 OK, well, shall we get started? So again, the important announcement to the day is that there is cake available after the lecture, second floor of noise in the Lewis orange room, middle of the hallway, if you don't know where it is. And it will be graded. Not the cake, your group participation. You know, I don't know, maybe. OK, now, we have lots of things to cover today because I've gotten overly ambitious here all of a sudden. But first of all, I need to correct something. So this is easy. We were talking about AC Voltametry last time. And I got a little bit confused on this graph I showed you out of Bard's book because I couldn't read it. And somebody did, who could add together, point out to me that the middle of a line is just the average between the two ends. So to clarify that, what this says here is that the midpoint here is just the solution resistance plus the charge transfer resistance over 2. That is, you start here with the solution resistance, you end over there with the sum of the solution and the charge transfer. That is, the diameter of this circle, our semicircle, is the charge transfer resistance. And so the middle here is this quantity, quite obviously. This line, due to the Warburg impedance, that is, the mass transfer limit does not hit, as I did say this correctly, in the middle of this semicircle. It's somewhere else. And it can be shown for reversible case, mass, transport limited, et cetera, et cetera, that this point where it intersects the real axis down here, the resistance axis, is the sum of these two resistances that is this point minus a quantity, which is 2 times the sigma squared times the double layer capacitance, where sigma is this sort of standard kinetic parameter, which I've actually cheated a little bit on, but it's close enough. Surface access is divided by the square root of the diffusion coefficients, assuming there's something on the surface. If there's not something on the surface, then this is what's near the surface. So that's where the cheating comes in here. And so that'll be a different point. And you could see in general, not a particularly useful point, because there's too many undefined parameters there. So presumably, if you're interested in the kinetics of the process and the convolution of the kinetics with the diffusion process, you're going to get that information using some other technique that we've discussed. That takes care of my last comment on impedance. So let's get rid of that one, end show, close it out, start with a new show here. So what I did not mention, I would like to go over with you, but I think it's a very nice way of summarizing what we talked about. And it was brought up by this comment that somebody made in class, or before class the other day, about doing electrochemistry on proteins. And you can blame him for that. Just about every electrochemist at some point looks like glucose oxidation via glucose oxidase. It's sort of a requirement if you want to be an electrochemist, you have to do this. And so there's a nice protein study. And so I thought I'd show you what we can do there. And actually, the question, we really weren't trying to make a sensor, although we did. Not a bad one either. But the question we were asking really is how far can you throw an electron? So what does that mean? Well, of course, we're talking about a nickel-ferrous cyanide rivetized electrode. But before we get there, let's look at glucose oxidase, which is this very impressive enzyme here. I stole this picture off of the Cambridge University website. This is a molecular dynamics calculation on glucose oxidase based on the X-ray crystal structure, and then how atoms and molecules are supposed to behave after that. So you can see it wiggling around there. But the key point is it's a dimer. It's got two identical subunits in it. Here's one of the units. It's not wiggling around. And what one finds is there is an active site, which has sort of a hole here. And then deep in that active site is a flavin unit, which is a redox-active species. And what this beast is supposed to do is selectively oxidize glucose to this material over here. And in doing that, it is believed, this is kind of interesting, it's believed that its oxygen is the actual oxidizing agent that supplies the charge. Oh, that's not really known for certain. But the idea is the oxygen would sort of seep into this protein structure. And it would oxidize the flavin unit, which is a quinoidal type of system, at the active site. And then the quinoid would oxidize the glucose. And so you make some hydrogen peroxide in doing that. And then your body has to worry about getting rid of that, if that's the case. But as I said, it's a little unclear if that actually happens. Where we know this happens, though, is if you've ever had to have your glucose levels tested, then essentially this is the reaction that is used. This glucose oxidase, by the way, is a non-mammalien enzymatic system. So this is not something that's happening inside of you. But it is very important, because all of our glucose sensors looking for diseases like diabetes and whatnot are based on using a glucose oxidase and then determining the turnover one way or the other of this reaction. Classically, the turnover has been monitored spectroscopically. And it's just been in the last few years that people have switched over to a redox-based, electrochemical-based system for doing the monitoring. And that's now available and is often used. So you have this material. And the idea is now one of the builders of the primary electrochemical sensor, I should say the builder, the author of the primary electrochemical sensor is Adam Heller at the University of Texas at Austin. And he has pointed out that you could consider all living organisms like you and me as just a bunch of batteries, which is a pretty depressing view of the world. So I'm not going to agree with it. But it is true. There's a tremendous number, of course, redox events that are happening inside of us. And if you were just to mix all the oxidants that together and reductions together in a beaker, everything would short out. Life wouldn't be as much fun as it is. And so you need these proteins to act as insulating areas that allow the right oxidant and the right reduction to come together. So in other words, this Flavin unit will oxidize lots of things. And presumably, the way it is selected for the glucose is by the size of the active site. And that's what it allows in. Based on that kind of thinking, it has long been stated that you're not, in general, able to oxidize a unit like this at an electrode. Because after all, the Flavin unit, which is the redox active part, which is surrounded by all this insulator, is not going to be able to come in contact with the electrode. So it's buried way down in this hole down here. And you're not going to be able to get to it. And so you shouldn't be able to do electrochemistry directly at an electrode with any redox enzyme. It has also been suggested that, therefore, what you need is a soluble mediator. That is, you need to throw something into solution that could be, say, oxidized at the electrode. And then it could swim over to this enzyme. And it has to be a small molecule. And it can get into the active site and get down to the Flavin unit in this case, or whatever the redox active component is. Oxidize that, swim out. And that's how you can turn over an enzyme at an electrode. One variation on this is that you might tether that redox unit to an electrode. So you might have it stuck on some long, alkyl chain. But the idea has been, it's got to be flexible. And the chain has to be long enough still that this guy can get down into the active site. And that's the basis for most of what's done. Adam Heller had a slight different approach. And that is, he partially denatured the enzyme and put a pathway of ruthenium hexamines, as one example, throughout the material going from the outer surface down into the active site, sort of a redox wire, if you will. And then discovered that you could take this wired enzyme and you could directly oxidize it, reduce it at an electrode surface. But again, you put the mediator in there. It's a small molecule mediator. He's isolated it and put several in. But that's the general idea. It's still following the general principle. And the other thing I wish to point out before I leave this transparency is in this sort of doorway, if you will, around the active site, there's a series of amino acids that have a net negative charge to them. That's going to become important later on. OK. So this idea is, instead of using oxygen to turn over the glucose oxidase, we'll use a redox mediator. And in doing that, we will simply collect the charge instead of looking for hydrogen peroxide as a product or something like that or disappearance of a mediator, spectroscopically. And by counting the charge, we can figure out how many times we turned over this glucose oxidase