 So, my name is Andy Bocarsley. I'm teaching this course on electrochemistry and I'm a professor of chemistry at Princeton University just to give you a second to background before you get started here. Although when people ask me where I'm from, I tell them, New Jersey these days. In fact, I spent the first 22 years of my life in LA as an undergraduate at UCLA. So I'm somewhat familiar with the area. And then after graduating from UCLA, I went to the East Coast where I've stayed. But the first stop was MIT for my graduate work. And I was in Mark Wrighton's group doing photo-electrochemistry with various people. But one of them that showed up about a year after I arrived at MIT was Nate Lewis. So I had the pleasure of teaching him a little bit about photo-electrochemistry actually. And that is actually a subject that I'm going to try and stay away from this term. We're going to deal with the other aspects of electrochemistry since Nate has a wonderful course going on if you want to hear about that. So we'll think about things that happen at metal electrodes and stay away from semiconductors. And unless you want me to talk about semiconductors a little bit, I don't know, we can arrange that. And what I'd like to do is the course textbook is a Barton Faulkner's book which is now in its second edition. This is a great book for learning the physical chemistry of electrochemistry. It's second edition is much better in terms of examples also, actually, like molecules that you might do something with, a grammatical improvement in the book there. So it's good for that. It's not really good if you want to kind of go into a lab and do an experiment and want to know how do you do this kind of a hands-on manual. And so I'm hoping to seriously supplement this course with that kind of practical information. If I want to run a cyclic voltamogram, what are the sorts of concerns I should have? What equipment should I be using? How do I select between different reference electrodes, issues like that? And I'm hoping that you will ask me questions, especially on that, as we go along because that will cue me in that I maybe haven't told you as much practical information. As I ought to be. In addition to that, I will be supplementing the book with examples from inorganic chemistry. In particular, the inorganic chemistry that we do at Princeton. Since I happen to know that a little bit, to give you some feeling for what you can learn from using these various techniques. Now, going along with this idea that Bard and Faulkner are wonderful on the PECAM, but if you want a more hands-on approach, there are better ways to do it probably. I'd like to suggest you two other texts. One is this book by Kissinger and Heinemann. It's hard to miss with that wonderful yellow cover. It just jumps out of the library from your laboratory techniques in electro-analytic chemistry. It's actually an edited text, each chapter is written by a different expert in the field. If you want to see a really fantastic chapter on photoelectrochemistry, this is the book to find it in. I can't remember who wrote it exactly. But it tells you a lot of practical things. You know, if you actually want to do a chrono-amperogram, how do you set it up and go about doing it and what are the pitfalls? And the other text along the same lines is this book by Gileotti. Gileotti actually has two textbooks. There's one called Interfacial Electrochemistry and this one called Electro-Connex for Chemists, Chemical Engineers and Material Scientists. This is a really wonderful hands-on text. That is the first half of the book is very physical chemistry. In fact, much more physical than even Bard gets. Worrying about the details of the interface between an electrode and an electrolyte. What are the ions doing? What is sort of happening in terms of free energy and chemical potential? If you want a lot of detail, the first half is good for that. But what's really wonderful about this book and also the other book that Gileotti has out, the second half is actually the same, I believe, or very similar in the two texts, is the lab manual. It goes through and it has a cyclic voltimetric experiment and if you were going to go and do that one, it has a recipe in there for doing that and chronoamperometry and AC techniques. And so this book is a really wonderful way if you just need to know how to do that. Now there's a wide variety of other texts out there and I think what I'll do next section is just hand out to you a little bibliography of other books that you might want to consider. But we will be using Bart and Faulkner. That is set up as a traditional textbook. It has problems at the end of the chapters which brings me to the point that it's a course and I guess I have to assign grades at some point and things like that. So there will be some problem sets which will be a combination of the chapter problems and some of my own original ideas that will give you. I'm thinking it's going to be about every other week in terms of sort of the problem set, something like that, that will go into your grade. We will have a mid-term type of exam, I'm not sure exactly in the middle, and some sort of a final exam for the course, so grades will be established. Okay, any questions on sort of administration before we get started on something more interesting? See you're already sitting there inhibited, no questions. Okay, electrochemistry. Let me take you back to freshman chemistry which is hopefully the first place you saw electrochemistry and remind you that a million years ago when you were taking your general chemistry course and you were introduced to charge transfer and electrochemistry there was probably two things that you learned and one of them was that you could oxidize and reduce molecules that is you could do electro synthesis essentially. So if you wanted to for example make chlorine then you could take something like sodium chloride and you could oxidize that and make chlorine gas from that. And of course you could do the reverse of that and that's called the battery that is we could take something where the free energy for the reaction was going to be negative and we could run the reaction in terms of two half cells and get it out and the other thing presumably that you learned hopefully was this thing called the Nernst equation. I said hopefully I'm sure you all learned about the Nernst equation but I remember several years ago when I was teaching a junior level inorganic chemistry course and I said of course you all saw this in freshman chemistry and they all denied ever having seen this equation before in freshman chemistry and most of them were in my freshman chemistry course and I remember seeing it but the point besides the fact that people tend to forget this is that the Nernst equation only tells you about potential and tells you about potential under equilibrium conditions. So in freshman chemistry there really is no current, there's just potential, there's the potential for the Nernst equation and then there obviously has to be a current flowing when you oxidize or reduce something in an electro synthetic cell or a battery but it's sort of ignored. You talk about it again in terms of free energy and that is essentially potential. So the big idea that we want to introduce in this course really is that there's current and potential and that they both interact with each other and if you understood that it's full details and I wouldn't have to give the rest of the course I suppose because that's really all there is in electrochemistry. So if we're going to take into account current also besides building batteries what else are we going to be able to do? That is up till let's say about 19, mid 1950s really electrochemistry really was the measurement of potentials and the use of the Nernst equation. And of course you can get pretty far with that, you have pH electrodes and ions, elective electrodes, you can determine redox potentials for various species and from that you can get free energies out so that's not a trivial point. In fact