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Impedances of thin and layered systems: Cells with even or odd numbers of interfaces

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Abstract

Impedance data, e.g., system responses, from perturbing small amplitude applied sinusoid signals of near DC to high kilohertz frequencies, give chemical information. Analysis of frequency-dependent imaginary and real impedance proceeds from equivalent analog circuit elements to chemical and physical significance determined from many model systems. Already, it is possible to interpret bulk transport processes, surface kinetic effects, diffusion phenomena, and dependencies on the type of contacts: symmetric ion contact, symmetric metal contact or asymmetric metal-ion interfaces, and cell design; even (battery or sensor) and odd numbered (constrained junction or immiscible liquid) interfaces in a system. These analyses cover the chemical origins, locations and meanings of the lumped resistances, capacitances and transmission lines that are introduced by engineers in their strict analog interpretations of the impedance data.

Examples cover simple ohmic, simple diffusive behavior, complex behavior with surface interfacial kinetics or surface resistances, and with finite (nonblocking) or infinite (blocking) DC impedance. High and low frequency responses may show socalled constant phase element character that suggests fractal behavior. Low frequency data occasionally appear in the second quadrant of impedance plane plots. These results are caused by negative capacitances and resistances.

In this paper, chemical interpretations of analog circuit elements are mainly based on theory and observations of thin cells of electrolytes and solid and liquid films (membranes) that are ionic or mixed ionic/electronic conductors. The information should carry over into thickened, gelled, and tissue electrolyte phases and serve as a basis for medically-oriented, perhaps diagnostic impedance measurement applications already pioneered by Herman Schwan.

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Abbreviations

A :

active area

a i :

ion activity

a red :

reduced species activity

a ox :

oxidized species activity

C :

capacitance or capacitance/unit area

C i :

ion concentration

C red :

reduced species concentration

C ox :

oxidized species concentration

D :

diffusion coefficient

d :

half film (membrane) thickness

F :

Faraday constant

J e :

electron flux

J i :

ion flux

n :

number of electrons in half cell reaction

R :

resistance

R :

gas constant appearing with T

T :

absolute temperature

u e :

electron mobility

u i :

ion mobility

Z(jω):

impedance

z i :

ion charge

z red :

reduced species charge

z ox :

oxidized species charge

α:

parameter of Cole-Cole plot

ε:

dielectric constant

References

  1. Armstrong, R.D. Impedance plane display for an electrode with diffusion restricted to a thin layer. J. Electroanal. Chem. 198:177–180; 1986.

    Article  CAS  Google Scholar 

  2. Armstrong, R.D.; Lindholm, B.; Sharp, M. Impedance characteristics of a modified electrode. J. Electroanal. Chem. 202:69–74; 1986.

    Article  CAS  Google Scholar 

  3. Bard, A.J.; Faulkner, L.R. Electrochemical methods. New York: John Wiley & Sons; 1980.

    Google Scholar 

  4. Berlouis, L.E.A.; Chatham, J.; Girault, H.H.J.; Schiffrin, D.J. Transport properties of phospholipid monolayer membrane models. Ext. Abstr. Electrochem. Soc. 83-1(620):935–936; 1983.

    Google Scholar 

  5. Brumleve, T.R.; Buck, R.P. Numerical solution of Nernst-Planck and Poisson equations systems: Applications to membrane electrochemistry and solid state physics. J. Electroanal. Chem. 90:1–31; 1978.

    Article  CAS  Google Scholar 

  6. Brumleve, T.R.; Buck, R.P. Potential reversals across site-free, passive membranes—A simulation analysis. J. Electroanal. Chem. 126:55–72; 1981.

    CAS  Google Scholar 

  7. Brumleve, T.R.; Buck, R.P. Transmission line equivalent circuit models for electrochemical impedances. J. Electroanal. Chem. 126:73–104; 1981.

    CAS  Google Scholar 

  8. Buck, R.P. Transient electrical behavior of glass membranes. J. Electroanal. Chem. 18:363–399; 1968.

    CAS  Google Scholar 

  9. Buck, R.P. Potential-generating processes at interfaces: From electrolyte/metal and electrolyte/membrane to electrolyte/semiconductor. In: Cheung, P.W.; Fleming, D.G.; Neuman, M.R.; Ko, W.H., eds. Theory, design, and biomedical applications of solid state chemical sensors. W. Palm Beach: CRC Press, Inc.; 1978: pp. 1–41.

