 Today, we will look at the application of mixed potential theory and in relation to the electrochemical testing for corrosion. You carry out electrochemical test in order to determine the electrochemical kinetics of corrosion. You one of the important the parameter that you might you might determine from this is the corrosion rate. But there are other parameters we call them as electrochemical kinetic parameters like the exchange current density, tuffle slopes and in case the metal is passivating what are the passive current density, critical condensity, pitting potential all these kind of stuffs that you are going to determine using electrochemical aspirant to detect. Now, you need to have a clarity in relating the data to the events diagram. So, far we looked at the events diagram and we looked at in fact, various parameters that affect the corrosion like velocity, the effect of oxidizers, the tuffle slopes of the anodic reaction, cathodic reactions, exchange current density. We all saw in a theoretical manner how they affect the corrosion rate. Now, you must have a method of determining all of them. How do you do it? It is not a very straightforward in the electrochemical technique. So, what we look at here is the electrochemical technique to determine corrosion kinetic data. Now, let us start with the so called events diagram. Let us take an example of iron corroding in hydrochloric acid ok. So, let us take this example of iron corroding in hydrochloric acid. It corrodes into ferrous chloride then hydrogen is avoided. We need to look at the corrosion kinetics of that. Now, for this you can write events diagram right. How many equilibria you have in this to start with? Two. One is hydrogen gas is in equilibrium with hydrogen ions. The second is iron is in equilibrium with Fe 2 plus ions. There are two equilibria right. And you have corresponding exchange current density, tuffle slopes, equilibrium potential these factors. So, let us represent here in the diagram ok right. So, you have a potential here log current current density rather and you can represent the two equilibria that you have right. And this corresponds to what? Hydrogen going as H plus plus electrons. Here H plus combines with electron forms hydrogen gas right. What is this? This one ion going as Fe 2 plus plus 2 electrons. And here the cathodic reaction Fe 2 plus plus 2 electron gives you ion here. And this is the equilibrium potential for hydrogen and this is the equilibrium potential for ion in equilibrium with Fe 2 plus. Now, we all know in this case right this is your I car and this is your. In the corrosion reaction here what are the governing governing relationship that that that affects the corrosion rate this particular kinetic this particular kinetics this does not really affect at all this does not really affect at all they do not affect do they affect they do not really affect at all. Now, I need to determine the tuffle slopes, the exchange current density, the tuffle slope, the exchange current density I need to determine. Of course, I need to determine of course, the I car and the I car value to start with. Let us look at a simple system ok. I just draw schematically suppose I have you know represent this corrosion process using this this schematic diagram. So, this is hydrochloric acid it is getting corroded simplicity it is deirated right. If I measure the potential of this one when it is corroding using a volt meter or electro meter and using a reference electrode what will be that potential called use use this diagram look at this diagram and tell me in this case which is this is called as a corrosion potential. I can measure the corrosion potential much easily using a reference electrode and in a electro meter. I want to also determine the I car value. Can I measure here? I cannot measure here directly because no current is coming out of this metal now. Why? The rate of iron oxidation is equal to the rate of reduction of H plus ions. The electrons liberated on the surface is consumed by the H plus ions. The no electrons they go out of the system now the current moves into system. So, you cannot measure the I car value directly in here though I can measure E car value you all with me I cannot use a meter right. If you use a meter what happens? Current does not flow out of this corroding system because the rate of oxidation here is equal to rate of reduction here at all or if I measure using ammeter suppose I measure using ammeter ok. Some means what will be the current there? The current will be 0 am I right? The current will be 0 I cannot measure any current right. So, at E car value the measurable current that is going out of this system is 0. Can I say that? So, that is the current. So, I I just represent in this diagram what is the corresponding current? The corresponding current at E car is 0 here agreed right. Now, what I am going to do is now I am going to now apply a potential on this right. I apply a potential on this how do I apply a potential? I use in another electrode here ok and this is is going to be let us say a platinum electrode. Now, I am going to apply using I use maybe a potential stat or whatever I use a potential stat. I will talk about what a potential stat is later. So, what I am going to do is now I am going