) =
4πε0 εr

7. Debye screening
1 Q
Φ(r) =
4πε0 εr
Potential profile Φ(r)
Structure of screening layer λD

8. 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

9. 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

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

11. 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)
¯

12. Interfaces: Electrolyte/non-conducting liquid

13. 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)

14. 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)

15. Electrolyte/electrode interface
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−

16. Electrolyte/electrode interface
Stern(1924)
diffuse layer (dl) + inner layer (il)
1 1 1
= + −−
C Cdl Cil −−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−

17. Electrolyte/electrode interface
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 −−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−

18. Electrolyte/electrode interface
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 −−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−

19. Electrolyte/electrode interface
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 −−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−

20. Electrolyte/electrode interface
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 −−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−
−−

21. Plan
• Electrolytes and interfaces
• Electrowetting - 1 conducting liquid
• Electrowetting - 2 conducting liquids
• Nanoparticles at interfaces

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

23. Electrowetting
The area of a liquid/fluid interface changes as a result of an
applied electric field.
G. Lippmann(1875)
−
Electrocapillarity: electrostatic charge
modifies capillary forces
∂γ
∂Φ = −Q
A
+

24. Electrowetting
The area of a liquid/fluid interface changes as a result of an
applied electric field.
G. Lippmann(1875)
−
Electrocapillarity: electrostatic charge
modifies capillary forces
∂γ
∂Φ = −Q
A
A. Frumkin(1930)
Chemical reactions at electrode surface, Hg
electrode
+

25. Electrowetting
The area of a liquid/fluid interface changes as a result of an
applied electric field.
G. Lippmann(1875)
Electrocapillarity: electrostatic charge
modifies capillary forces
∂γ
∂Φ = −Q
A
A. Frumkin(1930)
+ +
Chemical reactions at electrode surface, Hg
electrode
+++++

26. Electrowetting
The area of a liquid/fluid interface changes as a result of an
applied electric field.
G. Lippmann(1875)
Electrocapillarity: electrostatic charge
modifies capillary forces
∂γ
∂Φ = −Q
A
A. Frumkin(1930)
+ +
Chemical reactions at electrode surface, Hg
electrode
B. Berge(1993)
+++++
Polymer coating for applications - ewod

27. ewod
electrowetting on dielectric

28. ewod
electrowetting on dielectric
− +
− +
−
− +
− +
−
−− −− +
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
− − −− +
− +
−
− +
− +
−
− +

29. ewod
electrowetting on dielectric
+ + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + +

30. ewod
electrowetting on dielectric
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

31. ewod
theory
α
γsw − γso
Young-Laplace cos α0 =
γwo

32. ewod
theory
− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −
α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +
γsw − γso
Young-Laplace cos α0 =
γwo

33. ewod
theory
− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −
α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +
γsw − γso
Young-Laplace cos α0 =
γwo
C
Berge cos α = cos α0 + V2
2γwo

34. ewod
theory
− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −
α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +
γsw − γso
Young-Laplace cos α0 =
γwo
C
Berge cos α = cos α0 + V2
2γwo

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

36. ewod
challenges
• Practical
• Electric field divergence ⇒ dielectric coating ⇒ large
operation voltages (20 V) (CD Cdl )
• Theoretical - not thoroughly developed

37. ewod
challenges
• Practical
• Electric field divergence ⇒ dielectric coating ⇒ large
operation voltages (20 V) (CD Cdl )
• Theoretical - not thoroughly developed
• Electric field divergence ⇒ full analytical solution does not
exist
• Contact angle saturation
• No satisfactory model of dynamics

38. Electrowetting with ities
interface between two immiscible electrolyte solutions
α

39. Electrowetting with ities
interface between two immiscible electrolyte solutions
− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −
α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +

40. Electrowetting with ities
interface between two immiscible electrolyte solutions
− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −
• 2 back-to-back diffuse layers (in series)
α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +

41. Electrowetting with ities
interface between two immiscible electrolyte solutions
− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −
• 2 back-to-back diffuse layers (in series)
• ⇒ E ∼ 107 V/cm
α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +

42. Electrowetting with ities
interface between two immiscible electrolyte solutions
− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −
• 2 back-to-back diffuse layers (in series)
• ⇒ 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

43. Electrowetting with ities
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)

44. Electrowetting with ities
equilibrium theory
∆G = [γde − γse + εde − εse ] Ade + [γds + εds ] Ads + Vd ∆p
¯ ¯ ¯
− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −
> (ds): 2 x Cdl in series
> (de), (se): Cdl , Cil in series α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +
> spherical, macroscopic droplet
C. Monroe, M. Urbakh, A. Kornyshev. J. Electrochem. Soc., 156(2009)

45. Electrowetting with ities
equilibrium theory
∆G = [γde − γse + εde − εse ] Ade + [γds + εds ] Ads + Vd ∆p
¯ ¯ ¯
− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −
> (ds): 2 x Cdl in series
> (de), (se): Cdl , Cil in series α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +
> spherical, macroscopic droplet
Minimisation G(α) ⇒ α(V)
C. Monroe, M. Urbakh, A. Kornyshev. J. Electrochem. Soc., 156(2009)

