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Let us start lecture 2.And the subject of letter 2 will be same as subject the lecture 1 is basically a topicis recap on electrochemical polarization and will consider 2 aspects activation andconcentration polarization. Now we have already seen that energy distribution across doublelayer for an electrochemical reaction in the reversible situation M n plus plus n e M whereic ia, ic equal to ia equal to i0 when e equal to equilibrium equal to M.And this is generalized condition e equal to e0 when concentration of metal ions inthe solution is 1, otherwise it can have different other values depending on last equation whatwe have expressed in our previous lecture. Now energy distribution wise we saw that theyare on the same level and this is OHP M plus and this is n and we have an energy barrierequal to delta G star and for the thermally activated jump of metal ion as well as metalfrom one plane to another plane.This is OHP and this is IHP is in the same barrier and that what the rate of forwardas well as backward reactions are similar or same. Now we need to see what happens ifthere is any disturbance and this is equal to specifically anodic reaction and this iscathodic reaction, now if there is any disturbance and disturbance I mean to say that by manychance if there is an excess flow of electrons, this excess flow of electron would break thatequilibrium.This equilibrium will be broken. Now this excess flow of electron can be either a situationwhere electrons are supplied to the system and for example in this reaction if more electronis supplied that means this increases then of course in order to balance that particularcharge more metal ion would try to reduce. Similarly, if I take away electron from thesystem then this take away electron means metal has to send more electrons into that.So how can it sent, it can send by oxidation, so if the charge flow into the system in theform of electron per unit time per unit time area, if that increases means what means Iam increasing ic. So that means electron supply per unit time per unit time area increases,that is ic I am increasing, so the value of ic increasing, I’m increasing. So that meansin other words I am sending negative currents into the system.Similarly, ia would increase if electron taken away per unit time per unit time area, sothat increases then ia would increase, that is in this case rf, so this is rf, this isrb, rf increases in this case rb increases and that situation I would have changed inthis particular pattern, particular energy distribution. Now let us say I consideredrb that is increasing, if rb increases that means the rate of forward reaction is morethan the rate of backward reaction.Sorry in this case definitely rate of backward reaction is more than the rate of forwardreaction. So that means this reaction is taking place faster than this, so rb greater thanrf and as for Arrhenius theory if this rate is more than this that time delta G whichis the activation barrier for the backward process mass decrease as compared to the forwardprocess. So backward process is nothing but anodic process I can mention a here whichindicates the free energy barrier for the backward process or the anodic process.Must be lower than delta G of c which is the forward process of cathodic process this isthe activation energy felt by the metal ion for the jump from OHP to IHP. So this is activationbarrier again for metal ion going from OHP to IHP and in this case this is nothing butactivation barrier for metal going to metal ion or OHP this is IHP. Fine. So that meansthis particular activation energy should be lower than the activation energy felt by metalion for its own jump from OHP to IHP.So then energy distribution would be interestingly it will go up and then this should go down.Now interestingly you say the activation energy felt by metal for the jump from IHP to OHPis this much which is nothing but delta G a and what wouldbe then activation energy felt by metal ion for its movement from OHP to IHP isthis much. So this is delta Gc. So that means we could see that in this situation whichis basically the colored line that case my activation energy for the anodic process isless than activation energy for the cathodic process.So that time ia is actually more than in this case ia is more than ic, now I will put amode sign just to indicate that I am comparing the value, but still even at this conditionic is flowing opposite to value, now there could be the another situation where deltaGc can be less than delta Ga. So that time I will see that ic would be greater than ia,and what will be my energy distribution, if I put in different color, if I put in bluecolor.So that time this will go up and this will go down, thisside will go down. Fine. So now when this situation or let me put it in blue color,so that time the activation energy which is Ga is this much for case 2 this is case 1and activation energy which is felt by metal ion two. So now interestingly you could seethe forward rate which is the cathodic reaction rate is more than the anodic reaction rateor the magnitude of ic is more than the magnitude of ia that can be possible if case 2 is satisfied.Similarly, ia can be more than the magnitude of ic for the case 1 this is case 1. Now whenwe have such situation that case will experience that the potential shifts from this equilibriumpotential. Fine. So this equilibrium potential shift.So that means whenever I have situation like a less than delta Gc or ia greater than ic.On another hand delta Gc less than delta Ga or ic greater than ia those such cases I willhave shift in potential which is other than equilibrium and in this case we have considerede M plus M. Now let us consider the case 2. So in the case 2 I am sending more electronin to the system is not because I am increasing the negative current or ic.So if I send negative charge to a system its potential decreases, so that means in thiscase potential decreases, that means if I see that this potential goes after some currentflow E potential goes to E2 that time E2 which is the final potential, this is final minusE equilibrium should be negative. Now when we take out for example in case of case 1I am taking out electrons that is I am reducing the negative charge.In other way I can say that I am increasing the positive charge relatively that case Mminus n e = M n plus that is I am taking out this and so I am increasing this number, sothe positive charge increases so the