1 Electrochemical Measurements 1. Performance metrics vs. performance- and life-limiting mechanisms 2. General approach a. Reference electrodes b. Types of cells c. Inert electrodes 3. AC impedance 1. Performance metrics vs. performance- and life-limiting mechanisms For the last two lectures, we ve been learning about performance metrics. As a general rule, what do we mean by high performance? High power and high energy- pushing Ragone plot farther out and up. What does that mean in terms of battery properties? High voltage, high current, high capacity, low resistance. Side note: we ve been talking about performance metrics the last two lectures in terms of the whole battery. We call this cell-level performance- we are comparing cells (single batteries) to other cells. It s distinguished from what we call system-level performance, in which cells are themselves wired in series/parallel into a battery pack (your laptop has six, for example), and that might be evaluated differently from a single cell. We re not going to lecture too much about system-level performance in this class, but the distinction is something to be aware of- any added mass or volume for packaging will decrease the values of specific power and energy on the Ragone plot. The performance metrics discussed so far have been all about comparing cells to other cells. As you ll remember, we also learned in our electrochemistry unit how there are many processes going on inside a battery, which are all very complicated. We learned about what these are in the first three weeks of the course: electrochemical reactions (several) and ion transport (many species). Today s lecture is instead, hopefully, going to help bridge the gap between cell level performance the voltages and currents we put in and get out- to all that physics we did in the first three weeks the cause behind those voltages and currents. Many different physical processes go on inside the battery, and some of them are more important than others when it comes to limiting performance. Venkat showed a chart which showed how much of the potential loss in each battery is due to each process. How did they determine this? Another topic discussed on Tuesday was the presence of side reactions. We said that in addition to the main reactions that we ve been hearing so much about, there can be additional
2 chemical reactions in the battery. Why is this important? Mostly, for lifetime. We plot here capacity-cycle number, or capacity-time. It decreases with the cycle number- that means we are losing charge, and thus energy, as time goes on. This is called capacity fade, and you can see that it is faster at higher temperature. The cause of capacity fade is side reactions in the battery, so determining 1) what those reactions are, 2) what potential they occur at 3) how fast they occur is going to be crucial to predicting and controlling lifetime, because we don t want our high voltage to fall off after a few battery cycles, or our capacity to steadily decrease with a lifetime of six months. We should mention that aging studies - determining how and why batteries lose energy and power over the course of months or years- is a large and very active area of lithiumion battery research. Ultimately we care about the behavior of the entire cell, and without understanding of physical phenomena inside cell, extremely difficult to make improvements. How can we think about this? Performance-limiting mechanisms: Ohmic loss, concentration overpotential, surface overpotential. We want to know if transport, kinetics, etc are limiting performance. There is a lot going on inside the cell, and just looking at discharge curves can t tell us if there is resistance in the electrolyte or a slow reaction at an electrode or a concentration gradient building up. So we want some way to quantify the properties we ve discussed: rate constants, transport properties, etc Lifetime-limiting mechanisms: side reactions. What are they and how much are they occurring? Parameters to measure: thermodynamics: equilibrium potential (for main and side reactions) transport properties: conductivity, transference number, diffusivity kinetic properties: rate constants 2. Electrochemical measurements: general approach 3 variables: i, V, t. From these, get R and Q (capacity). Seems simple, but there are pretty much infinite variations on this. Some of the variations Control i, measure V (t): chronopotentiometry Control V, measure i (t): chronoamperometry
3 Variations: relaxation techniques, control V (t), measure i (t): linear sweep voltammetry, cyclic voltammetry, AC impedance. The math for most of these is pretty complex- we can t just plug into a simple equation. If you need to use these techniques, you re not going to learn them in an hour, and if you don t need to use them, the details are going to bore and confuse you, so we re instead going to talk about some really practical distinctions so that if you need to speak to somebody who works in this field, you can speak the same language. 