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So, what is that reactant and what is that product? That decides the voltage that is the chemistry involved. And therefore, this is of relevance from the perspective of thermodynamics ok. The thermodynamics of a system deals with what will happen under equilibrium conditions you will give it the best condition possible for the I mean you give enough time for some reaction to occur; what is that reaction that is going to occur, what is you know urge for the reaction to occur, what is the driving force for the reaction to occur that driving force represents itself as a voltage ok. So, thermodynamics which talks about what is possible; what is possible is thermodynamics. So, it predicts that you know given nature has certain tendencies; what is possible that prediction is thermodynamics and that relates to the chemistry that is involved which talks about which reactants are present and therefore, which products will it form. So, that is the voltage part of it. The current on the other hand relates to the rate at which the reaction is occurring ok. You have independently decided what is the reaction that will occur? That is the thermodynamics of it; what is the reaction that will occur is decided by the thermodynamics that that is involved. The rate at which the reaction is occurring in the current; rate at which the reaction occurs is current and therefore, this is referred to as kinetics ok. So, the current represents the rate at which the reaction is occurring and in the field of you know the science, we are referring to we look at it from the perspective of the kinetics of the reaction the voltage looks at what can occur and in the field of science that falls under the realm of thermodynamics. So, in some fundamental sense they have I mean you can think of multiple situations where the two of them don’t necessarily see eye to eye. So, you can have a good I main fairly high voltage, but you can also have extremely low current. So, which means there is a strong driving force for the reaction to occur. So, thermodynamics is saying that you know yes definitely this reaction can occur; there is a strong reason why these two chemicals should react with each other and release energy. But the circumstances in which that cell is situated are preventing the reaction from occurring at any appreciable rate; it is crawling along it is just crawling, crawling, crawling, crawling, crawling and therefore, the current that you are drawing from it is extremely slow okay. So, the point to remember here is in some ways the first starting point is the thermodynamics because supposing the reaction is not possible at all this thermodynamics says that this reaction is not possible. If it is not possible the chance that it will occur at any rate is anyway not there; so, it is going to be 0. So, the kinetics is automatically going to be 0. Once on the other hand once the thermodynamics says that the reaction is possible, then we have a choice of the kinetics you can select to you know either by your choice or simply because of the circumstances that are involved you can have a situation where the kinetics is slow or you can have a situation where the kinetics is fast. So, you can either have low current or high current. So, voltage is one aspect of it; the current is the other aspect of it and deals with the kinetics of it. From our from a user perspective, all this is in the background ok. So, I say user when I go and buy a cell and I put it into a remote or I put it into a toy I am not concerned about you to know what was the science involved in that you know deciding what chemicals are going to be involved there, what is you know is it set up to run naturally very well or it is set up to run naturally not. So, well those things are not relevant to me I want to draw good current. I want it at a good voltage only then some devices working. So, a scientist who is generating the cell bothers about these things; a user simply wants to know that it is delivering in a manner that is acceptable to him or her ok. So, that is the way we want to look at also we have this idea of current versus current density. As we discuss in this class I will focus more on current density rather than current and why is that? So, current, is the inherent quantity that represents the rate at which the reaction is occurring, but we do recognize that you know you can buy if you are talking of a cell; you can buy a triple-A cell or a double A cell or a D cell etcetera these are all of the different sizes right. So, they have different differing amounts of chemicals present in them. So, I can have a small electrode of the same set of chemicals or I can have a very large electrode with the same set of chemicals. Naturally, if let’s say one electrode is half the size of the other electrode; naturally everything else being the same, the larger electrode can produce twice as much current as of the smaller electrode because it has twice as many chemicals; twice as much opportunity to run the reactions etcetera. So, every other condition being the same the larger; the electrode larger is its ability to generate current a larger the number of locations where the current the reactions can occur. Therefore, the rate at which overall rate of the reaction occurring over that entire area will be higher. So, therefore, it is not a fair comparison I can make with everything else being the same; same manufacturer, same chemicals, same packaging, same kind of packaging etcetera I can make batteries or cells of a wide range of sizes. I can make something you know as big as a room and there is no comparison between that and a small double A cell or a triple-A cell that that may be there is no way of comparing. So, it is important to normalize for the size of the electrode. So, you have to compare against a similarly sized electrode and the best way