potential goes up. So if I consider this potential goesto E3, so E3 which is final potential after some current flow minus E equilibrium shouldbe positive. Now this change from the equilibrium non corroding situation is taking place becauseof either the relative increase of negative current of cathodic current as compared tothe positive current or the ia.And vice versa like ia is increasing with reference to ic magnitude wise that time mypotential shifts from the equilibrium non-coding situation which was corresponding to i0 theexchange current density. So this particular phenomenon we call it polarization and thispolarization is taking place because of this electrochemical reaction. Fine. So that whatwe called electrochemical polarization.Now if we understand this electrochemical polarization is nothing but a shift in potentialfrom the equilibrium value and this shift in potential can be measured ok and this isbasically due to the manifestation of current flow. So this is nothing but shift in potentialor this is a result of current flow and this measurement of polarization is nothing butdel E and del E here it is del E and here it is also del E. Fine. Now this del E whichis basically measure of polarization. We termed it as neeta or over voltage or over potential.Fine.So now in this case over potential is negative and in case where anodic current density ismore than cathodic current density over voltage is positive and just to indicate that whetherit is a negative change or positive change we can also term it as cathodic because thecathodic polarization over voltage is negative and we can put a subscript a which indicatesanodic. So now we could see that the polarization can be expressed in the form of overvoltageor meter.And cathodic voltage equal to nC neeta c anodic equal to neeta a, now this neeta a and neetac can have relation with the current density and in this case we can have a relation andwe have also proven it in our one in one of the lectures in corrosion part 1 you can goto that those lectures and find out the proof but for our convenience we can also writedown that particular expression final expression and the final expression we can mention inthe form of an equation with that equation is called as butler volmer equation.So the butler volmer equation which is the relation between I andovervoltage. So that can be written as i I can mention i applied or I net equal to izero exponential alpha nF neeta by RT minus exponential 1 minus alpha nF sorry small changethere will be minus sign 1 minus alpha nF neeta by rt. So this is the Butler volmerequation for a situation where the concentration change at the interface is not there. So thatmeans we are considering only thermally activated process that is metal is going to metal ionor metal ion is going to metal layer.So that is basically in the activation side, so we call it activation polarizationwhich is neeta in terms of overvoltage and that time i applied on i net can be expressedin the form of this equation. Now interestingly we need to know all the terms. Fine. So inthis equation the terms are let me write it again equal to i zero exponential alpha nFneeta by RT minus exponential minus 1 minus alpha nF neeta by RT.Here i0 of course is exchange current density, n and F we have already explained, neeta isovervoltage and in this case activation, alpha is nothing but symmetry factor. We have tojust understand what is alpha that is symmetry factor as well as overvoltage. Now if I considerthe condition for case 1 this is the condition where ia is more than ic that time this particularline is this line is applicable.Now in that case if neeta to be my overvoltage this is in volte this can be converted intofree energy with this expression nF neeta this is delta G. I’m just considering deltaG that is the value that is the change in value change in that particular energy distribution.So in the energy accessthis particular distance that means difference between this and this is nothing but nF neeta.And if I give notation A, B and C. This point is C. So alpha is nothing but AB divided byAC, hence the change in free energy for the anodic side isthis much which can be given as alpha nF neeta and change in cathodic side which is nothingbut this much or same as this value is nothing but 1 minus alpha this. So now we understandthat symmetry factor is nothing but the contribution of the total over voltage towards the changein free energy on the IHP as well as OHP.And in this case on the IHP the change is alpha nF neeta and on the cathodic side is1 minus alpha nF neeta. Now coming back to this so this is my expression. Now what isinet, i net is nothing but ia minus ic or ic minus ia. Now this case delta G a lessthan delta Gc or ia greater than ic and in this case delta Gc less than delta Ga or icgreater than ia. So now whenever we havethis forward reaction more than the rate of forward reaction is more than the rate ofbackward reaction.So this is rf this is rb that time this situation will prevail, you go back and then see thoseenergy distributions. So that time in the system there will be net current and thisnet current is nothing but the difference between these 2 currents why because these2 current flows in opposite direction. So this is ic this is ia. In case of I zero these2 are same length, but whenever I have ic more that time ia should be this one.So that case there will be net flow of current i net which is nothing but this and if icis less ia is more that time i net will be there which is nothing but this. So that isexpressed in this form, now we can separately write ic which is nothing but i0 exponentialminus 1 minus alpha nF neeta by RT and ic ia equal to i zero minus exponential alphanF neeta by RT. And I net you can see this is a i net or i applied which is the net flowof current into the system.Now interesting part is this 2 equations, these 2 equations leads us to one interestingequation for example if I consider ia equal to i zero exponential alpha nF neeta by RT.If we convert it into log scale so that time I can write neeta equal to RT alpha nf lnia by i zero. I can write this and where similarly I can write ic equal to i zero exponentialminus 1 minus alpha nF neeta by RT which goes to neeta equal to rt alpha 1 minus alpha nFln ic by i zero. So these 2 equations are very critical for our next few classes.So let me stop here, will continue our lecture on these 2 equations in our subsequent lectures,so thank you very much will continue our discussion in next lectures.