MIT10_626S11_lec27a

MIT10_626S11_lec27a - V Electrostatics Lecture 27a Diffuse charge at electrodes Notes by MIT Student We have talked about the electric double

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V. Electrostatics Lecture 27a: Diffuse charge at electrodes Notes by MIT Student We have talked about the electric double structures and corresponding models describing the ion and potential distribution in the double layer. Now we start to investigate the effect of double layer on the reaction kinetics, especially how the diffuse ionic charges affect the Faradaic half- cell reaction kinetics. 1. Frumkin Correction to Butler Volmer Kinetics First we assume that Faradaic reaction takes place at a reaction plane, which is roughly the same as stern plane. The charge carriers need to hop over this stern layer barrier (with a thickness of one solvent molecule) and pick up an electron to finish the Faradic reaction. This region is basically a solvation shell of the electrode surface. Remember that the Butler Volmer (B-V) kinetics is a molecular scale equation, thus, in order to introduce the Frumkin correction, we apply the B-V equation only across this compact layer and the reaction rate, where the reaction occurs. Then the B-V equation can be described as: (1 ) / / 0 1 0 0 [] : ln( ) S SS ne kT ne kT RO A eq S eq O O R R R e e k a a prefactor R overpotential across stern layer a kT ne a           Combining all these equations we will get: (1 ) ( ) ( ) 0 OO ne ne kT kT A R R a e a e   Note that for every charged species, activities or concentrations are all evaluated locally at the stern plane , which differs from the corresponding values in the neutral bulk electrolyte as we used in BV equation before. Now, in order to relate it to the bulk concentrations, we need a double layer model. For example, if the diffuse part of the double layer satisfies dilute solution approximation, then for ionic species i with charge z i e
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Lecture 27a: Diffuse charge at Electrodes 10.626 (2011) Bazant 2 / ( 0) ( 0) ( 0) ( 0) i z e kT o i x i ix o i x bulk D x c c e where c isconcentrationat stern plane c isbulk concentration    / i z e kT e is the Boltzman factor for charge across the diffuse layer.
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 20.410j taught by Professor Rogerd.kamm during the Spring '03 term at MIT.

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MIT10_626S11_lec27a - V Electrostatics Lecture 27a Diffuse charge at electrodes Notes by MIT Student We have talked about the electric double

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