Impedance of the Faradaic Reactions in the Presence of Mass Transfer

  • Andrzej Lasia
Chapter

Abstract

In Chap. 2 we saw the responses of electrical circuits containing the elements R, C, and L. Because these are linear elements, their impedance is independent of the ac amplitude used. However, in electrochemical systems, we do not have such elements; we have solution–electrode interfaces, redox species, adsorption, etc. In this and the following chapters, we will learn how to express the electrochemical interfaces and reactions in terms of equations that, in particular cases, can be represented by the electrical equivalent circuits. Of course, such circuits are only the electrical representations of physicochemical phenomena, and electrical elements such as resistance, capacitance, or inductance do not exist physically in cells. However, such a presentation is useful and helps in our understanding of the physicochemical phenomena taking place in electrochemical cells. Before presenting the case of electrochemical reactions, the case of an ideally polarizable electrode will be presented.

Keywords

Charge Transfer Resistance Total Impedance Diffusion Layer Thickness Electrical Equivalent Circuit Complex Plane Plot 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 8.
    E. Warburg, Ann. Phys. Chem. 67, 493 (1899)CrossRefGoogle Scholar
  2. 9.
    P.I. Dolin, B.V. Ershler, Acta Physicochem. URSS 13, 747 (1940)Google Scholar
  3. 10.
    J.E.B. Randles, Trans. Farad. Soc. 1, 11 (1947); J.E.B. Randles, in Transactions of the Symposium on Electrode Processes, ed. by E. Yeager, (Wiley, New York, 1961), p. 209Google Scholar
  4. 15.
    D.D. Macdonald, Transient Techniques in Electrochemistry (Plenum Press, New York, 1977)CrossRefGoogle Scholar
  5. 17.
    A.J. Bard, L.R. Faulkner, Electrochemical Methods. Fundamentals and Applications (Wiley, New York, 2001)Google Scholar
  6. 24.
    E. Barsoukov, J.R. Macdonald (eds.), Impedance Spectroscopy: Theory, Experiment, and Applications, 2nd edn. (Wiley-Interscience, Hoboken, 2005)Google Scholar
  7. 29.
    D.E. Smith, AC polarography and related techniques: theory and practice, in Electroanalytical Chemistry: A Series of Advances, ed. by A.J. Bard, vol. 1 (Marcel Dekker, New York, 1966), pp. 1–155Google Scholar
  8. 30.
    M. Sluyters-Rehbach, J.H. Sluyters, Sine wave methods in the study of electrode processes, in Electroanalytical Chemistry: A Series of Advances, ed. by A.J. Bard, vol. 4 (Marcel Dekker, New York, 1970), pp. 1–128Google Scholar
  9. 32.
    D.E. Smith, Applications of on-line digital computers in ac polarography and related techniques, in Electrochemistry: Calculations, Simulations, and Instrumentation, ed. by J.S. Mattson, H.B. Mark, H.C. MacDonald (Marcel Dekker, New York, 1972), pp. 369–422Google Scholar
  10. 39.