and hence how much glucose is around. And various solution mediators have been used, ferrocines, quinones. You can understand why these sorts of things would work, especially with a flavin unit. With enema means, I just mentioned, the hexamine system. Ferricinite has been reported. But I put a question mark there because I can't believe it would work because, based on our studies, it's got the wrong redox potential. But it is reported to work in solutions. So I'll just leave that standing, even though I think it's got a positive delta G for the reaction. And the one actually we're going to focus on is the hexocyanorhexanate system right here. There's other ways you can do this, it turns out, besides a soluble mediator. For example, if you take an electrode and just chemizorb onto it, 4, 4 prime bipyridine, then it acts, apparently, as an inner sphere sort of bridging ligand between the electrode and the active site in the glucose oxidase. And you get charged transfer and electrode that has this on the surface, even though this has never oxidized or reduced in the process. So it just gives you a pathway, somehow sticking off the electrode and into the active site. And how that works is really unclear. There may also be an effect due to some denaturization of the protein or something like that. But this works. It's never been totally understood why that works. And as I already mentioned, you can also play with the enzyme itself, denature it, wire it up with redox sites, and get it to work that way. And of course, this is in some ways similar, a little more sophisticated, but similar to the experiments that Harry Gray has done in terms of mounting, in this case, a photoredox active species on the outside of a cytochrome C type of moiety, and using that to inject charge into the active site to look at charged transfer processes. It's more sophisticated in that Adam had to come up with a series of mediators inside the enzyme that would take the electron from the outside to the inside active site. Yes? No, not necessarily. I'm saying that it would appear based on this result that there is an inner sphere pathway. And I'm just assuming that based on this result. But I'm not saying you can't do outer sphere. Well, I am simply arguing. The standard argument is an enzyme looks like this, if you will, with an active redox site right here. And then if you want to do this directly at an electrode, here's your electrode, right? You have no way, you have too large a distance here to do tunneling to the redox site. Well, the assumption here is, and it actually turns out to be true for glucose oxidase, is that this is the closest approach to the Flavin unit. That is, there's no sneaky little point back here that where D prime, where you actually could get closer together. There's a second very important point here. And even if that exists, clearly there's only one. If you think of this enzyme sort of in a spherical sense, there's really one part of the sphere that's going to allow the charge transfer pathway, whether it's this one or this one. And so you have all these collisions with the electrode going on. And so even if you can get close enough, very few of them will be productive charge transfer collisions because it's going to hit all different sorts of ways. So you would predict, even if that was the case, that you would have a very sluggish process with a very small rate constant for charge transfer and that it would be very hard to see a current from this system. So it could be right that it's not just that it's got to go through the active site, but simply you have a distance here, whether it's D or D prime, that you cannot handle in terms of tunneling. These are general statements. Yeah. Right. There could, in theory, be, but remember, remember that, well, I guess I shouldn't play God here, but the theory is that these redox sites, whether they're flavins or whether they're porphyrin-based systems or whether there's just a non-porphyrin iron in there, those are basically the redox sites, but those redox sites are wrapped in this protein to get selectivity. So in other words, proteins don't want tunneling to happen. They would prefer either some kind of a site-selective interaction based on sterics or an inner sphere process, which would only allow the right molecule to hook up with the redox site. There's got to be some selectively built in there, whether it's steric or an inner sphere mechanism. Some say. Yeah. So you've really, right, the assumption is the design is such that it's not going to work out in an electrode for these reasons, because to work out an electrode means you've lost your selectivity. OK. So as I said, as a requirement, you have to look at an enzyme if you want to be an electrochemist, and we had these nickel-ferrous cyanide rivatized electrodes, and so we thought we would utilize them. Now, based on what I've just told you, our working assumption was that we would never publish a paper on this, because this should fail miserably. And why is that? Well, we're putting this microcrystalline layer of nickel-ferrous cyanide on here, say. And although it's microcrystalline, the crystallite sizes still are on the order of, say, one micron. And while small, that is huge compared to the size of this enzyme. So if you have the requirement that the redox mediator get into the active site here, it's just not going to happen. You're throwing boulders at this thing. And so we assumed it would not work. And we were not surprised to discover that nickel-ferrous cyanide, in fact, does not oxidize cytochrome C when you put on the surface. We did discover that if you had on an electrode that had both nickel-ferrous cyanide on it and ruthenium hexacyano ferrate on it. So there's the nickel, the ferrous cyanide wave. There's the ruthenium cyanide wave. That effect, that was a mediator for the system. And of course, the argument still holds that you've got a solid surface here. How could the enzyme get close enough, active site, get close enough to it to make this work out? Now before I get to that, let me point out something that's a little bit unusual here. You see the cyclic voltamogram? Everything looks really beautiful, the iron and the ruthenium there. The way this electrode, excuse me, was made is firstly put down a layer of nickel-ferrous cyanide on the surface by anodizing the electrode in the presence of ferrous cyanide. And then we further anodized it in the presence now of hexacyano-ruthanate, removing the ferrous cyanide from the solution that hadn't reacted. Now given that piece of information, does this cyclic voltamogram labeled A here bother anybody? Well, you can't tell if it's reversible or not. I'll tell you it is reversible. Some scan right did over here, for example. But there's a different problem now. I've got an inner layer. Stepwise, what I did was I took a nickel electrode. And stepwise, I reacted that with ferrous cyanide, which unchecked it to see that I put a layer of a nickel-ferrous cyanide down. So I know I did that. And then I reacted it with ruthenium cyanide, which, after that, so I'm assuming that I now have a layer in here of ruthenium with six cyanides on it. There's a nickel out here, of course, from the electrode. Oh, yeah, there was enough to, yeah. We know how to corrode nickel electrodes well. We can always get them to make this layer in this model. Well, we'd have to integrate that. But it's approximately 100 angstroms thick. So that's OK. It could be that there are nickels in this ferrous cyanide layer, so maybe just grabbing those or something. Now, someone says something about it surprising that you see the ruthenium wave, I think. Who said that? You said that. Why did you say that? It's pretty far away from the electrode. OK, far enough. Well, OK. It's far away from the electrode. That's one surprise. But in fact, far enough away, if this in fact is 100 angstroms, since most of us don't believe electrons can tunnel over 100 angstroms in reasonable times, too far away. So I would argue what would have to happen when we have to do it by mediation. That is, we'll oxidize the irons on the surface first in this ferrous cyanide layer, and then they could oxidize the ruthenium. Does that sound good? Thank you. The potentials are absolutely wrong for that. That's right. The iron-3 is not oxidizing enough to oxidize ruthenium. That's a delta G there. Positive delta G, you'll notice, of about half a volt almost, which will never happen if you believe that delta G means anything. So the irons are not strong enough oxidizing agents based on the cyclic voltamogram to do this. So even though we laid this layer down sequentially, this can't be the right picture. We could never get that cyclic voltamogram from this picture. We should have just seen the nickel-ferrous cyanide if this was the right picture and not seen the ruthenium on there. So in fact, probably what happens is when the ruthenium goes in, it does steal nickels, ions out