 It is with great pleasure that I have the opportunity to introduce our speaker for today, Professor Lyndon Archer. He joined Cornell University faculty in 2000. He earned his PhD in chemical engineering from Stanford University and a BS in chemical engineering from the University of Southern California. He worked as a postdoc for a year at Bell's Laboratory, I think with Ron Larson. Is that correct? And he was on the faculty at Texas A&M from 94 to 99 in chemical engineering. And then in 2010, after joining Cornell University in 2000, to 2016 he served as the director of the School of Chemical and Biomolecular Engineering at Cornell. And in the fall of 2017 he was appointed director of Cornell's Energy Systems Institute. Professor Archer is a fellow of the American Physical Society and a member of the National Academy of Engineering. His research contributions have been recognized within a variety of awards including the National Science Foundation Award for Special Creativity, the American Institute for Chemical Engineers, Centennial Engineer, and Nanoscience and Engineering Forum Awards. He's also received the Thompson Rooters World's Most Influential Scientific Minds, and also this was in Material Science. And not only is he a great researcher, he's also an awesome teacher. This won the James and Mary Tien's Award for Excellence in Teaching. And thrice, he's achieved the Merrill's Presidential Fellows as the most influential member of the Cornell University faculty. His research interest focuses on structure dynamics and transport phenomena in liquid, solid interfaces. Can all of the students who love transport phenomena give a clap? Alright, so I expect him to receive a standing ovation at the end of his presentation. Professor Archer is currently the James A. Friend Family Distinguished Professor in Chemical and Biomedical Engineering. And I think I better stop there so that he will have plenty of time to give his presentation. But let's give him a hand. Alright, so I assume someone is going to switch to the talk. So thanks, Michael, for a very nice introduction and Arvind for the invitation. This is actually my third time visiting Purdue in two decades. And you've done well by spacing them out. Please, I have a chance to pretend that some of you forgot what I said last time. But this is quite an honor. And I think that it is true to say that there's a sort of incremental aspect to academic research. It begins with an idea to solve in this talk a big problem, a hard problem having to do with energy storage. And it does it in a field that is actually dominated by chemists and material scientists. And so when I entered this field about a decade ago, the question was what can a chemical engineer do? And what value can a chemical engineer add? And it turns out Michael is quite prescient or has a good memory. That transport phenomena is really very interesting, gives you very interesting opportunities. So that's a sort of subplot of the talk I'm going to give you today. So we are going to start big to give you a sense of why the questions I'm asking are potentially important. And then we're going to go small to talk about what are some of the solutions one can do to these problems from the perspective of molecules and material design. So like I said, I want to start by giving you a perspective and a big picture. And I was actually quite impressed with this list of 21st century grand challenges that the National Academy of Engineering came up with in the year 2008. And what caught my attention was the first two of these grand challenges. That the claim was that by, you know, for the next century, you, me, us engineers, should make a contribution that solves these 10 questions. And in particular, these first two questions, affordable solar energy and energy from fusion. And I think any of you who've spent any time thinking about, you know, how the sun produces energy, how solar energy is created, understand that actually it is from fusion. So what this list is telling us, you either learn how to use energy from our existing sun or learn how to make your own sun that is portable. So it's really about the sun, okay? Now what does that have to do with the topic of the talk, which is energy storage? Well, one of the real miracles I would say of the last half a decade or so has been the speed with which energy cost produced from solar has been dropping. Such that now levelized costs are about five cents per kilowatt hour for solar energy contracts. Which means that solar energy can compete, pound for pound, with energy generated from fossil fuel combustion, which is remarkable considering that just five years ago, the thought was that the NAE, you know, those goals were unrealistic even for a century. All right, so the question obviously then is why don't we have solar energy everywhere? Why don't we have solar farms everywhere? Why aren't we decarbonizing by essentially building our own suns or using the existing sun to generate energy? The answer is in the bottom bullet that the essence of solar energy is that it's actually intermittent. Meaning the sun isn't always shining. The end result obviously is that you either have to go where the sun is, basically, you know, rotate the panel with the rotation of the earth, which will definitely push the price back up, or you discover a way to store energy when it's in abundance to reuse it. And this is where batteries that I want to talk about come in. Now their costs have actually been also declining, but not fast enough. They're roughly about $800 a kilowatt hour in 2013 to order $200 a kilowatt hour just last year. So batteries have been coming down quite rapidly in cost, largely because of the innovations and so forth people have been implementing in manufacturing of lithium ion technology. Now obviously batteries are needed beyond just balancing renewables and that provides an additional driving force for innovation. So they're needing for leveling wind energy, which is also like solar, intermittent. They're needed by you, right? So you guys want smaller, more powerful machines. That is unfortunately still limited by the power and energy density of our batteries. And of course with every passing year, there's not a new application that needs better batteries, right? So I started off with these drones, then the cool cars. And now everywhere you look, it seems like these autonomous robots are dominating and