Let us start lecture 5.And topic will now get to gradually to concentration polarizationand mixed potential theory. Till now we have got the situation that activation polarizationhappens when there is activated jump of metal ion or metal atom across the double layerover an activation barrier. Now we have also seen that there could be situation of equilibriumand that time we will come across exchange current density and when polarization happensthis is the manifestation of current flow or other net current flow into the circuit.And that time either ia can go up as compared to ic or ic can go up as compared to ia andthat would lead to anodic polarization and cathodic polarization and you can measurethe polarization by over voltage which is neeta. Now again we have also seen that activationpolarization happens at lower current density when the concentration across the metal surfacedoes not change, the bulk concentration or as well as the interface composition of themetal species other reducing species would not change.But if we go to a higher current density that reducing species can change is concentrationat the interface of the metal. Now that time will come across concentration polarization.So if we see the concentration evolution of concentration polarization, so if we havedouble layer, so here we have situation like let say if I consider a situationwhere ic is greater than ia so in this case Mn plus. So this current ic and this currentia and ia less than ic.And the energy distribution plot will be the dotted green line, this happens, now thattime if I see the concentration C zero let’s say metal ion concentration C zero in thebulk that concentration remains same as C zero at the interface, but once ic becomesgreater than greater than ia then the rate at which this jump happen, the rate at whichthe metal ion is supplied by the bulk these 2 rates becomes different.So the rate this current density other reducing current density for the ic is so high thatthere will be a depleted iron layer across the interface. So now gradually the concentrationwill go down will keep going down across the interface because if this access is concentrationand this access is distance. So then the rate the reduction rate is so high that the metalion depletion happens across the interface.And the rate at which this happens and if I consider rate of metal ion supply is thenlower than ic for the reduction rate. So that time I will have a depleted layer. So if Itry to draw this one in the concentration profile mode so I will see that this is C1and this is the bulb consideration C zero then I will have a plot like this. So whenwe have a plot like this then I will have a diffusion distance which is delta is theboundary layer thickness.Now the entire reduction process will be decided by how quickly the metal ion is supplied frombulk to the interface and then that metal ion will get reduced. From this, this is ofcourse this line is distance, this is concentration, from this we can have one more polarization,let us see how we get to that, now I can see that J which is the flux nothing but moleper unit area per unit time I can write a simple Fick’s first law minus D dc dx andC is the concentration.Now this is nothing but I by nF. Why? Because W by area let us says a capital A area andtime is t that is I into let’s say let me mention it as small a which is area, thisis A which is the atomic weight nF for that. We have seen it before, so this unit is gramper unit area per unit time. So now if I want to convert into mole so that timethis is to be divided by atomic weight. So now W by at divided by A which becomes theunit like this. So then ia AnF.So these 2 cancels out and here small a is area and capital A is molecule atomic weightof the metal. Right. So now if I try to see the polarization situation when if you seethis particular C1 if the current density is extremely high that time the C1 can havethe extreme value which is zero, so this is very high very very high i. Ok. So that timeit can have the limiting value which is zero, that means whatever ions are coming from thebulk to the interface so the ions are immediately getting reduced.So now in one case I will have C1 and in one case I will have extreme situation the concentrationand interface goes to zero. Let us see that what will be the equation at this 2 boundaryconditions.So the one boundary condition is when C equal to C1 at the interface. So that time J equalto i by nF equal to minus D C zero minus C1 by delta and let me put it as J1 or let meput it as i1 corresponding to the condition C1 the interface condition. So that meanshere the situation is if I consider this is to be interface and this is the bulk concentrationI am having a situation like this. This is distance, this is concentration and this concentrationis C1.Now for a boundary condition when C equal to C zero sorry C equal to zero at the interfacethat time J2 equal to i2 nF, this i is nothing but the current density is equal to minusD C zero minus zero by delta. So this situation is like this, if this is the zero value, sonow this is C zero, this delta here it is delta. So this is C concentration, this isdistance. Right. So that condition I will have this equation like this. Now I couldimmediately make out this is i2 is the limiting value.Because I am reaching the limiting value of zero at the end, so i2 is right is consideredas i limiting or iL. So we see that i limiting is appearing when I am having this situation.Now let us considered the potential that is being developed at the interface. So in asituation like when C equal to C zero at interface that time potential M n plus by M equal toE zero M n plus by M plus RT nF, I can mention C zero since it is a pure metal and we havealready seen then the concentration of metal ion is nothing but C zero, so I am puttingC zero.Similarly, when C equal to C or 1 that time C so let say this C equal to C zero and hereC equal to C1, so M n plus M equal to E zero M n plus M plus RT nF ln C1. So these arethe 2 potential when the concentration at the interface are this, so if we see thisparticular