to change this potential of this electrode. I am going to now move from here towards a positive direction. Suppose I move towards like this suppose I move to let us say this potential. I moved from here to this particular potential I moved. Now, please look at this Evans diagram. What is the current that is corresponding to reduction? This is the reduction current and this is going to your oxidation current. So, iron is getting oxidized more than hydrogen is getting reduced or you are following me or not right. That means, there is going to be net flow of current in the system am I right or not? That means, if I want to rise it what happens now in this case? Now, when iron is dissolving the electrons move out of the system like this electrons move out and the current starts flowing like this. Now, I am going to use an ammeter use an ammeter now here the ammeter start measure in the current. What will be the current coming here? The current coming will be the difference between this current and this current right. For example, the iron is getting dissolved at this rate hydrogen is getting reduced this rate only the remaining electrons go out of the system right agreed. So, the current will be between these two points ok it is not going to be exactly this. So, I subtract this current from this current ok. So, what happens now? You find that at this particular place the current is going somewhere here ok the current starts increasing like that. Now, what I am going to do? I am going to rise the potential further I am going to rise it to this particular place I am going to move this to another potential here. What happens? In this case? The rate of oxidation increases even more and the rate of reduction is now decrease am I right or not? So, this current will be very close to this. Now, I come here this come very close to this because this current is less this is very high ok. Now, what happens now? Now, this current this starts going close to this it should be here actually ok it should be here ok. Now, again if I if I again extend this further what happens now? Extend further this curve will go and get merged with this because the reduction current is very small the oxidation current is more overall the current corresponds to oxidation current agree or not? So, that means, this curve will go and almost start merging with this and go like this of course, here what happens there is going to be one more oxidation things will start moving differently. So, up to this point you will find ok you find that this curve is going to be merging with this taffle line. Does it merging with this taffle line or not? It is merging with this taffle line here agreed anybody has any question? Yes. Yes. Suppose, I ok I will come to that point later what happens when decrease the potential right. Now, what happens now? At least have you have you understood the have you understood this behavior of potential current relationship that it is initially 0 it increases it goes like this and in this point of time it is just following the taffle behavior. Here is not following the taffle behavior not behaving the taffle behavior it starts behaving the taffle behavior here is it ok understood right. So, you ask the question what happens when I am going to bring the potential down in relation to e car right when I bring it down what happens now? When I bring it down let us say to I want to bring it down to this particular potential the anodic reaction to be is rate is less and the cathodic reaction rate is going to be more agreed ok. So, what happens? What happens? There is a net current the net current is going to lie somewhere here only. So, what happens now? This guy will start following similarly like this ok. So, I would get I would I would obtain you know the points will lie along this I am reversing it so that it will become easy for you to to understand ok. So, this is what you will get in an actual experiment. In an actual experiment you carry out in the laboratory you measure e car first you move from e car either way you can move either towards cathodically first and then you can start moving anodically later you will able to get this this this particular plot you get this particular plot here. So, this is how things will look like in all your experiments in all your experiments now and you using this you should able to now reconstruct the diagram now ok. So, if I have this this this this this polarization curve this polarization curve how do I get how do I get I car how do I get it? Simple right. You draw a tangent right you want to where do you draw a tangent do you draw a tangent here? No you draw a tangent here because it forms a Tafel equation. The Tafel behavior is coming here the Tafel behavior is not here the Tafel behavior is not here. So, you draw a tangent from here tangent from here and they extrapolate the tangent the intersection point gives you what is called as log I car. The intersection point ideally will give you the corrosion potential the car agreed agreed or not agreed. Now, I want to get the X n condensity right how do I get X n condensity? I want to get X n condensity for hydrogen H plus equilibrium right how do I get it? I have I have only this line I have only this line how do I get how do I get X n condensity ok