3. Reference electrodes and types of cells Remember, we re trying to get from the discharge curves we saw earlier to something specific, like a rate constant or diffusivity. Before we get into which techniques are used for which measurements, we should think about what we re going to be looking at. First problem: how do we know where the potential drops are? [draw Daniell cell diagram, relabel C6/LFP] This is the same problem we had before with standard potentials. Our solution then was to use one electrode as a comparison- we related everything to the reference reaction. We re still going to do that- use a reference electrode, but with a twist. Remember, we are trying to get kinetic and transport properties, which means passing current. When we measured an open circuit potential, we could be certain that the difference in potential was due to the different reaction. That was fine at equilibrium, but what happens when you pass current? There are now going to be losses at each interface, and it s going to be very difficult to attribute them correctly. The trick to this problem was invented by Hickling in 1942, and is that we actually put three electrodes in the cell. The potential is controlled (or measured) across this difference- working/reference. Current is passed across working/counter. [draw simple diagram- V, A] Why is this so good? Can eliminate interfacial resistance at counter electrode, measure reactions separately. Here s an example- we can see the graphite and cobalt oxide voltages as a function of state-of-charge. How do we choose a reference electrode? Depends on many things- two big ones are a) chemical compatibility; b) size. Show list of common references w/ reactions and photographs. Where do you use these? 1. Standard hydrogen- not practical, but it s the zero. What does it look like? 2. SCE (Saturated Calomel Electrode) Hg2Cl2 + 2e- 2Hg + 2Cl- U=0.241 V
4 3. Ag/Cl: Silver/Silver Chloride Electrode AgCl + e- Ag + Cl- U=0.199 V What assumptions do you make with a reference electrode? Biggest assumption: potential drop from reference wire to solution doesn t change. What would make it change? 1) reaction occurring- will generate overpotential. We go around that by passing only the tiniest negligible current, enough to measure voltage, but no more. If surface overpotential = 0, we measure the equilibrium potential- V = U. 2) Can the equilibrium potential change? Nernst equation- need to avoid concentration gradients at the reference, or the potential will drift. We typically keep concentration constant by the use of a Luggin capillary to isolate solutions- ions can t really go through the frit, at least not very fast. This first assumption can be problematic in some situations, such as when our reference electrode is an active metal. What does that mean? The metal reacts with the solvent or electrolyte without passing current. Lithium, for example, is actually extremely reactive with most things. This means there can be drift in the reference potential, which is bad, but sometimes there is no better alternative- I ll explain why in a minute. A common problem in measurements is uncompensated resistance between the working and reference electrode. Let s say we are trying to find the exchange current density for a new lithium-ion battery material. We do that by passing a certain amount of current and measuring the potential drop- that lets us get the overpotential as a function of current, which lets us fit the BV equation. [draw curve- relate to Ohm s Law] If there is a lot of resistance between the reference and working, we won t be measuring the overpotential we think we are, and that can interfere w/ measurement. This is a particularly big deal in nonaqueous electrochemistry, because the solvents are usually very resistive compared to water. It also limits our choice of reference electrodes when water is not the solvent. We generally want to keep water out of the system when the electrolyte is something like acetonitrile because water is a contaminant that can interfere with measurements. Even if the Luggin capillary frit keeps the water out, we can expect that the junction of these two insoluble liquids is going to cause some resistance. This is why we typically use lithium metal as a reference even though it goes in the face of everything you learn in electrochemistry books- the active metal can react without passing external current. How else do we address the problem of uncompensated resistance? We make the electrodes very close together. This is another reason to use lithium metal, because it can be made very small (like a wire). When you make an experimental lithium cell that includes a reference electrode,
5 you typically use what is called a Swagelok cell. The only reason to make a ssagelok cell is to have a reference in there- a little piece of lithium fits through the hole and you can attach a wire to the outside. There are several other compensation techniques for ohmic drop. One is to measure the resistance between working/reference and apply a correction to the data either during or after the experiment. How do you measure the resistance? Typically, AC impedance, which we ll come back to in a minute. We ve just said that lithium is not a good reference electrode, but that in lithium batteries it s often the best you have because you re so limited in terms of reactivity and space. People use these Swagelok cells in order to get the lithium in between the separator layers. A problem with Swagelok cells is that they leak a little bit through that hole, and so for long tests cycling for weeks or months- it s problematic to have even a tiny bit of air getting in the cell and reacting. In spaces this close, the presence of the reference can also be interfering- it can get in the way of ions and block the electrodes from each other. If these are serious problems, what we typically do in this case is to give up. We eliminate the reference electrode and make what s called a half cell, where we pair a lithium electrode with a porous electrode (usually some new material). Recall, earlier- we talked about half reactions. Does a half-cell measure a half reaction? No, of course not. The benefit is that it s easier, quicker, and less prone to leakage that using a Swagelok cell, while eliminating some of the uncertainty associated