of this lattice, out of this ferrous cyanide lattice. And in doing that, of course, the ferrous cyanide to some extent falls apart. And so we have regions now where we have ruthenium kind of getting down to the surface. And of course, by integrating the area under these cyclic voltamograms, we can determine exactly how much we have, because we have a little more ruthenium there just by eye than we have ferrous cyanide. And I wish to point out exactly one student on the exam cut and weighed the cyclic voltamogram to figure out what the area was. So I gave extra credit for that. OK. Now, you then go and you throw some glucose into this solution, which is buffered and things like that. And you get B. And you notice B looks identical to A. And that's because you can't oxidize glucose at a nickel ferrous cyanide or a ruthenium cyanide electrode or at a nickel electrode, for that matter, at room temperature. And then you throw in some of the enzyme. And you notice that it's quite obvious, obvious catalytic effect here, both an increase here indicating we're oxidizing something beyond the ruthenium that's there and a decrease in the return week telling us that we're changing the oxidation state of the ruthenium. So we're mediating through the ruthenium. The irons hasn't changed at all, you'll notice. So it's just going along for the ride. In fact, it has two purposes here. Number one is stopping the corrosion of the nickel electrode. And number two, it's an internal standard. I know exactly how much is there, right? But so there's your mediated charge transfer going on. Very easy to see in this case. Don't even need a scan rate dependence. But of course, you can't show up in my office without a scan rate dependence. So there is the scan rate dependence. And you will notice that the iron weighs over here. Now, first of all, this is not an ideal electrode. This is not the same electrode as this one. You'll notice there's a little peak-to-peak separation going on there, but it's still surface confined. And if you make a plot of the peak current here versus a scan rate, you'll find it's linear still. So everything's fine. We know that's on the surface. And on the ruthenium side here, you'll notice that the dependence is very different because it's actually now a soluble component that's being oxidized, the glucose. And you'll notice the return wave, for example, take this one. We got a big outgoing wave, but a small return wave because we more or less have consumed all the ruthenium that was in the oxidized state when we do that. So the catalysis is going on. And we can make the standard types of plots that Nicholson and Shane type plots. And everything works fine. Savian plots, actually, yes. What do you need the ferrous cyanide at all? If we make a nickel electrode without the ferrous cyanide there, it's not stable towards corrosion. So it's an anti-corrosion coating that's in there. And it's very convenient that it's an internal standard. That just is extra. And what we've done here is this is just a standard plot of the peak current versus a scan rate. You can see it's not linear because it's in solution. And then we said, well, what we're really interested in is the amount of glucose being oxidized. And so we'll subtract the peak current from, say, this one right here from that peak current in the solution. And that's what this shows right here. And as we can scan fast here, you notice we can beat out the kinetics at that point. And we don't see any turnover of the glucose oxidase and the glucose if we scan too fast. And you can play sort of standard games. Now looking at that difference in peak current and the cyclotamogram with coverage, and you find out at low coverages of the ruthenium there's a linear response, and then it saturates. Putting more on doesn't change anything. And likewise, you see a fairly linear response with the amount of glucose oxidase that you have out in solution. And it turns out that if you keep your glucose oxidase concentration below about 20 micromolar, then you follow nice, macalus meton kinetics for those of you who like biochemistry. So we did that just so we don't have to get the complications of having the kinetics of the enzyme mess things up. OK, so now we have this problem. This electrode works, and it shouldn't, right? Because it certainly is not accessing the active site, getting close enough to the Flavin unit in there to do charge transfer chemistry. And so we're very confused because this thing is working, and it's not supposed to be working. It turned out to make it work for some reason, we knew we had to throw in a few extra nickel ions, which was a little weird. We were, it was totally an accidental discovery. We were trying to figure out how to make these layers really nice, and we threw some extra nickel ions in. And we discovered we only see this catalysis in the presence of an excess of nickel ions. So that was a little confusing, so it works. It needs nickel ions around. And we're very confused by all of this. Yes, in preparing it. No, in preparing it. Yeah, you could prepare it. Yeah, so we started fooling around. We said, well, nickel ions, is there something special about nickel ions, or is it just cations in general that are important to have around? And so we made the film without any excess nickel ions around. And then in our electrochemical cell, where we have our glucose, our glucose oxidase, and whatnot, we have a supporting electrolyte, of course. We have a pH buffer also. We started throwing in different supporting electrolytes. So we started off with our standard one down here. This is sodium ions. And see, that's peak current difference there, and that's concentration of the ions we're adding. And that's zero. So if you don't have excess nickel ions around, and you just use sodium nitrate, which is what we normally use for this reaction, it is not a sensor. But as we switch over then to 2 plus cations, we find that there's nothing special about nickel. Any 2 plus cations will do good. So we look at calcium ions. Those are the black circles right there. They're quite nice. Magnesium ions are the pluses. They're similarly very nice. And then you can go to even more bizarre things like this cobalt pentamine chloro complex, 2 plus, only because it's 2 plus. And you notice all these, there are little differences here, but they all fall on the same plot more or less. They're not all that different. So 2 plus cations are good to have around. And 1 plus cations don't do a lot for you. And then we said, well, 2 plus is good. Maybe 3 plus or 4 plus is better. And so we started looking at all these complexes with very high charges on there. And I'll just point the highest charge we have here is a platinum hexamine 4 plus species that's down here. And it's our best one. It has some solubility issues. We couldn't go as high in concentration. But that's the best one. Although this cobalt hexamine 3 plus species is very similar. But the platinum beats it by a little bit. So the more charged the better. And then we did things like say, well, is it really, again, is it the charge? Let's look at a series of cobalt ions here, the hexamine, the hexamine chloro, and cyano, which will give us a negative charge on it. And see if it's cobalt maybe for some reason, or is it actually the charge. And again, if you have a negatively charged species around, there's no catalysis. And then the more charged the merrier. Here's what that's showing, the higher the charge, everything else being the same, the better off you are. So cationic charge is important in this system. So what we're thinking is, OK, so this enzyme comes up and it hits this electrode. And even if there is some magic spot where the Flavin unit gets close enough that we can actually push the electron in there, just tunnel it in, that on average, we're not going to hit at that spot. We're going to hit randomly. However, we know that this surface is net anionic. All the cyanide ligands on the surface. And we know that there is a ring of negative charge around the opening of the active site of glucose oxidase. So the hypothesis is then, and we can't actually prove it, so it's going to say hypothesis, but it seems to work really well, is that you have these cations that are gluing together, if you will, the negative charge around the active site and the negative charge on the electrode. So in other words, we get an orientation effect. If it hits the right way, everything lines up and it sticks. It turns out for this particular enzyme, this is not specific to enzymes, but for this particular enzyme, the only negative patch on the surface of the enzyme is around the active site. So this seems to work really well. So we're automatically orienting the enzyme with respect to the surface. If we had done this a few years later, we would have started talking about self-assembly, I suppose, or something like that, but it was too early for that. No. Yeah, no, there's a lot you