the very first measurements of activation activity coefficients was electrochemically, ferrocyanide, you have wonderful ways of getting your hands on delta H's in the lab, you can do bomb calorimetry and things like that but you don't have a delta G meter anywhere in the lab, the closest thing you have to a delta G meter is a volt meter, right? You can measure potentials and as you know the free energy of reaction, the potential are directly related within a few constants, in Faraday's constant and the number of electrons that travel in the circuit and so if you have a reaction that's amenable to electrochemical processing your volt meter gives you free energy and so up between say the early 1900s and 1950 that was the big deal thing, you could measure free energies and hence chemical potentials and activities with electrochemistry. It was good news also because in that time period people knew how to build volt meters that were extremely sensitive, we built them the same way today, it's a coil of wire. They were not very good at building ammeters, that is if you want to measure an amp or so that was okay but if you wanted to measure even a milliamp actually, not to mention a microamp or a picoamp, you were in big trouble, it was not a really precise way of doing that. In fact if you go back and when electricity was first ported into houses and the electrical company decided that they needed to be charged for the amount of electricity you used, is anybody aware of exactly how that was done? How they figured out how much electricity used? This even predates me, you'll be happy to know that. There were electrolysis cells on the outside of the house and little water in there and they would split the water and then you know the guy who reads the meter would come around and look at the amount of gas generated over you know the month and since they knew how much of electricity they were splitting off the electrolysis that ratio with the amount you were using and based on the amount of gas generated they could figure out how much electricity you used. So you had really no good way of keeping track of numbers of electrons or rate of electrical use to start with and it wasn't until we had things like transistors and nice integrated circuits and whatnot that you could get down to the precise measurements you needed for measuring current. So current came along a lot a lot later and it wasn't really until the 1950s that people started making good measurements on current and so that aspect of electrochemistry is really lagged behind the measurement of potential. However today we can do that so that opens up a lot of other possibilities. The most obvious thing that it opens up is the measurement of current. It's a direct measurement of the rate of reaction. Faraday told us that every time an electron flows that a redox event has taken place it turns out it's a false statement but it works pretty well. It worked for Faraday and we'll make a correction for that later on maybe by the end of the hour but that means that any time I measure a current if I believe Faraday then I'm looking directly at the rate of reaction. Obviously if I know the rate of reaction then I can start doing the kinetics and if I get the kinetics right I have a good chance of getting the mechanism. Well maybe a 50% chance of getting the mechanism depending how you feel about mechanism. And so the first thing that that current lets you do is look at charge transfer kinetics. Now let's see is everybody here an organic chemist or a physical chemist or do I have some real-life organic chemists that are willing to take this course? No one's least willing to identify themselves as an organic chemist. Okay good so when we look at I guess and when we look at there's nothing wrong with organic chemistry really but you know I of course I tell my class that organic chemistry is a horrible thing because in organic chemists we all realize it's the inferior science but there's no pretty colors in it really a few dyes but it is a science yes it is a science but but it's just not intrinsically beautiful science right however I do have to tell you remember that little experience over at UCLA not too far away from here organic chemistry junior year laboratory is where I met the person who eventually became my wife so there are some good aspects to organic chemistry can't totally put it down but so we will primarily be looking at inorganic examples which I guess will suit you just fine based on your inclinations here and there is an advantage to that it's rather interesting that redox reactions in terms of organic chemistry go far quite back in history that is it's a standard mechanism you all even if you're not organic chemists had to take probably a sophomore year again at chemistry course you probably have put that totally out of your mind it was a probably a life-threatening experience or something like that and you learned all these wonderful mechanistic things or at least you attempted to that have wonderful names associated with them right and then you had these oxidation reduction reactions I remember from when I was learning my initial organic chemistry there was just like it you know reduced and it was an arrow and it said ox over and there was product whereas all the other ones you had a page of arrows flying to the left and the right and what not I never understood why it wasn't that you know charge transfer reactions were just that simple or was there something else to it and of course the answer is that people just don't understand and even to this day really don't understand as well charge transfer reactions in terms of organic systems as they do in inorganic systems and so we have all the details we would like maybe a few more in terms of inorganic systems and the main reason for that is that the big component of the free energy that one just can't ignore whether it's organic or inorganic in a charge transfer reaction is the so-called reorganization energy that is what the solvent's doing immediately adjacent to the molecule when it's suddenly the molecule maybe it's neutral has a positive or a negative charge on and that could be something like half of the free energy and if you have an inorganic system if you have a transition metal complex then the first salvation sphere which takes most of the abuse when you do this is the coordination sphere and of course with the transition metal complex we can know exactly where those ligands are before and after the reaction so we have a big leg up on handling that energy but for some organic molecule which just has some solvent and some organization around the molecule that's really hard to figure out it's very very hard to get your handle on that reorganization energy and so mechanistically it's a big problem so we'll look at inorganic examples but don't want to leave out the organic and it takes a couple of the textbooks that I'll suggest you might want to look at when I give you the list next hour specifically electrochemistry for organic chemists because you have to approach it slightly differently because of these these unknowns so we have that mechanisms and we have kinetics a big area more recently in terms of electrochemistry has been this whole area of bio inorganic electrochemistry where one uses typically a measurement potential but sometimes current to learn first something about a metalloprotein active site and then secondly in a sensor application can I use an enzyme whether it's an inorganic based system or pure organic enzyme can I use that enzyme to sense some specific component and an obvious thing you might want to sense is some other biological component a third area that has been very active so over the last 20 years I was just gonna say 10 years I was forgetting how old I am but kind of going back to those in graduate schools the area of chemically modified electrodes we're gonna go and decorate the surface of an electrode with specific molecules to change the charge transfer dynamics at that interface we're gonna want to shut off some reactions