No data available.

Please log in to see this content.

You have no subscription access to this content.

No metrics data to plot.

The attempt to load metrics for this article has failed.

The attempt to plot a graph for these metrics has failed.

The full text of this article is not currently available.

oa

Nonlinear coupled equations for electrochemical cells as developed by the general equation for nonequilibrium reversible-irreversible coupling

### Abstract

We show how the Butler-Volmer and Nernst equations, as well as Peltier effects, are contained in the general equation for nonequilibrium reversible and irreversible coupling, GENERIC, with a unique definition of the overpotential. Linear flux-force relations are used to describe the transport in the homogeneous parts of the electrochemical system. For the electrode interface, we choose nonlinear flux-force relationships. We give the general thermodynamic basis for an example cell with oxygen electrodes and electrolyte from the solid oxide fuel cell. In the example cell, there are two activated chemical steps coupled also to thermal driving forces at the surface. The equilibrium exchange current density obtains contributions from both rate-limiting steps. The measured overpotential is identified at constant temperature and stationary states, in terms of the difference in electrochemical potential of products and reactants. Away from these conditions, new terms appear. The accompanying energy flux out of the surface, as well as the heat generation at the surface are formulated, adding to the general thermodynamic basis.

© 2014 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.

Received 22 May 2014
Accepted 25 August 2014
Published online 22 September 2014

Acknowledgments:
ETH Zurich is thanked for awarding guest professorships to D.B. and S.K.

Article outline:

I. INTRODUCTION
II. PROPERTIES OF GENERIC
III. THERMODYNAMIC VARIABLES OF CELL SUBSYSTEMS
A. Subsystem 3: The electrolyte
B. Subsystems 1 and 5: The electron conductor and gas supply channel
C. Subsystems 2 and 4: The electrode surfaces
IV. THE SYSTEM TOTAL ENERGY AND ENTROPY AND THEIR FUNCTIONAL DERIVATIVES
V. THE POISSON MATRICES
A. Subsystem 3: The electrolyte
B. Subsystems 1 and 5: The electron conductor and gas supply channels
C. Subsystems 2 and 4: The electrode surfaces
D. Remarks
VI. THE FRICTION MATRICES FOR LINEAR-FLUX FORCE RELATIONS
A. Subsystem 3: The electrolyte
B. Subsystems 1 and 5: The electron conductor and gas supply channels
C. Subsystems 2 and 4: The electrode surfaces
1. The isothermal linear regime
2. The general linear regime
3. Electrode Peltier heats
4. The friction matrix for the linear case
VII. NONLINEAR CONTRIBUTIONS TO THE EQUATION OF MOTION
VIII. GENERALIZED BUTLER-VOLMER EQUATIONS
A. The common Butler-Volmer equation
IX. DISCUSSION
A. GENERIC's contributions
1. The reversible contributions
2. The irreversible contributions
B. Assumptions
C. Coupled transport processes
D. The overpotential and the energy flux
X. CONCLUSIONS

/content/aip/journal/jcp/141/12/10.1063/1.4894759

1.

1. J. Newman and K. E. Thomas-Alyea, Electrochemical Systems, 3rd ed. (Wiley, Hoboken, 2004).

2.

2. J. O'M. Bockris, A. K. N. Reddy, and M. Gamboa-Aldeco, Modern Electrochemistry 2A (Klüwer-Academic Publishers, New York, 2002).

3.

3. A. J. Bard and L. R. Faulkner, Electrochemical Methods. Fundamentals and Applications, 2nd ed. (Wiley, Hoboken, 2001).

4.

4. S. H. Chan, X. J. Chen, and K. A. Khor, “Reliability and accuracy of measured overpotential in a three-electrode fuel cell system,” J. Appl. Electrochem. 31, 1163–1170 (2001).

http://dx.doi.org/10.1023/A:1012232301349
7.

7. S. Kjelstrup Ratkje and D. Bedeaux, “The overpotential as a surface singularity described by nonequilibrium thermodynamics,” J. Electrochem. Soc. 143, 779–789 (1996).

http://dx.doi.org/10.1149/1.1836538
8.

8. D. Bedeaux and S. Kjelstrup Ratkje, “The dissipated energy of electrode surfaces. Temperature jumps from coupled transport processes,” J. Electrochem. Soc. 143, 767–779 (1996).

http://dx.doi.org/10.1149/1.1836537
9.