could do here to prove that this is right. But this was sort of an aside, in a sense, a neat aside. But we still have the problem that even if you orient this thing correctly, you are too far away from the surface to do the oxidation on a reasonable time scale, according to what we thought we understood. So we said, ah, maybe. Maybe, in fact, we're being fooled. And what's happening here is that our electrode surface layer is dissolving and spitting out some ruthenium cyanides that are swimming in here and doing this. And if it happens slow enough, we won't notice it. And so the first thing we did is we did the brute force approach, which was we made up 50 of these electrodes. We made up an electrochemical cell with a volume of 1 milliliter. And we ran each electrode, cyclic voltammetry, we cycled it for 30 minutes, for 50 electrodes, in the same volume of solution. And then we went out and we looked for ruthenium in the solution by atomic absorption. And we found about 0.1 parts per million of ruthenium in there after all of this and said, this is not enough to do that. And this is after running this thing with 50 electrodes in it. How could we ever see it with 1? So that didn't sound too good. And then we did another experiment where we took a ring disc electrode and we derivatized the disc with this material, nickel disc. And then we have the ring set up potential where it will detect the ruthenium cyanide if it comes off the disc. And we're rotating it and simply ask, can we detect any ruthenium cyanide this way? And the answer is no, again. So we're now convinced that if there is some ruthenium coming off, it's not enough to do this catalysis at the rate that we are observing it. So we still have the problem of, how do I get an electron from here to here? Because everybody says, oh, an electron travels, maybe 10 angstroms, something like that. Then we said, OK, well, here's another possibility. People have talked about the fact that there's something funny maybe happening with the double layer. That is, the glucose oxidase will come up and it'll chemisorb on the electrode. It'll change the capacitance of the electrode, shift potentials around, and facilitate the oxidation of the glucose in this manner. This is sort of a hand-waving argument, but you could imagine, I guess, under just the right circumstances, something like that happening. And so we said, well, we better check and see if, in fact, something like that is happening and we're changing our double layer capacitance as we carry out this experiment. And so to do that, we used AC impedance. So we know already what the AC impedance looks like at the nickel-ferri-sinide-drivetized nickel electrode. And we get some data that looks like this over here. It's the diamonds. And the first reason I show this to you is that's not atypical of what real-life AC impedance data looks like. That is, the stuff I showed you on Tuesday was a little too good. So it wasn't perfect either. But the idea is, you expect there to be a semicircle, so you fit it to the best semicircle you have. So that's the semicircle fit to this data. And you do it under circumstances where you just have the drivetized electrode in buffer, and you have buffer plus glucose in there with the drivetized electrode, and you have buffer plus glucose oxidase plus glucose in there. And you do all of those. And you find it doesn't matter that much, which you do. Now you have to analyze this data to get out a double layer capacitance. Now we did not want to have to develop a full-fledged model electrical equivalent circuit for that interface, because all we were interested in was in the double layer capacitance. And so we took a shortcut here. We said there's going to be a solution resistance, R1. That's OK. There's going to be a charge transfer resistance, R2. We said there might be a Warburg effect, but we're not interested in that. In fact, there obviously is a Warburg out here. We're only interested in the double layer capacitance, so that's going to be at high frequency. So we can ignore the existence of a Warburg component in this. There could be several other resistances and capacitances besides the double layer capacitance. We're just going to put up with that. We're going to assume there's a capacitance up here. Now if it turns out it's coupled to other capacitances, that's going to be fine. Because, well, the question you want to ask is, is the double layer capacitance constant? And if it's one capacitor and a set of capacitors, if the data shows they're all constant, then we know that one is. So we have this constant phase element right here. This is a non-physical thing you put into a circuit. It's just an element that follows this equation right here. We're looking at a 90 degree that i is the imaginary i. We're looking at an output that's 90 degrees with respect to the incoming signal. And we're fitting it to this general equation. And what we're interested in is in this y0 value right there, which would be equal to the double layer capacitance plus any other capacitances that were in parallel with that double layer capacitance. And so if that's not changing, the double layer capacitance can't be changing. So we fit it to this simple circuit since that's all we're after. And we have a good fitting program to do this. It's not linearly squares. So that's the semicircle that you get out of that fit, by the way. And you see that independent of whether you have buffer around or enzyme or things like that, that as you, and we're doing this as a function of the cobalt hexa cyanide constant, hexa-amine, excuse me, concentration, which of course makes the things work better. That while there is some change in capacitance over with concentration, it's modest. We go from 140 microfarads per square centimeter to 180 microfarads per square centimeter. That's not enough to dramatically change the charge transfer kinetics again. It's a very modest change in the capacitance. So we rule out playing with the double layer as where this comes from. We stop along the way when we have this puzzle and say, well, we don't know how it works, but it sure makes a great sensor. So we have the cobalt hexa-amine in there because we decided that was the best cation to use for the highest sensitivity. We're just doing cyclical tamagrans. We have the glucose oxidase 10 micromolar in the solution, and we plot the difference between the modified electrode peak current in the absence of the glucose and in the presence of the glucose. And you see we get a plot like this as we increase the glucose. And we're actually going over a regime here, millimolar, from 0 millimolar to 20 millimolar. That goes way over the physiological regime unless you're seriously ill. And you can see that we have two regions. We have a low glucose concentration region and a higher region that we can both linearize if we want. So we have a nice sensor system. As long as you tell me which region you want to look in. This, it turns out, this one down here, if your glucose levels are that low, then you're not breathing too much or something. You need more glucose than you're in diabetic shock if you're down there. So it actually turns out this slope up here is the important one. Tells you kind of your blood sugar levels. So now, though, we still have to solve the problem. We have a sensor. We understand that we're getting this orientation, but how do we throw the electron far enough to get in the active site? It turns out it's not as much of a puzzle as we thought it was. Marcus and Hush have the answer already. So here's this equation, rate of charge transfer, there's some constants in there, what not, that has the standard Marcus type free energy and reorganization energy in it. But we've also added in the distance dependence that Marcus Hush there gives us. There's this beta term, which is a Caltech favorite discussion point somewhere around 1 inverse angstroms for proteins that the point we did this, people said the right number was 0.96. Some people like 1.1, it doesn't matter. It's going to work. And this distance is the nearest approach distance. That is, it's the distance from, in this case, the electrode to the edge of the flavin. And there's this offset of 3 in there that's supposed to get you to the center of the flavin, which is fanciful, but we didn't come up with this. It's in the literature. And again, it's close enough. And you find out that if delta G is somewhere around 0, that is, you're doing something close to a self-exchange, then this term kills you pretty quickly. And you cannot get to reasonable rate constants. However, delta G is not 0 in our system. We have the redox potential of the flavin here. And of course, we have the redox potential of the ruthenium on the surface. And so we simply do a plot here with different delta G's saying and different distances over here exactly what rate constant will we get for these. And so if you have a rate constant that is 10 per second, just