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Electrovariable Devices

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Electrovariable Devices

1. 1. Electriﬁed Liquid-Liquid Interfaces From Theory to Applications Monica Marinescu Imperial College London September 14, 2010 The University of Iowa
2. 2. Is geeky the new cool?
3. 3. Debye screening 1 QΦ(r) = 4πε0 r
4. 4. Debye screening 1 QΦ(r) = 4πε0 εr
5. 5. Debye screening 1 QΦ(r) = 4πε0 εr
6. 6. Debye screening 1 QΦ(r) = 4πε0 εr
7. 7. Debye screening 1 Q Φ(r) = 4πε0 εrPotential proﬁle Φ(r)Structure of screening layer λD
8. 8. Debye screening 1 Q Φ(r) = 4πε0 εrPotential 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. 9. Debye screening 1 Q Φ(r) = 4πε0 εr 1 Q e−r/λDPotential proﬁle Φ(r) = 4πε0 εr r ε0 εkB TStructure 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. 10. Debye screening examples• Pure water pH = 7 ⇒ c[H + ],[OH − ] = 10−7 M ⇒ λD ∼ 1 µm (cf. r = 1 ˚ ) ¯ A
11. 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. 12. Interfaces: Electrolyte/non-conducting liquid
13. 13. Interfaces: Electrolyte/non-conducting liquidGouy(1910), Chapman(1913) Cdl = 0 r λD cosh φ2 dl ∂ρ zeΦ C= ∂Φ , φ= kB T electric double layer, diﬀuse layer (dl)
14. 14. Interfaces: Electrolyte/non-conducting liquidGouy(1910), Chapman(1913) Cdl = 0 r λD cosh φ2 dl ∂ρ zeΦ C= ∂Φ , φ= kB T electric double layer, diﬀuse layer (dl)
15. 15. Electrolyte/electrode interface −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −−
16. 16. Electrolyte/electrode interfaceStern(1924)diﬀuse layer (dl) + inner layer (il) 1 1 1 = + −− C Cdl Cil −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −−
17. 17. Electrolyte/electrode interfaceStern(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. 18. Electrolyte/electrode interfaceStern(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. 19. Electrolyte/electrode interfaceStern(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. 20. Electrolyte/electrode interfaceStern(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. 21. Plan• Electrolytes and interfaces• Electrowetting - 1 conducting liquid• Electrowetting - 2 conducting liquids• Nanoparticles at interfaces
22. 22. ElectrowettingThe area of a liquid/ﬂuid interface changes as a result of an applied electric ﬁeld.
23. 23. ElectrowettingThe area of a liquid/ﬂuid interface changes as a result of an applied electric ﬁeld.G. Lippmann(1875) −Electrocapillarity: electrostatic chargemodiﬁes capillary forces ∂γ ∂Φ = −Q A +
24. 24. ElectrowettingThe area of a liquid/ﬂuid interface changes as a result of an applied electric ﬁeld.G. Lippmann(1875) −Electrocapillarity: electrostatic chargemodiﬁes capillary forces ∂γ ∂Φ = −Q AA. Frumkin(1930)Chemical reactions at electrode surface, Hgelectrode +
25. 25. ElectrowettingThe area of a liquid/ﬂuid interface changes as a result of an applied electric ﬁeld.G. Lippmann(1875)Electrocapillarity: electrostatic chargemodiﬁes capillary forces ∂γ ∂Φ = −Q AA. Frumkin(1930) + +Chemical reactions at electrode surface, Hgelectrode +++++
26. 26. ElectrowettingThe area of a liquid/ﬂuid interface changes as a result of an applied electric ﬁeld.G. Lippmann(1875)Electrocapillarity: electrostatic chargemodiﬁes capillary forces ∂γ ∂Φ = −Q AA. Frumkin(1930) + +Chemical reactions at electrode surface, HgelectrodeB. Berge(1993) +++++Polymer coating for applications - ewod
27. 27. ewodelectrowetting on dielectric
28. 28. ewodelectrowetting on dielectric − + − + − − + − + − −− −− + + + + + + + + + + + + + + + + + + + − − −− + − + − − + − + − − +
29. 29. ewodelectrowetting on dielectric + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
30. 30. ewod electrowetting on dielectric+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
31. 31. ewod theory α γsw − γsoYoung-Laplace cos α0 = γwo
32. 32. ewod theory − −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− − α + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + γsw − γsoYoung-Laplace cos α0 = γwo
