Encyclopedia of Applied Electrochemistry

2014 Edition
| Editors: Gerhard Kreysa, Ken-ichiro Ota, Robert F. Savinell

Ionic Mobility and Diffusivity

  • Charles W. Monroe
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-6996-5_325

Fundamental Concepts

Theories of mass transport in electrolytes or electrolytic solutions take into account that motion of dissolved species i can be driven by gradients in electric potential \( \Phi \)
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  1. 1.
    Planck M (1890) Ueber die Potentialdifferenz zwischen zwei verdünnten Lösungen binärer Electrolyte. Annalen der Physik und Chemie 40(8):561–576Google Scholar
  2. 2.
    Levich B (1942) The theory of concentration polarization. Acta Physicochimica URSS 17(5–6):257–307Google Scholar
  3. 3.
    MacInnes DA (1961) The principles of electrochemistry, 2nd edn. Dover Books, New YorkGoogle Scholar
  4. 4.
    Robinson RA, Stokes RH (1968) Electrolyte solutions, second edition (revised). Butterworths, LondonGoogle Scholar
  5. 5.
    Vanysek P (2011) Conductivity ionic diffusion at infinite dilution. In: Haynes WM, Lide DR (eds) CRC handbook of chemistry and physics, 92nd edn. CRC Press/Taylor and Francis Group, Boca Raton/Florida, pp 77–79Google Scholar
  6. 6.
    Kuiken GDC (1994) Thermodynamics of irreversible processes: applications to diffusion and rheology. Wiley, SussexGoogle Scholar
  7. 7.
    de Groot SR, Mazur P (1984) Non-equilibrium thermodynamics. Dover, MineolaGoogle Scholar
  8. 8.
    Onsager L (1945) Theories and problems of liquid diffusion. Ann N Y Acad Sci 46(5):241–265Google Scholar
  9. 9.
    von Smoluchowski M (1906) Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen. Ann Phys 326(14):756–780Google Scholar
  10. 10.
    Einstein A (1905) Über die von der molukularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann Phys 322(8):549–560Google Scholar
  11. 11.
    Newman J, Thomas-Alyea KE (2004) Electrochemical systems, 3rd edn. Wiley, HobokenGoogle Scholar
  12. 12.
    Hirschfelder JO, Curtiss CF, Bird RB (1964) Molecular theory of gases and liquidsGoogle Scholar
  13. 13.
    Newman J, Bennion D, Tobias CW (1965) Mass transfer in concentrated binary electrolytes. Berichte Der Bunsen-Gesellschaft Fur Physikalische Chemie 69(7):608Google Scholar
  14. 14.
    Monroe CW, Newman J (2009) Onsager’s shortcut to proper forces and fluxes. Chem Eng Sci 64(22):4804–4809Google Scholar
  15. 15.
    Monroe CW, Newman J (2006) Onsager reciprocal relations for Stefan-Maxwell diffusion. Ind Eng Chem Res 45(15):5361–5367Google Scholar
  16. 16.
    Helfand E (1960) On inversion of the linear laws of irreversible thermodynamics. J Chem Phys 33(2):319–322Google Scholar
  17. 17.
    Ma YP, Doyle M, Fuller TF, Doeff MM, Dejonghe LC, Newman J (1995) The measurement of a complete set of transport properties for a concentrated solid polymer electrolyte solution. J Electrochem Soc 142(6):1859–1868Google Scholar
  18. 18.
    Doeff MM, Edman L, Sloop SE, Kerr J, Jonghe LCD (2000) Transport properties of binary salt polymer electrolytes. J Power Sources 89(2):227–231Google Scholar
  19. 19.
    Doeff MM, Georen P, Qiao J, Kerr J, Jonghe LCD (1999) Transport properties of a high molecular weight poly(propylene oxide)-LiCF3SO3 system. J Electrochem Soc 146(6):2024–2028Google Scholar
  20. 20.
    Ferry A, Doeff MM, DeJonghe LC (1998) Transport property measurements of polymer electrolytes. Electrochim Acta 43(10–11):1387–1393Google Scholar
  21. 21.
    Nyman A, Behm M, Lindbergh G (2008) Electrochemical characterisation and modelling of the mass transport phenomena in LiPF6-EC-EMC electrolyte. Electrochim Acta 53(22):6356–6365Google Scholar
  22. 22.
    Valøen LO, Reimers JN (2005) Transport properties of LiPF6-based Li-ion battery electrolytes. J Electrochem Soc 152(5):A882–A891Google Scholar
  23. 23.
    Wang MH, Newman J (1995) The electrical conductivity of sodium polysulfide melts. J Electrochem Soc 142(3):761–764Google Scholar
  24. 24.
    Thompson SD, Newman J (1989) Differential diffusion coefficients of sodium polysulfide melts. J Electrochem Soc 136(11):3362–3369Google Scholar
  25. 25.
    Heintz A, Wiedemann E, Ziegler J (1997) Ion exchange diffusion in electromembranes and its description using the Maxwell-Stefan formalism. J Membr Sci 137(1–2):121–132Google Scholar
  26. 26.
    Wiedemann E, Heintz A, Lichtenthaler RN (1998) Transport properties of vanadium ions in cation exchange membranes: determination of diffusion coefficients using a dialysis cell. J Membr Sci 141(2):215–221Google Scholar
  27. 27.
    Delacourt C, Newman J (2008) Mathematical modeling of a cation-exchange membrane containing two cations. J Electrochem Soc 155(11):B1210–B1217Google Scholar
  28. 28.
    Okada T, Moller-Holst S, Gorseth O, Kjelstrup S (1998) Transport and equilibrium properties of Nafion (R) membranes with H + and Na + ions. J Electroanal Chem 442(1–2):137–145Google Scholar
  29. 29.
    Guggenheim EA (1967) Thermodynamics: an advanced treatment for chemists and physicists, 5th edn. North-Holland Publishing Company, AmsterdamGoogle Scholar
  30. 30.
    Smyrl WH, Newman J (1968) Potentials of cells with liquid junctions. J Phys Chem 72(13):4660Google Scholar
  31. 31.
    Harned HS, Nuttall RL (1949) The differential diffusion coefficient of potassium chloride in aqueous solutions. J Am Chem Soc 71(4):1460–1463Google Scholar
  32. 32.
    MacInnes DA, Cowperthwaite IA, Blanchard KC (1926) The moving-boundary method for determining transference numbers. V. A constant current apparatus. J Am Chem Soc 48:1909–1912Google Scholar
  33. 33.
    Hafezi H, Newman J (2000) Verification and analysis of transference number measurements by the galvanostatic polarization method. J Electrochem Soc 147(8):3036–3042Google Scholar

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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Chemical EngineeringUniversity of MichiganAnn ArborUSA