they need a supply of energy that is portable. So I was inspired by this chart that I didn't make, but I wish I had made. That's why I started adding to it, and you see my name now associated with this chart. But it was a chart made by my colleague Yetming Chan at MIT. So Yet basically did a technical economic assessment that looked at what it would take in terms of energy cost for batteries, or the cost of batteries per unit of energy stored to produce a mortise cost, right? So remember rechargeable battery doesn't just work one time. It works over some number of years, right? And the thought is that if the rechargeable battery operates trouble-free for over three years, what would the cost need to be so that we can get to the two to three cents a kilowatt hour a mortise cost? And he came up with this chart. So the red line is says that well, if we want to get there, the materials costs have to be at least $100 a kilowatt hour or lower. And so what Yet did is organize pretty much all of the couples, anode, cathode, chemistries that he could put his hands on and did this kind of assessment of materials cost. Now it is understood that the cost of the materials in the battery is not everything. That is just part of the cost. But the analysis that's going on in the background is that if you can keep this cost below $100 per kilowatt hour, you can maintain the overall a mortise cost below this two to three cents a kilowatt hour. That would be needed to be unbalanced with solar. So the interesting result, if you look at this chart, you will see that lithium ion technologies are largely bunched up near the $100 a kilowatt hour number and materials cost, which is a good thing, which is in fact why it is that solar is today important with lithium ion technology. But if you actually come down this chart to the chemistries that will cost a dollar a kilowatt hour, ten dollars per kilowatt hour, you see there are lots of chemistries, but if you look carefully you will notice that all of them use a metal as the battery anode. Sodium, zinc, lithium, aluminum. The more earth abundant the metal becomes and the more multivalent it is, it means the energy density and the cost are both, the energy density is going up, the cost is going down, and so the energy density per unit cost goes down very rapidly. Now the question then is why is it that we don't have batteries that use metals, sodium, zinc and so forth in current circulation? If these batteries have the propensity just on the basis of the energy density of the metal anode and on the basis of the earth abundance to produce the cost and performance criteria we need, why don't we have these batteries available today? And the answer is actually pretty simple and is the genesis of the idea that I had maybe about ten years ago that I'm going to describe to you today. So the first battery or the first lithium battery was in fact of the design that yet discovered would be cost effective. It was a so-called lithium metal battery discovered when this man who actually won the Nobel Prize in Chemistry just last year, Stan Whittingham, was employed by ExxonMobil of all places. And what Stan discovered is that a battery in which we stored charge essentially plating metallic lithium in the anode discharged the battery to store the lithium as lithium ions in a cathode that could be an intercalating material could produce lots of energy at a relatively low cost. These batteries were great in the laboratory but when they were brought into practice something very strange occurred and I want to start this lecture by showing you that animation of what that strange effect is. So again at first lithium is in the anode. When the battery discharges the lithium oxidizes becomes Li plus under the action of the electric field the Li plus moves from the anode to the cathode where it's hosted. When you discharge the battery you want exactly the same thing to happen and if you're going to get three years trouble free lifetime you want this to happen repeatedly over many cycles of charge and discharge. And so the animation is going to show you why we don't have batteries of this type today. So at first everything is going great. Charge this charge but then these structures known as dendrites begin to grow on the metal anode they very easily pierce this polymer separator cross over to the cathode short the battery internally the ohmic he generated as a consequence of that short is typically enough to ignite a liquid electrolyte in the space between the cell so these things are a safety hazard and no one will insure you if you put them in say an electric vehicle. Now what caught my attention was that this is a physical problem but at least that's what I thought at the beginning. This is a physical problem can we stop it using an understanding of physics? Can we stop the material from growing in this non-planar fashion to do something more planar by understanding fundamentally what causes it to form this instability and what are the factors that control the rate at which this instability develops and propagate. So I'm a planner so I wanted to understand what the literature understood about the source of this instability and the more I learned the more complicated it seems and so I'm going to try to tell you what I learned. So I learned that there are basically two effects one at low current that's driven primarily by chemistry and one at high current that is driven by fluid mechanics. In other words you can't escape whether you're at low or high current this instability happens. At low current it is thought that what occurs is at first the metal be it lithium, sodium, aluminum reacts with the electrolyte that's present in its vicinity to form what's called a solid electrolyte interface. So this is a new material that results from the chemical conversion of the electrolyte in contact with the metal. The trouble is that for reactive metals they're quite eager to participate in these reactions and so the end result is that they react everywhere they touch the electrolyte and the consequence is that you have this sort of patchy SEI a heterogeneous interface. Remember no one knows this right so don't get carried away. People just believe this is what occurs. And these heterogeneous interfaces as you can see from the differences in color are clearly different they might have different thicknesses they might have different transport properties and so the