can you can identify which is the which is the X n condensity in this event diagram where is it? This one right this corresponds to X n condensity H plus H and this corresponds to I naught Fe 2 plus and Fe ok. So, how do I how do I get this X n condensers? It should be much easier right is this is anybody discuss? So, you need to calculate the equilibrium and extrapolate the tangent to the equilibrium potentials why are you assistant right and we should not be assistant at this stage. You extrapolate to that particular place you get X n condensity and you get X n condensity. So, how do I calculate the equilibrium potential? Is there a way to calculate? Come quick. Suppose I say iron is here in the solution and I I you know in hydrochloric acid and I say that the ferrous iron concentration is 10 power minus 6 moles. Now, you tell me is there a way to calculate the the equilibrium potential? Can you can you not? Quick. Can you how? Nernst equation right. So, you can use the Nernst equation and calculate this and you will able to get the equilibrium potentials then you can able to get X n condensity you can get all these values why are these important? It is important because the X n condensity desires for should be corrosion rate of course, you have tuple slopes you have other factors. So, you we can determine that. You will see over a time period how we use this to design a new alloy system. You want a less X n condensity. For example, if if I move assume that the tuple slope is same right. If I lower X n condensity what will happen to corrosion rate? The tuple slope is same the equilibrium potential is same if I lower the X n condensity for this. So, what you will happen to I car value? Quick it will decrease right. So, these these are the things that that is what I meant the mechanisms of corrosion in this case. So, it is possible for us to determine all the electrochemical parameters using the the so called the polarization diagram ok. So, this is a an important thing and you might have done already I suppose this experiment if not you might be doing this very shortly and in this case you will only get you will get only the these lines get only these lines you are not going to get this. It is not possible why? The moment you immerse steel in in an hydrochloric acid you are not having any more equilibrium here you are not going to have any more equilibrium here. In fact, this this half of it this part of it you never able to get it off. You will only get only this part of it right. You will only get this part of it and we extrapolate and you can get the the electrochemical parameters understood ok. Now, let us go little further into it ok and try to use the so called Butler-Walmer equation and try to understand why does it really happen ok. I am going to now you know write briefly what the Butler-Walmer equation is. Now, we have seen now the current that is flowing in a system I current I measured I measured is equal to I anodic minus I cathodic. Please understand current as a sign so as a potential it is not independent ok. Cathodic current is generally negative and anodic current is generally positive because why in anodic current what happens in anodic current why why does it so why does you call this anodic current you take a metal right you take a metal there and when it dissolves the assume in the case of iron right. I have a electrode here iron dissolves as Fe 2 plus the current moves away from it and H ok whereas, when H plus is getting reduced the current moves in the counter directions. So, the current flow or the interface is different this anodic current or a cathodic current ok. So, the net current is given as anodic current minus the cathodic current that is the convention. We have seen earlier ok the so-called Butler-Walmer equation where I which is measured normally given as what is related to N B D still remember I anod exponential what exponential 1 minus alpha right and N number of electrons right and F ok and divided by RT into what into E applied minus E equilibrium right minus exponential minus alpha N F RT by E applied minus E we can use this bracket here and the first one what is this this is your anodic and this is your cathodic you can go back to your notes and check. Now, in in over here I am going to now put back this the Butler-Walmer equation talks about this and talks about this and talks about this I am going to apply this to corrosion also ok corrosion not equilibrium still you can apply this. So, I am going to apply to this this particular line here this particular line here the same Butler-Walmer equation ok. How do you do that? I slightly change this into this equation slightly change as I applied is equal to I car exponential 1 minus alpha N F RT E applied minus E car ok minus exponential minus alpha N F RT. What I have done here is of equilibrium potential I made as E car is of X n continuity I made as I car. So, from there only I am deviating right I am deviating from there right. So, I have moved from here to this for a this is for a corrosion system. So, this is for corroding system. Now, you tell me what does this correspond to yeah is it is inverse of tuple slope RT by alpha N F is tuple slope it is a inverse of tuple slope right. So, I write this equation like this I is equal