9. S. Kjelstrup and D. Bedeaux, Nonequilibrium Thermodynamics of Heterogeneous Systems. Series on Advances in Statistical Mechanics (World Scientific, 2008), Vol. 16.

11.

11. J. Ge, S. Kjelstrup, D. Bedeaux, J. M. Simon, and B. Rousseau, “Transfer coefficients for evaporation of a system with a Lennard-Jones long-range spline potential,” Phys. Rev. E 75, 061604 (2007).

http://dx.doi.org/10.1103/PhysRevE.75.061604
12.

12. J. M. Rubi and S. Kjelstrup, “Mesoscopic nonequilibrium thermodynamics gives the same thermodynamic basis to Butler-Volmer and Nernst equations,” J. Phys. Chem. B 107, 13471–13477 (2003).

http://dx.doi.org/10.1021/jp030572g
14.

14. T. van Erp, T. Trinh, S. Kjelstrup, and K. Glavatskiy, “On the relation between the Langmuir and thermodynamic flux equations,” Front. Phys. Phys. Chem. Chem. Phys. 1, 1–14 (2014).

http://dx.doi.org/10.3389/fphy.2013.00036
17.

17. H. C. Öttinger, Beyond Equilibrium Thermodynamics (Wiley-Interscience, Hoboken, 2005).

20.

20. A. M. Svensson, S. Sunde, and K. Nisancioglu, “Mathematical modeling of oxygen exchange and transport in air-perovskite-YSZ interface region. II. Direct exchange of oxygen vacancies,” J. Electrochem. Soc. 145, 1390–1400 (1998).

http://dx.doi.org/10.1149/1.1838471
21.

21. T. Kawada, J. Suzuki, M. Sase, A. Kamai, K. Yashiro, Y. Nigara, J. Mizusaki, K. Kawamura, and H. Yugami, J. Electrochem. Soc. 149, E252–E259 (2002).

http://dx.doi.org/10.1149/1.1479728
22.

22. S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics (North-Holland, 1962).

24.

24. J. Ross and P. Mazur, “Some deductions from a statistical mechanical theory of chemical kinetics,” J. Chem. Phys. 35, 19–28 (1961).

http://dx.doi.org/10.1063/1.1731889
25.

25. J. Xu, S. Kjelstrup, and D. Bedeaux, “Molecular dynamics simulations of a chemical reaction, conditions for local equilibrium in a temperature gradient,” Phys. Chem. Chem. Phys. 8, 2017–2027 (2006).

http://dx.doi.org/10.1039/b516704c
26.

26. D. Bedeaux, and S. Kjelstrup, “The measurable heat flux that accompanies active transport by Ca^{2 +}-ATPase,” Phys. Chem. Chem. Phys. 10, 7304–7317 (2008).

http://dx.doi.org/10.1039/b810374g
http://aip.metastore.ingenta.com/content/aip/journal/jcp/141/12/10.1063/1.4894759

Article metrics loading...

/content/aip/journal/jcp/141/12/10.1063/1.4894759

2014-09-22

2016-09-25

### Abstract

We show how the Butler-Volmer and Nernst equations, as well as Peltier effects, are contained in the general equation for nonequilibrium reversible and irreversible coupling, GENERIC, with a unique definition of the overpotential. Linear flux-force relations are used to describe the transport in the homogeneous parts of the electrochemical system. For the electrode interface, we choose nonlinear flux-force relationships. We give the general thermodynamic basis for an example cell with oxygen electrodes and electrolyte from the solid oxide fuel cell. In the example cell, there are two activated chemical steps coupled also to thermal driving forces at the surface. The equilibrium exchange current density obtains contributions from both rate-limiting steps. The measured overpotential is identified at constant temperature and stationary states, in terms of the difference in electrochemical potential of products and reactants. Away from these conditions, new terms appear. The accompanying energy flux out of the surface, as well as the heat generation at the surface are formulated, adding to the general thermodynamic basis.

Full text loading...

/deliver/fulltext/aip/journal/jcp/141/12/1.4894759.html;jsessionid=fQ-mADx9EtN5pFBAyG5UK4Eb.x-aip-live-03?itemId=/content/aip/journal/jcp/141/12/10.1063/1.4894759&mimeType=html&fmt=ahah&containerItemId=content/aip/journal/jcp

###
Most read this month

Article

content/aip/journal/jcp

Journal

5

3

true

true

Commenting has been disabled for this content