The Modifications of Wagner’s Equation and Electrochemistry for the 21st Century

Author(s)
Tomofumi Miyashita

ABSTRACT

The use of samarium-doped ceria (SDC) electrolytes in SOFCs (solid oxide fuel cells) lowers the open circuit voltage (OCV) below the Nernst voltage (Vth). The OCV is calculated with Wagner’s equation which is included in NernstPlanck equation. Considering the separation of Boltzmann distribution, the fundamental basis of this topic is discussed. A constant voltage loss without leakage currents due to a mixed ionic and electronic conducting (MIEC) dense anode was explained. Only carrier species having sufficient energy to overcome the activation energy can contribute to current conduction, which is determined by incorporating a different constant in the definitions of chemical potential and electrical potential. This difference explains the results using dense MIEC anodes. This topic is not an isolated and minor topic, but of vital importance to electrochemical engineering for the 21st Century.

The use of samarium-doped ceria (SDC) electrolytes in SOFCs (solid oxide fuel cells) lowers the open circuit voltage (OCV) below the Nernst voltage (Vth). The OCV is calculated with Wagner’s equation which is included in NernstPlanck equation. Considering the separation of Boltzmann distribution, the fundamental basis of this topic is discussed. A constant voltage loss without leakage currents due to a mixed ionic and electronic conducting (MIEC) dense anode was explained. Only carrier species having sufficient energy to overcome the activation energy can contribute to current conduction, which is determined by incorporating a different constant in the definitions of chemical potential and electrical potential. This difference explains the results using dense MIEC anodes. This topic is not an isolated and minor topic, but of vital importance to electrochemical engineering for the 21st Century.

KEYWORDS

SOFC, Ceria, Open Circuit Voltage, Mixed Ionic and Electronic Conductors, Wagner’s Equation, Boltzmann’s Distribution, Maxwell’s Demon

SOFC, Ceria, Open Circuit Voltage, Mixed Ionic and Electronic Conductors, Wagner’s Equation, Boltzmann’s Distribution, Maxwell’s Demon

Cite this paper

nullT. Miyashita, "The Modifications of Wagner’s Equation and Electrochemistry for the 21st Century,"*Materials Sciences and Applications*, Vol. 2 No. 3, 2011, pp. 180-186. doi: 10.4236/msa.2011.23022.

nullT. Miyashita, "The Modifications of Wagner’s Equation and Electrochemistry for the 21st Century,"

References

[1] C. Wagner, “Beitrag zur Theorie des Anlaufvorgangs,” Zeitschrift für Physikalische Chemie, Vol. B41, 1933, p. 42.

[2] H. Rickert, “Electrochemistry of Solids—An Introduction,” Springer, Berlin, Heidelberg, 1982.

[3] T. Miyashita, “Necessity of Verification of Leakage Currents Using Sm Doped Ceria Electrolytes in SOFCs,” Journal of Materials Science, Vol. 41, No. 10, 2006, pp. 3183-3184. doi:10.1007/s10853-006-6371-8

[4] T. Miyashita, “Current-Voltage Relationship Considering Electrode Degradation Using Sm-Doped Ceria Electrolytes in SOFCs,” ECS Transactions, Vol. 35, 2011. (In Press).

[5] T. Miyashita, “The Limitations of Wagner’s Equation in Solid-State Electrochemistry,” ECS Transactions, Vol. 33, 2011. (In Press).

[6] T. Miyashita, “Empirical Equation about Open Circuit Voltage in SOFC,” Journal of Materials Science,Vol. 40, No. 22, 2005, p. 6027. doi:10.1007/s10853-005-4560-5

[7] T. Miyashita, “Fundamental Thermodynamic Modifications in Wagner’s Equation in Solid State Electrochemistry,” ECS Transactions, Vol. 28, 2010, pp. 39-49. doi:10.1149/1.3502443

[8] T. Miyashita, “Quantum Physics can be Understood in Terms of Classical Thermodynamics,” Journal of Modern Physics, Vol. 2, 2011, pp. 26-29. doi:10.4236/jmp.2011.31005

[9] T. Miyashita, “Empirical Relations about the Number of Dimensions in Theoretical Physics with the Concept of Common and Unshared Dimensions,” Journal of Modern Physics, Vol. 2, 2010, pp. 147-149. doi:10.4236/jmp.2010.12021

[1] C. Wagner, “Beitrag zur Theorie des Anlaufvorgangs,” Zeitschrift für Physikalische Chemie, Vol. B41, 1933, p. 42.

[2] H. Rickert, “Electrochemistry of Solids—An Introduction,” Springer, Berlin, Heidelberg, 1982.

[3] T. Miyashita, “Necessity of Verification of Leakage Currents Using Sm Doped Ceria Electrolytes in SOFCs,” Journal of Materials Science, Vol. 41, No. 10, 2006, pp. 3183-3184. doi:10.1007/s10853-006-6371-8

[4] T. Miyashita, “Current-Voltage Relationship Considering Electrode Degradation Using Sm-Doped Ceria Electrolytes in SOFCs,” ECS Transactions, Vol. 35, 2011. (In Press).

[5] T. Miyashita, “The Limitations of Wagner’s Equation in Solid-State Electrochemistry,” ECS Transactions, Vol. 33, 2011. (In Press).

[6] T. Miyashita, “Empirical Equation about Open Circuit Voltage in SOFC,” Journal of Materials Science,Vol. 40, No. 22, 2005, p. 6027. doi:10.1007/s10853-005-4560-5

[7] T. Miyashita, “Fundamental Thermodynamic Modifications in Wagner’s Equation in Solid State Electrochemistry,” ECS Transactions, Vol. 28, 2010, pp. 39-49. doi:10.1149/1.3502443

[8] T. Miyashita, “Quantum Physics can be Understood in Terms of Classical Thermodynamics,” Journal of Modern Physics, Vol. 2, 2011, pp. 26-29. doi:10.4236/jmp.2011.31005

[9] T. Miyashita, “Empirical Relations about the Number of Dimensions in Theoretical Physics with the Concept of Common and Unshared Dimensions,” Journal of Modern Physics, Vol. 2, 2010, pp. 147-149. doi:10.4236/jmp.2010.12021