Question

1, Please use Butler-Volmer relation and polarization curve to explain the difference between the ideal polarizable electrode and non-polarizable electrode. For a good battery material, should it be more polarizable or less polarizable.

Answer 1

12 Electrodics : conducton (electrode) and a solution. roxn is very much dependerent on the the pe The most fundamental equation in elect "Butter-Volmer" equation (B-v equation). The electrodics je, electro-kinetics is concen oned with the rate of Chemical neaction at the interphase between a metallic on (electrode) and a solution. The nate of electrode sependeant on the the potential of electrode. mental equation in electrodics is known as izio Teci-emF/RT _e_BNF/RT 7 → It is a relationship between i and n. i- net cunnent - ?- i forward electronation rom (neduction) = i backwand de electronation non loxidation) n = oven voltage on oven potential. = 50-ode 1$ = measured potential unden working condition. (actually the potential difference) ope = equilibrium potential or thermodynamic potential. i = equilibrium exchange cunnent density. to an That means, io=i when i i & symmetry facton. ult B-vean shows how the current density ) depends on difference values of y. In a senuit (i) shows a dependence on actual non-eam and eam potential deffenence.

The electronation and deelectonation san may be written as follow- Atte D (electronation na Reduction, Ae- D Cbeebedronation mon) → oxidation. As these are chemical oxy they are associated with the energy change. let us consider the movement of the won' At from the soln side of the interphase across few Å distance of the layers to the metal surface, so for. electronation neaction, the At ons have to cross contain activation energy due to presence of the double Langen. to p potential energy! distance from the boss ut add electrode to votar The frequency with which an ion succesthully cross the energy bomien for diffusion may be given as-it sit bar Frequency = ke = Ket e RT (from collision theory) Frequency = ke = ket boot boot botsubab whene, bet stands fon stand and the energy of activation.mub Now, the rate for electronation van may be given as an oor Je = kai į but the Cat I unit of ke= unit of Ve unnt of CAT NA = No of moles aneals No of molecules aneat = st. e h C KT CAT.

When an electric field is applied further electron transfer to an electron accepton in sohn on movement of the sons from son to the electrode is opposed by the applied electric field. This for electronation on the work done by the con in climbing the potential energy had to mclude the work re, electrical Work. As the the son derend to more accross the double layers, it has to perform electrostatic work against the fuld between the innen potential difference through which the on passes and a part of the total. Dois required to pass through the energy banier. let the past be Bad whene p is a faeton which is greatter them zero but less than unity (ie, o<BL1), which is known on symmetry factor. B = bistomce crossed by the sons to cross oven the bamlen. Total distance b/w the electrode and the intenphese. Thus, BAOF is the ummount of energy which is to be added for electronation and (1-B) DOF be the enorgy which is to be deducted for de electronation sont In presence of appled field the total fru energy of activation for the electronation non is equal to the Chemical fru energy of activation. (boot) and the electrode distribution (BOOK). Thus, Boot = Got + BOOF . Now the rate constant, ke = ket e- (Brot & BD & F)/RT ke = ket e - Boute Roof

. Rate of electronation ron, de = kat & she - Bor CAT BDOF De - Recut e-Boot RT The rate Te is the noof moles of the lons neacting per second my crossing unit anca of interface and when this is multiplied by F we obtain the electronation current density to i. le = f.Je ab nie = F. Ke Ate BOOF duwee KT This expussion shows that ī is exponentially related to Do A small change in held will result a linge change in cuernment density. We will see later that equation (1) is nothing but a nulationship between to and de d icno tornare of Now we consider deekcronation process Fagot = Dut - (1-B) DOF Rate constant tom deelectronation proces is written co phode = kept e em (1-P) DPF/RT in de Rede de XBOP/R & Boot/RT Now As we know, da Tin = r. Dede

substituting the value of de de = F. Kde Cae e C1-B) There must have a centum value of appled field at which the noce of electronation and de electronation process will be scome. and the potential at which, ode=ie is given by Ale io = equilibrium exchange current density. we can write, влфF ) to the Cheet B) FØP/RTBF. Ke Care- RT 0 D¢ is the new equilebnium potential difference connes ponding to curment density. now $; no may be wonitten as A6 = 10 + (08-09) = $$+o Whene, Do The eam potential difference. n oven potential a substituting so=D80th meano We have, pa za i= FT de Cade e AB) APOF/RT (1-B) NF/RT – the CAT e-BoOoF/RT e Por 2

wow, when, n=o. DO = DOO and then, io-T i inio = Role Calef et-B) FDO0/RT man - ReCAT & e-BDQOF/RT - from equ f ③ we hame, i-iste (+B) FM/RT - e-BF N/RT] This is Butlen volmen en Graphical nynesentation of Butlen -volmen equation: 3 LH to mol-bres vitonsult sro This plot is not a symmetric one. and browulerson couture when, ß = a.s We have, i= ios en/ART – é art on ao boost a nt il eFn/PRT _ x-FN/ART en en ex - sinha = zi, sinh ( =aio - 2

We will have a symmetric curve. In this spometric currenralues will be sume on the either side of zero. and then it was produced egual cunnent ms equal furent electronation & de electronation curnent should produce equal values of n. case: 1 when, on value is very large EFN/ART » e-mart and en/287";. asmh (th nefn/RT This one can write that when the values of N is very longe then the and term of Ritus of Butlen -volmen equation vanishes and we have indummy staran i=io 84-13) FN/RT) here, i is neterred as anodic curnent density. case: 2 wher, y value is very small i=io [ e CI-H) In/ORT EBEN/RTy = io [ { 1 + [ltorney-(1-BFn 7

of on This is one form of chom's land. This for lower values of na Unear relationship be Curnent density (i) and over potential ( will be obtained. i =io [eltsen/et-e _149/x17 and i = dele is el-B) FM /R4 deelestronation T -io e-prn/rt → electronatwon so when the values of peame mean moneased, oven potenhet rahus are also mireased and the declectronation cunment: density Eide is also increased but there is a decnease in electronation cunent density (ie). when, n is very large n ime Room To tourisme In that case, i = (-B NF/RT :lt = etBra/RT Hore i stands for anodie crnent demily. Takmyboy m both side we here In t = (1-13) FN/RT . Ini = Inior (1-2 d.

net deelectronation strought une t o th excess curnent dinsity. net electronation Polarisable and non-polarisable mterphase : A non-pdaraisable mtersphase is one at which the potential difference does not change easily with the passage of current. Now for low values of n i= a ( in. n = 1) i This relation can be companed to that of Ohom's lun. v=IRtb otwarť = R. Ito raard al hann so here, y also comes and to the resistance lone at the interphase to the change transform neuition and depends only on the exchange cunnent density. This A is known as polemisaselity.

case: when, to is very lange. le, io & ndas so, for nonzero values of i, n . e Inspite of passage of curment density across the interphone, the oven potential (n) tends to zero. This that is the behaviour of an ideally non-polaris aste interphars. cesc: 2 When, is is very small re, ioo. Then, n a . re, there is a large change of the over potential value even with a small change in exchange curnent density. so, the interphose is highly polanisable. los MA