or want to catalyze other reactions or add some level of specificity to how the electrode interacts with some analyte in carrying this out also along those lines we can slip in energy conversion I mentioned photo electrochemistry earlier and certainly modifying a semiconductor surface with molecular species has been a very important approach in the conversion of light energy to electric energy likewise there's been a variety of suggestions that one might modify the electrodes of a fuel cell for example so that you can improve charge transfer kinetics and we'll want to look at that a little bit and see if that makes sense or not we'll also want to think a little bit about what we mean we say chemically modified surfaces that is on the one hand if I take well maybe one of my favorite pieces of material silicon I will slip into semiconductors I guess just for a second here and I oxidize it which is pretty easy to do by looking at it the wrong way then I'll end up with some silicon oxide on the surface and maybe I'll even do it carefully and end up with a silicon oxide of pretty well established oichiometry and some people say well that's a chemically modified electrode and I suppose it is in some sense in that change the surface this chemistry on the other hand I might go and take some nice molecule like ferrocene and attach a hydrolytically unstable silane to that and use that to anchor the ferrocene to a wide variety of surfaces and typically when people talk about a chemically modified surface that's what they're talking about where I have a well-defined molecular species that has certain properties that I want to take advantage of and I'm going to put that on the surface so in other words I'm taking if you will the the interfacial or the solid-state properties of the electrode and I'm going to endow them with some sort of molecular specificity as opposed to the silicon oxide example that I gave you and then finally I should mention electro synthesis I mentioned that as a very old technique but it is a new technique also in that there are a couple of species that are made electrosynthetically and not much else it has made many inmates so my example of of making chlorine actually is an old one and an industrially important one chloralkylide process in which you get chlorine sodium hydroxide from from Brian's solution beyond that the monomer that that Monsanto utilizes for making nylon is electrosynthesized and there's one or two other molecules and that's it so of all the things that you might make electrosynthetically there's very little that that really is from kind of an industrial pragmatic point of view and so development in that area is worth considering okay so that's where we're we're headed we're going to focus again most of our time on kinetics and mechanism this this term and then out of that sensor applications will grow and energy conversion applications so let's get started first we need some vocabulary let's start off with the electrolyte everybody knows what electrolyte is hopefully but let me point out that there's this other term supporting electrolyte which is a little confusing the electrolyte includes a solvent plus a salt the supporting electrolyte is the salt that we're adding that is anytime we're going to do electrochemistry we need some ions around that's the supporting electrolyte one would like to choose those ions that supporting electrolyte so it's the so-called spectator ions in the system it's innocent but that's not a given and I will show you examples where things that like sodium chloride that you would think we're just going along for the ride in fact are controlling the situation so one wants to be a little bit careful in this whole supporting electrolyte discussion typically from a practical point of view we would want to get the supporting electrolyte concentration up to something like 10th of a molar it's really nice you can get away with a little bit less depending what you're doing and it might go all the way up to one molar the other obvious thing from a pragmatic point of view to say about the supporting electrolyte is simply getting it dissolved isn't good enough you have to get it dissociated that is you can take a salt like tetrabutylammonium perchlorate which is a wonderful supporting electrolyte when you're doing non aqueous work and you can dissolve it in a cedar nitrile and it'll go in at close to one molar concentration and you'll have a wonderful electrolyte system but you can also take tetrabutylammonium perchlorate and dissolve it in methylene chloride or benzene close to one molar also and those are not electrolyte situations because of you have contact iron pairs still you never get free ions and nothing's happening so just dissolving the salt isn't isn't good enough this brings up actually a very very important point when you go and you do most analytical experiments you take a NMR or IR what if your favorite spectroscopic technique is then you can end up with a good spectrum or a bad spectrum depending on maybe how you prepare your sample but you will never break the spectrometer probably by preparing a bad sample I guess you could do it intentionally but by a large that doesn't happen and you can't get totally spurious data typically by preparing a bad sample although I if you work at it I suppose you could let's see Bruce a smiley back there do you want to confess something Bruce wrong answers well XPS is closely related to this I guess I stayed away from that technique it has electrons again the problem with an electrochemical experiment even worse than XPS is that when you go and you take your electrochemical cell and you attach it to a potentiostat it becomes an active element in the electrical circuit of the potentiostat and so depending how you prepare your sample your electrochemical cell you can get all sorts of artifactual answers and you can break the potentiostat for that matter in doing this so it's not just an innocent experiment anymore where okay I'm going to go and run a spectrum and you know see if there's a good sample and there have been more papers than I've been certainly I can count they've been published in the literature where somebody has seen this wonderful signal and they've interpreted in terms of this wonderful theory that has a molecular basis and in fact what they were seeing had nothing to do with what the molecules per se were doing in their electrochemical cell but simply the fact that you have resistors and capacitors in your potentiostat your cell for all intents and purposes looks like a series of resistors and capacitors and they had simply inadvertently modified their circuitry okay you know if you went into an NMR or even an XPS and you tore out the electronic guts and put in your own motherboard then you might guess that things would change and what you need to remember when you're doing electrochemical experiment is every time you connect your cell up that's what you're doing so one has to wonder whether what you observe is actually a molecular phenomena or is you know something else and the supporting electrolyte issue is a very good example because I can make the resistance of my electrical chemical cell exceptionally large either by forgetting to put in the supporting electrolyte or utilizing a solvent where I'm not getting much dissociation okay I can fool myself yes absolutely yeah shipped your solvent windows it's shipped your capacitance I haven't mentioned yet as well as your resistance but sometimes the electrolyte I said you would like something that's innocent and it's just spectator ions but if you're going for a big solvent window often you can hit the the potentials where you're going to oxidize or reduce the supporting electrolyte okay in effect it's also this capacitance which may shift your windows some also okay when you shift your resistance your capacitance then you shift the RTC time constant for your cell so your whole system response may change dramatically when you do this so there's almost nothing in the electrochemical cell that you