 OK, so we're going to get serious today. When I started the course, I told you that one of the concerns you have as an electrochemist is that unlike other sorts of analytical chemistry, such as spectroscopy, when you take your electrochemical cell and you attach it to your pretentious stat, you've modified the circuitry of the pretentious stat. And so you have to be certain about what you're doing or you can get some pretty exciting but unrealistic results, which is not all that uncommon, actually, unfortunately. So what we need to do is build the pretentious stat. So we understand what makes it tick. We're going to start this off by building what my students last term called a MacGyver pretentious stat. I'll remember this TV program MacGyver and this guy could get himself out of any problem with a few household items by building some sophisticated thing. So if you're locked in a closet and your life depends on being able to do an electrochemical experiment under potential control and all you have available is some wire and maybe a power supply and a couple of platinum electrodes, of course, then how are you going to go about doing it? So what you might do, let's see, is oh, you need a beaker also and some electrolyte. We'll give you that also. So you have some salt water here in beaker and you have a sheet of platinum. And so what you might do is you might cut two electrodes out of the platinum. Maybe one looks like that. And you're not too careful about this because you're locked in a closet. And so the other one looks like this maybe. And then you would go and you would take your power supply and we'll give you a variable power supply. So you have a little knob on it. You can change the voltage. And you'll drop a voltage across your two electrodes in the hope that some chemistry happens, some electrochemistry happens. Now, if you are so fortunate that you have picked a molecule that, let's say we're going to be reducing this molecule, that can be reduced and it can only go to one thing, then this will work just fine. That is, you can make this voltage as arbitrary large as you want and eventually it'll go. So in other words, what I'm telling you is if you're doing the kind of classic thermal experiment where you're going to carry out a chemical reaction by heating, if you picked a reactant that could only go to one product and as a result, you took that reactant in a flask and you just heated it up to 1,000 degrees. And since it could only go to one product, it does that, then no problem. And this experiment will work under the same conditions. However, can anybody think of a reaction that only goes to one product at 1,000 degrees? Maybe only go to one product at 1,000 degrees, but not the one you want. Typically, you've got lots of possibilities and the way we want to access those possibilities is by not controlling the voltage but controlling the potential of this electrode. We'll make this our working electrode. So if we could control that well, then if there's 29 different reactions that might happen, presumably we could pick out the one that we were interested in by knowing exactly what potential would give us a rate constant for the reaction of interest that would be suitable. And not rate constants for other reactions that would be suitable. Well, one way we might do that is we know what V is because we put it there. And so we might do with order, say, OK, let's assume that the voltage is evenly distributed across these two electrodes. So we have a phi 1 for our working electrode and a phi 2 for our counter electrode. There's a counter over here. And so V is just the difference in the potential of those two. And if it was evenly distributed in phi 1 and phi 2 would be equal. And so if I put 10 volts across there, then it's 5 volts over here and 5 volts over there. And I know that this is at 5 volts, my working electrode. And so I have some control now. Now, of course, for the situation I've drawn there, that is never going to happen because in order for the potential to distribute evenly around these two electrodes, the two electrodes have to be identical. And the two interfaces have to be identical. And you can see I have a huge electrode over here and a small one over there. So I go back and I whip out my platinum again. And I cut some new electrodes. And I do the same thing. But now I have two identical electrodes. They're identical, believe it or not. And now when I drop a voltage across them, in fact, it does distribute evenly of whatever voltage I drop there. Half of it goes there. And half of it goes over there for a very, very short period of time. Why is that? Well, initially, before I started this experiment, since both platinum electrodes are now identical, of course, since the solution has to be homogeneous, it is a solution, then everything is identical at these two interfaces before I start the experiment. But as soon as I start the experiment and a current flows in this circuit, of course, the ratio of reduced to oxidized changes at these two electrodes. So the quantity at this interface and the quantity at this interface are different. And of course, the Nernst equation tells us that if we have different oxidized to reduce, we had different potentials. So these two potentials at these two interfaces are different. So this experiment only works before you start it. And as soon as you pass any reasonable amount of charge, you no longer have that situation. Now, having said that, there are plenty of reactions, especially if you go back in the 1960s and look in the literature, where people did electrochemistry. And all they did was literally they took two electrodes and a battery, usually a lead acid battery, a car battery, put it together like I'm suggesting here. And they made something. And they made what they wanted, presumably. They didn't make 20 different products. They made one thing. And again, it's simply because there were no other reaction pathways available. And how the potential was falling across this circuit didn't matter as long as you had enough potential at the electrode so that you could change this ratio. Now, actually, when you typically do that, if you want to synthesize something, let me point out that you need to put a barrier in there. Or else, whatever you oxidize at one electrode is going to be reduced at the other electrode, so you're not going to get very far. So we need to have a separator. And of course, that separator has to let charged through, that is ions through, but not a lot of the oxidized and reduced species. So this is a gotionic transport, but not transport of the species of interest. So it's a semi-permeable membrane that we need to put in there. That'll work in some cases. In fact, sometimes it works better than doing it the right way, unfortunately. When I, the first year I was at Princeton, there was a particular molecule that I wanted to synthesize. And there was a prep for it. It was an organic molecule, believe it or not. I want to put it on an electrode surface. There was a prep for it in the literature. And it was a 1960s jacks communication. And this is how they did it. And they got something like 50% yield of this organic thing. And there I am, and I know everything there is to know about electrochemistry, of course. And so these guys, back in 1960 with their lead acid battery, there's a power supply actually, got 50%. I had my fancy