33. 33. ewod theory − −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− − α + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + γsw − γsoYoung-Laplace cos α0 = γwo CBerge cos α = cos α0 + V2 2γwo
34. 34. ewod theory − −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− − α + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + γsw − γsoYoung-Laplace cos α0 = γwo CBerge cos α = cos α0 + V2 2γwo
35. 35. ewod challenges• Practical • Electric ﬁeld divergence ⇒ dielectric coating ⇒ large operation voltages (20 V) (CD Cdl )
36. 36. ewod challenges• Practical • Electric ﬁeld divergence ⇒ dielectric coating ⇒ large operation voltages (20 V) (CD Cdl )• Theoretical - not thoroughly developed
37. 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. 38. Electrowetting with itiesinterface between two immiscible electrolyte solutions α
39. 39. Electrowetting with ities interface between two immiscible electrolyte solutions− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− − α+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +
40. 40. Electrowetting with ities interface between two immiscible electrolyte solutions− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− − • 2 back-to-back diﬀuse layers (in series) α+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +
41. 41. Electrowetting with ities interface between two immiscible electrolyte solutions− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− −− − • 2 back-to-back diﬀuse layers (in series) • ⇒ E ∼ 107 V/cm α+ + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + +
42. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 63. Electrowetting with ities remarks• Theoretical description the dynamics of electrowetting• Ultra-low electrowetting with ities is real
64. 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. 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. 66. Functionalised ities
67. 67. Functionalised ities−− +−− + +−− +−− + +−− + +−− +−− + +−− +−− + +−− + +−− +−− + +−− +−− + +−− + +−− +−− + +−− +−− + +−− + +−− +−− +−− + +−− + +
68. 68. Functionalised ities Use optical properties of monolayer (plasmon−− + + resonance)−− +−−−− + + + mirror−− + +−− +−− + +−− +−− + +−− + +−− +−− + +−− +−− + +−− + +−− +−− + +−− +−− + +−− + +−− +−− +−− + +−− + +
69. 69. Functionalised ities Use optical properties of monolayer (plasmon−− + + resonance)−− +−−−− + + + mirror−− + +−− +−− + +−− +−− +−−−− + + + + Reversible localization of nanoparticles with +−−−−−− + + + applied voltages ∼ 1 V +−− +−− + + + tunability−− +−− +−− + +−− + +−− +−− +−− + +−− + +
70. 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. 71. Functionalised ities reversible localisation −− + −− + + − + −−− + + −− + + − + −− +Wtot (x) = Wcap (x)+Wsolv (x)+Wext (x)+Wline (x) −− −− −− − − + + + + + + + −− + −− + + −−− + + −− + + − + −−− + + −− + −− + + −− + + − + −− + −− + + −−− + +
72. 72. Functionalised ities reversible localisation −− + −− + + − + −−− + + −− + + − + −− +Wtot (x) = Wcap (x)+Wsolv (x)+Wext (x)+Wline (x) −− −− −− − − + + + + + + + −− + −− + + −−− + + −− + + − + −−− + + −− + −− + > Interfacial energy ⇒ γow , α0 + −− + + − + −− + −− + + −−− + +
73. 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. 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. 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. 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. 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. 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 ⇒ µH. Girault(2010)Reversibility obtained experimentally (in print)
79. 79. Functionalised ities remarksTheory for coverage, reﬂection/transmission - awaitsexperimental proofTheory of Faraday rotation - in workMagnetic properties (spin, ferroﬂuids) - plannedBeyond ities:Functionalise electrolyte/electrode interface(E-Ink)
80. 80. Who is who in ities theory
81. 81. Who is who in ities theory
82. 82. Who is who in ities theory
83. 83. Who is who in ities experiment
84. 84. 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