    M. Sluyters-Rehbach, J. Sluyters, A.C. techniques (for electrode kinetics), in Comprehensive Treatise of Electrochemistry, ed. by J.O’M. Bockris, Yu.A. Chizmadzhev, B.E. Conway, S.U.M. Khan, S. Sarangapani, S. Srinivasan, R.E. White, E. Yeager, vol. 9 (Plenum Press, New York, 1984), pp. 177–292Google Scholar
  11. 61.
    A. Lasia, Applications of electrochemical impedance spectroscopy to hydrogen adsorption, evolution and absorption into metals, in Modern Aspects of Electrochemistry, vol. 35, ed. by B.E. Conway, R.E. White (Kluwer/Plenum, New York, 2002), p. 1Google Scholar
  12. 144.
    J. Crank, The Mathematics of Diffusion (Oxford University Press, Glasgow, 1970)Google Scholar
  13. 145.
    S.R. Taylor, E. Gileadi, Corrosion 51, 664 (1995)CrossRefGoogle Scholar
  14. 146.
    J. Sluyters, Rec. Trav. Chim. Pays-Bas 79, 1092 (1960)CrossRefGoogle Scholar
  15. 147.
    T.J. VanderNoot, J. Electroanal. Chem. 300, 199 (1991)CrossRefGoogle Scholar
  16. 148.
    J. Sluyters, J.J.C. Oomen, Rec. Trav. Chim. Pays-Bas 79, 1101 (1960)CrossRefGoogle Scholar
  17. 149.
    J.R. Delmastro, D.E. Smith, J. Electroanal. Chem. 9, 192 (1965)Google Scholar
  18. 150.
    G. Brisard, L’electroreduction du Cd2+ dans le DMSO en presence du perchlorate de tetraethylammonium, MSc Thesis, Universite de Sherbrooke, 1986Google Scholar
  19. 151.
    W.R. Fawcett, A. Lasia, J. Phys. Chem. 82, 1114 (1978)CrossRefGoogle Scholar
  20. 152.
    R. de Levie, A.A. Husovsky, J. Electroanal. Chem. 22, 29 (1969)CrossRefGoogle Scholar
  21. 153.
    D.E. Smith, Anal. Chem. 35, 610 (1963)CrossRefGoogle Scholar
  22. 154.
    C. Gabrielli, P.P. Grand, A. Lasia, H. Perrot, J. Electrochem. Soc. 151, A1943–A1949 (2004)CrossRefGoogle Scholar
  23. 155.
    L. Birry, A. Lasia, Electrochim. Acta 51, 3356 (2006)CrossRefGoogle Scholar
  24. 156.
    M.H. Martin, A. Lasia, Electrochim. Acta 53, 6317 (2008)CrossRefGoogle Scholar
  25. 157.
    C. Gabrielli, P.P. Grand, A. Lasia, H. Perrot, J. Electrochem. Soc. 151, A1943 (2004)CrossRefGoogle Scholar
  26. 158.
    J.R. Macdonald, J. Phys. Chem. 60, 343 (1974)CrossRefGoogle Scholar
  27. 164.
    J.R. Macdonald, J. Phys. Condens. Matter 24, 175004 (2012)CrossRefGoogle Scholar
  28. 165.
    M. Fleischmann, S. Pons, J. Daschbach, J. Electroanal. Chem. 317, 1 (1991)CrossRefGoogle Scholar
  29. 166.
    M. Fleischmann, S. Pons in Ultramicroelectrodes, ed. by M. Fleischmann, S. Pons, D.R. Rolison, P.P. Schmidt, (Datatech, Morganton, 1987), p. 52.Google Scholar
  30. 167.
    T. Jacobsen, K. West, Electrochim. Acta 40, 255 (1995)CrossRefGoogle Scholar
  31. 168.
    M. Fleischmann, S. Pons, J. Electroanal. Chem. 250, 277 (1988)CrossRefGoogle Scholar
  32. 169.
    R. Michel, C. Montella, C. Verdier, J.-P. Diard, Electrochim. Acta 55, 6263 (2010)CrossRefGoogle Scholar
  33. 170.
    V.G. Levich, Physicochemical Hydrodynamics (Prentice-Hall, Englewood Cliffs, 1962)Google Scholar
  34. 171.
    J.M. Coueignoux, D. Schuhmann, J. Electroanal. Chem. 17, 245 (1968)CrossRefGoogle Scholar