with another porous electrode. We know the distance between the electrodes, and we know the equilibrium potential of lithium. We don t actually know the potential drop across the lithium/electrolyte interface though, and so there s this implicit assumption that it s always the same when comparing different materials. Is this a good assumption? The last cell we ll talk about is a symmetric cell. An example is lithium-lithium, or for an aqueous system, platinum/platinum. This is good because we 1) know the area and distance between electrodes, no porous electrode confusion 2) equilibrium reaction potentials of electrodes are the same- OCP = 0, until we start messing around with concentrations. This cell is extremely useful for characterizing the transport properties of electrolytes. Relaxation and opencircuit techniques are what you typically use here- without getting into the math, the I-V relation can be related to the transference number, and the time it takes for concentration overpotential to relax can be related to the diffusion coefficient. For conductivity, you would use this type of cell
6 and AC-impedance. We ll come back to that one at the end of lecture because it is so commonly used. 4. Inert electrodes The original point of the lecture- we were trying to measure different transport and kinetic properties, which will in turn determine limits to performance and lifetime. We ve said that for electrolyte transport properties, we typically use symmetric cells. For kinetic measurements, we use either full cells with reference electrodes or half cells. For both of these, I ve been making the implicit assumption that by measuring current, I am measuring reaction rate. That s ok, because we know from Faraday s law the two are directly related. What happens, though, when there are several reactions going on at once? Such a situation is very common if there are side reactions in the battery, and it is very difficult to figure out how much current is caused by each. Here s an example, similar to what Venkat talked about on Tuesday. The capacity on charge exceeds the capacity on discharge, which causes this marching forward. How do we determine the relative amounts of current that go to each reaction? One way around this problem is to use an inert electrode. What do we mean by inert? Typically platinum, gold, or another material that doesn t oxidize easily. If the electrode doesn t oxidize, we can determine what reactions are going on in the solution. If you re doing electrochemistry but not developing a battery material, you probably use inert electrodes most of the time. But since this is a battery class, we re just going to talk about one application of these, which is determining the stability window of the electrolyte. We re showing here two different plots. These are both from a scholarly article on electrolytes for lithium ion batteries. The x axis is current and the y axis is voltage. What they did in this experiment is to put some electrolyte in a cell with inert working and counter electrodes, and an
7 Ag/AgCl reference. Then they applied a potential difference between the reference and working electrode and measured the current between the working and counter. Within this range (-3.5 to ~1.5), there is no current, but when they reach a certain limit they get a very high current, which corresponds to breaking down the electrolyte or the solvent. In this experiment they are comparing different lithium salts to see which ones are more reactive than the others. Thought question: in a battery, what would you want this plot to look like? Another example of using inert electrodes to measure electrolyte chemistry is in water splitting outside the range of 1.229 V. This idea of stability limits is very important for considering the voltage limits of the battery. There is a limited potential window in which we can operate. For aqueous systems (think NiMH, PbA), 1.2 V by water splitting. For nonaqueous, the reactions are much more complicated, depend on system, but typically anywhere from 3-4 V. Main point to take home: we use inert electrodes- platinum, gold, glassy carbon- because they don t react, which means we can separate main reactions (desired in battery) from side reactions. 5. AC impedance We re going to cover this last technique in more detail, because it s used so often. As soon as you start reading battery papers you will run into these circle diagrams, which are used to make all kinds of arguments that may or may not be true. Our goal with this section of the lecture is to give you a general idea of how it works and what this technique is used for. First I ll walk through a general idea of what we re doing, then I ll get to some math that explains what these charts mean. All of the techniques so far have applied a non-equilibrium current or voltage and measured the current or voltage that follows. AC impedance is a little bit different- we apply a tiny voltage and stay near equilibrium. How do we do that? We are going to put a signal in that oscillates. This has a set magnitude E (typically about 5-10 mv) and frequency, ω = 2pi/t. When you apply a voltage, you are leaving equilibrium, and so you will get a current. The amount of current depends on the system- how much resistance to reaction, how much ohmic resistance, etc. The different processes respond to voltage changes with different response times, so if we vary the frequency of the oscillation, we can separate out the different processes and see the relative magnitude of each. To summarize: we apply an oscillating voltage of varying frequency, measure the current, and from that get the resistance as a function of frequency.