brand new Potentia stat and my air-free cells. And really know what I'm doing. So I'm going to do this the right way and get 100% yield of this wonderful product. So we do it no air. We nice clean electrolyte, clean up our supporting electrolyte really well, hook it up to our fancy new Potentia stat, run the thing, zero product. And keep running. Don't understand. Try all the different things you might try, zero product. And finally, one night, the guy that was working on the project waits till I go home. This is always very important to do. And pops off the top of the cell so it's no longer under inert atmosphere. And ties together the electrodes so there's no reference electrodes so we just have a voltage across here now like I'm drawing here. And the next morning we have 50% product. So you have to take what I have to say here with a grain of salt, I guess. OK, so the good news about this is this first, for synthesis, this could work. This could be the way to do it. The bad news is, if you really want to know what's going on, if that's your goal, you're not going to know because these potentials here are going to be drifting in the Nernst equation guarantees that. So you don't know what potentials you're at. So you can now go and make your, let's see, your second generation electrochemical cell slash controlled potential experiment. What you might do is you might stay with your working electrode, your nice catalytic platinum working electrode. But instead of just throwing in another electrode, let's take a reference half cell. That is some electrode where we have the whole half reaction there. Maybe we have an iron electrode and iron 2 plus ions in solution. Some nice half cell like that as a reference. And we'll have to have that in a separate container here. And we will then put a little frit in here so that we can get ions to transfer between our reference half cell and our solution. And again, we'll apply our variable voltage power supply and drop a voltage across there. And now what we're going to do is we can now measure a lot of voltmeter in. We can measure now the voltage of this electrode versus whatever half cell I put there. So if I know the potential of this on some scale, and I can know that because I can look it up in terms of standard redox potentials, then I can say, OK, the potential of this electrode, my working electrode, is just x volts versus my standard reference cell. Now, the first thing you're going to find out is that although you go and set some voltage here and everything looks fine, then after a few minutes, the voltage that you read up here is different than the original voltage that you've set. And why is that? Well, again, the interface here is being undergoing a redox reaction. And so Nernst equation tells us that potential is changing. And so the voltage drop across these two things is changing. So now let's see, do I have any freshmen sitting here? Good. So what you do is you go and you find a friendly freshman. And you find a nice, comfortable stool. And you tell the freshman to sit down on the stool. And just while you're doing this experiment, which is only going to take 10 hours, stare at the voltmeter. And anytime the voltmeter deviates from the number that you want it set at, just turn the variable power supply to bring it back to whatever it is. And if you do that, now you now have a potential stat. That is, you have a built-in feedback loop, the freshman feedback loop. And that guarantees that that potential stays. So as the chemical environment around this working electrode changes, we adjust the overall voltage in the cell so that we maintain a constant voltage versus our reference electrode. Now after some time, you are going to run into a second problem that not even your freshman can solve. And that is, obviously, if I'm, say, reducing something at this electrode, then I am oxidizing something over here to compensate for that. So even though I start off with this cell with a given amount of oxidant and a given amount of reductant, over time that ratio changes. And so the potential I think this cell is at is varied. But if I use high concentrations over here, then I'd be, have some period of time anyway before I change that ratio significantly in the Nernst equation, not many trouble over here. A second problem you might have is this little frit down here. If there was a high resistance in that frit that connects you to the solution, then you do have a voltage, a temporal voltage across the solution, which is the current times the resistance. And that could be a big number if you had a big resistance and a decent current. And so this voltage would not actually then represent the potential of the working electrode. That is, in general, the potential of the working electrode, E, apparent potential, is equal to the actual potential of the interface, phi working electrode, plus the IR drop, which occurs between that working electrode and whatever your reference half cell is. And in this particular cell, since I want to pass some current so I can carry out a reaction, i is going to be pretty large, and therefore i times r is going to be pretty large. So this cell works for a short period of time. This cell over here worked for zero period of time, just right before the experiment was a good cell. This one is now working for a shorter period of time, but it's starting to work. And so we want to make our next modification now. We keep the freshman. That's very important. He's our feedback loop. So we have our cell. We have our working electrode. We have our reference electrode, which I'm just going to show as a line now, because things are going to get crowded. And I'm going to switch over to that reference electrode, even though that reference electrode is this reference half cell that I'm talking about over here. It's not an electrode, but some sloppiness has crept into the vocabulary. I have my variable power supply. I have my voltmeter. Let's get a little fancier here now and insert an amp meter so we can monitor the current also. So right in the circuit here, we'll put an amp meter in. Amp meters go in series. The current goes through them. They're a low impedance device, low resistance. Volt meters are in parallel. They're a high impedance device. I'm not carrying any current through there. OK. We have our stool and our helpful freshman smiling. The job it is to turn this knob to maintain that voltage constant, right? And now here's the change we're going to make. We're going to add a third electrode, which is the auxiliary or counter electrode. And what we're actually interested in is not the current between the reference electrode and the working electrode, but the current between these two electrodes. The reference, excuse me, the counter and the working electrode. That is, we want to pass our major current through those two electrodes, not through this circuit. So I want to get rid of this part of the circuit and just use that part of the circuit for voltage sensing. So let me redraw this a little bit. We'll leave the undergraduate out now. He's still there, but so we're going to have a voltmeter between our working and reference. We're going to have our power supply, variable power supply now, between our working and counter electrode. And we're going to monitor the current flow there. So I'm passing all my charge through this loop of the circuit, but I still