Electrochemical reaction mechanisms

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Garry Peters
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1 Eltrohmal raton mhansms Exampl: oppr rduton (): Cu + + Cu + slow (): Cu + + Cu fast Coppr also undrgos a dsproportonaton raton: Cu + Cu + + Cu Its qulbrum onstant s K. 6. As th frst stp s slow ompard to th nd stp t s rat-dtrmnng, and all Cu + formd n th frst raton rats mmdatly to Cu and w annot s two sparat stps n aquous solutons. Th sam appls also to Zn: Zn + + Zn k m/s and α.36 (ph 3)*. dssolvng dposton *A. Avaa t al. Thory of yl voltammtry for quas-rvrsbl ltrodposton ratons wth nsolubl produts, Br. Bunsn. Gs. 97 (993) 7-76.

2 Two-stp oxdaton, ntrmdat sps X: R X + X O + k k α,, E α,, E Total urrnt dnsty +, at stady-stat ½. Ignor onntraton polarzaton: F ( E E ) ( α ) f ( E ) X α f E k R F F ( E E ) ( α ) f ( E ) O α f E k X F At qulbrum, hn. E q and x,q an b alulatd from th qs. abov: E q RT O ( + ) + E E ln ; xp f ( E E ) F R X, q R o Exhang urrnt dnsts an b wrttn analogously:,, α ( ) α ( ) Fk X,q α ( ) α ( ) Fk O R X,q

3 Currnt-ovrpotntal quatons bom to th followng form α fη ( α ) fη X, X,q α fη ( α ) fη X, X,q Elmnatng ( x / x,q ) and notng that :, ( α ) fη fη + fη α fη ( ),, Eq. () Whn fη», fη α η.33 f RT η log ( α ) fη α, F, Whn fη «, log fη ( α ) η.33 f RT η α fη, ( α ) F,

4 For oppr,»,, hn at modrat ovrpotntals, < log /, ] < ( α + fη α fη [ ) ( ] ), Anod Tafl slop: 4 mv/dad Cathod Tafl slop: mv/dad If, «, and th ovrpotntal s modrat, α fη α fη [ ( ] ), Anod Tafl slop: mv/dad Cathod Tafl slop: 4 mv/dad At hgh ovrpotntals th Tafl slops ar ±,33RT/(α )F á dad. η / (mv) j //, j, log /, Smulaton to Eq. () wth th valus of, /, 3 ( ), ( ), ( ), ( ),.( ), ( ) ja 3 ( ) ; α α.5.

5 Anothr famous xampl s th rduton on mangans: Mn 4+ + Mn 3+ Th raton looks lk an ordnary on ltron transfr but t has bn notd that th onntraton of Mn 4+ has no fft on th urrnt, whras urrnt s proportonal to th onntraton of Mn 3+. Th mhansm that xplans ths bhavor s th followng: Mn 3+ + Mn + k, k (I) Mn + + Mn 4+ Mn 3+ k, k (II) Mn 4+ + Mn 3+ (I) + (II) Lt us dnot: [Mn + ], [Mn 3+ ] and [Mn 4+ ] 3. Not that n th lattr raton, thr s no ltron transfr, t s a dsproportonaton raton. Sn th rduton s don at suffntly athod (ngatv) ltrod potntals th nvrs of th uppr raton dos not nd to b takn nto aount (k - ). Makng th stady-stat approxmaton for th ntrmdat Mn + that dos not appar n th nt raton, t s obtand that d 3 3 d k k + k v k 3 k k dt dt Th last quaton provs that th nt raton s of th st ordr wth rspt of Mn 3+ and of th th ordr wth rspt to Mn 4+. Th raton shm s alld an EC mhansm.

6 Ths xampl hghlghts th mans of dtrmnng raton ordrs. Lt s assum a gnral rdox raton aa + bb n C + dd. Th rat quaton s nf α β [ A] [B] rd k ox k [C] [D] γ δ Not that not nssarly a α, b β, γ or d δ. At suffntly anod potntals, th rduton raton an b gnord, ladng to ln ln[a] α, ln ln[b] β ; E» E Analogously, at suffntly athod potntals, th oxdaton raton an b gnord: ln ln[c] γ, ln ln[d] δ ; E «E Ths analyss s possbl only n ltrohmstry baus ratons do not sgnfantly hang th onntratons of th ratants (f. Faraday s law), unlss vry hgh urrnt s drawn out of th ll for a long prod of tm. Comng bak to th mangans xampl, th fat that Mn 4+ has th th ordr dpndn tlls that t annot b assoatd wth a harg transfr raton.

