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Hello everyone, let’s start lecture 3.And topic, will continue our discussion on electrochemical polarizationand where we will consider activation and concentration polarizationand gradually will get into today at least Tafel equation. At the end of lecture 2 wecome across 1 equation which is i net is equal to i zero exponential alpha nF neeta by RTminus exponential minus 1 minus alpha nF neeta by RT, and then this is nothing but ia minusic, so separately we can write i equal to i zero exponential alpha nF neeta by RT.And ic equal to exponential minus 1 minus alpha nF neeta by RT and in this case we areconsidering a generalized equation this ic this is ia. Now if we start operatingon this 2 equations I can write overvoltage in the form of ia RT by alpha nF ln ia byi zero. Similarly, here minus RT 1 minus alpha nF ln ic by i zero. So if I convert into logwith base 10 I can write it as into 2.303 alpha nF log ia by i zero, similarly hereminus RT into 2.30 by 1 minus alpha nF log ic by i zero. Interestingly in our case thisalpha which is symmetry factor which is considered to be 0.5 it means thatthe contribution of this over potential towards anodic as well as cathodic side or let ussay IHP and OHP is similar or same.That means the distribution if I go back to that slide if I see this particular conditionthis is IHP OHP, this is a situation where i zero is setup, now if ia is more than icso this will be the situation that time this becomes my total neeta and ABC, so AB by ACequal to alpha which is 0.5. Now this part is alpha nF neeta and this part 1 minus alphanF neeta. So these 2 are equal. So I can say that alpha nF neeta equal to 1 minus alphanF neeta. So that is the situation we are considering.Now once we get this, so we can write neeta equal to 2.303 RT alpha nF log ia by i zero.Now interestingly since it is ia with reference to anodic current density I can write it asovervoltage to be anodic overvoltage. Now similarly I can write minus 2.303 RT 1 minusalpha nF log ic by i zero. Since we are considering the cathodic current density we can writeit as cathodic overvoltage. Now R alpha nF all are constant quantities because here nis constant for a particular reversible electrochemical reaction.F is constant, R is thus constant which is constant, also alpha have considered we haveconsidered 0.5, now if I fix temperature this is fixed, so these quantity in both the casesthey are fixed. So I can write in a straight line equation. So I can write C log ia minusC log i zero. Similarly, that means here C is nothing but 2.303 RT alpha nF and whereasC prime I can write it as minus 2.303 RT by 1 minus alpha nF, if that is the situationthen I can write it as C prime log ic minus C prime log i zero.Now little bit more on i zero so i zero is exchange current density, now this exchangecurrent density for a particular reversible reaction in this case it is M n plus M, thisis a reversible reaction we are considering. Now any electrochemical reaction happens ona particular surface, Now this i zero will see later that i zero is a strong functionof the surface on which that reversible reaction is taking place ok. So in this case the reactionthese particular reversible reaction is taking place on the metal surface.So I can write i zero for metal on metal surface, so this is the notation we will use, now thesesituation will be critical while we consider a gaseous reaction. For example hydrogen evolutionreaction let us say we consider this reaction that time i zero when it is non corrodingsituation that means a reversible situation. So i zero of hydrogen evolution I can writethis one as H2H plus H2, these particular i zero we fix all other parameters like allother factors like solution concentration, temperature.Al those things are constant, then depending on the surface this i zero of hydrogen evolutionreaction can change. Now in an acid solution we fix the pH also, but in the acid solutionin the same pH we can have hydrogen evolution reaction on zinc surface, we can have hydrogenevolution on platinum surface, we can have hydrogen evolution on gold surface ok. Solike that all the surface for example if zinc with dip in HCL we will see that hydrogenbubble on the zinc surface.So that means this particular reaction is taking place on zinc surface. Now even similarlyif I put a platinum in an acid will see that hydrogen evolution takes place on the platinumsurface. So that case this value will change greatly even if we fix the pH value and temperaturesummation all those things. Now that case we have to indicate that this is on what surface.So it is better to write i zero zinc hydrogen H2 or i zero 2H plus H2 on platinum or i zeroH2 on gold surface.So like that we have to write, so i zero bracket and then subscript superscript and this issubscript. So this is the surface on which that electrochemical reaction is taking placeand this is the reaction electrochemical reaction. So this is the notation will use, this isthe notation. So now in this case i zero for an electrochemical reaction which has achievedreversibility that means equilibrium, this is a fixed value.So that means this entire quantity is a constant, similarly here also this is a constant. Sonow I can indicate this one as a kind of straight line equation x plus B like this I can writeY equal to AX plus B which is the straight line equation, that the slope is nothing butA is a slope. So now if I try to plot this 2 equations. These 2 equations I can write.So this is another equation, equation 1, this is equation 2. These 2 equations are nothingbut Tafel equations.And this Tafel equitation is one case this is this side it is anodic this side is cathode,now if try to plot then let us plot them, one case I will plot with reference to