can't mess up by messing up the supporting electrolyte so one wants to think about that very very carefully and that of course is going to change the other aspect of supporting electrolyte is one often can run into a situation where there is either fizz or chemisorption of materials on the electrode and that would be sort of an unintentional chemically modified electrode it might be the supporting electrolyte ions that chemisor that could be an issue but you can also have various salting in and salting out effects that will deposit some other species upon addition of the supporting electrolyte on your electrode and so you know the second order effects that can be an equally big problem so we'll come back to that discussion a little later but that's a big one up front the supporting electrolyte is a is a is a critical issue okay then in addition to that of course you need to have some electrodes and it's probably more obvious that the electrode materials that you pick will affect the electrochemical response of the cell for all not all for a lot of the experiments will be talking about this term we're going to want to use a potential stat where we're focusing our potential control on one electrode and letting the other electrode do whatever it wants to as long as it doesn't get in the way and the problem with that is how do you know when that second electrode is getting in the way or not it is if suddenly it becomes the controlling factor then you're watching this auxiliary or counter electrode instead of the electrode that that you're trying to control and one way that it can become a factor is if its area is small compared to the area of the working electrode the electrode that you're trying to focus on okay so I've just thrown in a whole bunch of words here that maybe I should clarify so we have our working electrode that's going to be the electric that has potential control and something really important to recall it depends on you by your potential stat from but many of the manufacturers actually put the working electrode at ground which may sound counterintuitive but this is fine you can still have potential control this becomes really important if you're hooking up other equipment your electrochemical cell it's nice to know where your ground is or isn't and as I said it does depend on exactly what potential stat you purchase so it's important to know which side of the cell is grounded but often it is the working electrode side that is the grounded side you actually have more control that way then you're going to have either what's called an auxiliary electrode or a counter electrode and as I was saying you don't want that electrode to become limiting in any way in the easiest way to have that become a limitation is make the area of this electrode small compared to the area of the working electrode okay the important consideration here is is current density and so obviously if I'm passing an amp through my working electrode then I'm also passing an amp through my my counter electrode but if my working electrode is you know on the order of say one square centimeter then my current density there is an amp per square centimeter and if my counter electrode say is on the order of a square micron then you know I'm passing a million amps per square centimeter and obviously that's not going to happen and so things are going to happen on this side and I no longer have a system where I'm controlling this electrode and letting this one just respond so area here is critical we need large area now the other way you could fool yourself on the counter electrode is you could pick a material for your counter electrode which is kinetically sluggish so even though you have a large area the rate you can push electrons through it is slow and again that can become the controlling factor so typically for the counter electrode people would use platinum nice catalytic interface and then all you have to be concerned about is that the area of that counter electrode is large compared to the working electrode the geometry of the counter electrode isn't too critical at all the geometry of the working electrode it turns out is is quite critical so one can take for example a spiral of platinum wire or a sheet of platinum wires a little less expensive and that makes a great electrode for the counter electrode and then finally the third thing that we're going to want in this system isn't an electrode at all we won't always use it but for many of the experiments we're going to want three electrode cells we're going to have a reference electrode and I'll just either remind you or state you that a reference electrode is not an electrode it's a full half cell and again that's worth remembering that is there's more than just a piece of metal that can go wrong with a reference electrode since it's a half cell there and again you want to think about how that reference electrode is interfacing with the rest of the cell that's another area where you can get all kinds of wonderful artifactual results. Next piece of nomenclature that we have to clarify is this whole idea of whether a current is a positive current or a negative current which thanks to I guess a historical argument between chemistry and physics is never clear and in fact it's worse than that it's a historical argument I guess between chemistry and chemistry also so for example if you not only affects current but also potential so we'll start with with potential issue there they go together if you pick up a text or a journal article that was written prior to 1970 that has to do with chemistry or if you pick up a text or a journal article written after 1970 by somebody who was practicing electrochemistry prior to 1970 then you will find that things that have to do with oxidation are assigned a negative sign in general and things that have to do with reduction are assigned a positive sign so there's a very famous book which is a listing of redox potentials put up by Latimer and I think this is in the run in 1960s 1960 and so it was an oxidation he assigned that a positive potential 1970 IUPAC decided that they were going to have some rules about exactly how you do your your signage in electrochemistry and it turned out that internationally it was agreed that cathodic reactions would be associated with a negative sign and anodic reactions with a positive sign so if you learned electrochemistry after 1970 then you're dealing with a situation where we have potential when positive to the right and negative to the left and current when positive and negative and so things that are happening up here are oxidations and things that are happening down here reductions and if you're using the convention that was in place prior to 1970 then just go to the other side of the board and flip this over you'll be in great shape it's a mirror image okay and the key problem with this and I actually have to give Al Bard a lot of credit for this both the good and the bad actually this this older convention in fact has become known as the Texas convention because Bard and Faulkner at the University of Texas and basically when IUPAC came out with that they said fine but we've always done it the other way and why should we change and so if you look at all their journal articles they use the Texas convention not the IUPAC convention and it's it's a mirror image but when they went and wrote their textbook which was much more recently they did use the IUPAC convention in here so if you if you go and say okay I understand what they're saying in here I'm gonna go pull some of their journal articles now you can get yourself totally confused so be aware of that figure out which convention is being used on that now in terms of energy which is the other thing we like to relate this to typically if we're doing some kind of energy argument we like you know energy going up to be higher energy and again we have this relationship where we are going to relate our free energy of reaction to minus n Faraday's constant delta E and so you see there's a flip in sign that's going