using simple first-order rate constants right there, then you'll notice if the delta G is high enough, like negative 1 and 1 half electron volts, that's pretty impressive, you could throw an electron 30 angstroms plus. And as you go to smaller delta G's, you don't throw them as far. But when you have a rate constant that's only between 100 per second and 1,000 per second, that's going to give you a nice hefty current at the electrode. So if you take these two middle curves right here, you'll notice that if you generate something like a volt of free energy in that system, then you can easily throw an electron about 20, 25 angstroms. And that turns out to be plenty of distance to get it to the flavin. Because that flavin's only about 10 to 15 angstroms inside the protein. So nearest approach is probably between 15 and 20 angstroms. So you can throw an electron, 10 angstroms isn't bound at all unless you're looking at something that's a fairly iso energetic process. If you want to jack up your delta G on the order of a volt, which is what we're doing here, throwing an electron somewhere between 20 and 30 angstroms is not an issue. According to Marcus Hush, so you wouldn't have to do anything to modify it. And so you don't need a soluble mediator. You just need a big enough delta G to get in there. And presumably, you don't need an inner sphere reaction, but that doesn't mean you can't have an inner sphere reaction. Well, there is a question of exactly what do you use for this beta. And if beta gets too big, then that could be an issue. Probably the only way to do that would be to be in a vacuum or something. But there does seem to be this orientational effect. Now, it does turn out that the enzyme is closest to the enzyme surface at this opening to the active site. If you go around this side, it's about 20 angstroms of protein before you get close to the surface here. Oxygen is believed to go through this site, but that's because it turns out there's a little diffusion here, and it's actually getting in. But that is the point of closest approach, about 12 angstroms. 1% of the surface in a solution rate. Yeah, there is a big issue about how many of these enzymes you have sitting on the electrode per unit time, which has to do both with their size and how tightly, if you will, they're anchored here. You don't want them to stay there too long. So you wouldn't want some kind of a connection here which is too strong, which I think one of the advantages of a simple secondary cation effect is a very weak interaction. So it seems to orient things, but not keep them stuck there. So we have no information on that, because you need to know the dynamics of sticking in order to do that calculation. And if you say it only can react to the active site thing you say, it just makes it so that only some of the collisions are fruitful. So if the active site is, say, 1% of the surface area, you can say 1% of the collision would be. Yeah, whether the collision has to be correct or if there's an orienting effect here, and that once it's on the surface, it can wiggle around a little bit, and then it locks in when it charges, that's possible. We have no direct surface analysis on this system, which it's very hard to get because it's a dynamic system. On the SCM level, they're on the SCM level. That is, when you take an SCM, you see little crystallites with dimensions of the order of a few microns. So the SCM wouldn't let you see nanometer-sized protrusions, but it's not clear that you have those. I mean, it's possible. There's no behavior with respect to other redox systems and mediation that would suggest you have these hairs of nickel-fray cyanide whatever off the surface. We don't see any behavior that would suggest that. So we think it's just micron-sized things, that you don't have this red thing going in there. But it's speculative. There's no direct evidence on this. Other than that, the kinetics work really well. So this is exactly the same question that one asks when one does a pH titration with an indicator, and how close does the indicator PK have to be to the pH system that you're interested in, plus or minus one unit is the standard answer. So in this case, translating that to electrochemistry, you need to be about plus or minus 60 millivolts to get a reasonable equilibrium constant going there. So you can push it a little bit. You cannot mediate a little bit. You can have something on the surface that's got a given redox potential, something out in solution that's slightly more positive and make that work. But if it's out of that kind of 60 millivolt range, kind of broadly speaking, your rates fall off too fast. Well, so yeah, lots of people load lots of different numbers. That is, you can, of course, take the Flavin unit out and measure its redox potential in solution. However, most people would agree that's probably not the redox potential in that nice protein that's there to exclude water and all these things. And if you believe that that landed term has anything to do with anything, that's not a worthwhile discussion. The way people get at this number is by doing the titrations along the lines of what you were just suggesting. Put in various mediators and see which ones work at what concentrations and whatnot and kind of bracket your redox potential that way. And you can get a number that way, but it's a low resolution experiment. If you believe those numbers, then it's around the numbers I saw in the literature around, I believe, 0.35, 0.45 volts versus SCE somewhere in that area, which is why I can't understand why there's a report in the literature that says fairy cyanide in solution will work. Because that's only about 0.2, 0.3 volts versus SCE. It shouldn't be oxidizing enough. So it could be that the number for the flavin unit in the protein is off. It could be that there was something else happening. One of the pitfalls that you have to watch out for in this sort of chemistry is it's often very easy for the redox site to fall out of the enzyme. And this causes some interesting effects. So there was a group of people that initially said, you can go and you can turn over this glucose oxidase by using a gold electrode. You just have to pick the right electrode material. And they showed some nice little tamagrams. They showed the glucose oxidase being oxidized and that going off and oxidizing glucose, and everything was fine. And then another group came and looked at that. And they were more biochemically adept, the second group. And they couldn't make the gold electrode work. It was just dead out of gold electrode. Now, you'd like to say, ah, the first group must have the gold in touch, and the second group doesn't. But in fact, it turned out it's the other way around. The first group was not really biochemically capable. And so some of their enzyme was falling apart. And when it fell apart, the flavents came out and there was your soluble mediator. And the second group came along and they made sure their enzymes were pristine and intact and no soluble component. And they couldn't make it work. So any time you're doing the electrochemistry or the redox titration, you have the possibility of some of the flavin coming out. And you make, and then there's redox potential changes and you see things that not. So there certainly has to be some skepticism in the reported redox potentials. So that's what we stand on. That's what I have to say about protein. It's a very interesting field. There's a lot going on right now. But you really need to be very careful about the biochemistry. And presumably, you should do things like we just suggested. If you want to make these outlandish comments like I've made about changing the enzyme in terms of the types of manipulations one can do now and showing that everything works correctly. Yeah, we got numbers. We did the whole Michaelis-Metton kinetics thing and we have all the rate constants for everything and I don't know them off the top of my head, but you can look them up. There's an analytical chemistry paper. Yeah, so it all, all the rate constants fit together. Of course, there's several of them so that always helps make things fit together. It looked really nice on paper anyway. The story hangs together. Whether it's true or not, I don't know, but it does hang together. OK, so let's now totally change topics just for a really quick excursion into semiconductor electrochemistry. Just so I can feel self-fulfilled here. We have to wait for the glucose oxidase to be saved. OK, here we go. Now, the one thing I want to look at, a very specific thing, is just oxidation of water since you guys don't know how to do it. And neither do I, I'll say. Well, at least not with sunlight. And so we're going to use a semiconductor and we're going to attempt to split water. Here's a question. How many of you have no idea what band bending is? OK, let me give you a couple. So the two of you, the rest of you, sit back for a 10-second excursion