    Google Scholar 

  10. Buck, R.P. Transport properties of ionic conductors. Bergveld, P.; Zeme, J.; Middelhoek, S., eds; In: Chemically sensitive electronic devices. Amsterdam, Netherlands: Elsevier Pub. Co.; 1981: pp. 137–260.

    Google Scholar 

  11. Buck, R.P. The impedance methods applied to the investigation of ion-selective electrodes. Ion-Selective Electrode Rev. 4:3–74; 1982.

    CAS  Google Scholar 

  12. Buck, R.P. Electrochemistry of ion-selective electrodes. In: White, R.E.; Bockris, J.O.; Conway, B.E.; Yeager, E., eds. Comprehensive treatise of electrochemistry. New York: Plenum Pub. Co.; 1984: pp. 137–248.

    Google Scholar 

  13. Buck, R.P. Kinetics of bulk and interfacial ionic motion: Microscopic bases and limits for the Nernst-Planck equation applied to membrane systems. J. Membr. Sci. 17:1–62; 1984.

    Article  CAS  Google Scholar 

  14. Buck, R.P. Diffusion-migration impedances for finite, one-dimensional transport in thin layer and membrane cells: An analysis of derived electrical quantities and equivalent circuits. J. Electroanal. Chem. 210:1–19; 1986.

    Article  CAS  Google Scholar 

  15. Buck, R.P. Diffusion-migration impedances for finite, one-dimensional transport in thin-layer and membrane cells, mixed conduction cases: Os(III)/Os(II) ClO4. J. Electroanal. Chem. 219:23–48; 1987.

    Article  CAS  Google Scholar 

  16. Buck, R.P. Electron hopping in one dimension: Mixed conductor membranes. J. Phys. Chem. 92:4196–4200; 1988.

    CAS  Google Scholar 

  17. Buck, R.P. Steady state diffusion-migration potential differences in mixed conductor polymer films and thin layer cells. J. Electroanal. Chem. 271:1–14; 1989.

    Article  CAS  Google Scholar 

  18. Buck, R.P. Impedances of membrane systems with metal and/or ionic contacts. Electrochim. Acta 35:1609–1617; 1990.

    Article  CAS  Google Scholar 

  19. Buck, R.P.; Bronner, W.E. Prediction of salt effects on rates of single-ion crossings in ITIES experiments. J. Electroanal. Chem. 197:179–188, 1986.

    Article  CAS  Google Scholar 

  20. Buck, R.P.; Mathis, D.E.; Rhodes, R.K. Impedance measurements on purified silver chloride crystals using ionic vs electronic contacts. J. Electroanal. Chem. 80:245–257; 1977.

    Article  CAS  Google Scholar 

  21. Buck, R.P.; Stover, F.S.; Mathis, D.E. Site concentration determination in liquid ion exchange membranes: Theory and techniques. J. Electroanal. Chem. 82:345–360; 1977.

    Article  CAS  Google Scholar 

  22. Buck, R.P.; Stover, F.S.; Mathis, D.E. Site concentration determination in liquid ion exchange membranes: Experimental. J. Electroanal. Chem. 100:63–70; 1979.

    Article  CAS  Google Scholar 

  23. Buck, R.P.; Vanysck, P. Interfacial potential differences at mixed conductor interfaces: Nernst, Nerst-Donnan, Nernst Distribution and generalizations. J. Electroanal. Chem. 292:73–91; 1990.

    Article  CAS  Google Scholar 

  24. Cole, K.S. Membranes, ions, and impulses. Berkeley, CA: University of California Press; 1972; pp. 167–203.

    Google Scholar 

  25. Cole, K.S. Membranes, ions, and impulses. Berkeley, CA: University of California Press; 1972; p. 303.

    Google Scholar 

  26. Franceschetti, D.R.; Macdonald, J.R. Electrode kinetics, equivalent circuits, and system characterization: Small-signal conditions. J. Electroanal. Chem. 82:271–301; 1977.

    Article  Google Scholar 

  27. Franceschetti, D.R.; Macdonald, J.R. Diffusion of neutral and charged species under small-signal a.c. conditions. J. Electroanal. Chem. 101:307–316; 1979.

    Article  CAS  Google Scholar 

  28. Franceschetti, D.R.; Macdonald, J.R. Small-signal response theory for electrochomic thin films. J. Electroanal. Chem. 120:1754–1756; 1982.

