20:
1986:
382:" assumes that the concentrations at the electrode are practically equal to the concentrations in the bulk electrolyte, allowing the current to be expressed as a function of potential only. In other words, it assumes that the electrode mass transfer rate is much greater than the reaction rate, and that the reaction is dominated by the slower chemical reaction rate ".
780:
The following derivation of the extended Butler–Volmer equation is adapted from that of Bard and
Faulkner and Newman and Thomas-Alyea. the current is expressed as a function not only of potential (as in the simple version), but of the given concentrations as well. The mass-transfer rate may be
394:
The exchange current is the current at equilibrium, i.e. the rate at which oxidized and reduced species transfer electrons with the electrode. In other words, the exchange current density is the rate of reaction at the reversible potential (when the overpotential is zero by definition). At the
1695:
to an electrode causes the reaction to move in one direction, away from equilibrium. Tafel's law determines the new rate, and as long as the reaction kinetics are under control, the overpotential is proportional to the log of the corrosion current.
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It describes how the electrical current through an electrode depends on the voltage difference between the electrode and the bulk electrolyte for a simple, unimolecular redox reaction.
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relatively small, but its only effect on the chemical reaction is through the altered (given) concentrations. In effect, the concentrations are a function of the potential as well.
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The Tafel slope is measured experimentally. It can, however, be shown theoretically that when the dominant reaction mechanism involves the transfer of a single electron that
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reversible potential, the reaction is in equilibrium meaning that the forward and reverse reactions progress at the same rates. This rate is the exchange current density.
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51:. The Tafel equation was first deduced experimentally and was later shown to have a theoretical justification. The equation is named after Swiss chemist
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Also, at a given electrode the Tafel equation assumes that the reverse half reaction rate is negligible compared to the forward reaction rate.
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401:
1404:
1817:"Tafel Slope for Cathodic Reaction from Tafel Equation Calculator | Calculate Tafel Slope for Cathodic Reaction from Tafel Equation"
1776:"Tafel Slope for Anodic Reaction from Tafel Equation Calculator | Calculate Tafel Slope for Anodic Reaction from Tafel Equation"
336:
269:
125:, the Tafel equation is applied to each electrode separately. On a single electrode the Tafel equation can be stated as:
2011:
1744:
Bard, A. J.; Faulkner, L. R. “Electrochemical
Methods. Fundamentals and Applications” 2nd Ed. Wiley, New York. 2001.
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Burstein, G.T. (2005). "A century of Tafel's equation: 1905–2005 a commemorative issue of corrosion science".
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the plus sign under the exponent refers to an anodic reaction, and a minus sign to a cathodic reaction,
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the plus sign under the exponent refers to an anodic reaction, and a minus sign to a cathodic reaction,
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335:
A verification plus further explanation for this equation can be found here. The Tafel equation is an
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40:
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1599:. In such case, the dependence of current on polarization is usually linear (not logarithmic):
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524:{\displaystyle A={\frac {\lambda k_{\text{B}}T}{e\alpha }}={\frac {\lambda V_{T}}{\alpha }}}
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1123:{\displaystyle \eta =\pm A\cdot {\frac {\ln \left({\frac {i}{i_{0}}}\right)}{\ln(10)}},}
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Equation relating the rate of an electrochemical reaction to the overpotential
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develops is determined by the kinetics of the reactions involved, hence the
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1035:{\displaystyle \eta =\pm A\cdot \log _{10}\left({\frac {i}{i_{0}}}\right)}
193:{\displaystyle \eta =\pm A\cdot \log _{10}\left({\frac {i}{i_{0}}}\right)}
1277:{\displaystyle i=i_{0}\exp \left(\pm \alpha e{\frac {\eta }{kT}}\right),}
1761:
1394:{\displaystyle i=i_{0}\exp \left(\pm \alpha F{\frac {\eta }{RT}}\right)}
918:
is the reactive species concentration at the electrode surface in mol/m,
858:{\displaystyle i=nkFC\exp \left(\pm \alpha F{\frac {\eta }{RT}}\right)}
19:
1202:{\displaystyle i=i_{0}\exp \left(\pm {\frac {\ln(10)\eta }{A}}\right)}
1886:"Connection between the Avogadro constant and the Boltzmann constant"
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1900:"Link between the Avogadro constant Na and the Faraday constant F"
1473:{\displaystyle {\frac {e}{k}}={\frac {e/Na}{k/Na}}={\frac {F}{R}}}
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1985:
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An other equation is applicable at low values of polarization
24:
772:
Equation in case of non-negligible electrode mass transfer
1914:"Expression in terms of the standard rate constant k=k0"
439:{\displaystyle {\frac {\lambda k_{\text{B}}T}{e}}<A}
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1872:"Derivation of the extended Butler–Volmer equation"
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117:Where an electrochemical reaction occurs in two
1654:{\displaystyle i=i_{0}{\frac {nF}{RT}}\Delta E}
1532:Equation in case of low values of polarization
593:{\displaystyle \lambda =\ln(10)=2.302\ 585...}
957:, the value of which must be between 0 and 1.