  35. 172.
    D.A. Scherson, J. Newman, J. Electrochem. Soc. 111, 110 (1980)CrossRefGoogle Scholar
  36. 173.
    B. Tribollet, J. Newman, J. Electrochem. Soc. 130 (1983) 823; 2016Google Scholar
  37. 174.
    C. Deslouis, C. Gabrielli, B. Tribollet, J. Electrochem. Soc. 130, 2044 (1983)CrossRefGoogle Scholar
  38. 175.
    E. Levart, D. Schuhmann, J. Electroanal. Chem. 53, 77 (1974)CrossRefGoogle Scholar
  39. 176.
    B. Tribollet, J. Newman, W.H. Smyrl, J. Electrochem. Soc. 135, 134 (1988)CrossRefGoogle Scholar
  40. 177.
    C. Deslouis, I. Epelboin, M. Keddam, J.C. Lestrade, J. Electroanal. Chem. 28, 57 (1970)CrossRefGoogle Scholar
  41. 178.
    M.E. Orazem, M. Durbha, C. Deslouis, H. Takenouti, B. Tribollet, Electrochim. Acta 44, 4403 (1999)CrossRefGoogle Scholar
  42. 179.
    M. Durbha, M.E. Orazem, B. Tribollet, J. Electrochem. Soc. 146, 2199 (1999)CrossRefGoogle Scholar
  43. 180.
    J. Barber, S. Morin, B.E. Conway, J. Electroanal. Chem. 446, 125 (1998)CrossRefGoogle Scholar
  44. 181.
    D.E. Smith, Anal. Chem. 35, 602 (1963)CrossRefGoogle Scholar
  45. 183.
    T.G. McCord, D.E. Smith, J. Electroanal. Chem. 26, 61 (1970)CrossRefGoogle Scholar
  46. 184.
    T.G. McCord, D.E. Smith, Anal. Chem. 41, 1423 (1969)CrossRefGoogle Scholar
  47. 186.
    A.M. Band, R.J. O’Halloran, I. Ruzic, D.E. Smith, J. Electroanal. Chem. 132, 39 (1982)Google Scholar
  48. 187.
    J.W. Hayes, I. Ruzic, D.E. Smith, G.L. Booman, J.R. Delmastro, J. Electroanal. Chem. 51, 269 (1974)CrossRefGoogle Scholar
  49. 188.
    H.R. Sobel, D.E. Smith, J. Electroanal. Chem. 26, 271 (1970)CrossRefGoogle Scholar
  50. 189.
    I. Ruzic, H.R. Sobel, D.E. Smith, J. Electroanal. Chem. 65, 21 (1975)CrossRefGoogle Scholar
  51. 190.
    J. Hayes, I. Ruic, D.E. Smith, G.L. Booman, J.R. Delmastro, J. Electroanal. Chem. 51, 245 (1974)CrossRefGoogle Scholar
  52. 191.
    D.E. Smith, Anal. Chem. 35, 610 (1963)CrossRefGoogle Scholar
  53. 192.
    I. Ruzic, H.R. Sobel, D.E. Smith, J. Electroanal. Chem. 65, 21 (1975)CrossRefGoogle Scholar
  54. 195.
    T. Matusinovic, D.E. Smith, J. Electroanal. Chem. 98, 133 (1979)CrossRefGoogle Scholar
  55. 196.
    H. Gerischer, Z. Physik. Chem. 198, 286 (1951)Google Scholar
  56. 197.
    B.A. Boukamp, H.J.M. Bouwmeester, Solid State Ion. 157, 29 (2003)CrossRefGoogle Scholar
  57. 199.
    B.A. Boukamp, M. Verbraeken, D.H.A. Blank, P. Holtappels, Solid State Ion. 177, 2539 (2006)CrossRefGoogle Scholar
  58. 200.
    S.B. Adler, J.A. Lane, B.C.H. Steele, J. Electrochem. Soc. 143, 3554 (1996)CrossRefGoogle Scholar
  59. 201.
    R.U. Atangulov, I.V. Murygin, Solid State Ion. 67, 9 (1993)CrossRefGoogle Scholar
  60. 202.
    S. Havriliak, S. Negami, Polymer 8, 161 (1967)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Andrzej Lasia
    • 1
  1. 1.Département de chimieUniversité de SherbrookeSherbrookeCanada

Personalised recommendations