can monitor the potential of my working electrode versus the reference electrode. So now in the words, I'm still saying, OK, sit there, watch this voltmeter, and any time this voltmeter deviates from whatever number I want on it, change this power supply so that it comes back to what I want. Now the first thing you'll notice is there is now no longer a direct relationship between what's coming out of that power supply in terms of the voltage and what you read up here. So this is a safety consideration. You're sitting there now with a real life potential stat that does not have an undergraduate mounted on the inside. And somehow it's doing exactly the same thing, developing a feedback loop where it monitors the voltage between the working and reference electrodes and then changes the output of its power supply between the working and the counter electrode. So you're sitting there saying, oh, look, it's at 2 volts versus my reference electrode. I can't be hurt because it's 2 volts. And what could 2 volts do to me? And what you're not realizing that is that if there's enough resistance in this circuit and if the kinetics are sluggish enough and things like that, that power supply might be putting out 100 volts between the working and counter electrode when you read 2 volts on this meter. So you can have a very hefty voltage going between your working and your counter electrode. And it's not a good idea, for example, to take the working and counter electrode and put them up to your tongue, even though the reference electrode is only reading 0.1 or 0.2 volts. There's a lot of potential across there, depending on the size of the power supply you're using in your potential stat. I tell you that because I have, from time to time, decided to take the full output of the power supply across me when I've done electrochemistry. And it's less than ideal. So that's something to think about. OK. Now, the interesting thing about this design that I've just shown you is that since this is the operational equation, if we can go and have a very high impedance here between our reference electrode and our working electrode and everything else. And if we have very high resistance, that means that the current will be very, very low. So we'll be typically talking about a current that's somewhere between, say, a nano amp and a pico amp. That's going to get through this resistance. This resistance could just be a fine frit. OK. Now, since that resistance is high, r will be a large number. But it guarantees I will be a small number. And as a result, i times r is a small number. And so now, when my undergraduate reads e here versus my reference, even though e is equal to the actual potential of interest at the interface of the working electrode plus IR, we can ignore that last term. So we have a potential compensated circuit now. Now, we have a potential stat. As long as we can keep our undergraduate there, right? This r is the solution resistance here. Plus the frit. Yeah, I said solution, I should be more careful. It's the whole cell resistance. So the frit would be in series with the solution. Right, so i times r is a small number. Well, by a high resistance, I might put a mega ohm. That'd be a high resistance. A mega ohm of resistance, say, between these two electrodes. I probably don't even have that much to have it high. Mega ohm is definitely high. But still, if I'm only passing a pico amp, i times r is still a small number. If you look at the specs on most commercial potential stats, they will tell you that they'll hold the voltage plus or minus 10 millivolts. Most people don't bother to read that and often report their potentials to greater significant figures in that. But typically, and of course, you could buy a better potential stat, and it would be better. But 10 millivolts is sort of a typical number. So if I can keep i times r below 10 millivolts, I'm in great shape. And you can see what the numbers I just gave you, keeping it below a millivolts isn't going to be around a millivolts isn't going to be very hard. That is below the accuracy of the potential stats, so I'm fine. So yeah, we could certainly, when I say zero here, we could handle a millivolts, no problem. And of course, one could actually build a reference electrode with a low resistance here and just be subject to the resistance of the cell. But from day to day, you make different cells with different resistances, and you can therefore not be guaranteed that the current flow through that part of the circuit will be small. And so you actually want to put a high resistance there, which is going to be in series with your solution resistance since series resistances add so that you are certain that your current is small. Now having said that, if you work at it really, really hard, you can mess yourself up and get such a high resistance between your working electrode and your reference electrode that even the trivial current is a problem. So if you really want to mess this thing up, then do things like put a five foot long salt bridge between your working electrode and some other container with your reference electrode in it. And make sure, of course, that reference electrode is absolutely as far away from the working electrode as possible, and the salt concentration is as low as possible. And if you worked at it, you could get it up there. Now is an important point. What if you're using, you go on to an experiment and you want to use a classic H cell, which would be a two-compartment cell, have two compartments with a frit there in the center, everybody immediately realizes that I'm going to have the working electrode in one of these compartments and the counter electrode in the other, so I don't reduce what I just oxidized. But the question is, where do I put the reference electrode in this case? And there is a right answer. It's got to be in this compartment right here. Because if you put it over there, now you have the frit that's built into the reference electrode plus the frit in your cell plus the solution resistance. And that's a good way to get to very, very high resistance. And you can have this take on a significant value at that point. So it's easy to be off by a couple hundred millivolts if you're not careful about this. And likewise, if you're just working in a single compartment in a beaker, put the working electrode in the reference electrode as close together as is reasonable. Don't try and get them far apart from each other. Try and minimize this, and that way you won't have too much concern about it. So now we have our cell built. Now the only problem is this freshman we have sitting there maintaining our potential is a little bit problematic. He likes to eat, time off to listen to his iPod or whatever. And it just won't work through the night. This isn't a freshman story. This is a graduate student's story. One of the problems we have when we're doing our fuel cell work is that we have something called a fuel cell test station that tests our fuel cells. And what it does is it measures the current and the potential. But it also humidifies the gases and controls the flow and the pressure of the gases going into our fuel cell. And fuel cell test stations have heated bottles of water in them that you have to fill up from time to time. The gases bubble through that. And that's how you set the humidity level for your cell. And it's set up so that if you're