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

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