situation, now when we are having activation polarization that time the concentrationat the interface is maintained C zero all the time, so this is that time we alreadyget activation polarization.And that we can express in the form of tafel equation, but once we have a very high currentdensity that means reduction current density ic that time the concentration will startreducing at the interface so will get up depleted zone and then these 2 potential values mustbe different and this is the condition we are getting when we are having very high ic.Fine. So this condition is getting. So now if I try to see what is the polarization dueto this concentration change is nothing but E M plus n C equal to C1 minus E C equal toC zero M n plus M.So these 2 values are same because the standard potential, so this is I can write it as nFln C1 by C zero. This is nothing but concentration, we shortly write as concentration is equalto then RT by nF ln I can see C1 by C zero I can do little bit of juggling here RT bynF ln 1 minus 1 plus C1 by C zero we can write it as RT by nF ln 1 minus C zero by C1 i Czero. I can write this. I can convert into log and if I consider 25 degree Celsius 1atmosphere pressure that time this factor will become factor multiplied by. So thatmeans RT f 2.303 log 1 minus C zero by C1 by C zero by n, this factor would become 0.059Mlog of 1 minus C zero minus C1 C zero ok.So I can for that write 0.059 by n log of now get to this particular 2 situations thisand this, so I tried to write J1 equal to iL nF equal to minus D C zero minusC1 by deltaand J2 equal to il by nF equal to minus D C zero by delta. So then I can see that Czero minus C1 by C zero is nothing but i1 by iL. We can get to this. In both the casesD would be same because it is at a particular temperature n and F for both the cases aresame. So this ratio we are getting so I can write it as 1 minus i1 by iL.So this is concentration polarization, if I would like to plot it, so this is n concentrationequal to 0.059 n log 1 minus i1 by iL. Now here instead of 1 I just put i because thegeneralized equation then this step it is valid for any other compositions. This C1could be anything other than C zero and once I reaches to iL that time this quantity becomesinfinite. So if I try to plot it, the plot nature would be.So this is the situationif you see this the situation this is the value zero overvoltage zero and this is logi, so when it can go to zero when ic equal to ia equal to i zero. So that means I willhave situation like this. These are the activation region and now at this point I equal to iL,so that was concentration polarization becomes infinite, so it goes down directly straight.So this value corresponds to iL, i limiting.Now you could see that before I achieve this situation the concentration polarization orthe change in concentration change in potential due to concentration effect is not that significant,but there is a change in potential due to activation. Now the activation will take thepotential down but the concentration affect will not allow the potential to be down significantly,it will be in significant.So initially at the lower current level the activation current will try to take activationpolarization leading to the ic that will take the potential down and finally when the icreaches this particular criteria it will merge with this. Fine. So the final plot would beso this is for ia, this is for ic, this is i zero, this is zero voltage correspondingto E equilibrium, this is the corresponding iL. So this combines. So, up to this we arehaving activation polarization and after this we are getting concentration polarization.Fine.So this is the significance of this is the in the log scale is the significance of concentrationpolarization and this plot shows the combination of both activation and concentration. Nowif I try to see the mixed potential theory here also, now in case of zinc and hydrogenthese 2 reactions you could see that the plots were like this. So this is the and these pointI am not indicating you just go back and see that what are those points.This is for hydrogen, this is for zinc and now this point is nothing but i corr equalto ic hydrogen and this is E mix, and this is the potential axis. This is the situationwhat we had in case of activation site activation, when the polarization is control polarizationis nothing but activation polarization. Now if we have a situation like this let say 1metal which is having its own activation polarization in the cathodic side this is ia for metalminus ne equal to M n plus.And this is ic for that metal. Fine. And this is i zero of that metal on the metal surface,this is E equilibrium of that particular metal. Fine. Now if I consider the hydrogen evolutionon that particular metal and if we consider the hydrogen reaction is taking place likethis and before it reaches the mix potential I will have achieved if I achieve concentrationpolarization in case of hydrogen. This is the concentration polarization line.This is ic hydrogen on that metal surface, if we have a situation like this, this isia for hydrogen, this is i zero hydrogen on that metal surface and this is E equilibriumhydrogen. So that time the mix potential be this one. Fine. And at this point i limitinghydrogen on that metal surface is equal to ia of that metal or i corrosion. Fine. Thisis the situation. this is the mixed potential theory for in the situation when we have interactionof concentration polarization with activation part of that metal.And these 2 extreme points they try to reach a mix potential where total cathodic currentdensity is equal to total anodic current density. We will have interaction like this. So thisis the interaction of activation polarization for both ia and ic and this is interactionof concentration polarization of ic and activation polarization of ia.So these 2 situation we have just now explained. So let us stop here, now we have understooda kind of we will basically this is the recap, now will get to understand lot of corrosionphenomena with the help of mixed potential theory one after another, thank you.