running your normal PEM fuel cell, it'll go for a week without having to put any more water in there. But of course, we like to run our cells hot, as you know. And water evaporates really quite well above 100 degrees. And so we discovered that we can only keep water in our test station for about six hours, even though it's designed for about a week. And so people keep on asking me when I give fuel cell talks, how long have you tested this fuel cell for? Is this just a transient effect? Are you telling us something interesting? And the answer is 60 hours, which is considered an OK amount of time, but not an exceptionally long period of time, because people would like fuel cells to last for 5,000 hours. And the reason is it turns out that the graduate student working on the project, every six hours, had to refill the test station with water. And after three nights of no sleep, he gave up on it. So see, there's a problem doing it this way. So we need some kind of electronic device that is going to take care of this for us. So how are we going to actually go about do this when we buy our commercial potentiostat? And actually, even though I'm joking about this, when I arrived at Princeton, I was kind of scavenging around in the basement where I found some really old, old, old equipment. And I found a, I guess, an early prototype. It was sold by Fisher of a potentiostat. Yeah, big, big, heavy steel box, huge thing. I opened up it. See, how in the world, there was a date on it. It was 1950. How in the world in 1950 could they build a potentiostat? As you'll see in a second, they're built with integrated circuits. They didn't have those in 1950. And this is how they did it. They didn't have a student in there. What they had was they had a little mercury battery, which holds a very constant potential for a long time. Turns out not from 1950, 1980, but a long time. And they balanced off the potential coming out of their reference electrode against this battery. And there was literally, there was a voltmeter. And as this voltmeter turned, it had a, instead of having a needle on it, it had a pulley. And this pulley had a rubber band wrapped around it that went to a knob on a power supply. And so if the voltage got away from what the battery was saying, then that would cause this null reading to turn. And then turn the pulley, and it would turn the power supply. It's hard to believe it worked. It probably didn't. That's why it was in the subbasement. But you could do it that way, sort of. But the way we're going to do it, the thing that made electrochemistry possible for the world, people that weren't dedicated, crazed electrochemists, was the advent of the integrated circuit in a specific one called an operational amplifier, an op amp. Close. Now op amps are symbolized by these triangles. This is not the picture I wanted. And we have three wires coming out of an op amp. Two inputs, a plus and a minus input and an output. And these are good for all kinds of exciting things. There's a couple things you want to know about them. Just some rules. We don't have to worry about why they work. But what the op amp wants to do is the op amp wants to have the voltage at the plus input equal to the voltage at the minus input. It'll do whatever it has to do that. That's rule number one. Rule number two, it doesn't like current. It's high impedance. And rule number three is the way you can assure these things is by changing the output voltage. So you can take this device, and as its name suggests, you could build an amplifier out of it. You could use it for doing integrations of currents. You can use it for current and voltage converters, all this wonderful stuff. What it depends on is the sorts of resistors and capacitors and whatnot that you're going to attach to the rest of the circuit. So we'll just look at one configuration, a non-inverting amplifier that is what's used in terms of controlling your potential stat. So the idea is going to be then that we are going to set a line at ground down here, and we'll apply a voltage over here, v in, against ground, and that will generate a voltage over here, v out. And then we can add in a resistor here, resistance, that we can hook in over here, and a second resistor over here, which would be an input resistance, and we can ground that whole thing so we have a complete circuit. So the thing that we're going to control is that v in, and we let the op amp in control v out. And whatever voltage we apply over here has got to show up over here because of this first rule. So we're going to generate a voltage over here by applying a voltage over here. And that will generate a current because we're taking that voltage through some resistors, and so we have a current that we could associate with that. And we're just going to follow Ohm's law and Kirchhoff's rules and all that wonderful stuff. And I don't think we're going to get too concerned in that because that goes back to freshman physics. And you probably remember that somewhere way back when. So I will simply tell you if you do this, you will find out that the ratio of v out to v in is equal to a constant. That constant happens to be 1 plus RF. So those of you interested in building an amplifier, you could see how this works. If you pick your resistors the right way, then you'll notice that you can get that ratio so that one of those numbers is bigger than the other. So you can amplify a voltage by doing this. Well, you'll notice by flipping this, changing these so you can never get below 1. So your gain is always 1 out of this particular system. It can go above that. But the key point here I want to make is if you change v in, you have to change v out. Because this is all fixed for the circuit. And likewise, if you change v out, you have to change v in. So if we made v out, the potential between our working electrode, excuse me, if we made v in, the potential between our working electrode and our reference electrode, then if that were to change, the potential versus reference electrode, this op amp would change v out so that that ratio was re-established. So we would re-establish the potential. So we could have v out go between our working electrode and our counter electrode and have this work out. So let me now throw in an electrochemical cell into this picture. So we take our op amp, going to drop an extra little resistor in here, which is a precision resistor R, and then take a precision voltmeter and drop across that R. And now if there's a current that flows here, a current is allowed to flow here. I remember our rule is there's no currents over here. So if we have a current flowing out of our op amp, we can measure it. And so I'll connect that to my counter electrode. Here's my electrochemical cell right here. I'll have a working electrode over here. This is somewhat counterintuitive, but not all potential stats, but most potential stats ground the working electrode. You would think, I'm trying to adjust the potential there, so why would I ground it? But we're talking about different zeros. So typically, certainly in your PAR type of potential stat, you ground the working electrode. And the way we're then going to adjust this whole thing is by applying a variable v in here. Let me just write that. If that's variable, we can adjust that. And then on our second input lead, we'll just take it around to the reference electrode. So we have a v