46. Electrowetting with ities
equilibrium theory
∆G = [γde − γse + εde − εse ] Ade + [γds + εds ] Ads + Vd ∆p
¯ ¯ ¯
− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −
> (ds): 2 x Cdl in series
> (de), (se): Cdl , Cil in series α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +
> spherical, macroscopic droplet
Minimisation G(α) ⇒ α(V)
→ large contact angle variation Φ < 1 V
C. Monroe, M. Urbakh, A. Kornyshev. J. Electrochem. Soc., 156(2009)

47. Electrowetting with ities
equilibrium theory
∆G = [γde − γse + εde − εse ] Ade + [γds + εds ] Ads + Vd ∆p
¯ ¯ ¯
− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −
> (ds): 2 x Cdl in series
> (de), (se): Cdl , Cil in series α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +
> spherical, macroscopic droplet
Minimisation G(α) ⇒ α(V)
→ large contact angle variation Φ < 1 V
→ effect of α0
C. Monroe, M. Urbakh, A. Kornyshev. J. Electrochem. Soc., 156(2009)

48. Electrowetting with ities
equilibrium theory
∆G = [γde − γse + εde − εse ] Ade + [γds + εds ] Ads + Vd ∆p
¯ ¯ ¯
− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −
> (ds): 2 x Cdl in series
> (de), (se): Cdl , Cil in series α
+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +
> spherical, macroscopic droplet
Minimisation G(α) ⇒ α(V)
→ large contact angle variation Φ < 1 V
→ effect of α0 ,c
C. Monroe, M. Urbakh, A. Kornyshev. J. Electrochem. Soc., 156(2009)

49. Electrowetting with ities
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

50. Electrowetting with ities
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

51. Electrowetting with ities
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

52. Electrowetting with ities
experiment
A. Kucernak(2010)
> non-ideal electrode ⇒ hysteresis
> new pulsing technique
• eliminate hysteresis
• strong α(V) dependence
• stick-slip motion, step size
A. Kornyshev, A. Kucernak, M. Marinescu, C. Monroe, A. Sleightholme, M. Urbakh. J. Phys. Chem. C, in print

53. Electrowetting with ities
experiment
A. Kucernak(2010)
> non-ideal electrode ⇒ hysteresis
> new pulsing technique
• eliminate hysteresis
• strong α(V) dependence
electric pulsing ←→ effect of
• stick-slip motion, step size
roughness?
A. Kornyshev, A. Kucernak, M. Marinescu, C. Monroe, A. Sleightholme, M. Urbakh. J. Phys. Chem. C, in print

54. Electrowetting with ities
theory of pulsing R(t)
¨
Ff + Fd = mR
M. Marinescu, M. Urbakh, T. Barnea, A. Kucernak, A. Kornyshev. J. Phys. Chem. C, submitted

55. Electrowetting with ities
theory of pulsing R(t)
Ff + Fd = mR¨
¨ ˙ ˙
mR + η R = k(Re − R) − F0 sign(R)
M. Marinescu, M. Urbakh, T. Barnea, A. Kucernak, A. Kornyshev. J. Phys. Chem. C, submitted

56. Electrowetting with ities
theory of pulsing R(t)
Ff + Fd = mR¨
¨ ˙ ˙
mR + η R = k(Re − R) − F0 sign(R)
M. Marinescu, M. Urbakh, T. Barnea, A. Kucernak, A. Kornyshev. J. Phys. Chem. C, submitted

57. Electrowetting with ities
theory of pulsing R(t)
Ff + Fd = mR¨
¨ ˙ ˙
mR + η R = k(Re − R) − F0 sign(R)
k(V ) = ∂ 2 G/∂R2
Re (V )
M. Marinescu, M. Urbakh, T. Barnea, A. Kucernak, A. Kornyshev. J. Phys. Chem. C, submitted

58. Electrowetting with ities
theory of pulsing R(t)
Ff + Fd = mR¨
¨ ˙ ˙
mR + η R = k(Re − R) − F0 sign(R)
k(V ) = ∂ 2 G/∂R2
Re (V )
M. Marinescu, M. Urbakh, T. Barnea, A. Kucernak, A. Kornyshev. J. Phys. Chem. C, submitted

59. Electrowetting with ities
theory of pulsing R(t)
Ff + Fd = mR¨
¨ ˙ ˙
mR + η R = k(Re − R) − F0 sign(R)
k(V ) = ∂ 2 G/∂R2
Re (V )
→ qualitative success
M. Marinescu, M. Urbakh, T. Barnea, A. Kucernak, A. Kornyshev. J. Phys. Chem. C, submitted

60. Electrowetting with ities
theory of pulsing R(t)
Ff + Fd = mR¨
¨ ˙ ˙
mR + η R = k(Re − R) − F0 sign(R)
k(V ) = ∂ 2 G/∂R2
Re (V )
→ qualitative success
→ need better system characterisation
M. Marinescu, M. Urbakh, T. Barnea, A. Kucernak, A. Kornyshev. J. Phys. Chem. C, submitted