logia and here overvoltage and here I have to put neeta a similarly on the other side Iwill plot log of ic neeta c. Now interestingly this slope C, if you see this, this is a positiveslope and here C prime is a negative slope. Fine. So if I try to see that one side theplot would be like this another side the plot would be like this with a negative slope.So this is the slope which is called C and this is the slope which is C prime and theseslope in electrochemistry we write it as a tafel slope, this is also a Tafel slope andthese are popularly termed it as beta c and hear it is beta a, why this is the Tafel slopefor anodic reaction anodic side, this is the tafel slope for cathodic side and this isa negative and this is positive. And this is also matching with our concept that wheneverwe send positive current.That means ia increases with reference to with respect to ic, the potential goes positiveside and here also it is C that that means more and more ia ic that overvoltage increasingand overvoltage is nothing but the measure of polarization. And similarly on the otherside if beta C has the slope negative slope. So that means with increase in the magnitudeof ic I would always fine that neeta C is decreasing.And here it is increasing, so that means this is also perfectly fine as per our convention,now what happens when ia equal to i zero. Let us say this i zero and here also thisis i zero. So i zero when it is achieved when ia equal to ic equal to i zero when E equalto E equilibrium or we considered it as has M n plus M. Fine, so this is the conditionthat an i zero is similar to same as ia as well as ic. So that means if we combine this2 curves we can get a curve like this.So this is neeta, so this plot is like this and another plot would be like this, so thisis nothing but beta c slope and this slope is beta a and what is this value and thattime this will be log i, now at this point is nothing but i zero because I see that atthis point ic equal to ia equal to i zero and that time what is the over voltage becausethis is at equilibrium potential over voltage should be zero and as we go upward then overvoltagegoes up.And as we are going down overvoltage goes down from the equilibrium potential, so thisis going down. Now we have to see that what is the net current because our actual equationis this one. So we have actually going to get the net current this is the differencebetween these 2 current. Now net current if you see let us say this particular value youassume some value 10 to the power minus 6 ampere per centimeter square.So now if I go to this potential, then this value is let’s say 10 to the power minus4, these value goes to 10 to the power minus 8. So then what is i net equal to ia minusic equal to 10 to the power minus 4 minus 10 to the power minus 8 which is nothing butminus 4 ampere per centimeter square. So now if I would like to plot i net what will bethe point the that locus point in this particular diagram, that time that point would be lyinghere. Because it is exactly same as nothing but ia.Because this current is ia and this current is ic. Now as we go down if we keep goingdown I could see the difference between ic and ia that is decreasing. So that time atsome point of time that means that are very low overvoltage, I will not get this approximation.that time this difference will be some finite difference and then once we get that finitedifference then we have to take the log. Ok.Because we are taking log of i net, so then that time this gradually these points willkeep shifting, so here it is this, now I am finding that the difference is coming up wego down further, I could see the difference is here. Now as you are coming closer to thisovervoltage zero that place at this point I could see that this difference is goingto be zero. So once we have zero then these point will go asymptotically towards thispoint.So then the plot nature would be like this. Similar, thing happens on the bottom side,on the cathodic side this should be this. So what would be my experimental plot, experimentalplot would beand then from this experimental plot because experiment wise I will only get the i netwhich is the experimental current density I will measure. So then the straight linepart I could see the straight line part is happening at the higher overvoltage.Here also higher over voltage from that I will draw a straight line and similarly herealso I draw a straight line. Fine. These are crossing point which is nothing but i zerook and this straight line slope is nothing but beta c, this line is beta a and this isthe polarization line which is nothing but this and this is the polarization line nothingbut this. Though these are invisibly present, but we can have an idea that where are thoselines from the polarization line polarization diagram.So the experimental polarization plots, so this green line here and the black line here,this in this case black line, in this case the green line, these are the polarizationplots, these plots we can have.Now coming to this is for a single electrode system, for example here what we are gettingfor a single system M n plus plus ne, in this case we are getting a plot like this. So weare having a situation like this but the plot would be definitely like this. Fine. No issues.So this is over voltage equal to zero, this goes up, this goes down, this is neeta a,this is neeta c and this is log scale log i and interesting this is a straight lineof course this is a straight line we have already explain because this is a straightline equation.Now coming to a situation where we have 2 such reactions taking place where we can experiencesuch reactions. Let us say we have a situation like zinc rod let us say pure is dipped inHCl solution of pH 1, lets say. Ok. Now the solution has a condition what