Linear-fractional programming: Difference between revisions

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'''Charge transfer coefficient''', and '''symmetry factor''' (symbols ''α'' and ''β'', respectively) are two related parameters used in description of the [[chemical kinetics|kinetics]] of [[Electrochemistry|electrochemical]] [[electrochemical reaction|reaction]]s. They appear in the [[Butler-Volmer equation]] and related expressions.


The symmetry factor and the charge transfer coefficient are dimensionless.<ref>IUPAC. "Quantities, Units and Symbols in Physical Chemistry" ("The Green Book"), 2nd edition, Blackwell Science, 1993. [http://www.scribd.com/doc/44380146/Iupac-The-Green-Book-Quantities-Units-and-Symbols-in-Physical-Chemistry (on line)]</ref>


According to an [[IUPAC]] definition,<ref>IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. {{doi|10.1351/goldbook}}. [http://goldbook.iupac.org/C00906.html Entry: "Cathodic transfer coefficient".]</ref> for a reaction with a single rate-determining step, the charge transfer coefficient for a cathodic reaction ('''the cathodic transfer coefficient''', ''α<sub>c</sub>'') is defined as:
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:<math>\frac {\alpha_c} {\nu} = - \left(\frac {RT} {nF} \right) \left( \frac {\partial ln(|I_{red}|)} {\partial E}\right)_{T,p,c_{i,interface}}</math>
 
The '''anodic transfer coefficient''' (''α<sub>a</sub>'') is defined by analogy:<ref>http://goldbook.iupac.org/A00371.html</ref>
:<math>\frac {\alpha_a} {\nu} =  \left( \frac {RT} {nF} \right)  \left( \frac {\partial ln(|I_{ox }|)} {\partial E}\right)_{T,p,c_{i,interface}}</math>
 
where:
*<math>\nu</math>: [[Stoichiometry#Stoichiometric coefficient|stoichometric number]], i.e., the number of activated complexes formed and destroyed in the overall reaction (with n electrons)
* <math>R</math>: [[universal gas constant]]
* <math>T</math>: [[absolute temperature]]
* <math>n</math>: number of electrons involved in the electrode reaction
* <math>F</math>: [[Faraday constant]]
* <math>E</math>: [[electrode potential]]
* <math>I</math>: [[partial current|partial cathodic (anodic) current]]<ref>http://goldbook.iupac.org/P04407.html</ref><ref>IUPAC. ''ELECTRODE REACTION ORDERS, TRANSFER COEFFICIENTS AND RATE CONSTANTS. APPLICATION OF DEFINITIONS AND RECOMMENDATIONS FOR PUBLICATION OF PARAMETERS.'' Pure & Appi. Chern., Vol. 52, pp.233—240, 1979. [http://www.iupac.org/publications/pac/1980/pdf/5201x0233.pdf (pdf)]</ref>
 
==Interpretation==
 
The charge transfer coefficient signifies the fraction of the interfacial potential at an [[electrode]]-[[electrolyte]] interface that helps in lowering the free [[energy barrier]] for the electrochemical reaction. The electroactive [[ion]] present in the interfacial region experiences the interfacial potential and electrostatic work is done on the ion by ''a part'' of the interfacial electric field. It is charge transfer coefficient that signifies ''this part'' that is utilized in activating the ion to the top of the free energy barrier.
 
==Batteries and fuel cells==
 
In operating [[Battery (electricity)|batteries]] and [[fuel cell]]s, charge transfer coefficient is the parameter that signifies the fraction of [[overpotential]] that affects the [[current density]]. This parameter has had a mysterious significance in electrochemical kinetics for over three quarters of the previous century. It can also be said that charge transfer coefficient is the heart of electrode kinetics.
 
==Symmetry factor==
 
The symmetry factor (or barrier symmetry factor) is a coefficient similar to the transfer coefficient, but applicable only to single-step reactions.
 
The sum of anodic symmetry factor and cathodic symmetry factor is equal to one:
 
:<math>\beta_c + \beta_a = 1</math>
 
===Interpretation===
{{Empty section|date=October 2011}}
 
==References==
{{Reflist}}
 
[[Category:Dimensionless numbers of chemistry]]
[[Category:Electrochemistry]]

Latest revision as of 18:23, 28 December 2014


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