in over there, and we have a v out over here. And we see from this analysis that we can't change one without changing the other. So v in, remember, whatever we put over here, that voltage has to show up over here. So if we get a difference in voltage between our working and reference electrode, it has to be adjusted back here. So that's why it's variable. And that will lead to a different voltage between our working and our counter electrode. So this is set up with negative feedback. That is, if one gets bigger, the other one's going to get bigger until it zeros out again. And we can measure the current flow associated with this. So now we don't need our undergraduate anymore, our freshman. We're in great shape. This little guy will do it. This is a negative feedback loop. It does exactly what our freshman was going to do for us. Now, as I pointed out, you could think of the region between the reference electrode and the working electrode as a resistance. And you could think of a second resistance between the working electrode and the counter electrode. Now, this resistance we're stuck with, that is, our current's going to go through that. So r prime times i does have some value. But that's OK, because we do not measure our voltage there. We're measuring it over here. However, our voltage measurement in this circuit is only as good as our compliance with this equation. So if rs, not rs prime, but if rs becomes large, that can be an issue. We essentially have a total cell resistance, which can be thought of as the sum of these two resistances, rs plus rs prime. We're knocking out rs prime, essentially, by using a high impedance, low current pathway there. And we put up with whatever's left over. But remember, it's always there. Now, modern potential stats often have a resistance compensating circuit in them. And this is sort of good news and bad news. I don't know if you guys have tried to use this. But there's an interesting thing about these operational amplifiers. Now, what I've drawn here in the equations that one uses over here, just the simple equations, is for a so-called ideal amplifier. What it doesn't tell you is what a real amplifier does. A real amplifier has a very interesting situation in that as your potential approaches the exact potential that you want it to be, the amplifier goes into uncontrolled oscillations. We kind of count on the resistances that we've put into the circuit. And we know we're there from the electrochemical cell to avoid this situation. But the way you have the same problem, say, in the thermostat and the heater in your home. Any thermostat and negative feedback loop will do this. If you pop open your thermostat, you'll find there's always a resistor in there. Because if the house temperature, if it wasn't there, the house temperature would get up to exactly what you said it. And that would tell, of course, the thermostat would tell the furnace to turn off. But then that would cause the temperature to drop a tenth of a degree or something like that. And so that would tell the furnace to turn on. And then it would get up to temperature almost instantaneously because it's only a tenth away. And so it would turn off. And you start getting oscillation. And it turns out that is an ever-growing oscillation. It just does the opposite of damping out. It goes into uncontrolled oscillations, the parasitic oscillation. So you have exactly the same problem here. And you are depending on the fact that there is a little IR drop to make sure that the actual potential that you want and the actual potential that this guy is seeing are slightly different so that you don't go into this oscillation. The way these resistance-compensating currents work is they apply a current or potential. You want to think of it that's opposite to this IR current. Goes in the opposite direction. You put the current in the other direction. And it's set up so it will measure it so an example exactly equals the opposite of this number. Now, if you do that, you've removed all the resistance from your circuit. And you end up in oscillations. This works really well when all people used for electrochemistry were mercury electrodes. Because when the potential goes uncontrolled, you blow up your drop of mercury. You burn it. You back off a little bit on your IR compensation so that you have a tiny little value here. And the next drop of mercury comes down, and everything is fine. But if you're using a solid electrode, if you're using a platinum electrode, like I was suggesting, or a semiconductor, they burn really well, it turns out. And you use IR compensation, and you get it right on the money. You throw away your electrode after that. So IR compensation is an interesting issue. Now, more recently, circuits use a current interrupt technique to get at this. That is, they actually go to open circuit at the point that they want to make a measurement. And they look at the decay of the circuit potential or current and get the RC time constant out. And based on that, calculate resistance and then can put a value in here that makes sense when you're doing your compensation. So if you have a computer-controlled interface that can do all that calculation very quickly, that helps, and you don't run into this problem. But if you're using a analog potentiostat with IR compensation, don't use it. Don't use the IR compensation. The analog potentiostat is wonderful. Another point to make is, if you go and take the circuit I've drawn here and decide you're going to run back to your lab now and whip out your box of resistors and 741 op amps or whatnot, and solder it together to make your own home-built potentiostat, it won't work. Why not? Real-life potentiostats usually have at least two often three stages of operational amplifiers so that they can get into this region of fine potential control. And if you use a single op amp like I've drawn here, then you will not be able to hold your potential. So conceptually, this is the right circuit. But in fact, you've got to do a fair amount of engineering to make this circuit work. And there's usually a series of stages of amplification that allow you to hold the potential. OK, so that's the potentiostat. What about the reference electrode? We understand the working electrode. The counter electrode we don't have to be too concerned about now. It's just off doing its own thing. But what about that reference electrode? What are we going to use over there? Over there. So of course, anybody who's opened up a freshman chemistry textbook knows that what you're supposed to use, obviously, because the tables are all like this, is the standard hydrogen electrode. Must be, right? We are told in our tables that all our potentials are measured against one molar of protons and one atmosphere of hydrogen. And we need a catalytic electrode because it's hard to get current to flow there. So we would use, say, platinum, which is a great electrocatalyst, as we've already discussed, for hydrogen. So that would be our standard hydrogen electrode, SHE. Sometimes, instead of the SHE, you'll see it referred to as the NHE, which stands for normal hydrogen electrode. Do the same thing as long as the acid you're using is a one proton acid, basically. And sometimes, you find it referred to as the RHE, the rational hydrogen electrode. In all cases, they're the same thing. Now, having told you this, although there are measurements in the literature that use the hydrogen electrode, if you will use it because the hydrogen's there, nine times out of 10, nobody uses a hydrogen electrode when they're doing electrochemistry, even though, of course, we've decided that's what everything should be referenced against. So why is this? Well, you have, first, the obvious issue of safety. That is, how are you going to get one molar, one atmosphere of hydrogen gas? Well, you're just going to bubble hydrogen gas out into the air, right, over your platinum electrode and out into the air. And then your lab mate's going to come along smoking his or her cigar, and experiments over, right? So that's not so good. Although, to be honest, hydrogen isn't all that flammable. And it's not going to be a problem, even if you're smoking. It really isn't a problem. But what is a problem? It isn't a problem. Well, smoking might be a problem, but smoking's bad. But the hydrogen isn't the problem. There's a DOE study. There was a question, if you had a fuel cell car and the tank of hydrogen started leaking and it was in your garage at night and the garage doors closed and all the windows in your garage are closed, will your house blow up? And so they did a simulation. And if you believe the simulation, the answer is no. Because hydrogen has such a high velocity, it fuses so quickly that you never build up to the explosive concentration in a garage just by the cracks that are there under the doors and things like that. It's not too bad, really. After you believe the computer simulation, depends on your faith and that sort of thing. Well, what is bad is that hydrogen gas is going to bubble through this aqueous electrolyte and it's going to cause the water to evaporate rather quickly if you take gas through electrolyte. And so your one molar protons are not going to stay one molar. And that cell drifts just horribly as a result of that. So people don't use it because of that. Now, so what do you use? Well, probably the cell that most people use is the SCE, saturated-calamel electrode. This is a mercury-micurus chloride couple in saturated KCl, aqueous KCl. Now, this cell has all kinds of things going for it. Not only will it not blow up, you have a pure liquid here, mercury, and you have a sparingly soluble salt right here. And so the concentration of the mercury ions, the macurus ions, in the solution and mercury in the mercury is a constant. That ratio in the Nernst equation simply doesn't change until 1,000 years have passed and the macurus chloride finally decides to dissolve. But this has a KSP. That's a really small number. And if some of the water in the cell evaporates, that doesn't change anything either, because this is already at saturation. You put KCl in that saturated to start with. So a little bit of KCl will crystallize out of some of your water evaporates. You can always just throw a little more water. And as long as you keep it saturated, that's always the same. So there's nothing there that can affect the concentration term in the Nernst equation. So this is what people favor, because it gives you a very, very stable potential. The only downside to this is that there is a fair temperature dependence to that couple in the Nernst equation. It's somewhat temperature sensitive. You can get around that problem by switching over to the silver chloride reference electrode. Same idea, silver metal. So we have an activity of 1 for that. Silver chloride, it's very soluble with a KSP about 10 to minus 10. And for reasons I never quite understood, people have settled on four molar KCl instead of saturated for that electrode. But I guess the difference between four molar and saturated KCl isn't big enough that it has a big impact on the Nernst equation. This electrode has all the advantages of that electrode, but a fairly small temperature coefficient. So when you go and buy one of those fancy combination pH electrodes that measures the pH for you and has a built-in reference electrode, typically it's this material. Because there, sometimes you like to measure pH at weird temperatures. And SC would be a little problematic there. Exactly the same idea. Of course, there is another problem here, but it's pretty easy to solve. And that is that the silver chloride is somewhat light sensitive. And so the assumption is you'll always have silver chloride there, and therefore the right number of silver ions, whatever, it's soluble in water. And if you leave this thing lying under the fluorescent lights in your lab, you can convert all the silver chloride over to silver metal and wipe out that part of the redox couple. It won't work anymore. So from that point of view, the SC, if you're not worried about temperature stability, is the way to go. What else do we have? Sometimes potassium is an issue in an electrochemical cell. You don't want any potassium ions around. For example, if some of you like to use perchlorate salts as you're supporting electrolytes, usually you use sodium perchlorate. It works great in aqueous solution. However, it turns out potassium perchlorate is much less soluble than sodium perchlorate. And as a result, if you take your wonderful SCE, brand new SCE, and let it sit in a solution of sodium perchlorate for a few hours, you will start to precipitate potassium perchlorate in the reference junction, in the frit. And you go from high resistance to ridiculously high resistance when you do that and start with a new reference electrode after that. So in that case, what you want to do is you would like to substitute sodium chloride over here. Obviously, that couple doesn't matter whether it's potassium chloride or sodium chloride. But it does turn out there is a slight difference in potential between having sodium chloride there and potassium chloride there. So you will see people talk about either the NASCE, the sodium SCE, or sometimes the SSCE. Same thing. They've just taken the KCL out and put in saturated sodium chloride in place of that. It's a shift of a few tens of millivolts when you do that. Another issue you can run into is you might decide that you do not want to do your electrochemistry in water. In fact, you want no water around, because whatever molecules you're interested in are going to die if they see water. And of course, all of these are aqueous systems. So that isn't an issue. The typical way of getting around that issue is to switch over to a silver nitrate in acetone nitrile, usually with something like tetrabutylammonium perchloride as a supporting reference electrode. So I can have a silver wire here. And of course, that has activity 1. Now I need a solution of a silver nitrate. And so I'm going back to some of the negatives of the SHE. But there's no water around. And people use anywhere from 10 millimolar to 100 millimolar silver nitrate. And of course, what you pick here does change the potential of your reference electrode. So you have to figure that out. And then you have acetone nitrile, and usually between 0.1 and 1 molar tetrabutylammonium perchloride as a supporting electrolyte. So what's the downside of this? Well, at least you're not bubbling a gas through this. So you're not rapidly evaporating your solvent. So this concentration shouldn't change too much. But this is not a sparingly soluble salt, remember. So if there's any way the acetone nitrile can evaporate, you will change your concentration here. That's