are those condition,this is dipped, there is no oxygen dissolve oxygen, no oxygen. Fine, no impurity, thesecondition only we are considering.And the temperature is let us say room temperature which is 25 degree Celsius, pressure is 1atmosphere. Fine. Now in this case will have 2 reactions 2 half cell reactions, one reactionwould be taking place on zinc plate, so the zinc plate will see what are the observation,observation would be we will see that on the zinc surface will get little bit of bubblingformation and those bubbles and nothing but hydrogen bubbles.And reaction would be zinc plus HCl equal to it will form zinc chloride plus H2, thisis the balance reaction. Now if we break them and then try to see whether they are electrochemicalin nature we can easily see that, we see that zinc if it releases 2 electron it goes tozinc plus plus whereas 2 hydrogen plus it access 2 electron and goes to hydrogen. Nowimmediately it is very easy to understand that this is the cathodic reaction and thisis the anodic reaction.And since we are considering our context to be only corrosion so though we can easilysee that zinc is corroding. Fine, now if we allow them this particularly take them separatelylet us say I put zinc in a zinc ion zinc ion present, then I can have an equilibrium reactionlike this. Similarly, if we have a hydrogen cell where I can have an equilibrium likethis. So the both this equilibrium would have some E equilibrium reaction.And both these cases would have a separate like this diagram. Similarly, here also E,I will get an equilibrium potential like this, if we allow them to equilibrate in a separatelyif we are not mixing them.Now that case both the cases will have separate diagrams, so that means in this case I willhave a diagram like this log i, I have a diagram like this and this is nothing but i zero andthese i zero is nothing but zinc on zinc surface. Similarly, and this is ia, this is ic, thisis the slope beta a, this is the slope beta c for the zinc case, this is the zinc siteand these corresponds to zero which is nothing but E zinc plus plus zinc.On the hydrogen side if I see so it will be again like this, and now here it is happeningon some this is i zero on some surface. So I will say that metal surface it must be happeninga metal surface, hydrogen H2 this is i zero and correspondingly its potential would beE H plus H2 which is nothing but zero overvoltage zero. Now here we are considering 1 pH equalto 1. So then what will be this equilibrium potential E would be thenequal to E zero H2 minus 0.059 pH.And we know that this value is zero is nothing but 0.059 and pH equal to 1 volt equal tominus 0.0594. Now here depending on the zinc concentration I can change this particularvalue. Now when you add when you mix them immediately there will be some finite zincconcentration in that. Now before the reaction starts it will have some finite values. Nowwhat happens if we mix then, now we have to understand this, this reaction from this diagramszinc plus HCl equal to zinc, zinc chlorine plus H2.These reaction we have to understand with the help of these 2 diagrams. How do we dothat? In order to understand these particular reactions with the reference of these 2 reactionsthese 2 plots we need to get to the mix potential theory. This mix potential theory we havealready discussed in lecture 1 that is in corrosion one will not go detail of thosediscussions you can go back to those lectures and then follow up.We will just put forward a brief of it. Ok. So now this mix potential theory what arethose 2 major postulates, 1 postulate says that there could be number of cathodic andanodic reactions. There could be number of cathodic and anodic reactions it could be1 cathodic plus 2 anodic or 2 cathodic plus 1 anodic. Fine. So like that there could bemultiple cathodic multiple anodic reactions. For example this example you can easily sitethat iron and zinc.They are coupled, and if they are put up in acid, so that case cathode reaction wouldbe hydrogen evolution if it is deaerated that means there is no dissolve oxygen or impurityare there. So that case is 1 cathode reaction which is hydrogen gas evolution and 2 anodicreactions that means iron in this case I can say that iron releases 2 electrons and thenform 2 iron plus plus iron plus plus ion and zinc releases 2 electron and forms zinc plusplus. Fine.So now these are the 2 anodic reactions and what are the cathode reaction is H plus H2.So this is cathodic reaction. Now I can have example of 2 cathodic 1 anodic where let sayzinc in HCl where we have Fe plus 3 impurity. So that case what are the 2 cathodic reactionsH plus 2E equal to H2 and Fe plus 3 plus e equal to Fe. These are the 2 cathodic reaction,this is in this case 2 anodic, 1 cathodic and in this case 2 cathodic and 1 anodic.What is that anodic reaction zinc releases 2 electron and form zinc plus plus. So thisis 1 anodic, in this case 2 anodic 1 cathodic and this is 2 cathodic 1 anodic. Fine. Sowe can have several such examples. So this is the simplest example that could be multipleof cathodic and anodic reactions and the second postulate says that the charge balance.There could be global charge balance and for that the system would achieve a potentialwhich is call mixed potential where summation of ic ic equal to summation of ia.So that means the total current density due to anodic reactions and total current densitydue to cathodic reaction, cathodic reactions will be same. So on the basis of these 2 postulateswe can have a mixed potential theory and then we will see that this 2 separate plots canbe combined and we will get to mix potential which is nothing but the corrosion potentialas well as we can get to the corrosion current density. Let us stop here will continue ourdiscussion in our next lecture, Thank you