to do it is to look at current density there where we are talking of the number of amperes that can be delivered per centimetre square ok. So, once you talk of amperes per centimetre square; you have normalized concerning area right. Once you have normalized concerning area it doesn’t matter how big the electrodes; however, big the electrodes you may have a large amount of current, but you also have a large amount of area. Once you divide it the large current by the large area you will have the same value a small current by small area assuming everything else is the same. Therefore once you look at current density; you have normalized for the area and therefore, the quantities become comparable ok. As I mentioned voltage simply talks of what reaction is going to occur and simply talks of what are the chemicals that are present. So, there whether it’s a large electrode or a small electrode doesn’t matter if only looks at what is that electrode is it some particular reaction there is going to occur then that is going to be 1 voltage the size is irrelevant because it's only doing that what is the electrode ok. So, it is only looking at the quality or. So, to speak one characteristic of the chemical composition of the electrode it doesn’t care about the size of the electrode. So, by looking at composition it is sort of already doing a normalization because it is looking composition is some kind of a concentration that is already normalized in some sense. So, therefore, voltage is unaffected by size current is affected by size. So, current we need to look at as in the terms of current density. So, in this discussion on this slide, these are two important points that I wanted you to stay alert to one is a voltage versus current the fact that voltage refers to thermodynamics or the chemistry of the system. And current refers to the kinetics or the rate at which some reaction is going to occur. And the fact that more than current it is the current density that is of interest because that is when you can do a comparison between different devices ok. (Refer Slide Time: 27:04) So, we now have you know as I said a constant setpoint operation which means you can have typically as a function of time. You usually look at a voltage or current density which is you know often represented by small I and you see how that it functions as a function of time. So, let me say the opens open circuit voltage was 1 volt or the voltage under some operating condition happens to be 1 volt; then you would like to see how this voltage stays as a function of time. So, for example, ideally, you want it to just stay flat. So, you are drawing current for a long period and the voltage stays the same value for this entire period. Usually, this is not what you will see usually you will see that it steadily deteriorates. So, this is what you will typically see for almost any electrochemical device you tend to see this deterioration. So, this is a deterioration ok; so, deterioration of the functioning of the device. So, if for example, you are looking at if we if it were a battery for example, then you would run out of charge altogether; so, then that performance characteristic would look different. But let’s say it is an energy conversion device like a fuel cell then you would see your behaviour that looks like this over some time then you have to find a way in which you can you need to recover this performance. So, sometimes there are ways schemes by which you can recover this performance and then again you let it run for some time and then it does this kind of thing. So, a lot of diagnoses is done using this to a first of all people look at degradation rates. So, they look at the slope of this curve at of this line here and that represents a degradation rate. So, we talk of it in terms of you know millivolts per hour; degradation rate millivolts per hour degradation rate is something that people try to actively keep track of for many electrochemical devices. And so, they will have a target; so, if you are looking at any device you know other people who have looked at the device in a more holistic sense will set a target saying that you know if you have a device we want a degradation rate that is less than so, many millivolts per hour. So, it means it is degrading at a much slower rate. So, that is something that we want to accomplish and that is the parameter that we want to keep track off as they characterize these devices. It also turns out that this rate of degradation the slope that I have just shown you on the on this slide can vary significantly with time. So, in other words, you may have a very gentle slope in the first say 500 hours of operation and then you may have a much steeper slope from 500 to 800 hours of operation and it may just precipitously drop off after 800 hours of operation. So, this is not even a constant slope. So, a lot of research is done to understand what is causing that slope to be a certain value for the first 500 hours, what is causing the slope to change between 500 and 800 hours and what is causing the slope to completely collapse after 800 hours of operation?. So, that’s just to give you some idea of you know the kind of work that is done; you can do this at a constant voltage or constant current correspondingly the other parameter gets measured and then you see that as a function of time ok. (Refer Slide Time: 30:09) The other parameter that you looked at a lot is the polarization curve ok. So, polarization curve is a very important diagnostic tool where basically what we do is; as supposed to the constant set-point operation where you are looking at you know the operation of that device over may be several hundreds of hours may be several thousands of hours or if it is a battery you are looking at operation over several cycles several hundreds of cycles ok. So, that’s it’s a long you know process during which you find out what