8 Ok so that s the general idea. Now we ll get to a little more math. First, let s think about a resistor. What is the relationship between I and V? V= IR, constant. Why is the resistor relevant to the battery? Ohmic resistance in the electrolyte, R ohm = L/KA. Also charge transfer resistance, R ct = F/RTi 0. How about a capacitor? I = C dv/dt. Why is this relevant? If ions are mobile, they can accumulate at the interface- we call this double layer charging, where the electrolyte acts as a capacitor. If you think about the capacitor equation, without doing any real math, you will see that as we increase the rate of change of voltage, the current in the capacitor will increase. That means the resistance will decrease. If you go infinitely fast, the current becomes very high, and resistance in the capacitor will be basically zero. If you have a circuit with a resistor and a capacitor in series and you oscillate the signal fast enough, the capacitor eventually will short out the circuit and the resistance goes to zero. This is relevant to a battery- if we have an interface, the double layer can charge and discharge in parallel with the faradic reaction (energy storage). If we oscillate fast enough, we ll short out any charge transfer resistance via the double-layer capacitance. I ll explain why we would want to do this in a minute. Now let s take this signal and represent it mathematically. V = E sin( ωt) From Ohm s Law, V = IR, so through the resistor I = E sin( ωt) R For the capacitor, what is the relation? dv I = C = Cω E cos( ωt) = CωE sin( ωt + φ) dt We can rewrite the cosine term as a sine term plus a delay. This isn t too important for here but if you into the theory more for your own reasons it becomes more important. What we care about is the relation between I and V, which we can rewrite as E I = sin( ω t + φ) where X X 1 = ωc Now we take this resistance, R, and the reactance, X, and combine them into one term which is called impedance. Z = R + jx, or Z Re + jz Im. j is the imaginary square root of -1. We see from this definition that one of these terms depends on frequency, and the other one doesn t. What that means if that you plot real vs. imaginary resistance for different frequencies for this little circuit, you get this semicircle. This is called a Nyquist plot. At high frequencies, the capacitor shorts out
9 the resistor, and at low frequencies the capacitor is totally insulating, which means the diameter of the circle is the resistance of the resistor. That was a little abstract, so let s relate it back to the battery. We can think of the cell as an equivalent circuit. In addition to the interface, which was already discussed, there is ohmic resistance in the electrolyte. So, if you can short out processes at the interfaces, you will measure the pure resistance of the electrolyte. This is how we measure conductivity- we know the separation and area between electrodes, go to high frequency, and get the real resistance. [slide]. We also know that the diameter of the semicircle is the charge transfer resistance, which means we can get out exchange current densities and thus rate constants. Here is an example in which the authors compared different materials, and found that the charge-transfer resistance of one was much higher than the others. You can also use AC impedance as a tool in aging studies- it is very easy to run, and one of the few non-destructive techniques. Here is an example in which the authors took a fresh lithium ion battery, measured impedance, let it sit 24 hrs, and measured again. The arc is much bigger, possibly showing that the reactions are slower. What is the drawback of AC impedance? Mostly, that real systems do not simplify to this little circuit, and most things don t fit nearly so nicely. You can represent the system with more complicated circuits, but they then start to involve a lot of fitting parameters that may or may not be physically relevant. The technique is also very sensitive to noise- small currents are easy to distort- and there can be nonlinear effects from, say, electromagnetic fields generated by other equipment in the lab. The take-home for this technique is that it can give a lot of information about different processes, but it is easy to oversimplify and draw unwarranted conclusions.
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