    Google Scholar 

  29. Franceschetti, D.R.; Macdonald, J.R.; Buck, R.P. Interpretation of finite-length-Warburg-type impedances in supported and unsupported electrochemical cells with kinetically reversible electrodes. J. Electrochem. Soc. 138:1368–1371; 1991.

    CAS  Google Scholar 

  30. Gratzl, M.; Pungor, E.; Buck, R.P. Impedance measurements for pressed-pellet electrode membranes based on silver iodide and silver iodide/silver sulfide with solution contacts. Anal. Chim. Acta 189: 217–228; 1986.

    Article  CAS  Google Scholar 

  31. Hebb, M.B. Electrical conductivity of silver sulfide. J. Chem. Phys. 20:185–190; 1952.

    Article  CAS  Google Scholar 

  32. Hills, G.J.; Jacobs, P.W.M.; Lakshminarayanaiah, N. Membrane potentials: Part I The theory of the e.m.f. of cells containing ion-exchanging membranes. Part II The measurement of the e.m.f. of cells containing the cation-exchange membrane, cross-linked polymethacrylic acid. Proc. Roy. Soc. A262: 246–279; 1961.

    Google Scholar 

  33. Ho, C.; Raistrick, I.D.; Huggins, R.A. Application of a-c techniques to the study of lithium diffusion in tungsten trioxide thin films. J. Electrochem. Soc. 127:343–350; 1980.

    CAS  Google Scholar 

  34. Horval, G.; Graf, E.; Toth, K.; Pungor, E.; Buck, R.P. Plasticized poly(vinyl chloride) properties and characteristics of valinomycin electrodes: High-frequency resistances and dielectric properties. Anal. Chem. 58:2735–2740; 1986.

    Google Scholar 

  35. Hunter, T.B.; Tyler, P.S.; Smyrl, W.H.; White, H.S. Impedance analysis of poly(vinylferrocene) films. J. Electrochem. Soc. 134:2198–2204; 1987.

    CAS  Google Scholar 

  36. Iglehart, M.L.; Buck, R.P. Ion transport properties of cyclic and acyclic neutral carrier-containing membranes. Talanta. 36:89–98; 1989.

    Article  CAS  Google Scholar 

  37. Labes, R.; Lullies, H. Analyses der nerveneigenschaften durch wechselstrommessungen mit hilfe der membrankernleitertheorie. Arch. Ges. Physiol. 230:738–770; 1932.

    Article  Google Scholar 

  38. Lindner, E.; Niegreisz, Zs.; Toth, K.; Pungor, E.; Berube, T.R.; Buck, R.P. Electrical and dynamic properties of non-plasticized potassium selective membranes. J. Electroanal. Chem. 259: 67–80; 1989.

    Article  CAS  Google Scholar 

  39. Macdonald, J.R. Theory of space-charge polarization and electrode-discharge effects. J. Chem. Phys. 58:4982–5001; 1973.

    Article  CAS  Google Scholar 

  40. Macdonald, J.R. Simplified impedance/frequency-response results for intrinsically conducting solids and liquids. J. Chem. Phys. 61:3977–3996; 1974.

    Article  CAS  Google Scholar 

  41. Macdonald, J.R. Binary electrolyte small-signal frequency response. J. Electroanal. Chem. 53:1–55; 1974.

    Article  CAS  Google Scholar 

  42. Macdonald, J.R. Some a.c. response results for solids with recombining space charge. J. Phys. C7:L327-L331; 1974.

    Google Scholar 

  43. Macdonald, J.R. Complex rate constant for an electrochemical system involving an adsorbed intermediate. J. Electroanal. Chem. 70:17–26; 1976.

    CAS  Google Scholar 

  44. Macdonald, J.R. Interpretation of ac impedance measurements in solids. In: Mahan, G.D.; Roth, W.L., eds. Superionic conductors. New York: Plenum Press; 1976: pp. 81–97.

    Google Scholar 

  45. Macdonald, J.R. Space charge polarisation. In: Kleitz, M.; Dupuy, J., eds. Electrode processes in solid state ionics. Dordrecht: Reidel; 1976: pp. 149–180.

    Google Scholar 

  46. Macdonald, J.R. Impedance spectroscopy—Emphasizing solid materials and systems. New York: Wiley-Interscience Pubs.; 1987.