are the degradation rates and then you figure out what you can do to recover. This, on the other hand, the polarization curve, on the other hand, is relatively instantaneous okay relatively instantaneous; meaning it’s not instantaneous it takes maybe a few minutes to acquire this data, but it gives you a sense of the health of your electrochemical device at that instant in time okay. So, what do we see here? So, it is something where you are first of all not at one operating point you are steadily changing the operating point in a small span of in an in several minutes okay. So, you will have an open-circuit voltage which means you can see here we have current density plotted here. As I said you know this normalizes for the area of the cell and you have voltage plotted here on the y axis. So, when you have 0 current in the system which is this point out here then you have some open-circuit voltage which is that point that you see over there ok. So, that is the open-circuit voltage which if you know go by the device and you just put a voltmeter on either side of the device and you measure the voltage that’s the voltage you will see then you start drawing current. So, this device now has to be attached to some you know unit which can predictably draw current. I should be able to say draw 0.05 amps per centimetre square that is the current density I want. So, it will draw 0.05 amps per square centimetre and then at that point, it will tell me what is the voltage. So, let’s say that is somewhere here then I will see this voltage ok. So, gradually I will increase the current density; I will go to various points out here and I will keep measuring and in at each condition I know exactly what current density I am using and for that corresponding current density it is measuring the voltage. So, it is measuring the voltages along the y axis for each of those current density values that I have just marked out there. So, when I; so, this is a process that I said you know it will happen over just a few minutes. So, it will what the instrument will do is; it will take this device it will set the current density to be 0.01 or 0.1 amp per square centimetre it will measure the voltage it will stay at this point for let’s say 10 seconds or 5 seconds; measure the voltage then it will go to 0.2 amps per square centimetre. Again sit there for 5 seconds, measure the voltage record those two go to 0.3; sit there for 5 seconds, measure the voltage record the voltage and so, on. So, this process continues till you suddenly see that the voltage begins to drop precipitously right and so, you can set some cutoff saying you know if the voltage drops in this case that is set at 1.5 volts let’s say I just give some value here let me say this is 0.3 volts. So, I will set some cutoff voltage say you know if you reached 0.3 volts stop the curve and we reverse the direction of the current this gradually start decreasing the current. So, invariably you will see a curve of the nature that you see on your screen here; it starts at a high value out here of a voltage and then it starts sliding down. And then you see this curve that that is generated here it just goes down and then it precipitously begins to dropdown. So, this is a polarization curve ok; so, that’s a polarization curve. So, now we want to understand what does this convey to us about the cell ok. So, it is a very useful technique because it conveys several interesting things about the cell to us; the first thing is different regions of this curve correspond to different aspects associated with the cell. So, what you see in the initial part of this curve here relates to the; manner in which the reaction is occurring at the reaction site ok. So, you have some reaction occurring at various reaction sites maybe there are catalyst sites that are present, maybe that there are anode materials that are present, cathode materials are present there is the reaction that is occurring at the reaction site right. So, at the reaction site whatever reaction is occurring; whatever difficulty it is facing in completing the reaction that is what is conveyed in this initial part of the curve. Then in all electrochemical devices as we have seen before you have an anode, a cathode and an electrolyte anode-cathode and electrolyte so, in all electrochemical devices you have some ion; some ion that goes. So, some you know let’s say a positive ion is being transferred through the electrolyte. So, some ion is being transferred it doesn’t have to be positive ion; I am just you know putting a positively charged ion get being transferred. So, let’s say it is a proton; so, H plus I have just to just for something that you can keep in mind some ion is being transferred. So, there is a conductivity associated with that transfer process usually that is the lowest of the conductivities that are there in that circuit ok. So, that conductivity impacts the slope associated with this region of the curve. And that is why this region of the curve is referred to as an ohmic loss okay this early part of the region is referred to as an activation loss; refers to the ease or difficulty with which a reaction can occur at the reaction site; this ohmic loss represents the ease or difficulty with which the ion can be transferred through the circuit. And finally, we have concentration losses or mass transport losses this represents the difficulty with which the reaction sorry the reactant is being brought to the reaction site ok. The difficulty or ease or difficulty with which the reactant is being brought to the reaction site which means what; So, for example, if you were in a few if you are considering a fuel cell the gases that you supply hydrogen and oxygen that you supply have to find their way to the reaction site right. So, they have to go through some force to arrive at the reaction site. Now, you can have a situation where you know where there