61. Electrowetting with ities
theory of pulsing R(t)
Ff + Fd = mR¨
¨ ˙ ˙
mR + η R = k(Re − R) − F0 sign(R)
k(V ) = ∂ 2 G/∂R2
Re (V )
→ qualitative success
→ need better system characterisation
M. Marinescu, M. Urbakh, T. Barnea, A. Kucernak, A. Kornyshev. J. Phys. Chem. C, submitted

62. Electrowetting with ities
theory of pulsing R(t)
Ff + Fd = mR¨
¨ ˙ ˙
mR + η R = k(Re − R) − F0 sign(R)
k(V ) = ∂ 2 G/∂R2
Re (V )
→ qualitative success
→ need better system characterisation
F0 F0
→ F0 ⇒ Re − k , Re + k metastable
M. Marinescu, M. Urbakh, T. Barnea, A. Kucernak, A. Kornyshev. J. Phys. Chem. C, submitted

63. Electrowetting with ities
remarks
• Theoretical description the dynamics of electrowetting
• Ultra-low electrowetting with ities is real

64. Electrowetting with ities
remarks
• Theoretical description the dynamics of electrowetting
• Ultra-low electrowetting with ities is real
• Pulsing technique
− tool for facilitating electrowetting
− a new electroanalytical method for wetting dynamics

65. Electrowetting with ities
remarks
• Theoretical description the dynamics of electrowetting
• Ultra-low electrowetting with ities is real
• Pulsing technique
− tool for facilitating electrowetting
− a new electroanalytical method for wetting dynamics
• Current focus on minimising F0 (A. Kucernak, N. Cousens)

66. Functionalised ities

67. Functionalised ities
−− +
−− +
+
−− +
−− +
+
−− +
+
−− +
−− +
+
−− +
−− +
+
−− +
+
−− +
−− +
+
−− +
−− +
+
−− +
+
−− +
−− +
+
−− +
−− +
+
−− +
+
−− +
−− +
−− +
+
−− +
+

68. Functionalised ities
Use optical properties of monolayer (plasmon
−− +
+
resonance)
−− +
−−
−− +
+
+
mirror
−− +
+
−− +
−− +
+
−− +
−− +
+
−− +
+
−− +
−− +
+
−− +
−− +
+
−− +
+
−− +
−− +
+
−− +
−− +
+
−− +
+
−− +
−− +
−− +
+
−− +
+

69. Functionalised ities
Use optical properties of monolayer (plasmon
−− +
+
resonance)
−− +
−−
−− +
+
+
mirror
−− +
+
−− +
−− +
+
−− +
−− +
−−
−−
+
+
+
+ Reversible localization of nanoparticles with
+
−−
−−
−−
+
+
+ applied voltages ∼ 1 V
+
−− +
−− +
+
+
tunability
−− +
−− +
−− +
+
−− +
+
−− +
−− +
−− +
+
−− +
+

70. Functionalised ities
Use optical properties of monolayer (plasmon
−− +
+
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?

71. Functionalised ities
reversible localisation
−− +
−− +
+
− +
−−−
+
+
−− +
+
− +
−− +
Wtot (x) = Wcap (x)+Wsolv (x)+Wext (x)+Wline (x) −−
−−
−−
−
−
+
+
+
+
+
+
+
−− +
−− +
+
−−−
+
+
−− +
+
− +
−−− +
+
−− +
−− +
+
−− +
+
− +
−− +
−− +
+
−−− +
+

72. Functionalised ities
reversible localisation
−− +
−− +
+
− +
−−−
+
+
−− +
+
− +
−− +
Wtot (x) = Wcap (x)+Wsolv (x)+Wext (x)+Wline (x) −−
−−
−−
−
−
+
+
+
+
+
+
+
−− +
−− +
+
−−−
+
+
−− +
+
− +
−−− +
+
−− +
−− +
> Interfacial energy ⇒ γow , α0
+
−− +
+
− +
−− +
−− +
+
−−− +
+

73. Functionalised ities
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 )

74. Functionalised ities
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 )
> Energy in electric field ⇒ dl prop, zn , V

75. Functionalised ities
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 )
> Energy in electric field ⇒ dl prop, zn , V
> Line tension effects ⇒ µ

76. Functionalised ities
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 )
> Energy in electric field ⇒ dl prop, zn , V
> Line tension effects ⇒ µ

77. Functionalised ities
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 )
> Energy in electric field ⇒ dl prop, zn , V
> Line tension effects ⇒ µ

78. Functionalised ities
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 )
> Energy in electric field ⇒ dl prop, zn , V
> Line tension effects ⇒ µ
H. Girault(2010)
Reversibility obtained experimentally (in print)

79. Functionalised ities
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)

80. Who is who in ities
theory

81. Who is who in ities
theory

82. Who is who in ities
theory

83. Who is who in ities
experiment

85. 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