    Google Scholar 

  47. Macdonald, J.R.; Franceschetti, D.R. Theory of small-signal a.c. response of solids and liquids with recombining mobile charges. J. Chem. Phys. 68:1614–1637; 1978.

    CAS  Google Scholar 

  48. Mathis, D.E.; Buck, R.P. Ion transport in free and supported nitrobenzene aliquat nitrate liquid membrane ion-selective electrodes I: Bulk electrical properties including ion association and dielectric constant. II: Interfacial kinetics and time-dependent phenomena. J. Membr. Sci. 4:379–414; 1979.

    CAS  Google Scholar 

  49. Nyikos, L.; Pajkossy, T. Diffusion to fractal surfaces parts I, II, and III. Electrochim. Acta 31:1347, 1986; 34:171–186; 1989.

    Article  CAS  Google Scholar 

  50. Reid, J.D.; Vanysck, P.; Buck, R.P. Potential dependence of capacitance at a polarizable (blocked) liquid/liquid interface. J. Electroanal. Chem. 161:1–15; 1984.

    Article  CAS  Google Scholar 

  51. Reid, J.D.; Vanysck, P.; Buck, R.P. Potential dependence of capacitance at a liquid/liquid interface, unblocked interface. J. Electroanal. Chem. 170:109–125; 1984.

    Article  CAS  Google Scholar 

  52. Rhodes, R.K.; Buck, R.P. Impedance measurements using ionic contacts on purified and doped silver bromide crystals. J. Electroanal. Chem. 86:349–360; 1978.

    Article  CAS  Google Scholar 

  53. Rubinstein, I.; Rishpon, J.; Gottesfeld, S. An a.c.-impedance study of electrochemical processes at Nafion-coated electrodes. J. Electrochem. Soc. 133:729–734; 1986.

    CAS  Google Scholar 

  54. Sandifer, J.R.; Buck, R.P. Impedance characteristics of ion selective glass electrodes. J. Electroanal. Chem. 56:385–398; 1974.

    Article  CAS  Google Scholar 

  55. Stover, F.S.; Brumleve, T.R.; Buck, R.P. Comparison of time constants for liquid ion-exchange membrane electrode responses determined by an impedance method and an activity step method. Anal. Chim. Acta 109:259–278; 1979.

    Article  CAS  Google Scholar 

  56. Stover, F.S.; Buck, R.P. Site concentration determination in liquid ion exchange membranes. J. Electroanal. Chem. 94:59–66; 1978.

    Article  CAS  Google Scholar 

  57. Stover, F.S.; Buck, R.P. Electrical properties of mobile site ion exchange membranes with interfacial permselectivity breakdown: Non-zero current properties. J. Electroanal. Chem. 107:165–175; 1980.

    Article  CAS  Google Scholar 

  58. Toth, K.; Graf, E.; Horvai, G.; Pungor, E.; Buck, R.P. Plasticized poly(vinylchloride) properties and characteristics of valinomyvcin electrodes. Part 2: Low-frequency, surface-rate and Warburg impedance characteristics. Anal. Chem. 58:2741–2744; 1986.

    Article  CAS  Google Scholar 

  59. Vanysck, P. Electrochemistry on liquid/liquid interfaces: Lecture notes in chemistry No. 39. Berlin: Springer-Verlag; 1985.

    Google Scholar 

  60. Wagner, C. Galvanic cells with solid electrolytes involving ionic and electronic conduction. In: Proceedings of the 7th Meeting of the International Commission of Electrochemical Thermodynamics and Kinetics, London: Butterworths; 1957: pp. 361–377.

    Google Scholar 

  61. Wandlowski, T.; Marecek, V.; Samec, Z. Kinetic analysis of the picrate ion transfer across the interface between two immiscible electrolyte solutions from impedance measurements at the equilibrium potential. j. Electroanal. Chem. 242:291–302; 1988.

    CAS  Google Scholar 

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  1. Department of Chemistry, University of North Carolina, 27599-3290, Chapel Hill, NC

    Richard P. Buck

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Buck, R.P. Impedances of thin and layered systems: Cells with even or odd numbers of interfaces. Ann Biomed Eng 20, 363–383 (1992). https://doi.org/10.1007/BF02368537

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  • DOI: https://doi.org/10.1007/BF02368537

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