Annals of Biomedical Engineering

, Volume 20, Issue 3, pp 269–288 | Cite as

Linear and nonlinear electrode polarization and biological materials

  • H. P. Schwan


Electrode polarization is a major nuisance while determining dielectric properties of cell and particle suspensions and tissues, particularly at low frequencies. Understanding of these interfacial phenomena and appropriate modelling are essential in order to correct for its distortion of the dielectric properties of the sample of interest. I survey the following topics, concentrating on contributions from our laboratory:

Linear properties of electrode polarization and relevant models

Effects of electrode polarization on sample impedance

Effects of sample on polarization impedance

Techniques of correction

Extension of linear to nonlinear models

Harmonics generated in the nonlinear range.


Bioelectrodes Electrodes Linear Nonlinear Impedance Polarization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Buck, R.P. Impedances of thin and layered systems: Cells with even or odd numbers of interfaces. Ann. Biomed. Eng. 20:363–383; 1992.PubMedGoogle Scholar
  2. 2.
    Cole, K.S.; Cole, R.H. Dispersion and absorption in dielectrics. I. Alternating current characteristics. J. Chem. Phys. 9:341–351; 1941.Google Scholar
  3. 3.
    Davidson, D.W.; Cole, R.H. Dielectric relaxation in glycerine. J. Chem. Phys. 18:1417; 1950.CrossRefGoogle Scholar
  4. 4.
    de Levie, R. The admittance of the interface between a metal electrode and an aqueous electrolyte solution: Some problems and pitfalls. Ann. Biomed. Eng. 20:337–347; 1992.PubMedGoogle Scholar
  5. 5.
    Fricke, H. The theory of electrolytic polarization. Phil. Mag. 14:310–318; 1932.Google Scholar
  6. 6.
    Geddes, L.A. Electrodes and the measurement of bioelectric events. New York: Wiley Interscience; 1972.Google Scholar
  7. 7.
    Geddes, L.A.; Baker, L.E. Principles of applied biomedical instrumentation. (2nd ed.) New York: Wiley Interscience; 1975.Google Scholar
  8. 8.
    Geddes, L.A.; DaCosta, C.P.; Wise, G. The impedance of stainless steel electrodes. Med. Biol. Eng. Comput. 9:511–521; 1971.Google Scholar
  9. 9.
    Geddes, L.A.; Foster, K.S.; Reilly, J.; Voorhees, W.D.; Bourland, J.D.; Ragheb, T.; Fearnot, N.E. The rectification properties of an electrode-electrolyte interface operated at high current density. IEEE Trans. Biomed. Eng. 34:669–672; 1987.PubMedGoogle Scholar
  10. 10.
    Jaron, D.; Briller, S.A.; Schwan, H.P.; Geselowitz, D. Nonlinearity of pacemaker electrodes. IEEE Trans. Biomed. Eng. 16:132–138; 1969.PubMedGoogle Scholar
  11. 11.
    Jaron, D.; Schwan, H.P.; Geselowitz, D.B. A mathematical model for the polarization impedance of cardiac pacemaker electrodes. Med. Biol. Eng. 6:579–594; 1968.PubMedGoogle Scholar
  12. 12.
    Kohlrausch, F.; Holborn, L. “Das Leitvermoegen der Elektrolyte.” Leipzig: Teubner; 1898.Google Scholar
  13. 13.
    Kronig, R. On the theory of dispersion of x-rays. J. Opt. Soc. Am. 12:547; 1926 (See also Kramers, H.A. Atti Congr. dei Fisici. Como. 1927: p. 545.)Google Scholar
  14. 14.
    McAdams, E.T.; Jossinet, J. DC nonlinearity of the solid electrode-electrolyte interface-impedance. Innovation et Technologie en Biol. et Med. 12:329–343; 1991.Google Scholar
  15. 15.
