Lagrangian and Network Formulations of Nonlinear Electrochemical Systems
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.
KeywordsElectrochemical Cell Entropy Generation Electrical Load Dissipative Process Dissipation Function
Unable to display preview. Download preview PDF.
- 3.Prigogine, I. (1967) Introduction to thermodynamics of irreversible processes, Wiley, New York.Google Scholar
- 7.de Donder, T. (1928) L’Affinite, Gauthier-Villars, Paris.Google Scholar
- 10.Keizer, J. (1987) Statistical Thermodynamics of Nonequilibrium Processes, Springer, New York.Google Scholar
- 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.Shiner, J.S. (1990) Biophys. J. 57, 194a.Google Scholar
- 20.Shiner, J.S. (1993) Biophys. J. 64, A244.Google Scholar
- 22.Koryta, J. and Stulik, K. (1983) Ion-selective Electrodes, Cambridge University Press, Cambridge,.Google Scholar
- 23.Alberty, R.A. and Silbey, R.J. (1992) Physical Chemistry, Wiley, New York.Google Scholar
- 27.Shiner, J.S. and Sieniutycz, S. (1996) in J.S. Shiner (ed.), Entropy and Entropy Generation, Kluwer, Dordrecht, this volume.Google Scholar