into band bending. That's all it takes. I will use the Nate Lewis hyper-special approach to explaining band bending. All right, there is a problem, by the way, when people that are trained as pure electrochemists try and use semiconductors. They miss this subtle point. So here's a semiconductor. And here's a surface. And out here is an electrolyte. And on this scheme, we have energy. And it's going in that direction. A semiconductor consists of a band structure. And so we have a low-energy band, which is called the valence band, and a high-energy band, which is called the conduction band. There could be a whole bunch of these, but let's assume there's just one valence band and one conduction band. And we have a region and energy in between those two where we have no allowed states called the band gap. And this is what gives your semiconductor its typical color. So silicon is black because it's got a band gap of 1.1 electron volts, which corresponds to absorption of 1,100 nanometers. That's in the near IR. It's black. It absorbs all the light greater in energy than the band gap energy. Essentially, these bands, in other words, are very thick. There's lots of states in them. OK, now you know everything you need to know about semiconductor physics. Wasn't that easy? Except for one minor little thing. And that is semiconductors are characterized by something called the Fermi level. And the Fermi level is just the free energy of the semiconductor. And it follows an equation just like the redox potential, minus nf e is equal to delta g. It's just the free energy. Typically, in a semiconductor, this bottom set of states would be totally filled. The top ones would be empty, filled with electrons. That is the electrons up here in your so-called intrinsic semiconductor. Your idealized semiconductor interface. And so the average energy of the electrons will be halfway in between the filled and empty states, right in the middle of the band gap. We can dope semiconductors. In fact, not only can we dope them, but they tend to dope themselves if you're not very careful. If you add in a material to this lattice, that's going to withdraw some electrons from the lattice. That is more electronegative to the lattice. You move the Fermi level down. So we're adding something that's electron withdrawing. That is more electronegative than the lattice. On the other hand, if we add something that is less electronegative than the lattice, we will donate electrons from that dopant to the lattice and things move up. When we add materials that are giving electrons to the lattice, that would be a n-tightened dopant. When we are sucking electrons, if you will, out of the lattice, it's a p-type dopant. If I got it right so far? I'm good? I'm good. OK. So I have time in the next few minutes to consider just one case. So I will consider the case of an n-type dopant. So now we have our semiconductor. We have our band edges. And we have our Fermi level. That's up here somewhere near the conduction band edge because we have picked an n-type semiconductor. It's in an electrolyte. That electrolyte has a redox potential. Probably not the same as the Fermi level, so let me just put it right there arbitrarily somewhere else. OK. What's going to happen? Just in the dark, there's the free energy of this material. There's the free energy of this solution. They're different. We want to go to delta G equals 0. And so things are going to change. How are they going to change? Well, what's supposed to happen is this guy's supposed to move down, right? And this guy's supposed to move up, and they meet somewhere in the middle. How do they move? Well, if I have an n-type material, I put electrons into it. Where did I put those electrons? These states were filled. So I'm going to end up with some electrons up near the edge of the conduction band and doing that doping. So if I take some of those electrons and move them out to solution, that will solve the problem for me. That will lower this Fermi level and raise the redox potential according to the Nernst equation. So far so good. According to Professor Lewis, when you do this, the redox potential doesn't really move at all because there's a lot of molecules out in solution. And this is a semiconductor with a limited number of charges in it. So this is like taking a bucket, going down to the ocean. You've heard this one, right? But they haven't. Stole this right from Nate. Filling the bucket up with water, and you'll notice that the water level in the bucket has changed dramatically. And in fact, you changed the ocean level also, but not enough that you can detect it. So this is the ocean out here. And yes, this has moved up an imperceptible amount. And we have the Fermi level of the semiconductor moving down, therefore, to meet the redox potential. So at equilibrium, these two levels come together, and they come together at the standard redox potential. Or I should say, I shouldn't use a standard there. At the redox potential, whatever you set it at in solution. Now in doing that, what's happened? I have moved charge across the interface. So I have negative charge on this side of the interface, and obviously positive charge remaining on this side of the interface now since everything was neutral to start with. Now take a negative test charge like an electron and drop it on this interface. Which way does it go? It's going to be repelled by these charges and attracted to these charges, and so it will be accelerated through the interface like that. In other words, there's an electric field at this interface. And this particular field pushes things this way. If the charges had gone in the opposite direction, I'd have the opposite electric field and negative charges would be shot out. So we need a way of symbolizing that electric field at the interface. It's going to be cumbersome to draw pictures like this. And the way we're going to do it is by band bending. That is, we are going to say that the edges of the conduction band and valence band are fixed at the semiconductor electrolyte interface. They have to be fixed. This is an arbitrary for one very good reason. The interface is a line, a geometric line. And so this is one point on the line. It has a potential, which is both determined by the semiconductor and by the electrolyte. But it's one point, so there can only be one potential associated with it. Same thing down here. It becomes pinned, if you will, not Fermi level pinned. It just pinned by the fact that you have two different conditions that generate the constraint on the potential at that point. Since that point can only have one potential associated with it. Now, way back in the bulk of the semiconductor, since the semiconductor is a lousy conductor, the electrons way back in the bulk have got no idea what's happening on the surface. There's all this excitement going on the surface, and they're just clueless, bad communication. OK, so they don't know anything that's happened. So if at the beginning of my story, I have that energy, the difference in energy between the Fermi level and the conduction band edge, then way back here in the bulk, later on in my story, I have to maintain that energy difference. So my conduction band edge better be down there, the same place as it is up here, if I'm in a frame of reference, which is inside the semiconductor. Now, the semiconductor does not change color when I dip it into the electrolyte and it comes into equilibrium, so the band gap has to stay the same. So I take this band gap spacing and I move it over here somewhere, and that hasn't changed. That can't change anywhere. But at the surface, I have set these potentials and I have imposed an electric field at the surface, which is going to change the energy of the surface. So I connect everything together so that the band gap stays constant everywhere. And I have this band bending. And all that band bending is saying is that, again, if I take a test charge and I drop it down here and electron, it'll roll down the band if it's an electron. On the other hand, if it's a hole, it'll move up the band. So it's just a way of symbolizing the electric field that is at the interface. It is identical. That is exactly right. So the formation of the double layer on this side and the formation of the space charge layer on this side is one and the same. There's no mathematical difference between them, really, other than the charge carriers. This is the space charge layer. This is the double layer. And if we want to describe the capacitance of that interface, in terms of an equivalent circuit, we take two capacitors. The same two parallel plate capacitors. OK. If I now irradiate the surface with energy of equal to or greater than the band gap transition, I'll promote an electron from down here to up here, leaving a hole down here. And of course, an electron up here. If there's no band bending when that happens, then I just get rapid recombination. But if there is band bending, the