to occur here so we're going higher in energy if we want to compare that to a potential scale we need to put energy that's higher as negative and energy as lower as positive this was all done just to make life that confusing for all of us it's not that it's hard enough to start with okay so if you want to measure energy for example an electron volts which is particularly easy if you'd like to compare that to a potential scale or working in volts then just remember that more negative electron volts is a more negative potential that works fine but it's higher in energy as if I'm on this scale here and I find out molecule doesn't reduce until I get way out here I'm using more energy to reduce it then if it reduced at a more modest potential less negative potential so the IUPAC and the energy scheme do go together so a simple way we could put this together then would simply say we have an electrode here right there on this side we have an electrolyte on this side we have the electrode assuming the electrode is made out of a metal then I can apply a potential to that metal and that potential will control where the Fermi level of the metal is highest occupied molecular orbital if you will of the metals Fermi level of turn that you're all familiar with no problems good so I have a bunch of filled states below that bunch of empty states above that of course I get to move that around by applying a potential back here out of the electrolyte I have some molecule that has highest occupied orbital and unoccupied orbital and the simple argument is that if I am energetically at a potential where electrons can flow into an empty orbital which can't happen right here and a charge transfer will take place that's not possible because I have totally filled states here so I'm going to have to move my Fermi level positive in order for that to occur that's the oxidation right on the other hand if I want to populate this molecule out here with an electron obviously the first orbital I could put an electron in is something up here and again that's going to require an electron over here of similar energy or higher energy and I have nothing over here so there's no way I can do that right now but if I move my Fermi level more negative then I will populate the states below it and I can get the reduction to occur so this IU pack formalism and this concept of energy flow work together okay now we can go that's nomenclature we're doing great here now we can go and we can divide the world down into essentially two types of experiments that we can do electro chemically we have to control the potential or control the current we don't get to do both at the same time right one of those are dependent variable the other is an independent variable if you look back at the earliest electric chemistry experiments once people were starting to flow current 1950s even 1960 the initial experiments that were most favorable were those in which you controlled the current and again that was because measuring current was problematic you couldn't do it to the extent you wanted and so you could set a current and then you can measure potential and so a so-called chrono potential metric experiment is sort of the first historically of the modern electrochemical experiments where you're setting a constant current using a galvanostat and watching a flow of current as monitored by change of potential so experimentally it's easiest experiment to do in terms of interpreting results it's one of the hardest experiments to do and so once people could get a handle on measuring current then you came up with a set of potential controlled experiments in which current was the parameter of interest now in doing this I have a colleague my biggest research effort right now at Princeton is in the area of fuel cells and order to a fuel cell fuel cell is a really strange thing in that chemists only understand about half of fuel cells what a fuel cell does and engineers understand only about half and they're the opposite house and so you really have to work with an engineer make a fuel cell work right one of the reasons is a fuel cell does not have a reference electrode in it and introduces all kinds of interesting engineering complications as a result there are other interesting engineering complications besides the reference electrode anyhow a lot of fuel cell research has been done by electrochemists as opposed to chemical engineers and electrochemists think more or less the way I've been telling you to think for the last 45 minutes that is in terms of potential and current and in terms of this sort of thinking in a three electrode type of cell engineers don't think about three electrode cells to any large extent they might but what they're interested in is making something that could be used you know to put energy into something else fuel cell for example and so when you're running a fuel cell what are you doing you're generating some current and some potential and you're running it through an external load simplest one say being just a simple resistor okay so the question is when you're doing that which parameter are you controlling and I promise you if you go out on Colorado Boulevard and you know find some electric chemists and ask them they'll tell you that really you're controlling potential if you do that and the current's doing whatever it wants to do but in fact that's really not true you're controlling resistance when you do that and the current and potential are allowed to do whatever one wants to do that is when you're using a potential stat you have designed a system very specifically that lets you control potential and monitor current if you're not using a potential stat if you're just using a load then you're controlling either even though they're two link parameters you're not controlling either one you're simply controlling cell resistance so if you want to build a fuel cell that's they're going to run a car or something like that you don't want to look at it as a system that is a potential control experiment that's generating a current that's going to run the electric motors in your car you want to look at the car as a load and you want to ask yourself how does the load impact the fuel cell performance we'll get to that but we'll throw that out right in front that what I've had to say here only applies to potential-statted circuits okay so something we're potential-statted and that we're going to monitor current and we're using a three electrode cell with our potential stat so that we're working under the conditions the very specific conditions that I've laid out here then what sorts of experiments can we carry out start over fresh here so let me let me shoot up on the board over here a outline of what's possible my machine has been sleeping too long there okay so we're going to do a potential control experiment is this can you guys in the back see this this is like an eye exam right now we're okay we've got great eyesight on this side have on that side okay sort of so I'm gonna go over this and I think I'll use the board also but I divided the world into two things we can do a static potential experiment we just pick a potential and we're gonna stay there in the story and we're not going to even look at the what's happening in this cell immediately after we pick it we'll let everything come into steady state and then we'll consider what's happening or we can dynamically change our potential so that's what's on the right hand side of the chart over there if and I'd say again this is sort of the historically the early experiment the static potential experiments kind of 1950s and more recent and in dynamic experiments were we're actually changing the potential are it's nineteen just starting in the 1950s and then coming up to today so just really reviewing what I've already told you in terms of the static experiment the the classic static experiment is would be an experiment where I am in thermodynamic equilibrium and obviously by definition of equilibrium that means that the current I here has to be zero we don't have