to I car exponential what is that E applied minus E car by beta A exponential E applied minus E car can I say these are not got it. Let us now look at this equation I hope you guys are following right let us look at this equation ok. Now, look at this condition 1 ok E applied minus E car is positive and large let us say very large ok large quite large ok quite large. So, what allowed equation look at your equation tell me what happens ok. I think I made a mistake here please go back to this go back to this equation yeah see there is a mistake here please correct it. I equal to I car exponential E app minus E car beta minus exponential of minus ok please look at that please make this change. So, having this let us go to the condition 1 ok in condition 1 E applied minus E car is positive and quite large. So, what will happen to this equation the equation will be equal to I is equal to I car what happens exponential E applied minus E car by beta A understood condition 2 E applied minus E car is negative and very large ok. What happens to I car I equal to? I equal to what? I equal to I car minus exponential minus ok. So, this is a very interesting thing what is what can you say about see you can also say E applied minus E car can be considered as over voltage here you know in a sense of over voltage I do not want to call in that true sense it is over voltage in a different sense of that ok deviation from E car actually. So, this is what is this relation called anybody this is called a Tafel equation this is called a Tafel equation right. So, go back to this diagram go back to this diagram or so, this is the Tafel equation Tafel 1. So, that means, if I if I represent this go back to the go back to the I am going to make a small diagram here I versus E ok this is your experimental data right. This is your experimental data please go back and see your diagram I am not giving the events diagram completely. So, these are the measured values. Now, equation 1 and the equation 2 equation 1 is applied here right equation 2 agreed and is not valid here not valid here. That means, where do I extrapolate? I extrapolate from this point to this continuously and I extrapolate from here and get this. If I do any extrapolation in these regions as that becomes wrong because it is not valid equation you understood not understood ok. So, that is why when you carry out an experiment you normally get E versus log I curves and in order to get I curve value you make a Tafel extrapolation when when is the condition the condition is E applied minus E curve is large please look at this E applied minus E curve is large and negative you get this here. So, it has to be higher value then only you can able to extrapolate and get these things here ok. So, you can extrapolate and you can extrapolate and you can get E curve and I curve ok. So, any other place extrapolation is incorrect you must clear your doubts here if you are not you are going to have perennial problem in understanding polarization curves anybody ask any questions. Do not be hesitant you just tell me I am ready to spend some more time and make it clear to you that what it really means. So, do not draw a tangent anywhere you want you should draw a tangent where the over voltage is is higher ok because that is where the Tafel's Tafel relation is valid other places it is not really valid ok that is the important thing in you should keep in mind. Now, the question now there comes is how much you can do that ok how much that you can do? Let us look at some complications here ok now it goes something like that now it goes like this. Can you do this here? Can you do it here? You cannot do because very likely they are effusion controlled in some cases large IR drop I am not going to talk about right now IR drop and let us not worry about right now. So, you cannot do either at too large they need a value because the Tafel equation is not valid anymore. So, it is valid. So, you should not look at which region the Tafel equation is valid and you should make an extrapolation that is a very important thing getting the electrochemical kinetics of corrosion ok. So, I think this should you should keep in mind when I talk about when I talk about ok problems in Tafel extrapolation. So, it is not that simple I mean you had to be you had to know what is going on if you do not know what is going on in the system you simply cannot use this plots to extrapolate the way you need to do that ok yeah. Yeah right now we will not talk about it and it is now it is going to take you know quite a bit of time it will rather digression maybe at some other point we will discuss otherwise you will be discussing this in the other course Experimental Techniques for Corrosion there you might discuss in details just note down that or we can discuss of the class ok. It is it is a big subject by itself ok. Let me let me go back to this equation again and see what it really means actually ok. I go back to this equation otherwise let me let me put this equation here. Let us look at the equation one more time I is equal to I car exponential E applied minus E car beta A minus exponential minus E applied minus E car beta C. Let us look at this equation now let me this put another condition right E applied minus E car is very small. So, what