is let’s say water being generated and blocking the excess of the gas to the electrode; then this mass transport becomes bad. So, in other words, it is unable to get enough hydrogen and oxygen to the reaction site and therefore, this drop off that you see will occur under much poorer conditions ok. And what are poorer conditions? Those are all that are listed here in your you know x-axis and y-axis. If everything were ideal; you will be able to draw a current at this open circuit voltage itself; if everything were you know the beautifully ideal world that you have then you will get a considerable current at open-circuit voltage. You keep on drawing higher and higher current voltage of the cell will not draw; it will stay some standard fixed value. Real-world nothing happens that way; as you draw current you are trying to make that reaction happen faster and faster and faster. When it tries to happen faster and faster it happens inefficiently these three parameters that I showed you the activation loss, the ohmic loss and the mass transport loss or concentration loss are inefficiencies that are present in the system because the reaction is struggling some energy is wasted there. So, that is your activation loss because the transport of ion is struggling. After all, you are trying to drive it faster and faster and faster; some energy is lost in the process in trying to drive the ion to get across the membrane. So, that is a loss that is an ohmic loss some energy is lost in trying to push this ion along and it is it happens to be struggling. For some reason; the gas is struggling to reach the reaction site again your you know you know driving it too hard for the process and therefore, some energy is lost in the process. So, therefore, that is the reason these are referred to as losses in electrochemical terms they are referred to as polarization. So, polarization is a loss; so, this wherever I talk of a loss and I use this term polarization they mean the same. So, is based on the book you look at; we will talk of activation polarization, ohmic polarization and concentration polarization here I am referring to it as a loss they are the same idea is being used. So, ideally, you should not have any loss; you should just have this nice flat you know profile for voltage and you should be able to get you to know indefinitely get current at high voltage that is not what is happening, you are losing all this voltage. So, whereas, your battery was you know capable of giving you 1.5 volts, you put you know voltmeter across it and it showed 1.5 volts. When you start drawing current, you find that it is giving a much lower voltage which corresponds to this value here line here; if I just draw this line here. So, here, for example, let’s say in this scale that I have drawn here this may be about 1 volt. So, as opposed to being 1.5 volts that the battery was capable of giving when you draw current from it and at some appreciable level; it is only giving you 1 volt right. So, this is the loss and this is the energy that has been lost from the system. So, you are only getting about two-thirds energy that it is capable of giving you it does not give giving you the full energy. So, this is a specific degradation of the system as a function of just the operating condition; it is got nothing to do with them; so, if you relaxed the operating condition you can operate the device with fewer losses. But this is a very very nice way of characterizing your cell because first of all, it takes only a very small amount of time to do this characterization. And at the same time, it is giving you information about three different processes that are happening in your system, you have an activation process, you have an ohmic process and a concentration process. So, all three processes it is trying to give you good information. So, for example, if you compare two different cells or the same cell under two different conditions after two different operating conditions.
 
 
 
 
 
 
 
 
 
 
(Refer Slide Time: 39:51) You may have something like this; we will look at this briefly let’s say there are two different cells cell A and cell B; you can see here that these two have two different polarization curves ok. Let’s just assume that these are two brand new cells ok. So, if you go to the shop; if you go to a store and you go and try to purchase a double-A battery you can see that you know it will say 1.2 volts or something like that, but let’s say it say says 1.5 volts. So, you take a brand new battery from our brand new cell from one manufacturer, you put a voltmeter across it shows you 1.5 volts. You take a brand new cell from another manufacturer and you put a voltmeter across it; it also shows you 1.5 volts. So, both of them coincide at this point. Now, you take these two cells and you put them to a test ok. So, every manufacturer says you know my cell is better than the other person cell right; they all say that everybody advertises they say my cell is so, much better than the other person cell, you should buy it kind of thing. How do you know that it is better or not? This is the kind of test you do you take that cell and you put it through a polarization curve ok. So, you can see here, for example, cell A as I said in the ideal condition you should see no drop in voltage that is an idea. That is never going to happen; so, this is just for you know the frame of reference. So, what is going to happen is there is going to be some loss of performance as you draw current from it, but you want to minimize that loss that’s all it is. So, in other words, this gap between this ideal performance and this actual performance; you want to minimize that gap because that gap represents a loss. So, you want to minimize it; so, you want a polarization curve that looks closer and closer to the ideal curve right. So, in other words, this cell this second cell that you see a cell B