a process occurring so we have no rate for process occurring so we have zero current there and again that would lead us to something like the Nernst equation over here right so that I have an equilibrium potential just to remind you here that is related to a standard redox potential plus a term that takes into account our concentration of reduced species that's reduced over a concentration of oxidized and let me just remind you when when Nernst wrote this down originally he didn't use a natural logarithm he used a base 10 log so you have to throw in a factor of 2.3 logarithm of red over ox so instead of writing a concentration and whatnot down all the time I'm going to talk about reduced over oxidized is red over ox for the rest of the term and take you back to that discussion we had a couple minutes ago about IUPAC in making that sign convention what they were essentially saying is that the standard way you will write out all reactions all half reaction as is as a reduction reaction so again if you go back to Latimer's book then all the half cell reactions are oxidation reactions in Latimer's book if you go more recently Bard and Parsons put out a more up-to-date compilation of redox potentials a wonderful book that has about every redox potential you could think of in the world in it and they've written everything as as reductions so our generic reaction is that one right there if we are operating at room temperature then this term right here is 59 millivolts divided by n the number of electrons that transverse so you can see we obviously have a way now of relating potentials to concentrations and a very powerful analytical way that's our pH electrode essentially alliance elective electrode and that's all done under an equilibrium sort of our pseudo equilibrium condition on the other hand holding the potential static doesn't mean that current doesn't have to flow that is when we don't do a measurement like this we use a high impedance system to ensure that current doesn't flow but we can let current flow in these systems obviously the Nernst equation isn't going to apply then and then when we have current flowing we have two options we can have very fast charge transfer kinetics if we had that situation even though we're not in a static equilibrium we are approaching something that is close to equilibrium at the electrode electrolyte interface and going back to a Nernstian condition is very reasonable on the other hand we may have slower kinetics where the rate of charge transfer is the rate limiting step in our reaction and then we have to develop some sort of a kinetic scheme that allows us to follow that and initially this was worked out by a gentleman by the name of taffel this was an empirical equation the taffel equation that described the relationship between a potential and a current and then a more detailed physical chemical understanding of that equation was provided by Butler and Volmer relating it back to concentrations and rates of reactions things like that so we will look at that that's basically what we have possible in terms of a static experiment if we're going to change our potential then we have two situations also one I've already mentioned is we can have a ferdaic reaction that is a reaction where what we have over here is happening electron flows through the circuit and something gets oxidized or reduced question yeah no no there's all potential controlled experiments so the question is yeah when I say dynamic potential am I controlling the current no I'm I'm I'm dynamically controlling the potential so I'm doing something like a cyclic volt amogram or a chrono amperogram where I'm sluying my potential or jumping my potential these are all potential controlled and the simplest experiment would be a potential jump a chrono amperogram for example and I could sort of zero authority what I expect there then is that I'll end up with something that Faraday's law describes that is I oxidize well if it was Faraday it was silver I oxidize silver to silver ions and every time I see one electron in the external circuit I end up with one redox event that's occurred okay this by the way that silver experiment is the genesis of the Coulomb right that is at the point the Coulomb the fundamental unit of electrons was was defined we didn't quite understand moles and Coulomb's were somehow related unfortunately as a physicist Faraday was a physicist that day I guess was doing his Coulomb experiment and Faraday on a different day was doing more experiments but there was an understanding of what was happening there so they needed a fundamental unit and he knew that he could do something like reduce a gram of silver which was the basis for this and he could very precisely weigh the amount of silver that he had and so he said the amount of electricity it takes to reduce a gram of silver ions the silver metal will define as the fundamental unit there's your Coulomb and that's why we're stuck with Faraday's constant in here today by the way that that is a script F the way I write it because last term when I was teaching this course three weeks into the course a student came up to me and said what is this it's just an F and of course that's just the ratio of Coulomb's to moles which turns out to be if you like sort of zero significant figures 10 to the fifth 96,496 if you like a few more significant figures so on the one hand we can say that's happening on the other hand what what Faraday sort of didn't understand was the first thing that happens when you pass charge to an interface is that you get rid of some entropy at the interface that is if I have an electrode there's case one the case two if I have an electrode sitting in solution again there's my electrode there's my electrolyte if I suddenly go and dump say some electrons on this interface I have a bunch of negative charge there and this electrolyte which is out here which has supporting electrolyte in it as well as dipoles that are associated with the actual solution molecules it's going to respond to that and so obviously I'm going to bring up things like cations to that interface or perhaps if I'm using say water as my solvent I have a nice dipole moment I might be arranging my solvent dipoles something like that and of course as soon as I do that the rest of the solution is going to look at that and not be happy with that because you're well positive charge there is going to bring up negative charge to balance that out or potentially some dipole moments I go in the other direction and that will keep going until eventually fuzz is out and I'm way out here in both solution and I have just a random assortment of charges again now that's work and work takes energy we have to get that energy from somewhere and what where are we going to do it there's going to be a flow of electrons associated with this so we have non-faraday processes and it's just the organization of this interface when we apply a charge to it and Faraday misses whole thing because for some reason his I don't know his his laptop computer really couldn't see things happening on a millisecond time scale given that I think his stopwatch actually was probably a thing with sand in it right or so he didn't see that but now that we can you know look on a millisecond or a shorter time scale we find that this whole organizational process dominates the early time charge transfer chemistry and so we had these non-faraday processes and one either has to say you know I'm not really interested in that I'm interested in the Faraday part and so I will do things to minimize this aspect so it doesn't confuse me or one might say well I'm building this whole organization at the interface can I use that to interrogate the nature of the interface so I might actually use the non-faraday component as a way of studying the interface take it either way so we have those two possibilities going on there if we want to minimize this because we're really not interested in it we can never make it go away but we can minimize it there's two things that we can do the