electron feels the effect of the field. And it moves into the bulk of the semiconductor. And the hole also feels the effect of the field light as long as I do this near the surface where the band bending is. And it moves up to the surface. And when it gets to the surface, it can oxidize something. So an n-type semiconductor is a photo anode. It oxidizes things in the light. That's what this first little picture shows over here. Here's your whole electrochemical cell. This is your semiconductor. Here's your counter electrode. There's your redox potential in the dark. All three Fermi levels or redox potential and Fermi levels come into equilibrium. We get the band bending I just described. I now photo-lize that interface with the photons of this energy or greater. I set it up so that they're absorbed in this band bending region. I promote electrons up here. And as I do that, the band bending decreases. Because I have a couple ways of looking at it. If I want to look, there's a double layer effect. I have shifted around the capacitance. I'm charging up the capacitor, right? If I want to look at this just in terms of electrons moving around, as I move electrons up here, the Fermi level has to move up in energy. And eventually, I'll get to the point where the Fermi level started off in the non-equilibrium state, so-called flat band potential. Well, there's no band bending. At that point, I can't separate charge anymore. It just recombines. And so I don't go beyond the flat band potential. So that's the most I can do. When I do that, the hole that's generated here can come out at the surface and oxidize whatever I have in solution. The electron, which is generated in the conduction band, goes through the external circuit to the counter electrode. And we carry out a dark reduction over there. So if we're taking water, and this is an anti-semiconductor, we'll generate oxygen here and hydrogen over there on a good day. Because I happen to meet a ex-member of the Lewis group this week, who was doing organic semiconductors. And I said, where's the photo-action spectrum? And the answer was, we don't have one yet. You have to have a photo-action spectrum, right? That is, if you want to know what the energetics of this interface is that we're looking at, you can tell me this band gap. And you can tell me where these edges are. And you more or less, in the redox potential, you more or less have set everything once you do that. So the first question is, what's the band gap? Well, there are actually potentially a lot of transitions in a semiconductor. So the only transition I'm interested is the one that does this chemistry I just described. So I can, for example, collect photocurrent, which is what I was showing you here as a function of wavelength. This is for gallium phosphide. I'll see an onset of photocurrent when I hit the band edge. It should go up, and it should not come down. This says, do another absorption out in solution in this particular cell that I'm using. So this should just go up. Once I hit the band edge, I have lots of charge carriers and a real depth of orbitals. And so it's not going to come back down. Just going to go out. And from that, from this onset, I can determine things like this is a band gap, a 2.24 electron volts for the gallium phosphide interface. Another experiment I can do is take advantage of the fact that this is a double layer capacitor type of fact. And I can measure the capacitance of this interface. And I can do that as a function of potential and hence the amount of band bending. When the bands go flat, then the capacitance shoots off to infinity, right? Putting it the other way around, 1 over the capacitance goes to 0. And it turns out when you run through the mathematics, it's actually 1 over the capacitance squared. That is the quantity one needs to look at in an equation that Matt and Shockey came up with. You can look that up. And so I make a plot of electrode potential versus 1 over c squared. How do I get this capacitance? Usually by an AC impedance experiment. This all this data was done at 1 kilo hertz long, long time ago. This is on a TIO2 electrode. And then I get data where the points are and I extrapolate to infinite capacitance. And that's the flat band potential. That is, that would be the energy of the Fermi level under this condition where the bands are not bent. That energy is close to the energy of the conduction band. And if you tell me how much dopamine is around, I can tell you exactly what that spacing is. But usually close is good enough. And so I know this point, that means when I measure that. And I know the band gap from the prior photo-action spectrum. And therefore, I know this point. And then, of course, I know the redox potential from whatever I put in solution. You will notice in the case of TIO2 that this band edge is pH sensitive. It's just 60 millivolts approximately per pH unit, which has to do with protonation and deprotonation of the metal oxide surface here. According to the Machakhi equation, all these lines are parallel to each other because they depend on the semiconductor dopant concentration. You can see there's a little problem there, but we won't get into that today. However, if you have a question about this, the Lewis group would love to explain this to you. And Tom Hatch is an expert at this. He was just taking this data recently. You don't notice the same thing. So you can go through now at some fixed pH, say 14, because that's a good place to generate oxygen. Hydroxide oxidations we talked about before. And you can look at a series of semiconductors, and you can put them on a common potential axis. And we have the valence bands down here, and the conduction bands up here. And I think I borrowed this from a paper by Garrischer. Could be barred, though. You find there's lots of places. These are the redox potentials for water, oxygen evolution, hydrogen evolution. And you can see since the electrons will come out of the conduction band, I had to pick a conduction band that is negative of the hydrogen evolution potential in order to generate hydrogen of the water. And since the holes will come out of the valence band, I need to pick a valence band that is positive of the oxygen potential in order to thermodynamically get oxygen out of water. And you'll notice for this variety of metal oxides here, we can do the oxygen side no problem. They're all oxidizing enough to do oxygen. But only some of them are reducing enough to reduce water. The first one studied was a TIO2 by a Japanese group led by Honda, the professor, not the car. And he published a very excited nature paper saying, you put this out in sunlight, and you split water into hydrogen and oxygen. And the fuel crisis is not a fuel crisis. Well, he didn't know it was going to be a fuel crisis because he published it about one year before the Arabs decided that they should embargo us and cut off all of our oil from the Middle East. But people got really excited because the two things happened about the same time. He made a modest mistake. He saw the oxygen coming off the semiconductor and said, ah, I'm splitting water. He did not look for the hydrogen. And then other researchers like Mark Wrighton and Adam Heller and Alan Bard came along and pointed out that this TIO2 electrode really wasn't splitting water. It was oxidizing water over here, but it was actually reducing oxygen that was dissolved in the water, which is easier to do than reducing water over here. It sort of doesn't matter in that everybody got interested in this. Yeah, it made electricity. Just didn't split water. But it made everybody interested. And so all these people started studying this. And that's how they figure this out and been studying it ever since. So it started this whole field even though it was only a 80% correct observation. It also turns out that by applying a little extra potential, you can obviously get these electrons at higher energy, and you can split water. And so with a little battery in that circuit, maybe 300 millivolts or so, you'll split water. So that was OK. My favorite material, though, is this material right here, strontium titanate. Very underutilized. It's not really good in the sense that on the Earth, we don't have a lot of photons that are that big. And you notice you're throwing away an awful lot of that energy. But it does straddle the band edges. So if we happen to live on, say, the moon, this wouldn't be such a bad material. We've got more UV photons coming out. The band gap here is about 3 and 1 half electron volts, a little less than that, 3.2, actually. I think we'll skip this one. Let's go right to some data. That was too complicated. So how are we going to study this? We are going to do a scan where we change the electrode potential, and we're going to monitor the current. If you think like an electrochemist, everything goes wrong at this point. You see, when I change the electrode potential, I change the potential. My