7 Anothr way of analyzng raton mhansms s to look at th rat dtrmnng stp. Lt s assum qut arbtrarly that th sond stp n th mangans rduton s rat lmtng. Ths mans that th frst raton has tm to sttl to qulbrum,.. at all tms ( E E ) K RT F E E ln xp F RT If w assum furthr that k «k, any Mn + ratd wth Mn 4+ s radly rplad wth anothr Mn + va th frst raton that nluds ltron transfr. Thrfor, ltr urrnt s gvn by th rat of th sond raton, although t nluds no ltron transfr. F v d dt 3 K k 3 log F ( ) ~ ( E E ).33RT Baus k s ndpndnt of potntal, th Tafl slop would b 59 mv/dad. In that as th raton would b of th st ordr wth rspt to both Mn 3+ and Mn 4+. Fndng th raton mhansm thus s rathr a formdabl task and usually prods va lmnatng th mpossbl raton routs. Th analyss of paralll ltron transfr ratons s rathr straghtforward: total urrnt s th sum of ndvdual raton urrnts.

Eltron transfr ratons ar oftn aompand by lgand xhang. For xampl, oppr s dssolvd n th on lqud -butyl--mthylpyrroldnum bs(trfluoromthylsulfonyl)- md (BMPTf N) only as a hlord omplx. Hn, addng.g. BMPCl n th soluton, th dposton of oppr n BMPTf N an b studd.

8 Eltron transfr ratons ar oftn aompand by lgand xhang. For xampl, oppr s dssolvd n th on lqud -butyl--mthylpyrroldnum bs(trfluoromthylsulfonyl)- md (BMPTf N) only as a hlord omplx. Hn, addng.g. BMPCl n th soluton, th dposton of oppr n BMPTf N an b studd. Cu(I) s not stabl but oxdzs asly by atmosphr oxygn. Thrfor, Cu(I) solutons ar mad n a glov box utlzng th dsproportonaton raton. BMP + Cu + + Cu Cu + Tf N T. Vankka t al., Eltrohmal study of oppr hlord omplxs n th RTIL -butyl--mthylpyrroldnum bs(trfluoromthylsulfonyl)md, Eltrohm. Ata, 87 (3) Yllow: Cu(II) soluton Clar: Cu(I) soluton

9 Cu(I) oxdaton. Cu(I) oxdaton. Cu(I) oxdaton Abov: Currnt-voltag urv of Cu(I) oxdaton. Blow: Mhansm that xplans th urv; k 3 dm 3 mol s, k /k 5 dm 3 mol. Abov: Cyl voltammogram of Cu(I) at varyng hlord onntratons: addng hlord rmovs th sond wav at a.. V. Conluson: Cu(I) s found manly as a trhloro omplx, but stohomtry of th lgand xhang stll s unknown sn th addton of a small amount of hlord (39 mm (- - -), 435 mm ( ), 48 mm ( )) rmovs th sond wav. That would rqur a raton of th 3 rd ordr wth rspt to hlord.

10 Cu(II) rduton / µa I / µa Cu(I) + Cu Cu(I) + Cu E / V Cu(II) + Cu(I) Cu(II) + Cu(I) E / V Lft: Rduton of Cu(II) to mtall oppr on platnum n two stps. Th dffrn of th two stps s a. V whh mpls to th hang n th oordnaton of th omplx. Rght: Th frst rduton wav at varyng tmpratur ( 96 C) : dots data, ln ft. Raton mhansm (shm-of-squars) that xplans th urvs at ah tmpratur. Yt, th valus of th rat onstants do not vary monotonously as th funton of th tmpratur. Hn, th modl had to b rjtd.

11 Cu Cu + + N + + N Eltrolss platng of nkl on a oppr rod. Lft: NCl soluton; rght: N(Tf N) soluton. Usng a hloro omplx a smoothr and brghtr surfa s ahvd. Solvnt s BMPTf N.

Advances in the study of intrinsic rotation with flux tube gyrokinetics

Advances in the study of intrinsic rotation with flux tube gyrokinetics Adans n th study o ntrns rotaton wth lux tub gyroknts F.I. Parra and M. arns Unrsty o Oxord Wolgang Paul Insttut, Vnna, Aprl 0 Introduton In th absn o obous momntum nput (apart rom th dg), tokamak plasmas