first is again what I said earlier if we have a lot of supporting electrolyte around then you see we don't have to do as much work to bring these things up and so we can minimize the amount of energy that's needed to do that and that will help quite a bit this is also by the way the reason that you never do electrochemistry without supporting electrolyte around if all you're going to rely on is the dipole say you know distilled water to do all of this it's going to take a tremendous amount of energy much of which will release this heat to do it so you'll have a you'll have a lot of heat generated in B it's going to be very sluggish type of thing so you'll never see the nice beautiful electrochemistry you want to see you'll just see this organizational thing going on another way we might do this is simply say okay for the conditions that we're operating under we know that it's going to take four milliseconds for the interface to organize itself and so we'll just look later in time than that or we know for the first four milliseconds there's something going on here and so we will somehow deconvolute that process because we want to look in that four millisecond time window now if we want to do that then you simply have to realize that that interface for all intents and purposes looks like a parallel plate capacitor and so we could describe this process of building up this so-called double layer as the charging of a discharging of a parallel plate capacitor so the first thing that would pop into mind is that we're going to have an exponential drop-off in the current associated with this that's dependent on an RC time constant again the R will depend on exactly how much supporting electrolyte is out here in the in the bulk because that can be a major resistance the C will depend on exactly what you have available to organize that double layer those of you who are more familiar with semiconductors then you have a space charge layer and a semiconductor on this side and it is the mirror image of what's happening out here they are identical okay so if you understand space charge layers you already understand the double layer if you don't you understand neither I guess but we'll get back to that in a couple minutes okay so we have a non-ferdaic response we have a ferdaic response if we're doing a ferdaic response then we can talk about kinetics again and we can divide the world down into fast and slow charge transfer kinetics through the interface and as I said before if it's fast then at the interface even though we are not officially in equilibrium obviously because current is flowing we're going to have a situation since the rate limiting step is not the charge transfer itself that the Nernst equation applies it'll be a pseudo equilibrium situation that we could use to define what the interface looks like what will presumably be limiting and what typically is limiting when we have fast charge transfer kinetics then is bringing up molecules from out in solution to be oxidized reduced at this interface and typically we would set up a situation where that's a diffusion controlled process more generally we can say it's a certainly a mass transport controlled process okay so by taking the Nernst equation as a boundary condition along with whatever mass transport we're using then we define what's happening in terms of a fast charge transfer reaction if it's a slow charge transfer reaction then obviously we're never in an equilibrium situation that is I'm talking about the heterogeneous charge transfer of electrons across the semiconductor electrolyte interface and now we need some sort of a kinetics statement such as Butler-Volmer that will define what's happening there so when we're fast we're Nernstian plus mass transfer control and when we're slow it's charge transfer kinetics okay doing okay everybody's hanging in there okay so let's start off with since this non-fair day business has to occur whether we have a fair day process or not let's let's look at that and so we understand what it can do for us or what it can do to us as we just show you terms of some experimental data what I'm talking about here this actually there's there's two two purposes for this first one is I actually took this data so you should be really impressed that I can use an oscilloscope and it was a sort of a circa 1980 it was that Princeton already though so and but we didn't really have computers yet so it's just Polaroid on the oscilloscope wonderful old technology look at that even today you know I haven't inadvertently had a gamma ray come through here and erase my my data never lost the second is what I have here this is an acetonitrile electrolyte so fairly high resistance I have tetrabutyl ammonium perchloride in there's a supporting electrolyte my box here is a two millisecond box and with a one milliamp full-scale and I'm doing a potential step experiment here a chronoamperometric experiment and so I start down here and I jump up here I get this response you can see in this system I have a millimolar of ferrocene in solution so I'm looking at the oxidation of the ferrocene experiment down here exactly the same experiment with the same electrodes nothing has changed this potential jump happens to be a point six volt jump I'm doing a point six volt jump down here the only difference is I didn't put the ferrocene into the cell and there's your current response okay and you can see just qualitatively they're different exactly the same cell in fact it really is exactly the same cell because I didn't do it the way I just told you I did it what I did over here is I jumped to a 600 millivolt window where I knew ferrocene would go from its reduced state to its oxidized state and over here I jumped through the same 600 millivolt window but I picked a region where ferrocene was going to stay in its reduced state there was not going to be any charge transfer chemistry so I was certain whatever interesting structure I had at the interface didn't change because I changed the electrolyte or anything like that and yet you get this very different response but probably you can't tell for certain by eye is that is an exponential decrease in the current right there in fact you can take that curve and you can back out that I have 85 ohms of resistance there and a capacitance that's about 2.3 microfarads if you need a ballpark number for just about any metal electrode it's about 20 microfarads per square centimeter of electrode about a tenth of a square centimeter that I have there so it works right so if you know great rule of thumb if you just need to have a guess at the RC time constant 20 microfarads per square centimeter and in this particular cell I get a RC time constant of 0.2 milliseconds when I carry out that experiment and I've really loaded that cell up with supporting electrolytes so that's about as good as you can do in a in a non aqueous electrolyte and it'd be a good idea if you really wanted to study the a current that had to do with the periodic process you might go three time constants beyond that to make sure that you're really down there so again it's it's two milliseconds per box here and so if I go from this point if I go out three boxes so I have a little or two millisecond lifetime I'm over there and you can see my current is essentially negligible at that point so if I were to wait in this particular case to to two millisecond to six milliseconds I can be very certain that any current I saw at that point was going to be from a periodic process and you'll notice when I have the ferrocene around where I have this I have a very different shape and probably by eye you can't tell that is a tiny the minus one-half response but if you go plot it out that's what it'll work out to be you can see if I go out a similar distance three boxes out here that although I'm missing a big chunk of current there's a lot of current over here my zeroes down here so I have quite a bit of current out here to play with still so two choices assuming I'm not going to change the chemical composition of the