767:, the value of which must be between 0 and 1.
106:{\displaystyle Ox+ne^{-}\leftrightarrows Red}
1928:"Kinetics of Corrosion - the Tafel Equation"
785:The Tafel equation can be also written as:
1803:"Limiting cases of Butler–Volmer equation"
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1592:{\displaystyle |vert\eta |vert\simeq 0V}
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730:{\displaystyle V_{T}=k_{\text{B}}T/e}
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337:approximation of the Butler–Volmer
14:
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1978:
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1792:
1522:, which finally yields equation (
1984:
1841:"Verification of Tafel Equation"
1668:due to its formal similarity to
1321:{\displaystyle \lambda =\ln(10)}
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371:{\displaystyle |\eta |>0.1V}
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1970:10.1016/j.corsci.2005.07.002
621:{\displaystyle k_{\text{B}}}
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1515:{\displaystyle i_{0}=nkFC}
2012:Electrochemical equations
776:In a more general case,
339:equation in the case of
329:exchange current density
43:relating the rate of an
41:electrochemical kinetics
1686:electrical double layer
1666:polarization resistance
946:{\displaystyle \alpha }
756:{\displaystyle \alpha }
1821:www.calculatoratoz.com
1780:www.calculatoratoz.com
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320:{\displaystyle i_{0}}
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235:{\displaystyle \eta }
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1993:at Wikimedia Commons
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2017:Physical chemistry
1932:www.doitpoms.ac.uk
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23:Tafel plot for an
2007:Chemical kinetics
1989:Media related to
1964:(12): 2858–2870.
1958:Corrosion Science
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1156:
1153:
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1140:
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1117:
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1099:
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1057:
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1017:
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1008:
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982:
979:
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962:Demonstration
956:
940:
933:
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926:
923:
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914:
911:
907:
904:
901:
900:rate constant
897:
894:
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884:
883:
882:
875:
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837:
832:
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800:
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789:
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743:
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686:
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601:
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548:
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532:
516:
510:
506:
502:
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490:
487:
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453:
452:
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430:
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421:
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387:
383:
379:
365:
362:
359:
351:
338:
330:
312:
308:
300:
297:
281:
274:
271:
255:
248:
245:
244:overpotential
229:
222:
219:
218:
217:
210:
203:
201:
186:
179:
175:
171:
166:
162:
157:
153:
149:
146:
143:
140:
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130:
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126:
124:
120:
100:
97:
94:
86:
82:
78:
75:
72:
69:
62:
61:
60:
56:
54:
50:
49:overpotential
46:
42:
38:
30:
26:
21:
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1957:
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1931:
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121:on separate
116:
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53:Julius Tafel
36:
34:
270:Tafel slope
2001:Categories
1937:2024-05-28
1826:2024-05-28
1785:2024-05-28
1732:References
123:electrodes
1682:corrosion
1670:Ohm's law
1646:Δ
1581:≃
1561:η
1374:η
1366:α
1363:±
1355:
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1254:η
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138:η
92:⇆
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29:oxidation
27:process (
1700:See also
1401:because
294: :
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898:is the
763:is the
737:is the
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588:585...
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547:where
216:where
25:anodic
741:, and
582:2.302
1746:ISBN
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1966:doi
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