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Butler-Volmer kinetics
Posted 10.11.2014, 10:15 GMT-5 Battery Design, Electrochemistry 3 Replies
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As an electrochemist I cannot understand the formulation of the equation of the electrode reaction kinetics (attached). Why is there (n - eta) in the first exponent, instead of 1- eta? The formulation does return Nernst looking equation at zero current, but it neither agrees with the documentation of Comsol. Is this simply a cosmetic bug, or how is Comsol calculating reaction kinetics?
Note also that zero overpotential does not mean the C_Ox = C_red, as Comsol appears to define, but that the ratio (C_Ox/C_red) defines the value of the equilibrium potential.
The current-overpotential and the exchange current density equations are usually written in textbooks as in the other attachment. The formula that Comsol uses thus is a mixture of Butler-Volmer and current-overpotential equations. Literature is admittedly a bit confusing in these issues.; I follow the treatment of Bard & Faulkner.
Note also that zero overpotential does not mean the C_Ox = C_red, as Comsol appears to define, but that the ratio (C_Ox/C_red) defines the value of the equilibrium potential.
The current-overpotential and the exchange current density equations are usually written in textbooks as in the other attachment. The formula that Comsol uses thus is a mixture of Butler-Volmer and current-overpotential equations. Literature is admittedly a bit confusing in these issues.; I follow the treatment of Bard & Faulkner.
Attachments:
3 Replies Last Post 12.11.2014, 08:50 GMT-5
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Posted:
1 decade ago
COMSOL follows the definition, common in the modern literature, that the transfer coefficient alpha takes values between 0 and n rather than between 0 and 1. So in place of n*(1-alpha) one writes (n-alpha). This has the benefit that the transfer coefficient alpha can be interpreted physically as a "number of electrons". You may be interested in the discussion of the relative virtues of the two definitions in Pure Appl. Chem. 2014, 86, 245-258.
The expression quoted in the documentation is specifically the one-electron equation.
The condition of zero current implies a condition of (dynamic) equilibrium. Substitution of i_loc = 0 into the Butler-Volmer equation as quoted yields the Nernst equation, which for a unimolecular reaction of dilute species states in turn that at zero overpotential, cOx = cRed.
The expression quoted in the documentation is specifically the one-electron equation.
The condition of zero current implies a condition of (dynamic) equilibrium. Substitution of i_loc = 0 into the Butler-Volmer equation as quoted yields the Nernst equation, which for a unimolecular reaction of dilute species states in turn that at zero overpotential, cOx = cRed.
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Posted:
1 decade ago
Thanks for a prompt reply. I'll check that paper you referred to, and perhaps comment later on.
I have to disagree with the claim that zero overpotential means C_ox = C_red. Let us say that in the solution we have [Fe(II)] = 0.1 M and [Fe(III)] = 0.5 M. Then clearly at equilibrium, i = 0, the concentrations are not equal, and
E_eq = E^0 + RT/F*ln(5).
It appears that Comsol is defining overpotential as E - E^0, while it should be defined E - E_eq.
After all, I am not that purist, the main point that I know what I am calculating, and now how Comsol is writing the equations.
Best regards
Lasse
I have to disagree with the claim that zero overpotential means C_ox = C_red. Let us say that in the solution we have [Fe(II)] = 0.1 M and [Fe(III)] = 0.5 M. Then clearly at equilibrium, i = 0, the concentrations are not equal, and
E_eq = E^0 + RT/F*ln(5).
It appears that Comsol is defining overpotential as E - E^0, while it should be defined E - E_eq.
After all, I am not that purist, the main point that I know what I am calculating, and now how Comsol is writing the equations.
Best regards
Lasse
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Posted:
1 decade ago
Hi again
I have now read the paper you referred to, and also checked the new edition of Bard & Faulkner. You probably refer to eq. (16) in the paper:
alpha_c + alpha_a = n
which includes the possibility of a multistep reaction mechanism, whereas I was thinking of a simple electron transfer reaction.
Nevertheless, I was not able to reproduce the equation in the attached file.
BR
Lasse
I have now read the paper you referred to, and also checked the new edition of Bard & Faulkner. You probably refer to eq. (16) in the paper:
alpha_c + alpha_a = n
which includes the possibility of a multistep reaction mechanism, whereas I was thinking of a simple electron transfer reaction.
Nevertheless, I was not able to reproduce the equation in the attached file.
BR
Lasse
Attachments: