 Most people. OK, so we have the cyclical tamagram. And the issue that we have to deal with now is how to utilize the diagnostics or how to actually use the diagnostics. And really, in addition to the issue of, you need to have a large range of scan rates. Not necessarily by the way, a lot of separate cyclical tamagrams. Not necessarily a lot of different scan rates, but a large range on the scan rates. Typically, a number like five would be a good number. But again, spread over at least two hours of magnitude, and preferably if you can stand at three hours of magnitude. So some number like that. So we have that to utilize the diagnostics. But the other is this issue of baseline, because a lot of the diagnostics depend on peak current. In order to measure the peak current, you need to measure the baseline. So you have three methods for measuring the baseline. Now, let me remind you, I've already stayed what the problem is. You know what the problem is. If I start a cyclical tamagram over here, and I'm going up and down, and there's my land to point, and I come back down here, it's easy to measure this peak current. I just go to my 0 of current and measure up, and that's my peak current. The challenge comes in determining the peak current over here. So for example, if I'm using that third diagnostic, which is the ratio of ionic over ionic cathodic, I have to measure both of them. There's no way around it. And the challenge is, how do I get my hand on that? And the problem is, it's very easy to see when you flip open the cyclical tamagram, that is make it this a time axis instead of a potential axis, that is shown by these dashed lines here. You have a varying baseline. You should be measuring from that baseline. And that baseline value can vary both depending on exactly what scan rate you're using, because that determines the time, as well as where your land to point is. So quite obviously, if I turn here, I'm measuring a baseline from there versus turning here, I'm measuring a baseline from there. That is a big difference. So what do you do? Well, you have three options, and they're listed there. The first option and the option that most people utilize is you kind of guess where the baseline is. You kind of say, well, look, if I can get past this peak, it kind of goes out like so. And so it's kind of folded over and you guess. And that sounds real hokey, but it actually works pretty well. It's not a bad way to do it, because the error you make will be a constant error when you do that. And so in comparing a series of anodotic orthotic currents, you don't introduce an error, but not a huge error when you do it that way. So it tends to be OK. Where you can get into a lot of problems with all the techniques, but in particularly the guessing technique, is it would be wonderful if every cyclical tamagram looked like this one right here, which is some theoretical construction. But often, you have a secondary process, electrochemical process, that occurs somewhere out here, not too much beyond the peak. And so you don't get. You can't see this nice limiting current over here. And you run into trouble when that happens. That is, what if your cyclic voltamogram looks more like this? Never like that. That's annoying my little artwork. That's not too unusual. You're not getting this nice thing down here and whatnot that allows you to do that. So what do you do? Guessing becomes hard then. It's easy if you have a nice cyclic voltamogram to guess, but it becomes difficult if you have this. Probably one of the best ways, I think, of getting at the baseline, if you need a good baseline. And by the way, this baseline issue is one of the reasons that you'll find people, say, favoring using just one of the peak currents or the peak-to-peak separation, because it's hard to do this. And again, Nichols and Shane say you should do all of them. But obviously, if I only use this peak right here, that's easy to get. So if I do the current function just for the first peak, no problem. If I do the peak-to-peak separation, this is unaffected. But you can't get all your results that way, unfortunately. So the way that is best is run a cyclic voltamogram. Let's say it looks like that evil red curve that I've put right there. And then run a second cyclic voltamogram. However, what you're going to do is you're going to stop your potential, hold your potential at this point right here, and continue pulling the current on a time axis. So switch over from a potential axis here to a time axis. And now you see, just by folding that over, you have a wonderful baseline. You're just holding it, just this potential, whatever that last potential is. You're not turning it off, but you continue. And you get the petroleum behavior at that potential then. That's a great way to do it. Now, it used to be actually a very easy way to do it. And the day of X-ray recorders and strip-chart recorders, this was very straightforward. You could either use a strip-chart recorder, in which case you get the unfolded cyclic voltamogram like that. And then you would just run a second one, but hold at that potential. That makes it very easy. Or in the case of an X-ray recorder, they often have time bases on them also. So you could run one that was a regular current voltage, and then right on top of that a current time plot. Give you the same result, just holding your potential right there. Scan at the normal speed, hold your potential right there. So that's a very good way to do that. That becomes a little bit tricky with a computer and memory and all that. But you could dust off that old X-ray recorder you have in the corner of the lab if you need it and do it this way. There's a third way. You could. Yeah, I haven't seen one, but there's no reason you couldn't. Yeah, but yeah. Actually, the answer is going to be an answer that you already know, and we'll get to in a minute. Third way to do this is a method that Nicholson suggested in 1966 in this analytical chemistry paper. And he looked at, for the reversible or near-reversible cases, the shape of the cyclical tamagram, and points out that there are geometric relationships between the various peak currents and the lambda currents and things like that, and comes up with a simple ratioing approach. And I apologize for the fuzziness of that equation. Not the equation, it's the equation is fine, but the fuzziness of the numbers, I guess, but it didn't xerox well. So that is another way that one might do it just by taking these values and calculating it. And again, this will work well as long as there's no, he's assuming, you'll notice from that figure, there's nothing weird happening out here. And to the extent that you do not have a figure that looks like his, that's not going to work well. And one could argue if you have a figure that looks as nice as that one on the screen, guessing will work pretty well also. So, but if you want to be a little bit more analytic about it, then there we have it. Okay, so as I mentioned, if you come in my office with a single scan rate, then you only slice the pie one way and that's not good enough. And if you come in my office without a separate cyclic voltamogram, not a single scan rate, this is fine, that does not have the redox active species in it, that's problematic also, okay? Because this is not the only issue, the baseline of the second peak is not the only issue. But consider the following, this is out of Gileade's book. The cyclic voltamogram on the top here is a platinum electrode in one molar sulfuric acid. Nope, I lie, half a molar sulfuric acid. Okay, no redox active species intentionally added to solution, they're just water, sulfuric acid and platinum electrode. That's the baseline, okay. What's going on there? Well, what happens if you start your scan right around here and you scan positive, then you get an oxide growing on the surface, that's the first thing, fairly ill-defined. And then when you get out here that's oxygen evolution and then you scan back and that is the reduction of this oxide and removal of that oxide, this nice so-called stripping peak, which I'll come back to in a minute. And then as you go negative here, you make a surface hydride, a second surface hydride, often you can pull out a third surface hydride and then you get hydrogen evolution, which is cut here. And the formation of those hydrides is all reversible, so you can see peaks for them, okay. So the way you see these peaks are fairly small, but obviously easily seen. So if you have your current scale set so that it's fairly sensitive, your baseline instead of being a fairly flat thing, will look like this. Now, someone could get a cyclical tamagrand that looked like that when they intentionally added some electroactive species in there and try and assign some of these peaks to some of the stuff they added to solution, they would be fooled. So it's very important to have a baseline before you add in your electroactive material. In addition, this is just intrinsic to the system, but sometimes you have some impurity in your solvent or in your supporting electrolyte or whatnot and it gives you a redox active species that you don't intend to be there. And again, you might interpret that as the interesting species if you don't have this baseline. The baseline can be a little tricky. If you take this, by the way, if you're using a platinum electrode, scan it in half a more sulfuric acid before you do anything else and make sure you get this pattern. Because that means you have a clean electrode. There's nothing on that surface. That is a clean platinum electrode. And it's very easy to get a gummed up platinum electrode and you get a very different response. This peak, you'll notice that it's very sharp compared to the most cyclic voltimetric peaks and it's asymmetric. It goes up here slower and then down here very quickly. And that's classic of a stripping peak. That is something on the electrode surface that is coming off, folding out into solution, when you carry out the redox process. Not just the surface oxide, but if you see a peak like that, sharp peak that's asymmetric, nine times out of 10, that's a stripping peak. That means you have some chemisorption on your electrode and there's something on it that is coming off when you do that. So if you don't expect that, if you don't want that to be happening, if you really have something out of solution, keep an eye out for that. Okay. You take this beautifully cleaned platinum electrode and now you put it in the same electrolyte but you add in a small amount of benzene. And that cyclic voltamogram changes to this one. The first scan is the solid scan here. And then the second scan is the dash scan. It looks totally different. What this is, is that you can see way out here there's some kind of an oxidation. You've lost mostly oxide formation in here. There's some kind of a stripping feature here. There's no hydrogen evolution. Benzene, initially, physisorbs and chemisorbs onto the electrode surface. It turns out you cannot oxidize that a platinum electrode, benzene, in solution. But you can oxidize benzene on the electrode surface and once the surface is coated with whatever left over after you've oxidized the benzene, that new surface can oxidize solution benzene. So the dash curve now, you've got this non-platinum surface and it does oxidize benzene to some extent. But you get this chemisorption and you see it totally changes this pattern. So first of all, this pattern is very sensitive to having an impurity around. So it tells you you have a clean surface. And second of all, you have to be certain even when you have the baseline for a clean surface that the molecules you add aren't going and totally changing the nature of the surface. You just want to know that that's happening. One way of doing this is to do a diagnostic that Nicholson and Chene did not talk about and we haven't talked about. And that is look at a plot of peak current versus concentration. Now, obviously in this case, you don't even have to do that. It's not going to take anybody too much time to figure out that this cyclotamogram is different from this one over here and that something's happening. But sometimes the chemisorptions much more subtle. These equations that we're dealing with, I lost my peak current equation, didn't I? Well, you'll recall that the peak current is linear in concentration, in bulk concentration. If you have chemisorption, that will no longer be the case. So typically, in a chemisorptive system, you start at very low concentration and you start to see the linear dependence on peak current developing because you don't have enough material yet to really chemisorb a lot of material on the electrode surface. But at some point, the chemisorption starts and you saturate the surface with a monolayer or whatever it is of this material and you lose your linear plot. So a non-linearity in the peak current versus concentration plot is a great indicator diagnostic for chemisorption on the surface. And that's worth checking if something funny is happening. Okay. This is platinum again. Obviously, if I use a different material, gold, carbon, whatever, it's going to be a, I don't expect to see this particular shape. Platinum shape is one of the cleanest, easiest ones to see, though. Questions on that? Because being able to see that is usually very important. If you don't see that, by the way, you throw your electrode in and it looks more like the bottom panel than the top panel and you want to get it to the top panel. Often, you can just scan in the end, so furic acid is a good one, one molar, half molar, between oxygen evolution and hydrogen evolution. Just keep scanning back and forth, usually for a couple hours. 100 millivolts a second, maybe. And you will develop this pattern over time and once it's developed, you have a clean electrode. If after a couple hours it still hasn't developed and you're getting a little frustrated, then you have two other options. Nitric acid often will clean off the electrode and then you'll have to scan it again because you put some oxide on the surface. When you do that, you've got to get back to this pattern. And if that one fails, you can stick it in a flame and assuming that whatever is chemistry sort is organic, that will take care of it. But now you have a lot of oxide and you have to scan for a long time to get back to this pattern. And in fact, often after a flame, you want to abrade the electrode surface because there's so much oxide to remove, you just want to mechanically remove it and then you have to cycle. Okay, that's the baseline. Now, one thing I haven't really said too much about is I gave you a range of scan rates that you might think about, but kind of one of the normal ones. And most people sort of start around 100 millivolts per second for their first scan rate. That seems to be a kind of convenient number. It's easy to access and often will hit the sort of exciting region of the cyclical tamagrand. And then you can see going down to fit 20 or 50 millivolts up to 500 or one volt per second is pretty straightforward. An important point when you do this, when you do a scan rate dependence, don't do 20, 50, 100, 200, 500, one volt, right? Because you're doing it in time. And if there's a change, how do you know if it's through the scan rate or the fact that you did it in a time sequence? So mix them up. Okay, so let's look at a result here. Now, there's something a little bogus about this, but I won't tell you what it is. I'll just use it for what I want to demonstrate right here. So this is a cyclical tamagrand I've been able to publish several years ago on hydrazine oxidation. Just to show you the sort of thing that you might expect. So we're looking at a peak here that we will not usually say is the oxidation of hydrazine to say nitrogen. And you see we start with five millivolts per second and go all the way to 500 millivolts per second here. So we've gone over a fair region in terms of scan rate. And you can see that there is some sort of a scan rate dependence here that is obviously not linear. For example, there's 200 and there's 500 and 500 would be a little more than twice as big as 200 if there was linear, so it's not linear. If we make a plot of that, we can see it's not linear and you can see actually by eyeballing it, it looks like it probably goes as a square root of the scan rate dependence, which it does in this case. And so we can conclude based on that plot right there that this is either a reversible or an irreversible system. Now, given that you're seeing two waves here, you might actually conclude in this case that it might be a reversible system, but in fact there's two components in there and what you're looking at is an irreversible system. What is a reversible component and an irreversible component? And it's the irreversible component that's giving rise to the scan rate dependence here. So that's how one might use that sort of data. And again, we started these scans over here. We go up this way and there's our lambda point and come back. And so this peak, we can read off that chart just from our initial current over here up to the peak. But for this peak and that's actually what I'm plotting over here, we have to go out here. And we do have a very nice return side here. We're not messed up at all. And we have to make a correction for the baseline and come back. We did that using this chart technique here, but I also went back and did that data just by guessing and I get the same result. That is, a cyclical timogram looks that good. You can come up and just sort of guess at the baseline. Yes, it depends on the mechanism. For a reversible, it's scan rate independent. Assuming you have zero uncompensated resistance. So again, there is always in the real world some sufficiently fast scan rate where these peak currents get large enough that i times r is a number that comes into play. And you see some peak to peak separation. And this particular system is rather resistive, actually. OK, to see how one might use the Nicholson and Sheen diagnostics and for something a little more complex, let's go back to the example that I gave you the other day of this tungsten tetra carbonyl bipuridine system, where I use it as an example of how one used double step chronoamperometry to get at a rate constant for, in this case, loss of the CO ligand from the system, one of the CO ligands from the system. Now, I could not have done all this stuff unless I knew the part that I pinned in there first. What working curves I should have used and what I should have jumped between and all that nonsense would have been unknowable unless I already knew that when I dumped an electron into this system, first I reduced the complex and then a CO ligand falls off. I need to know that first. So how did I know that? Because I'm certainly not going to figure that out by looking at a set of curves that looks like that. And the answer is we did cyclical tammetry to start with. So this is the study before the study. So what we have here, we have cyclical tammograms. This one is the chromium tetra carbonyl bipuridine complex, the molybdenum and the tungsten. So we were looking at the data for this one down here. And what you can see, this is only at one scan rate. These are at 100 millivolts a second. That one might guess is a reversible reduction over here followed by a re-oxidation. We're starting in the middle here. And over here for the chromium, again, it looks like it might be a reversible system out there for the oxidation. So as we're starting here, we scan, we see the reversible, we scan back, we see the reduction like that. Over here, again, reversible reduction, perhaps, again, with the caveat that I'm going to show you one scan rate, and clearly a non-reversible oxidation. And the same thing down here, non-reversible. This might be reversible again. Well, if one does a scan rate dependence, then it turns out these peaks are reversible. And you notice they all fall independent of the metal at the same potential. The halfway potentials are the same. So we associate that with a reduction of an electron into the bipurity. Now, by reversible, I should be a little bit careful here. This really would be a good example of a quasi-reversible system for these two down here. It's quite reversible in the chromium case. But this is the thing we're looking at by chronoamperometry in the prior slide. That is, the jump we're doing here is right through that reduction wave. We start over here, and we jump to this side of the wave. We make it a big enough jump that we have the coutrelle limiting current over there. And we were doing that not for the chromium system that I'm pointing to, but for the molybdenum system in that case. So at this particular scan rate, 100 millivolts per second, it looks reversible, but we're fooled. If we go fast enough, something else is going to happen. Over here, we're clearly non-reversible. Now, let's talk about this a little bit. This would be an oxidation, and all cases that's moving around is different. That is metal-centered. So we have metals there that are in the zero-oxidation state. The complex is neutral, and we're pulling an electron out. It's a de-electron on the metal that's coming out. And in the case of the chromium system, it's a fairly reversible process. But in these other cases, that's clearly not the case. Now, you can't just look at that, though, and say, oh, that is an irreversible process. Irreversible means it's easy to pull the electron out, but you can't shove it back in. There's a big rate constant for moving it out, but not back in. Because it is equally likely that what's happening here is there's some chemical process, like the molecule falls apart after you pull an electron out. And there's no return wave, because there's no molecule there to push an electron back into. So it could be an EC mechanism just as well. So I really would have to do a scan rate dependence here and figure out whether it was a case 2 mechanism, irreversible, or a case 5, or whatever it might be to do that. Or maybe instead of that, I could do some spectroscopy or something like that. OK, what we've done is over here we have, and this is another eye exam, but these are the current function versus scan rate for a set of cyclotamograms, again, chromium, molybdenum, tungsten. And that is the ratio of cathodic to ionotic for this set of peaks, again, for the three systems. And here you can see now that we are not reversible. That is the chromium one, which is the most reversible. You can still see a slow scan rates down here. We lose that horizontal line in our current function. We're not plotting peak current, but this current function there. And it's more obvious in the molybdenum case and the tungsten case is similar. And likewise, when you make the plots of peak currents, in particular for these two, you can see that reversible case, it would be a horizontal line. That is the anodic current would equally cathodic current. And this is baseline corrected stuff. And obviously those are not horizontal lines. So we have a mechanism going on here. And again, that mechanism is the loss of one of the ligands. The idea is I do a cyclotamogram. If I do it at sufficiently fast speed, and the ligand falls off pretty slowly in this case. So sufficiently fast isn't that fast. Then by the time I get all the way around here, none of the COs have had the opportunity to fall off, basically. And so I can reduce all the molecules that I oxidized over here if I'm scanning fast enough. If I scan sufficiently slow, then between when I do this reduction here and come back and do the oxidation, I've lost the CO. And so I can't put the electron back into it. And so I predict that this peak, as I increase the scan rate, will increase linearly with scan rate to the 1 half power. But this peak is going to fall off because I'm missing some of the molecules as I do that. And the faster I scan, though, this will be less of an impact because I can beat out that process. Now, this brings up an important point. Cyclotametry for determining non-electric chemical rate constants is only good in a certain time regime. That is, if the chemical step, if the rate constant for that is super fast, then we're not going to see it. OK, it'll just look irreversible. We'll miss that point. On the other hand, if it's super slow, we won't be able to scan slow enough to see it. And so there's only an intermediate set of rate constants. This is a good technique for intermediate rate constants. It is not good for really slow things or really fast sorts of things. Now, everything I have shown you here on these last two transparencies is based on 1964 technology. And it has a caveat that we don't have our IR correction in there and the caveat that we need a good baseline. And it still is a pretty good way of doing things. But there is another way of analyzing this sort of data. And that is, today one has access to our commercial packages of programs that digitally simulate a cyclic voltamogram. They don't really base it on a specific mechanistic analog or picture. The idea would be that you would consider your electrode here, and you take the space in front of your electrode, mathematically speaking, and you divide it into a grid. Of course, the finer the grid, the better the simulation is going to be. But you put a certain number of particles into this space, molecules that are going to be oxidized or reduced, and you tell those particles that they have to follow the laws of diffusion and chemistry, rate constants and whatnot. And you just set the thing into motion and generate a cyclic voltamogram based on a digital simulation. And if you do that, you can simulate any mechanism you want, and you can then compare your data to that mechanism. And now you're not comparing just a peak here or a peak-to-peak separation, what have you, you're comparing all the data. So in a sense, with all this Nicholson and Shane stuff, we're throwing away most of the data. We only use the peaks and the peak-to-peak separation. There's a lot more data in there. If you would be more confident, obviously, that you had the right mechanism, if every single point here matched up with what the mechanism predicted. And that would be difficult in Nicholson and Shane's day using those tables and numbers they generated. But using this approach, you can do that. So there's a program, for example, called DigiSim. And Bruce tells me that now some code has been released publicly, so you don't have to pay for it maybe. That'll let you do this. But you can take your cyclic voltamogram, and you can simulate it. And then you'd be very certain of the mechanism. And of course, if your mechanism is very complex, not just EC, but lots of steps in it, then the only way you could be very confident that you have the right mechanism would be a simulation like that. Barr talks about, mathematically, how you go about doing that in the appendix section of the textbook. So you might want to look at that. I'm not going to say a lot about it, but that is available as an alternative to all of this. Nonetheless, even if you're doing that, that's a big deal thing, you're not going to start off with, here's my brand new molecule, and I'm going to take a set of cyclic voltamograms, and then step two is going to be a digital simulation. You won't even know what to digitally simulate. You still are going to want to take a look at these cyclic voltamograms and the diagnostics and say, oh, it looks like an EC mechanism, or what have you, or reversible, or what it might be. You need to start there. So although you have a more powerful technique, it's not useful until you've done this, really. And of course, when you do that wonderful simulation, it will take into account the baseline differences. And you don't have to worry about that. OK, let's see, though, staying with the good old fashion way of doing things and some real good inorganic chemistry here. Let's see exactly how this works out if we have something a little more sophisticated than just a simple reversible mechanism. So this was a study carried out by Reitn with Luang as a graduate student, and Naesha was a visiting professor. Actually, just to make this a little more interesting, when I joined Mark Reitn's group, I actually had been a professor for four years in a discovered photo-electrochemistry and was considered a really important guy. The year before that, he had bought his first potential stat up to that point that had borrowed him from the undergraduate lab. The PR174 is very proud. He showed it to me so I could use it. And I thought this was all great. And then it turned out he knew no electrochemistry. However, to his credit, one of the first things I did is I went out, I decided I should learn some electrochemistry. So I bought some textbooks on it. I bought the Giliati book, actually. And I bought this two-volume set by Bacchus and Reddy, a modern electrochemistry that I bought. And I had them on my desk. And I was kind of just reading them at my leisure. This was just my own edification. Because we weren't really doing electrochemistry. We were doing photo-electrochemistry. I just wanted to learn this. And so I'm sitting at my desk. I was TA-ing at that time. So it's a little around dinner time. And I'm grading lab reports. And Mark Ray walks in and asks what's going on. And he sees the books on my desk. And he asks what they're doing there. And I said, well, I wanted to learn about this. So I bought these books. And I guess they're OK. I've glanced through them, but I haven't really read them. And he says, oh, would you mind if I borrow them? And so I say, sure. So he takes them. And he comes back the next day. And he goes back to me and says, thanks for letting him borrow them. They're really great books. You should read them. He'd read them all over the night. He'd do the stuff it up. So that was very impressive. But the other thing he did is he got Louie Nagio to come. And Louie had been in Savion's lab in France and was a highly-trained electrochemist on his way to becoming a professor. In fact, he went back and today is a professor. He took a professorship right after he left us. And he really taught the group electrochemistry. And then John Long said, I'm just a wonderful graduate student that was there. So this had nothing to do with me, but it was happening at the same time I was there. And they were interested. The other half of the research group that wasn't doing photoelectric chemistry was doing organometallic chemistry, mainly photochemistry. And one of their favorite photochemical species at that time was this chloro-rhenium trinocarbonyl fennanthroling complex. So a little bit like the compound I showed you on the prior transparency. We have a rhenium. That's a difference now. We had bipuridine before, but fennanthroline and bipuridine are close cousins to each other. We have some carbonyl ligands. And in addition to this, we have a different oxidation state. We have a rhenium one here and a chloral ligand. That balances out that charge. And this electrochemistry that they were looking at in the Cedarnite trial with tetrabutylammonium perchlorate supporting electrolyte. And they published this paper in Jack's on this. So the first thing we have is a relatively long-range scan rate dependence over here. I don't know if you can read the numbers, but plus 2 on the positive side. That's minus 1 and 1 half. We're there, so almost minus 2 on the negative side. And at first glance, you'll notice this one right here. It looks pretty much like the ones I was just showing you. Some kind of potentially reversible phenomenon over there. And it's something that doesn't look very reversible over there. First item to point out, there's the baseline. That is the Cedarnite trial, TBAP, platinum electrode system. And you'll notice there's a little bit of gunk in here. There's some waves right there. And you can see them right there in the cyclotamogram of interest. So if you did not have this baseline, you might say, ah, I'm going to interpret these waves in terms of having something to do with the chloral rhenium tricarbonyl complex. So that's why you want to do a baseline. And likewise, you'll notice out here, just past where this wave is, that is important. There is something happening. And suddenly down here, it turns out, if you have a little bit of water in your Cedarnite trial, they're both oxidation reduction events that can occur, especially oxidation. That's the organic chemistry that you have to look out for. So again, just to stress, that baseline is really a critical thing to do. OK, so once you have the baseline, and so now we know which peaks are rhenium-based peaks, chloral rhenium tricarbonyl-based peaks, then you can ice like this and just do a scan rate dependence over this region of potential. And you see something that turns out, when you plot that out, it looks reversible. That is, it goes with the scan rate to the 1 half. You see there's very little shift in the peak to peak potential by eye there. That's a reversible system. On the other hand, when you do the oxidation, looking over there, as you change the scan rate, the peak goes up. But you might start to think that that is an irreversible system based on that. There's one peak. It doesn't seem to change with scan rate. It's not moving around too much. And yet, one has to be a little bit careful. So what we did, this was all done on an xy recorder where you couldn't run fast about 500 millivolts per second before overcoming the mechanical limitation of the xy recorder. This is actually helped them with these down here. This was done in a oscilloscope. This is really wonderful technology. It's a oscilloscope, a Polaroid camera. Amazing stuff. Take the picture, tell it to smile. And I took those. Can you see all the credit I got on this paper for that? There's an acknowledgment. All I did was take the pictures and set up the oscilloscope. You didn't push the button on the screen. No, I'd set up, you know, I got the oscilloscope working and figured out the right exposure. All that oscillographic stuff. This wasn't a digital oscilloscope, by the way, guys. This was the real thing. Anyhow, so we start here, and we're starting at, I believe it's 10, excuse me, 1 volt per second, 2 volts per second. I believe it's 20 and 50 volts per second as we drop down there. And we're a little off the screen there. Yes, I'm right. 20 and 50 volts per second. Anyhow, one volt a second, again, you can see it. There's no return peak as far as one can discern. But when you get to 2 volts per second, you start to see there is a little bit of a return peak that's starting to show up there. And by 10 volts per second, it's very clear there is a return wave there. And at 50 or 20, whatever I said, I think it's 50, it looks pretty reversible now. So you can see without doing any plotting, this is an EC mechanism. And it turns out that the C part of this thing goes pretty fast. And so until you get up to 10s of volts per second, you cannot trap this molecule. That is, as soon as you pull the electron, it's an oxidation, pull the electron out of this molecule, it falls apart. And you have to do some chemical analysis to figure this out. Some spectroscopy, but what's happening is you are losing the chlorine ligand when that happens. And if you do this in acetonitrile electrolyte, then acetonitrile happens to go in as the new ligand in that system. So that would be a very nice example of how Nicholson and Sheen works. And the fact that if you don't go over a large enough dynamic range and scan rate, you're going to misinterpret the mechanism. So there we did the full three orders like we were required to do. OK, this one will be, this is like a walk down history lane or something. This will be of interest to a fair number of people in the class. And that this is another right in study, some general interest. But this is a right in study which involved the Bokarsley-Lewis duo. Nate and I did this along with a couple other people, actually, back in the day. And the question was this. The question had to do, as we posed at that point, with semiconductor photoelectrochemistry and the behavior of ferrocene and stabilizing silicon electrodes. But it was a bigger question. That is, we know if you have, say, two molecules out in solution floating around that they don't communicate with each other. That is, one molecule swims up the electrode, gets oxidized, and the molecule next to it doesn't know that that's happened. But what if you go and you start sticking two molecules together, two redox centers together? So those two ferrocenes are stuck together. At what point do they start to communicate with each other? And so this is a problem not only for issues of putting ferrocene on silicon and things like that, but if you want to make sensors, this becomes an important problem. If you want to do catalysis, it's an important problem. It's a fundamental issue in electrochemistry. When does one side of a molecule know that the other side of the molecule has been oxidized? If you want to think about molecular electronics and data storage, again, this issue comes up. How far can that information diffuse? So we started off, first of all, with these two ferrocene units. And they're hooked together just by a single bond there. And ferrocene oxidizes at about 0.25 volts versus SC and acetonitrosyl around there, depending on exact conditions. And what we see now is we see two redox events. So in other words, one of these ferrocenes oxidizes. And then the second ferrocene had a much more positive potential oxidizes. Now if the two centers were not in communication, they'd both oxidize at the same potential. And we'd just see a single n equals 2, a two electron charge transfer there. We wouldn't know that. But to the extent that we get a separation here, clearly the second ferrocene knows that the first one has been oxidized. And so it's harder to oxidize the second ferrocene. It knows the first one's missing an electron. And so to pull an electron out of the second one becomes more challenging. So they're in communication. And you could use this peak to peak this way separation as an indicator of the communication. Further that is apart, the stronger the communication is. If they're right on top of each other, no communication. Now this molecule, although I've drawn it this way, you'll notice there is free rotation around this bond. So this ferrocene could be flipped up in a shape like that as well as the way it is. And in fact, for steric reasons, one might guess that in solution when you're doing this electrochemistry, it adopts that second configuration, not the one that's drawn there. So the next question was, if we guarantee that that configuration is the only one available, that we can't flip it around by putting a second bond in there, can we then enhance the charge transfer communication? So you do that. By the way, those of you who know Professor Lewis know that he did not synthesize these molecules because he would be totally incapable of doing that. And I will tell you, since you don't know me as well, I am equally incapable of doing that. There was a wonderful postdoc, Michael Palazzardo, who did all the synthesis for us. So you make this structure, and now do the cyclotamogram, and this is a lot of platinum, acetone, nitrile, TBAP. And again, two reversible ways, and we did do the scan rate dependence, et cetera. I'm not showing you, but they are reversible. And you'll notice that the peaks are even more spread out. There's a bigger separation. So we have even stronger communication when we say those two irons have to be facing each other. And the next question you can ask is, what if we start inserting some molecules in between here and pull those ferricenes apart? So let's take a CH2 group and put it in between there. And if you do that, we happen to have a bit of a scan rate dependence there, then there's only one set of peaks. So one methylene group is enough to break the communication. They're far enough apart now, the two ferricenes between that. You're actually doing two things, to be honest. One is you're obviously separating them further apart by putting that methylene group in there. But you'll notice, this is a conjugated system, these two. We have two aromatic rings, and we've broken the conjugation here. So it could be due to that also. This one, this one, these are in solution. This one's on the surface. Yes, right, very good. You see, you've learned your lessons as well, yeah. But we don't know that in this class yet. But yeah, it works out in solution also, but I happen to have that data set easily accessible. And now you know that Nate did it since I've confessed it's on a surface. The other thing you could do is instead of putting a carbon there, you could put a silo group there, a silicon. This is a dimethyl silo group in there. And one thing naively you might think is, well, a silicon is bigger than a carbon. And so they're even further apart. And so there should be no communication because there was no communication with the carbons. On the other hand, the silicon has these fairly low lying d orbitals, and they might facilitate communication between the two aromatic rings. And sure enough, when you put the silicon in there, you start to see the communications going back. It's not a big splitting compared to what we saw up there, but clearly there is a splitting. And so the two irons now know when one is oxidized and the other is reduced. So both distance and in the nature of the orbitals, these things you know now are important. It wasn't so obvious in that what those different parameters did in the late 70s when that work was done. Okay, so that is examples. Let's now turn our attention to a few just practical issues when you're done. We've hit on a lot of practical issues. We're doing a single-volta hemograms, but there's a few more that we need to think about. I've already pointed out that your land of potential will have some impact on exactly where your peaks are, your peak-to-peak separation and issues like that, so you're aware of that. I've pointed out the issues of baseline on the peak current, especially the return peak and how you have to be very careful about correcting that. And by the way, I pointed out that you can guess and get a pretty good correction and you won't make too much of an error, but I do promise you, if you make no correction, you will get an answer that has nothing to do with the chemical dynamics of the system. So you need to make some kind of correction, even if it's a guess. One thing that we haven't talked a lot about is the instrument, okay? You can see a lot of, you can go theory to any scan rate you want, but if you go to a scan rate in which something is limiting that isn't your electrochemical cell, you run into problems. So I've already given you one example. If you were using a mechanical XY recorder, you might have a system that's beautifully reversible at 10 volts per second, but I promise you your mechanical XY recorder is not reversible at 10 volts per second. It can't keep up with that. And so you would run into a limitation. That might be kind of obvious, but what about the potentiostat itself? There's a couple of things you have to watch out for here. Number one is there are some potentiostats that will allow you to drive them faster than they're designed to be driven for some reason. That is there are knobs or buttons on them that let you go at 10 or 100 or 1,000 volts per second, and yet actually the electronics of the potentiostat can't necessarily keep up with that. That is you may be able to ramp your power supply at that rate, but that doesn't mean that your current following can occur at that rate. Okay, so one has to make sure one has a potentiostat that can do what it's promised to do. You might want to look at a system that you're sure is reversible like the ferricing system, for example. When you have a brand new potentiostat, put it through its paces and see just because the knob says it goes at 100,000 volts per second if it really does. Okay, the second thing is, although the manufacturer is responsible for what happens inside the box, you're sort of responsible for what happens outside the box. So for example, you have your voltage and your current outputs and you decide, my students have done this actually, that you'd like the potentiostat on that side of the lab and your electrochemical cell on that side of the lab. Okay, now they're not scanning at 100,000 volts per second, but this is still annoying. You know, there's gonna be IR laws in that line and whatnot and you could expect that at some very high scan rate, things are gonna mess up. Likewise, if you decide you're not gonna use coax cables, you expect to pick up all kinds of noise that you might interpret as cyclic voltometric events. If you decide in your electrochemical cell, your cell is close to your, I should point something out, if you use an old 173 potentiostat, it has an external electrometer and the reason for that is a little cylinder, remember that she said, and the reason for that is PAR, the real PAR, knew that it was important to have a short distance between the electrometer and the reference electrode because if you put a long wire in, there would be a resistive loss there that your most sensitive electrometer would say it's part of the system. So they built it now. Ever since then, and actually before then, every other electrometer has had a, potentiostat has an internal electrometer. Okay, and the manufacturers are just assuming that you will not put five miles of wire in between your reference electrode and your electrometer. But there's not that stops you from doing it. Okay, so keep that in mind. Next, in your electrochemical cell, even if you have short wires and whatnot, it is quite possible to develop high resistance by some obvious things like forgetting to putting in the supporting electrolyte, having a reference, a frit in between your reference and your working electrode. If you're gonna use a two compartment cell with a frit in it, make sure the reference electrode and the working electrode are in the same compartment. The counter electrode could be in a separate compartment. Right, but you don't want excessive resistance. You want high resistance, but not excessive because that extra frit is an uncompensated resistance. The frit that's associated with the reference electrode is a compensated resistance. Okay, so you need that in there or simply having your working and your reference electrodes too far apart. Or if you were to go and design a working electrode, say that was a flat square centimeter or something and you covered the back so it was insulating and you faced that working electrode towards the edge of your beaker, that's your electrochemical cell, and then you put your reference electrode at the other end of the beaker to the back of your electrode. You can induce high uncompensated resistances and to the extent that you do that, it will affect, even before it starts to do really ugly things, it'll affect your peak to peak separation here, which is an important diagnostic, but it's resistance that you're measuring. Does that enter into, so qualitatively, is that in? Yes, until things get really, really bad. At some point, the whole waveform is distorted, but it affects the peak to peak separation long before it does that. Now, even modest resistances, uncompensated resistances can have effect on this, especially to get to these very high scan rates, like the ones I was showing you in the tens of volts per second, because the current's pretty high there, and so I times R can be pretty large. So in fact, if you were looking at that data a little more closely than I'm sure you did, you'll actually see for that chloroenium system that you are starting to get a little bit of bigger peak to peak separation at the tens of volts per second. And that's not because of anything chemical that's happening, it's just that the currents have gotten big enough now that I times R is a reasonable number and we're getting a separation there due to that. You could do an IR correction if you wanted to, most potential steps will do that these days to get around that, but you should be aware of it. The other thing that can happen, in particular, if you have either not a lot of an electroactive species around, or one where the rate constants aren't so fast, is that the peaks can start to dissolve into the baseline. And again, if you have a reasonable amount of resistance in your system, then the baseline, instead of being a flat line, like we'd like to think it is, you know, I'm assuming when I draw this, sort of that the baseline is more or less like that, we can get some thickness there to that. And that thickness is due to the RC constant, the system, in fact, Bard has suggested that, you know, if you want a poor man's way of measuring the RC time constant for your cell, run a scan rate in a region where there is no electroactive thing going on, and measure that baseline, and you can calculate an RC constant from doing that quite easily. So, in the case where you have either a very small amount of material, or a sufficiently small rate constant, such that the peaks are getting small, if you have a lot of resistance, you'll have a big baseline, and it'll be hard to see your peaks over the baseline. Now, sometimes this is a situation that is hard to avoid. For example, there's been a whole cottage industry of alkane files on gold, which you're probably all aware of, and within that industry, some of them very interesting experiments were done in which you use the alkane part as a spacer and put a redox-active species, such as a ferrocene at the outer distance, and ask yourself exactly how far away can a redox-active species be from the surface in order to get charged transfer chemistry to occur? And there's some very nice and expected relationships that have come out of that, but they've confirmed what we expect in terms of tunneling issues and charged transfer and whatnot. It's really nice studies. But when you go and you put a monolayer of, say, a C18 alkane on your surface, it is resistant. You can't get around that. It's very high resistance there, so your cell has an uncompensated resistance in it, which is that monolayer, and then you put your ferrocene or whatever you want on the outside of that, and you don't have a lock because you only have a monolayer of those, and so there's a system that has a low number of redox-active species on the one hand and is highly resistive. And so you are gonna have a big baseline there, and anybody that's done that knows that, and you have a huge RC constant, and you just have to deal with it. You can't say increase the supporting electrolyte, things like that, because the resistance comes from that alkane-file layer, and you simply have to know it's there and calculate it and pull out your data from that. So sometimes the baseline issue simply goes with the problem. Finally, everything I think I've shown you so far, we've had sycovolta-metric ways that are spaced fairly far apart. Even in that ferrocene case, if I go back to that for a minute, you'll notice that even in the closest way, well, this would be actually a good example that I wanna talk about, but I was gonna say in these ways, if I wanna make measurements of peak currents, this peak right here is an easy one to measure. I start here, and this one just measures from baseline. If I wanna measure the peak current here, it's not fair to go back to baseline. I have to extrapolate the petroleum current out in here and measure off of that. That's pretty easy to do when they're this far apart. That is, the petroleum current has fallen off quite a bit, and so I can guess and come up with a reasonable answer, or better yet, I could do the strip chart trick and come up with a great answer. That is, just run a one sycovoltaenogram that goes all the way through this thing, a second one that stops here, and then turn on my time axis here and go out and get it. So I need to do it for all three of these peaks, in other words, a baseline correction. However, what do I do when I have something like this? Where those peaks are coming almost on top of each other. Clearly, there's two peaks there. There's no question about that, but equally well, it's clear that the error in measuring this peak current, if I were to measure it off baseline, would be horrendous. And likewise, I don't have enough of this peak showing that I know exactly how to sketch in the baseline here. So when I have two peaks like that, this is a case where the Nicholson approach works pretty well, actually, because you can just do it on the first wave and calculate a baseline for the second wave doing that approach. The strip chart can work well, however, if you have to stop your potential at a point where this peak is already being oxidized, the strip chart isn't gonna work right either. So in this one, it's too close together. I really can't get past that peak and not be in a region where this peak isn't being oxidized. So I really have to either guess or use the Nicholson approach to this. Okay, let's see. Those were probably the main points that I needed to make. One last point, there really is such a thing as a two electron oxidation, whatever that means. That is, there are systems where you see a single peak and the peak-to-peak separation is 30, or 60 divided by two, and the amount of current you get indicates two electrons are going into the molecule. Now, you can sit here and debate whether that really means both electrons are going in simultaneously or whether there's a slight difference in time between the two, and I'll leave that up to you. Probably the interesting example of this, and by the way, when I say two, I mean some number greater than one, I guess, not necessarily just two. The classic example of two, which is two, is the hydroquinone-benzoquinone system, which in the presence of protons gives one wave that has two electrons in it for all intents and purposes, and the absence of protons, such as in the pseudonite trial, you get two perfectly separated one electron waves. But there's two electrons and two protons, and things happen so fast on the cyclic-volta-metric time scale that you have to say it's a two-electron process. The limiting example of this was some work that Barr did. He was looking at polyvinyl ferricine in solution, and they had oligomers, really, of these materials, with 30, I think the largest one had 30 ferricine units on this vinyl polymer, and you take the cyclic-volta-mogram of that and you get one wave, one wave with 30 electrons in it. So the peak-to-peak separation was more or less zero because it was 60 divided by 30, okay? Two millivolt peak-to-peak separation. Actually, there's a little bit of different theory that one has to use. It turns out when you have something like that, but very small peak-to-peak separation, you use a statistical model, it has a logarithmic dependence instead of a simple 60 divided by 30. But it looks like when one of these ferricine oligomers hits the electrode, that every ferricine gets oxidized like that, you can't distinguish between them. Now, in the vinyl ferricine, you have that extra carbon in between the two ferricine units, so the ferricines don't communicate with each other like I was just showing you, and so one doesn't know the next one's been oxidized, and they all just go at the same time. Okay, that is cyclic-volta-metry. Now, I want to make a, well, I'm just gonna say subtle, but it's not so subtle, it's sort of a change now in how I'm presenting the information to you in this class. We've gotten to a point now, we've covered lots of mechanisms, you know a lot of experimental details and whatnot. We have not hit absolutely every electrochemical technique that I'd like to talk about. We'll see if I get to talk about them all before I leave town, but we have quite a few under our belts, and we have, I think, an appreciation of how you develop the analytical chemistry, the physical chemistry of this, those sorts of issues. So far, I've looked at this sort of technique-wise. Well, how does this technique work? How does that technique work? Now, for perhaps a remainder of the lectures, I'd like to switch over to a more chemical approach to things and start looking at chemical systems and ask how do they behave using these various techniques? And then we will bring in new techniques as needed to study the systems. Now, before I can do that, I need to talk about one other thing that we haven't spent any time on yet, and that is charge transfer mechanisms. We've talked about kinetics at an electrode, but I want to talk more generally about charge transfer mechanisms so that we can correlate our data with real-life chemistry. So perhaps, yeah, actually, you know what I'd like you all to do? I need to just find out something quickly. So take a piece of blank paper and write the following thing on it. Write K12 equals, and then fill in what goes beyond that. And if you don't know what goes beyond that, just write question mark there. But everybody has to turn in a piece of paper. Don't put your name on it. And I am clear on all these boards, right? Does he sense? Does he have a right to it? I clear it out. It's clear, right? I have a question. It should have been a dogmatic statement. I am clear on all these boards. Well, I will be. Okay, why are you doing that? We have two charge transfer mechanisms. We have an inner-sphere mechanism and an outer-sphere mechanism. Inner-sphere mechanism was developed by Henry Taube. We see the Nobel Prize. And I forget the guy who did the outer-sphere thing. No. Your favorite professor? Yes, he did. Taube absolutely did do both. But we'll give him credit for it. Yeah, well, yes, I suppose I am. Marcus did the theory to be explicit for outer-sphere. Taube certainly did that both because you will recall the inner-sphere mechanism is a mechanism in which the electron transfers for some sort of a molecular bridge from point A to point B. And of course, to think about that, you need to understand that there is a possibility that the electron just flies through space from point A to point B. So that's the outer-sphere. It just goes A to A+, and the inner-sphere would involve some sort of a bridge like that where the electron somehow travels through the bridge to get to the other side. And Taube certainly did look at both, but is well-known for finding this particular mechanism. And Marcus is well-known for teaching us how to understand this particular mechanism. Now there's one thing that I always found really fascinating. I took general chemistry, of course, and I took organic chemistry like the rest of you. And in organic chemistry like everybody else here, I had to learn all these mechanisms. And there's all these really intricate mechanisms, arrows flying to the left and the right and electrons hopping everywhere and bonds being made and broken and all this in terms of organic chemistry. And then you get to a section of whatever textbook you're using and they talk about oxidation reactions. And invariably, all you see is not pages and pages, but mechanisms, but something like this usually. And even as a young undergraduate, I said there's something wrong here. Is it really true that oxidation mechanisms just happened? And whereas every other mechanism involves electrons moving around and bonds being formed and broken and this and that and the other, I couldn't figure this out. And I didn't understand until, I didn't understand actually until I became a graduate student and Henry Tavley came to MIT and gave a lecture that of course the problem is that if there's a detailed mechanism such as the inner sphere mechanism, then the species immediately adjacent to the charge transfer center get involved. This is true in outer sphere also, but it's obvious in inner sphere, the things that are connected to the charge transfer centers have to get involved in the reaction. When you have an organic reaction, you probably have no idea exactly what is immediately adjacent to your molecule. It's solvent obviously, but what's its orientation and how many solvents and what else is in between your molecule and wherever the electron's gonna end up, et cetera, et cetera. Whereas of course, if you have a coordination complex, then your cohesion sphere, which you know well is your first salvation sphere. And so you have a built-in way of handling this issue of the fact that it's not just the molecule itself that's important. And poor organic chemists really don't have a way of handling that. So they've gotten a lot better at understanding redox reactions in recent years, but they still have to struggle with this problem of that it's the molecules that they are not interested in fundamentally that play a key role in all of this chemistry. So we have our inner sphere mechanism. Now with regard to that, inner sphere mechanism, I'd like to introduce you to, well first let me go over Taube's historical experiment that led everybody to believe that an inner sphere charge transfer mechanism really existed. Yeah, wing it. Taube started off with a very simple elegant experiment, which was the reduction of a cobalt complex by a chromium complex. This is in water. And the idea is that we're gonna end up with a chromium-3 in a cobalt-2 out of this. And one of the really interesting things about Taube, something that is that he was able to teach us an awful lot about charge transfer chemistry, not because he knew a lot about charge transfer chemistry, but because he knew a lot about coordination chemistry. And so he picked this thing just right in that, and it isn't by accident, he knew exactly what he was doing. Chromium-2 is a labial complex. It exchanges its ligands very, very rapidly. And Taube's definition of labial, which no one seems to use anymore, they just talk about labial, is that all the ligands fall off in one minute or less. That was his definition. So it changes its ligands very rapidly. Chromium-3 does not. Its ligand sphere is more or less locked into position. Cobalt-3 likewise is not labial, its ligands will stay on, but cobalt-2 is labial. So when this redox reaction took place to form this, whatever ligands were transiently on the chromium at the point that the electron transferred got locked onto the chromium. Whereas, of course, all the ligands fell off the cobalt at that point. So it's not surprising that he ended up with aquated a cobalt complex plus ammonias. But what he was looking for was whether or not this happened. If that happened, then that meant that there was a chloro that transferred from the cobalt to the chromium at the same time that the electron was transferring. And that could only really happen if there was an activated complex, if you will. That looked like this. So right before the electron transfers, there must have been a bridge there. And when the only way the electron's gonna transfer is when that bridge is there. And that argues that the electron went through the bridge. So that was his evidence. Now, when people first saw that, they were impressed by that, but they still were wondering if perhaps there was some way that the chloride kind of fell off and was swimming around in solution and then happened to come together with the chromium at the time it was being oxidized to make this complex. So this didn't really exist. So he did a second very clever experiment in which he put a radio labeled chlorine onto this complex and then a ton of regular chloride out in solution, sodium chloride. And showed that all of the label shows up over here. And then he did the reverse experiment also just to make sure everything was working right. So at that point it's unambiguous. This bridge must be here. So that is the inner sphere mechanism. Now, prior to that experiment, there were other experiments that suggested that inner sphere types of things probably were happening, but this was the definitive experiment. Hems had a set of experiments where you look at one complex being oxidized by a whole series of different complexes. And you find out that depending which complex you use, you get different rates for the redox reaction. And these rates will vary over many, many orders of magnitude. I think on the order of 10 orders of magnitude difference depending what you use. This is polypyridol complexes that were being used. And some of the oxidizing molecules had ligands on them that could potentially act as bridges. And some of them did not. And so just based on the fact that it's very unlikely that you have the same mechanism when you're seeing many, many orders of magnitude change. And right, there was a suggestion that you had a different mechanism. And the inner sphere was postulated. And that was happening about the same time actually as Taube was doing his experiment. So this all came together. And many people will say, based on those experiments now and understanding that there is an inner sphere charge transfer mechanism, that one could just look at the rate of the reaction and decide whether it's inner sphere or outer sphere. That is, inner sphere should go fast compared to outer spheres. The problem with that is, as Bruce said, Taube looked at both. And that's not always a true statement based on what Taube said, because there are important subtleties to these mechanisms. And you can have inner sphere mechanisms that go slower than outer sphere mechanisms. Taube showed, in the case of the outer sphere mechanism, that the exact amount of orbital overlap between the oxidized species and the reduced species was critical to how fast the rate was. So you could make an outer sphere mechanism go fast or slow depending on orbital overlap. Likewise, Taube showed that, depending on exactly which orbitals you're using on your donor and your acceptor and your bridge, you can make this go fast or slow. In particular, he showed that if everything goes through a pi system, your electron starts in a pi system, ends up in a pi system, and goes through a pi system on the bridge, that was a great way to do things. On the other hand, if you start within a pi system, maybe end in a pi system, but have to go through a sigma framework on the ligand, then things are going to go slower. So there's all kinds of interesting subtleties like that. And you have the wonderful Quetz-Taube ion and the related ions. Bruce knows a little bit about this, just a little, that show these very nice relationships. Cal Creutz, he was at Brookhaven with Bruce, so he has a direct relationship to all this. And all this follows very nicely. Keep the electrons in the same kind of orbitals, nice orbital overlap, things will go fast, put them into different orbitals, or have poor orbital overlap, things will slow down. And that holds for the inner sphere and the outer sphere. So now we have our inner sphere mechanism, that goes. Now, my favorite inner sphere complex is also a complex that Bruce is aware, because he's helped us with it. We discovered several years ago now that if you take ferricyanide and react it with Platinum II by tetramine, that you get a redox reaction. The ferricyanide oxidizes the Platinum II to Platinum IV. This is just an aqueous solution. There's nothing too fancy here. What you end up with is this guy. Two iron IIs, two ferricyanides on the ends, and a Platinum in the middle, and the Platinum has, we can be colorful here, these four ammonia groups on it still. So here's a redox reaction, and clearly inner sphere that we've trapped, the inner sphere intermediate. It is our product in this case. So one can have a debate about still, I guess, does the electron transfer first, or the bridges form first, but that's the species that you see when you do that. It turns out that a species has an intense red color. This is a white solid, so it doesn't give you much of a solution, color, gives you a great solution. This is a orange solid, light orange solution, and then you get this intense red color. So you kind of pour these two things together, and it's a classic make blood reaction. And that intense red color is due to an intervalent charge transfer that takes an electron off the iron and puts it onto the Platinum. But you can see what we have here is we have a reaction that involves both a charge transfer to make it and the formation of new chemical bonds. That is, the Platinum II likes to be square planar, the Platinum IV likes to be octahedral, and so it's going to borrow the lone pairs on the cyanides to make the octahedral complex that it needs. So we have an inner sphere process here, and we've done a lot of studies to show that, in fact, it is inner sphere, and it's not an outer sphere that then comes together after the fact to look like an inner sphere mechanism. Now, by the way, if you take this complex and you run a cyclic volt-tamogram on this, just to get back to electric chemistry for a minute, in fact, you see a single oxidation, and in that oxidation, there's two electrons. That is, the wave is twice as big as you'd expect 30 millivolts peak-to-peak separation, approximately. Well, actually under 60 millivolts peak-to-peak separation is what I should say to be technically correct, and that indicates that's an oxidation for the two irons, and that this structure in between insulates the two irons from each other, so that one of them does not know that the other one is oxidized, and you would expect that, actually, based on the molecular orbitals that are involved here. So then we have inner sphere, and then the next thing we have to look at is outer sphere, and I think that would be a great place to start tomorrow. So let's call it quits for the day, and I will see you tomorrow afternoon at 2.45.