    McAdams, E.T.; Jossinet, J. A physical interpretation of Schwan's limit current of linearity. Ann. Biomed. Eng. 20:307–319; 1992.PubMedGoogle Scholar
  16. 16.
    Moussavi, M.; Sun, H.H.; Schwan, H.P.; Richter, A. Nonlinear phenomenon of interfacial polarization immittance of a Pt electrode. Ann. Biomed. Eng. 18:505–518; 1990.PubMedGoogle Scholar
  17. 17.
    Onaral, B.; Schwan, H.P. Linear and nonlinear properties of platinum electrode polarization. Part I: Frequency dependence at very low frequencies. Med. Biol. Eng. Comp. 20:299–306; 1982a.Google Scholar
  18. 18.
    Onaral, B.; Schwan, H.P. Linear and nonlinear properties of platinum electrode polarization. Part II: Time domain analysis. Med. Biol. Eng. Comp. 21:210–216; 1982b.Google Scholar
  19. 19.
    Ragheb, T.; Geddes, L.A. Electrical properties of metallic electrodes. Med. Biol. Eng. Comp. 28:182–186; 1990.Google Scholar
  20. 20.
    Schwan, H.P. Electrical properties of tissues and cells. In: Lawrence, J.H.; Tobias, C.A., eds. Advances biological medical physics, Vol. 5 New York: Academic Press; 1957: pp. 147–209.Google Scholar
  21. 21.
    Schwan, H.P. Determination of biological impedances. In: Nastuk, W.L., ed. Physical techniques in biological research, Vol. 6. New York: Academic Press; 1963: pp. 323–406.Google Scholar
  22. 22.
    Schwan, H.P. Alternating current electrode polarization. Biophysik 3:181–201; 1966.CrossRefPubMedGoogle Scholar
  23. 23.
    Schwan, H.P. Electrode polarization impedance and measurements in biological materials. Ann. New York Acad. Sci. 148:191–209; 1968.Google Scholar
  24. 24.
    Schwan, H.P.; Ferris, C.D. Four electrode null techniques for impedance measurement with high resolution. Rev. Sci. Inst. 39:481–485; 1968.Google Scholar
  25. 25.
    Schwan, H.P.; Maczuk, J.G. Electrode polarization impedance: Limits of linearity. Proc. 18th Ann. Conf. Med. Biol. IEEE-ISA. Philadelphia, PA: 1965.Google Scholar
  26. 26.
    Schwan, H.P.; Onaral, B. Linear and nonlinear properties of platinum electrode polarization. Part III: Equivalence of frequency- and time domain behavior. Med. Biol. Eng. Comp. 23:28–32; 1985.Google Scholar
  27. 27.
    Schwan, H.P.; Sittel, K. Wheatstone bridge for admittance determinations of highly conducting materials at low frequencies. Trans. AIEE. (Comm. & Elec.) May:114; 1953.Google Scholar
  28. 28.
    Simpson, R.W.; Berberian, J.G.; Schwan, H.P. Nonlinear AC and DC polarization of platinum electrodes. IEEE Trans. Biomed. Eng. 27:166–171; 1980.PubMedGoogle Scholar
  29. 29.
    Sun, H.H.; Charef, A.; Tsao, Y.; Onaral, B. Analysis of polarization dynamics by singularity decomposition method. Ann. Biol. Eng. 20:321–335; 1992.Google Scholar
  30. 30.
    Sun, H.H.; Onaral, B. A unified approach to represent metal electrode polarization. IEEE Trans. Biomed. Eng. 30:399–406; 1983.PubMedGoogle Scholar
  31. 31.
    Warburg, E. Ueber das Verhalten sogenannter unpolarisierbarer Elektroden gegen Wechselstrom. Ann. d. Physik 67:493–499; 1899.Google Scholar
  32. 32.
    Warburg, E. Ueber die Polarisationskapazitaet des Platins. Ann. d. Physik. 6:125–135; 1901.Google Scholar

Copyright information

© Pergamon Press Ltd. 1992

Authors and Affiliations

  • H. P. Schwan
    • 1
    • 2
  1. 1.Department of BioengineeringUniversity of PennsylvaniaPhiladelphia
  2. 2.Biomedical Engineering and Science InstituteDrexel UniversityPhiladelphia

Personalised recommendations