Lagrangian and Network Formulations of Nonlinear Electrochemical Systems

  • J. S. Shiner
  • S. Fassari
  • Stanislaw Sieniutycz
Part of the Understanding Chemical Reactivity book series (UCRE, volume 18)


We show that the equations of motion for systems with electrochemical coupling can be derived from a dissipative Lagrangian formalism and that these systems can also be cast into an equivalent network formulation. These formulations are possible since we have shown how to cast chemical reaction kinetics into the formalisms common to electrical networks and other nonchemical systems. The examples treated are simple electrochemical cells obeying Butler-Vollmer kinetics at the electrodes and mass action kinetics for the other reactions. The chemical reactions are coupled to an electrical load and in one example to an additional electrical potential source. For the latter case we show that the stationary state is described by equations of the form of the phenomenological equations of nonequilibrium thermodynamics and that these equations display an algebraic symmetry but not the differential symmetry of Onsager reciprocity in general.


Electrochemical Cell Entropy Generation Electrical Load Dissipative Process Dissipation Function 
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  1. 1.
    Onsager, L. (1931) Phys. Rev. 37, 405–426.CrossRefADSzbMATHGoogle Scholar
  2. 2.
    Onsager, L. (1931) Phys. Rev. 38, 2265–2279.CrossRefADSzbMATHGoogle Scholar
  3. 3.
    Prigogine, I. (1967) Introduction to thermodynamics of irreversible processes, Wiley, New York.Google Scholar
  4. 4.
    Glansdorff, P. and Prigogine, I. (1971) Thermodynamic Theory of Structure, Stability and Fluctuations, Wiley, New York.zbMATHGoogle Scholar
  5. 5.
    Nicolis, G. and Prigogine, I. (1977) Self-Organization in Nonequilibrium Systems, Wiley, New York.zbMATHGoogle Scholar
  6. 6.
    Keizer, J. (1977) BioSystems. 8, 219–226.CrossRefGoogle Scholar
  7. 7.
    de Donder, T. (1928) L’Affinite, Gauthier-Villars, Paris.Google Scholar
  8. 8.
    Goldstein, H. (1980) Classical Mechanics, Addison-Wesley, Reading.zbMATHGoogle Scholar
  9. 9.
    MacFarlane, A.G.J. (1970) Dynamical System Models, Harrap, London.zbMATHGoogle Scholar
  10. 10.
    Keizer, J. (1987) Statistical Thermodynamics of Nonequilibrium Processes, Springer, New York.Google Scholar
  11. 11.
    Shiner, J.S. (1992) in S. Sieniutycz and P. Salamon (eds.) Flow, Diffusion and Rate Processes, Taylor & Francis, New York, pp. 248–282.Google Scholar
  12. 12.
    Shiner, J.S. (1990) Biophys. J. 57, 194a.Google Scholar
  13. 13.
    Sieniutycz, S. (1987) Chem. Eng. Sci. 42, 2697–2711.CrossRefGoogle Scholar
  14. 14.
    Sieniutycz, S. and Shiner, J.S. (1992) Open Sys. Information Dyn. 1, 149–182.zbMATHCrossRefGoogle Scholar
  15. 15.
    Sieniutycz, S. and Shiner, J.S. (1992) Open Sys. Information Dyn. 1, 327–348.zbMATHCrossRefGoogle Scholar
  16. 16.
    Rayleigh, J.W.S. (1945) The Theory of Sound, Dover, New York.zbMATHGoogle Scholar
  17. 17.
    Oster, G.F., Perelson, A. and Katchalsky, A. (1973) Q. Rev. Biophys. 6, 1–134.CrossRefGoogle Scholar
  18. 18.
    Wyatt, J.L. (1978) Computer Programs in Biomedicine 8, 180–195.CrossRefGoogle Scholar
  19. 19.
    Shiner, J.S., Lüscher, H.-R. and Sieniutycz, S. (1992) Experientia 48, A91.CrossRefGoogle Scholar
  20. 20.
    Shiner, J.S. (1993) Biophys. J. 64, A244.Google Scholar
  21. 21.
    Hjelmfelt, A., Schreiber, I. and Ross J. (1991) J. Phys. Chem. 95, 6048–6053.CrossRefGoogle Scholar
  22. 22.
    Koryta, J. and Stulik, K. (1983) Ion-selective Electrodes, Cambridge University Press, Cambridge,.Google Scholar
  23. 23.
    Alberty, R.A. and Silbey, R.J. (1992) Physical Chemistry, Wiley, New York.Google Scholar
  24. 24.
    Grabert, H., Hänggi, P. and Oppenheim, I. (1983) physica 117A, 300–316.ADSGoogle Scholar
  25. 25.
    Shiner, J.S. (1987) J. Chem. Phys. 87, 1089–1094.CrossRefADSGoogle Scholar
  26. 26.
    Schlögl, F. (1972) Z. Phys. 253, 147–161.CrossRefADSGoogle Scholar
  27. 27.
    Shiner, J.S. and Sieniutycz, S. (1996) in J.S. Shiner (ed.), Entropy and Entropy Generation, Kluwer, Dordrecht, this volume.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • J. S. Shiner
    • 1
  • S. Fassari
    • 1
  • Stanislaw Sieniutycz
    • 2
  1. 1.Physiologisches InstitutUniversität BernBernSwitzerland
  2. 2.Department of Chemical EngineeringWarsaw Technical UniversityWarsawPoland

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