has a much more significant loss compared to cell A right. So, if you were trying to draw some significant amount of current from cell B you will find that when we once you reach this point for example; it is unable to deliver any higher current than that. If we try drawing any further current from it the voltage completely drops precipitously drops; the voltage precipitously drops. And once and voltage represents the driving force if you don’t have voltage; nothing is going to go through your circuit and then basically it comes to once you have 0 voltage it means there is no further driving force for any current to go through your circuit, nothing is going to happen; it’s all going to come to a halt. So, clearly for any current density higher than this operating point that I am marking here; you cannot use cell B you can only use cell A right. This is even though at the starting point; they both look the same right. So, when you purchase this from a store it looks like you have got two cells of the identical you know capabilities, but when you put them to use; they are dramatically different they are not in a position to perform anywhere close to each other. So, this is I will come back to this in just a moment. So, as I said you know the voltage times current is the power. (Refer Slide Time: 42:53) And so, that is shown to you in this curve here, where we are taking the polarization curve and also adding the power curve corresponding to it. It means so, for example, if you see here you have high voltage 1.5 volts right that’s the open-circuit voltage at that instant in time you are drawing 0 current. So, the power you are drawing from the cell is 0; 0 watts you are drawing ok. So, 0 0 watts I have put current here you can put current density also here; so, its 0 watts. So, as you start drawing more and more current, as you go up I mean along this axis; correspondingly the voltage is coming down. So, if you take the product, but the voltage is coming down gradually; the current is going up fairly significantly it’s it is only a gradual drop here, but the current has gone up this much. So, you have a fair bit of power; so, power is going up. So, power keeps increasing along this line power is continuously going up. So, this continues this process continues; so, you see this continuous increase in power, then you reach a point where you have now reached a value of current where if you cross this value of current the voltage is beginning to drop precipitously. Because the voltage drops precipitously the overall power is also dropping precipitously. So, the power begins to drop precipitously right. So, therefore, this represents the maximum power that this you know electrical chemical device can deliver; this represents the maximum power that this electrochemical device can be delivered. So, if you are doing a project and you know what you are doing; you are doing a project you have some number of devices that need to be powered by a power source. You need to figure out how much power those devices require right; you need to understand what is that power that is required by those devices that are now in your circuit and that total power that it that is required when you buy a power source for that device for that circuit that you have created that power source should have a maximum power that is distinctly higher than that maximum power that you are going to draw. If on the other hand, the maximum power that the power source can give is less than the maximum power that your device can be required; your device will not function it will or it will at least not function as well as you want it to function, it will just struggle it will struggle may be parts of it will work parts of it will not work or it will completely not work it will basically either work sluggishly or completely not work. So, you may think that you know because of the components that you have got; it will function very well, but because the power source that you have selected is such that you know its power maximum power is less it is not in a position to support this end-use that you are putting into. So in fact, if we go back here you can see again in these two cells that you have here the two the maximum power point that you can get from these two cells will also be very different. So, if I plot a power on this and had a power axis also on the y axis; then let’s say I put power here in watts, then you will see that the corresponding to that you will have for one; one cell you will have a curve that looks like this. And for the other, you will have a curve that looks like that something like that; so, this is a schematic. So, you can see that you know this is a much higher maximum power that it is delivering to you; this is a much lower maximum power that it is delivering to you. So, clearly for whatever end-use you are putting to you know; cell A is a much better position to deal with that end-use than cell Bright. So, the this is how these two cells compare; so if you look at our polarization curve and you see a few different ways in which the system might have deteriorated with time. So, we will see them show up in certain interesting ways concerning the polarization curve. So, first, let me just draw here the polarization curve schematic of a polarization curve that looks okay. (Refer Slide Time: 46:51) So, we have V, and we have met, and you see a curve that looks like this right. So, now if for example, after some hours of operation; the let’s say the catalyst or the reaction site has alone become bad and everything else is fine with that cell, then you will see a polarization curve that will change to something like this. So, I will still draw the original one here and then we will look at how that is changed. So, we will assume that this is the original one that has done something like this; you will now see the new polarization curve that looks like this.