does it mean? Eta over voltage is very small. So, what do you think will happen? You guys all you know experts in mathematics right if if this is small it could be either positive or negative whatever it is very small what happens? So, you have a series right right. So, this can be written as I is equal to I car 1 plus E car beta I can keep having the series right and I can have this then I have minus of ok what happens 1 minus square nor goes right way is not it goes like that am I right? So, what will happen now? If I make this is delta ok now what I do then is equal to I I car delta E by Eta plus beta C am I right it can also be I. So, when I put a see when I have a delta E what will happen to this this I also becomes delta I upon delta E is equal to I car 1 by beta A beta C. What is I by E generally R right ok. So, is equal to 1 by is it right? Look at the now the relation between between between E and I are linear now look at this this is a linear relationship or not and this is called as is called as stone gary equations. Now, what is beta I A beta C they are all constants ok these are constants and R and I I mean I car or interrelated to each other ok. So, this is another way of determining the I car value ok. So, how to do this here? How does it work? It works this way this is called as linear polarization technique once again. Please notice here we have plotted not on log scale we have plotted in simply linear scale, linear current, linear voltage and and you see that there is a region what is this place? It is a over voltage is 0 here right Eta is equal to 0 here I odd is equal to 0 here right. So, origin goes to an origin here ok and of course, here it becomes exponential and it becomes exponential and that is how the equation is valid. Now, the bottle warm equation is valid all through please look at if you use a bottle warm equation it is valid everywhere. The Tafel equation is valid here here the stone gary equation is valid here because they are all special case of the over voltage ok. So, slope of that is what this is what gives you what is slope is equal to and this is where you are supposed to go the way should go where it goes here. Now, why do you use a linear polarization technique as compared to Tafel technique ok. Let us go to the now what are the advantages and disadvantages is technique ok merits, demerits, Tafel ok can get so many parameters is is independent is what is the demerit is a destructive test. If I do for if I want to follow the corrosion rate with time see sometimes metals may not corrode the same way you know with the time the corrosion rate may increase or decrease you cannot use a Tafel slope because once you polarize metal corrodes the surface is getting destroyed the destructive technique right. You go to linear polarization it is non-destructive why we apply only a few millivolts the range is in the range of 5 20 millivolts you apply plus or minus 5 to 20 millivolts you apply actually. So, the corrosion is so small the sample is not really changing its characteristics it is a non-destructive technique. What is the demerit? The demerit is you need Tafel slopes. One more I just mentioned I am not going to discuss too much and cannot be used in highly resistive environment. What I mean the conductivity of the electrolyte is very small you will not get it ok. Again I will not discuss it requires some other background ok. So, for the time being it is sufficient to understand and be aware that linear polarization cannot be used in some conditions. I am sure of course, the next course you are taking electrochemical techniques there these things will be discussed more in details ok. So, I think we have discussed so far the relation between experimentally obtainable polarization data and how you can use that to determine the electrochemical parameters like corrosion current density, ecore values, exchange current densities, Tafel slopes and all this like that we can we can able to get this. And I also it is necessary to connect them to events diagram because you need to get a clear picture about what are the mechanisms are happening. So, that we have done it. We have also seen that they are all related to the the mother equation we call it. The mother equation is a Butler-Walmer equation. We have not derived that those who are interested you can read Buchanan and or maybe you read the Bakris and Reddy book they are very nice you know derivations are given there. But you know that if you know that the Tafel equation and what are the significance of that you can see how from that equation the Tafel relationship emerges from that equation how the Stain Gray equation emerges and the merit and demerit of these equations see. The point again is clear they are special case of Butler-Walmer equation that means the electrochemical data should be properly interpreted you cannot diverse that from the Tafel relationship or the Stain Gray because there are certain regions they are applicable certain regions they are not applicable. So, then only you can able to get the proper data otherwise you get some some Icar value we may not really know whether there is any relevance at all ok. With this I think we will finish the discussion related to Icar Icar as a electrochemical parameters and ok.