cell either I go out some distance like that and and you can decide maybe you don't want to go out three constants maybe you're happy with a little bit of a you know an error in here and only want to go out two constants or one constant and just pick off the points out here or you can try and deconvolute these two curves which is pretty challenging it turns out if you needed time that was going to be say within the first couple milliseconds this you have you have two problems here first if you want to go a very short time you've actually lost potential control it goes off scale here and it's not it's not because I've miss set the oscilloscope it's going off sale because you you you lose potential control in the very earliest time period you have to wait for the potential stat to get back and reestablish the potential that you're dealing with but in addition to that even if you go beyond that you're looking at a subtraction of two very large numbers to come up with a small number and the chance of doing that successfully are pretty limited so you'd have to have exceptionally good data set in order to do that deconvolution and the other way by the way to make this whole thing faster if you need to is to have a smaller current flowing and limit our current and the way we might do that is since the current is proportional to the area of the electrode if we use smaller electrodes then we can limit it so one can go for example down to ultra micro electrodes these would be electrodes that say if we're looking at a circular electrode would have a diameter of 10 microns or less and 10 microns is sort of the official cutoff point for an ultra micro electrode and we get a lot less current flowing through the system we'd be talking about you know picoamps of current and much faster charge transfer process could be followed as as a result of that small current also by having this smaller area our RC time constants dropping way down because the capacitance remember is 20 microfarads per square centimeter and if I drop down to a minor fraction of a square centimeter then RC is is wonderful okay so that's what we're talking about from a very physical point of view now what's actually happening here when I go and do this and grossly this is what's what's happening but of course that that graph right there doesn't tell us anything about what the ions are doing it tells us that we have a complex current potential relationship that that's an involved there so once this thing is set up what do I have that is when I'm out here I'm out here because I have developed this whole structure in here and it's there now that double layer is there and and so exactly what do I have I will just tell you we can divide that double layer into two regions that's divided yeah the double layer in two regions but let me go out here and remind you that there is a bulk electrolyte out there with random ions and solvent around and that we have this double layer structure and that double layer structure is going to have a region in it right adjacent to the electrode where we have a lot of ions and a lot of organized solvent and that's called the compact double layer and often this plane here is referred to as the inner inner Hema-Holtz plane and that typically is about what I've drawn there it's about two molecular layers thick you have a lot of organization the first two molecular layers and after that you get into this region where you have some organization but not really like I've shown you there and that is the diffuse double layer and then that goes out to the outer Hema-Holtz plane well at which point we arbitrarily say we have bulk solution if I was to look at that now not in terms of where the ions are but in terms of the potential of what I'm measuring potential versus distance then what I'm telling you is I start off right at the electrode at zero and I've applied some potential or the electrode is established some potential phi that's what it is somehow it's established and then I excuse me let me call that phi sub m yes in fact you know what I'd like to do actually let me reverse this whole thing let me put my metal potential down here that is my electro potential right down here and when I get way far away from the electrode out in in solution there's some potential associated with the solution so phi sub s up there so I'm going to start over here I'm going to end up or I'm going to start over here so I'm going to end up over here and that potential drop has to occur through this double layer so I'm going to every very steep potential drop that's going to take me to the through the inner Hema-Holtz plane Hp inner Hema-Holtz plane and then a smoother drop-off and potential until I get out here to the outer Hema-Holtz plane OHP so I'm dropping a huge potential across that that double layer yes this is this this is an m for metal okay potential the metal potential the solution and I'm going to apologize in that I'm not used to quite such small board space and things are getting congested there pardon I HP the inner Hema-Holtz plane right here right there so you're dropping a large amount of potential there you drop a lot of potential over a short distance you're dropping out quite a bit of potential here also but over a larger distance and again exactly what those numbers are depends on exactly what your solvent is what you're supporting electrolyte is but this is these are fairly large numbers so for example there was an experiment that was first done in the early 1980s where carbon oxide was chemisored onto a platinum electrode in an electrochemical cell and the IR spectrum the CO was observed and as a function of the electrode potential so we're not doing any charge transfer chemistry CO is just sitting there and what it's experiencing is whatever is happening out here in terms of all this organization and what you observe is as you change the electrode potential away from so-called point of zero charge as there is some potential on this electrode where this potential and this potential happen to be the same and if I find that then there is no potential drop across this thing so we have and therefore there are no ions in other words that are generating an iron gradient out here so that's the point of zero charge I have nothing ionically physique zorbed onto that surface so if I can find that point presumably the CO is just like a CO bound to a platinum and a platinum complex and then as I apply a potential I'm doing all this stuff and move away from the point of zero charge and one observes experimentally that the vibrational frequency of the CO shifts so the question is actually somewhat debated now but not as much is what's that shift do the fact that I had this huge electric field here this is this a stark effect spectrum where I take in CO and if I take in CO and I put it across two plates in a Bruce type experiment actually I'd see shifts in CO as I apply a big electric field to that system so am I doing that or is this an effect that's due to the pi back bonding of the CO that is as I change the potential in the electrode not only am I doing all this stuff but again I'm moving the Fermi level of the electrode around and so I may be pushing electron density into the pi star orbital of the CO and changing the bond order of the CO so there's a huge debate about this to start with actually initially there wasn't a huge debate because it was a bunch of inorganic chemistry said oh obviously it's it's back bonding and you're changing the bond order of the CO because that's what inorganic chemists think about and then other people came along and said well this is a possibility also and you know the truth is some of both actually so it's going on there so but this is a big effect you can you can subject a molecule to a field of a million volts per centimeter at an interface it's a non-trivial thing okay it looks to me like this is a good point to stop at that things up we will continue then next Tuesday we'll pick it up from the non-fair day current and work our way into a third day of response