number one. Number two is it is a light-sensitive electrode. Quite a light-sensitive electrode. And you will change your concentration again by converting silver ions into silver metal over here. So again, if you're going to go and store that electrode on your desktop, you're going to run into trouble because of the lighting around. Electrode like this, if it's well taken care of, will usually last about three weeks. And it's a really good idea to recheck the potential of that electrode every so often and make sure it's what you think it is. Because if it's a good number on day one, and 21 days later, it's going to be a bad number. There's probably different numbers in between. So it has to be checked, say, at least once a week. And it's very simple to check it. Just take a voltmeter, take your SCE, what you have, put the voltmeter between the reference and the silver and the SCE, and make sure you know what your reference is versus SCE. And then you can go off and do whatever experiment you're interested in. Sometimes you need an electrode that either has low resistance. That is, you do not want to have that frit in here. Or you need an electrode where you have to be certain that the material in the half cell is totally compatible with whatever you have in your electrolyte. That is. Another source of potential here, potential drop that I really haven't mentioned, I should add another term on, is junction potential. So if I have one solvent in my electrochemical cell and a second solvent in my reference electrode and I put them together and there's a frit in between them, I develop a potential just because there's a free energy difference, obviously, between two different solutions made of totally different things. And I should have that junction potential or free energy in here as another drop in potential. Now often that number is small. 10, 20 millivolts and electric chemists aren't so concerned about that. And so you get away with it. But every once in a while, it can become a large number because you're using some very strange electrolytes and you have an incompatibility, a big junction potential between what you have in your cell and what you have in your reference compartment. In that case, one would tend to go to a pseudo reference. And the easiest way to do a pseudo reference is just a silver wire. So the idea is going to be you're going to put that silver wire in in place of your reference electrode. And there's going to be some current flow that will cause some ions to be generated, silver ions. And they will stay near the silver wire for some short period of time. But of course, you're making more ions as time goes on. And so you have more or less a constant concentration of silver ions near your electrode as long as you don't need it to stay constant for a long period of time. So let's say you're doing a very high speed experiment. You really want to change your potential very, very quickly. If you do that, the RC time constant of a standard frit will do you in. So you'd like to have a low impedance interface. And so you're just going to have a silver wire, no frit. And since the high speed experiment will last long, and over the time period of that experiment, you can be fairly certain that the concentration of silver ions, whatever it is, will be constant. So you won't know what the potential is. You'll never be able to take that experiment and say, that's at 0.5 volts versus a standard hydrogen electrode. But you will know you're measuring again some arbitrary constant. And so you can compare one experiment to the next experiment because of that. So that will be used for a pseudo reference. A second use, again, would be if you need total compatibility of the electrolyte, because it's sitting in the electrolyte. A really bad time to use a silver pseudo reference is if you have anything around, that could react with silver ions. So for example, you decide to use sodium chloride as you're supporting electrolyte. You really don't want to use a silver pseudo reference because you'll have no constant potential there. Because as soon as you generate silver ions, since silver chloride is sparingly soluble, you make silver chloride. And so you can't hold that population of ions near your electrode surface. You'll end up with silver chloride coating it. At some point, you'll get to this electrode, but it's going to take some time. So you will have no idea. You'll have a constantly shifting reference potential. In the case where you have something reactive, if you're doing a very, very fast experiment, you often can get away with just a platinum wire as your reference electrode. Platinum tends to be electrocatolic for a wide variety of couples. You're hoping there's some little bit of garbage, oxygen, or something in your cell, water, or a little bit of something that platinum would be catalytic for. And it'll just latch onto that potential. And for the short time you need it, it'll hold it. OK, that was my short list of reference electrodes. Does anybody have another reference electrode they want to discuss? Favorite reference electrode of use? Couple seconds. You're good for? Enough time to do a cyclical tamagram at a reasonable rate, for example. But not over, even a minute will be pushing it. That's about, let's call a minute as the outside that you want. It's also going to depend what kind of mass transport you might have going through your cell. Because you're really depending on the area right around this wire, being very stagnant. Yes, exactly, yeah. So you don't have any junction or whatever? Yeah, you just use some supporting electrolyte with a high concentration of salt in it so that you don't have a problem. That's open, yeah. Yeah, you take your favorite supporting electrolyte, put your two references in there, and just put a voltmeter across. A voltmeter is high impedance. It's open circuit for all practical purposes. This one is the easiest one to build. The silver-silver chloride is the easiest reference electrode to build if you want to do a homemade one. And what I would do is I just take a silver wire and put it in your four molar KCL. Or maybe if it's home built, you'll want to use saturated KCL here, break with convention. And then I just pass a little oxidizing current that will oxidize some silver ions, which will cause silver chloride to precipitate on the silver wire. And you're done. That works well. You don't like that one? And you actually passed the current and made some silver chloride? I haven't seen a lot of drift in that one. Pass a little more current. I mean, can you actually see the coating of silver chloride on the wire? It should be good. Of course, this one's easy also. But again, you've got to keep it. If drifting is your issue, I'm not sure this is your solution. This is easy to make, but it does drift someone on you. And again, I would define drifting as changes that are bigger than 10 millivolts, since I don't think your pretentious deck can read better than 10 millivolts. So if you're looking at all look, it's shifted to millivolts today, I don't think it's an issue. But 10s of millivolts is an issue. Over a what period of time? Shouldn't do that. Really, that's how they make them for. Well, when they make this, they actually, if you look at it, they actually take silver chloride and they pack it into like a little glass tube that's open at the bottom and they shove