potential is set, obviously. And that's attached to the back of my electrode. And if this was a metal, of course, that potential would be transmitted to the front of my electrode, and it would just go a mock step, no problem. However, it's a semiconductor, and there's no states here. So the only place that holes can come out is at this energy right here, electrons or lower. And the electrons are going to come out at this energy or higher. So changing the potential at the back of a semiconductor does not change the oxidizing power of the hole, or necessarily the reducing power, of the electrons over a certain range. All it does is it changes the band bending. So if I move the Fermi level up, I can down. I can change the band bending, but I haven't changed these fixed points. So what do we see here for strontium titanate? Well, in the dark, there are no electrons up here, so there is no current. Until I get very negative, at which point I have gone to the flat band potential right there and then beyond the flat band potential and inverted the bands. And now I have the bands putting down this way, and electrons can come out and reduce something. And so I get water oxidation, or, excuse me, reduction, in the dark at this anti-material. That's a general phenomenon. I can't ever oxidize the water because there's no holes here to oxidize it down in the valence band. So an anti-material is not only a photo anode, but it is a dark cathode. I shine light on it, and now I have holes down here. And so as long as there's enough band bending to do the electron hole separation, those holes come out, and I oxidize water. So I'm hitting this now with about 2 and 1 half watts of UV light in a about one millimeter squared area. So that's on the order of 300 plus suns, intensity that I'm hitting this semiconductor with. And it's very happy under these conditions, believe it or not. And it's generating, you can see here, on the order of 40, 35, maybe we'll call it, milliamps per square millimeter. And the reason this line is jiggling here is this electrochemical cell looks pretty much like a coke can that you have shaken up. And you've got so much hydrogen and oxygen bubbling out of this solution that it's scattering the light everywhere. And that's what that jiggling is, the light shooting in all different directions. Very stable semiconductor. Works at amazingly high intensities with a quantum yield for a charge transfer of one. And the only problem is it requires UV light. So wonderful semiconductor. And it was my first publication of the Reiting Group. Everybody's favorite is TIO2. So here's non-dysensitized for those that care TIO2, the real thing. And again, operating at these high intensities. And once again, you can see when I have band bending available, I separate charge and I generate oxygen. And as I go to higher intensities, I generate more oxygen and the light starts to scatter. I get a flat band potential right around here. And all of these, whether it's in the light or in the dark, will reduce water when I invert the bands over here. You'll notice that this one doesn't saturate. And it's true also. You'll notice the strontium titanate. We don't see the saturation current until we have run through about 300 millivolts of band bending. So once you have 300 millivolts of band bending, you are going to separate as many charges as you can. Less than that, you get some recombination. More than that, it doesn't help you. And you'll notice again that this is not exactly as ideal as the strontium titanate. There's a little slope to that line. But again, on the ballpark of 40 milliamps of current from the same size electrode, it's a lot of current at these high laser intensities. You can do this in the other direction also instead of using an n-type semiconductor. We use a p-type semiconductor. And everything flips around. So an n-type semiconductor was a photoanode and a dark cathode. A p-type semiconductor is a photocathode and a dark anode. And so in other words, if we photolyze a p-type semiconductor, we'll generate hydrogen from water, not oxygen. And of course, there's a counter electrode where the oxygen comes off of. So this is p-gallium phosphates. Whoa, p-gallium phosphide, not p-gallium phosphate. Phosphide, boy. I shouldn't type that fast. And in the dark again, you have a blocking current, because you have no electron hole pairs. If you go far enough positive here, you'll get dark oxidation. Everything's reversed now. Unfortunately, it's not dark oxidation of water. In this case, it's dark oxidation of the semiconductor. So we don't go there. And then as you turn on the light at higher and higher intensities, you see a generation of hydrogen. And again, about 300 millivolts of band-bending needed for efficient electron hole separation. What you may not be noticing here, but I'm sure Bruce has, is the currents are much smaller here than in the other scheme. So this microamps, by the way, per square centimeter, only refers to this line right here, which is at very low intensity. And the milliamps per square centimeter, these three lines right here. But we're only getting up to about, what, 6, 7 milliamps per square centimeter, as opposed to 40 before. Why is that? Because other ugly things start to happen when you go to higher intensity. You run into both kinetic limitations and decomposition of the semiconductor. So what you should be taking away from all of this is a very simple idea. You can use a large band-gap semiconductor, such as a metal oxide. And you can split water just fine, with a quantum yield at least approaching one, if not one. And it will work great, except you live on the wrong planet for that, because you don't have photons of that energy striking the Earth's surface, which is good news for other reasons. But we'd like to live through it. On the other hand, if you go to a smaller band-gap semiconductor, such as the gallium phosphide here, you start to run into problems with the semiconductor photodecomposes. And so you're limited in intensity, but even that will eventually become problematic. And so one has to come up with chemical schemes, if you will, that shut off the rate constants for photodecomposition while allowing the useful chemistry, such as hydrogen evolution, to continue. And there's a variety of ways one might do that. You might go hunting around for a semiconductor. That just happens to have the right kinds of kinetics, electro-catalytic for what you want, and stable in terms of the semiconductor decomposing. That's certainly for the wide band-gap materials works well, but nobody has really found, for some pretty solid thermodynamic reasons, small band-gap materials that won't photodecompose themselves. Another way you might do this is play with the charge transfer kinetics at the interface, which the Lewis group has specialized in, and tweak that interface either by changing the nature of the semiconductor at the surface or by doing something like chemically modifying the interface or throwing in an appropriate solution redox couple so that you can get the rate constants for what you want to be large and the decomposition rate constants to be small. Typically where people have been successful in doing this, they've had to shut off the rate constants for oxidation of water also to do that. So perhaps the most successful cell, not perhaps, clearly the most successful cell is the so-called Gretzl cell, which is a TiO2-based cell. And to get around the fact that it's wide band-gap, when Michael Gretzl, I guess, absorbs a ruthenium-based dye on the surface of the TiO2, and the light is absorbed into the dye. The dye injects charge in the semiconductor, and we take advantage of the band-bending to keep the charge from recombining. But in doing that, we're no longer splitting water. We're just making electricity. We put a redox couple out in solution that can be oxidized and reduced, something like iodine is the Gretzl couple. And so we sacrifice the water splitting for the stability and the good photo response. And that has been the bottom line after studying these systems for since about 1972 when that Honda paper originally came out. Or actually, if you want to be more pessimistic, since 1839, when a gentleman by the name of Beckroll first described the photoelectric chemical effect. In that paper, he used a silver chloride electrode as his semiconducting electrode. And he made two comments in the paper. It's a French paper. He says, number one, you can generate a photo current. And number two, the electrode photo decomposes. And those two comments have been the ruling comments in this discipline since he made them in 1839. So on that note, I am going to close out my discussions with you. I'd like to thank you all for your willingness to listen to me for the last couple of months. I appreciate it. I've had a great time. And hopefully you'll continue to enjoy the good weather. And I can go back to some reasonable cool weather. Thank you.