the silver wire into it. But the way I did it, I suggested you do it. And the way, apparently, you do it, should actually be a little bit better in that by electro chemically generating the silver chloride, you get a better silver-silver chloride interface. Any other comments? OK, now, we'll do a whole file there. Let's see. We have a few more minutes, we can get to the next file. So now, we have our potentiologist, that we have our electrodes. Ah, one other comment I do have to make. When you go out and you buy a reference electrode or reference electrode body, you have the option to buy a variety of different junctions there. The most common one is a ceramic frit, which typically has a leak rate of five microliters per day. That's before you start banging it around. When you take it out of the box, very, very low leak rate, high impedance, but enough ions through it. And so, in that condition, you can see, even if you want to work, say, in a non-aqueous electrolyte and are concerned about water, if you can put up with five microliters of water in your cell, then you're still OK. Sometimes you can't even put up with that. But you can do that. If you need to have a lower leak rate, then there are these reference hassles that use a cracked glass bead. When you've taken a tiny little glass bead, heated it up, thrown it in water, you get a thermal crack going through it. And the leak rate on that is ridiculously small. So if you're really concerned about intermixing, that's another way to do it. On the other hand, if you have the possibility of anything precipitating into your frit, that one clogs up really quickly. So that's a trade-off. Sometimes you like a free flow because you're not concerned about that. And so there are junctions that are just a fiber. It used to be asbestos. I'm not sure what they're using now, but just fiberglass probably. Just a fiber that goes through. And now you have much faster transport of salts and liquids between the two compartments. Doesn't bother you. And finally, the other possibility is just pull your reference tip out into a capillary. And you get a fairly slow, it's nothing like a ceramic frit or a crack bead, but you get a fairly slow transfer solution through a good capillary. And it's only moderate impedance. And so if you wanted, for example, to a high-speed experiment, that's another way of getting around that. Just have a capillary at the end of your reference. This brings up one other issue. And that is, I have not been too concerned so far about the shape of a working electrode. I've been drawing squares and told you it should be small. But we haven't talked about the shape. We're going to come back to that and talk about that a bit. But let's think a little bit about the implications of the shape of the working electrode. So let's think about, we'll make this an easy shape. And work out, classically, this is a good shape to use. The dropping mercury electrode not only is it made out of mercury, but has another big advantage. It's spherical. So let's take an electrode where the electroactive part is a little sphere. And think about the electric potential as you move out into solution away from that sphere. And you'd have lines of force that would go out like that. So you'd have equipotential surfaces, et cetera, as you move out. Now, in fact, when you go and you take your reference electrode, let's see, let's have another equipotential surface way out here, what you're actually measuring is where the tip of your reference electrode is. So if that's right there, you're going to measure the potential of that potential surface. Now, if that potential is close to the potential right here, no problem. But again, on the other hand, if instead of putting my reference electrode over here, I go out into the next building and put my reference electrode, then it's going to be cutting a potential surface. This is a very big cell I have now. It's cutting a potential surface. That's nowhere near this one, and it's the wrong number. So I've already argued that you would like to get your reference electrode as close to your working electrode as possible. As you'd like to cut one of these potential surfaces when you dump it in there, that's close to the potential of the electrode. But another thing you can do is make a so-called Luggins capillary where you start off with a widebore tube, and you draw it down to a capillary. That's a J-shaped device. And so you put your reference electrode right in there. Just insert it right down that tube. And this is all filled now with supporting electrolyte. And you have a capillary at the end. This is lots of fun if you liked it. It's one of the simpler things you can do in glass blowing. Really fulfilling. If you're not good at glass blowing, try this one. It makes you feel real good. Pull out a capillary, bend it, and break it. First of all, just physically, this lets you get your reference electrode close to your working electrode. You've got a sort of a J-shaped device here, so you can get it close to your electrode. But it turns out if you pick standard capillary dimensions over there, what you essentially do is you capture the potential surface that's right at the mouth of the Luggins capillary, and you transmit it through the capillary. So you're not changing potential. There's no potential drop here if you do it this way. And so if you're very concerned about the potential of your working electrode, then this is the way to do it with a Luggins capillary. And if you want to see the details of exactly how that works out in terms of the E&M, then Giliotti's book discusses this in detail. You do not have to have a spherical electrode to have this be an advantage. It will work with any shape. So I just drew spherical, so I could draw the lines of equi-potential easily. But you could imagine I could have a flag electrode, which I do like that, and I could drop my Luggins capillary right below it, and I could get a very good measurement of the electrode potential right there. So if you need a critical potential measurement, that's the way to do it. Now we have ourselves. Now we have everything. And now I think the next thing we want to do is we want to do some electrochemistry. We want to think about the potential control experiment, but this is a great time to stop. So I think we will call it quits for today here, and we'll pick up next hour with the situation where we are mass transport limited. That is, we've actually already worked out the case where we're charge transfer limited. That's the Tafel case. Let's go to the other extreme where the charge transfer reactions happen like that. We don't have to worry about it. And all that we're limited by is moving stuff up to the electrode. We'll look at how that works out. And that gets us in the range, then, of the kind of experiments that probably you are interested in doing in the lab. One other comment on the homework. When Bard says, tell me how to build a cell that turns A into B, he's not thinking like an engineer. He's saying design, if you will, and quotes a cell for me that has a negative free energy. So not what reference electrodes you're going to use, and what's the shape of your working electrode, and things like that. So when you do the homework, those are simple problems. They're not complicated problems. What chemicals do you pour into your two half cells to make this thing work?