thought is that the next step in this process is that the places along the surface that have faster lithium transport are better hosts for lithium. The end result is that when lithium deposits during the first cycle it deposits in these bumps and these bumps are called dendrite nucleates. Now many of you have heard of the lightning rod effect the lightning rod effect basically goes something like this your odds of being struck by lightning if you're going to thunderstorm is like one in a million but if you go outside with a pointy metal pole your odds are one that you will be struck. And the reason for that is that the pointy metal pole concentrates electric field lines at a point and this then makes it an attractor for the lightning strikes exactly the same thing occurs inside the battery where these bumps become essentially like lightning rods the electric field lines concentrate on the rods accelerates the lithium deposition on the bumps and off to the races and the dendrites are formed. Alright so the first step is chemistry the second step is deposition and the third step is electrodynamics or electrohydrodynamics the deposition of the metal on the bumps so you've got to understand all of that in principle to solve this problem. The second pathway is actually somewhat more interesting and one that I will start with in terms of proposing solutions that basically any electrolyte that contains cations and anions driven at a current above a certain special value called the diffusion limit which is sort of like the speed limit at which ions can move in a liquid electrolyte develops a hydrodynamic instability that looks like turbulence the fluid mechanical turbulence and that instability in a closed cell has a certain pattern and the pattern is actually illustrated here in this very nice work by Hoof since the 1990s it has this very nice roll cell structure where it has the configuration that it dumps material to certain specialized spots at the interface between the electrolyte and the electrode with the end result that you produce not by chemistry but by hydrodynamics a configuration that's very similar to the one produced by chemistry bumps that are distributed on the surface and just as in this case once those bumps are formed they concentrate felines and off to the races the dendrites grow so what in the world can one do? So we spent a lot of time now classifying the types of instabilities that could occur as a consequence of the two pathways I just described and we know that they're essentially four there's a hydrodynamic which is the last thing I told you about this sort of idea that fluid mechanics produces turbulent like effects at the interface between the electrolyte and the electrode and then there's a first phenomenon a chemical that produces the bumps that act as lightning rods that ends up causing so-called morphological instability Now there are others there's a mechanical instability that I had some really nice discussions this morning with some people interested in mechanics of how dendrites form and break and there's also a kind of chemical corrosion type instability that is quite important but in the interest of keeping this stock under five hours I will just focus on the two and the intention is not to tell you everything but to give you a perspective on how we think what we do and what the results are So let's begin here and we're going to begin with a bit of an introduction to electrokinetics which is transport inside a battery So the equations of electrokinetics are written here and they look kind of foreboding but they're simple equations so the first one is the conservation of mass the second one is the conservation of momentum this one here is the conservation of mass in an incompressible fluid grad dot u equals to zero uf means the velocity of the fluid f means fluid and this one here is the so-called Planck equation or Coulomb's equation that basically tells you that all of this is happening inside an electric chemical system it's driven by an electric field Now in principle these equations are a set of very complicated coupled differential equations that could also be time dependent that you have to solve to determine the concentration of ions and how ions move the velocity in the electric chemical cell Now people are lazy and with some justification in general and they say well it's a battery it's a closed cell so we don't expect any fluid flow to occur so we set uf to be zero we say well we're going to wait long enough and we're going to consider this problem to reach steady state and so we set the time dependent terms to be zero and we say well in principle electroneutrality is typically right in liquids so we're going to basically set the right hand side of the Poisson equation to also be zero Now when you do that you get a very nice and interesting solution to this problem that's illustrated in the right where I plot basically the flux of ions or a current J as a function in this case of the potential V that I apply in other words the driving force what we find is that the current at low potentials is actually proportional to the potential this is a so-called Ohm's law-like response right V is equal to IR so the current just responds in proportion to the potential but when you get above a current this is a dimensionless potential of order four you notice the current saturates a certain value such that this ratio J over JL is one and that value is called the diffusion limit this is where J becomes JL the so-called limiting current so it's telling you that in an electrochemical cell there's a maximum current that you can operate at once you get to that maximum current it doesn't matter how hard you drive this system you can't get any more current out of this system that's what these equations tell us reality is very different in fact what people typically find is that if you measure the current versus voltage in an actual electrochemical cell you in fact get the Ohm's law regime as predicted at low potentials the linear regime you in fact get this transition to the limiting current regime but if you keep driving the system what you deserve is that you get an additional regime where the current starts to increase with voltage and this is referred to as over limiting conductance now when this was first discovered it was highly controversial it was controversial because most of the discoveries were made in electrolytes that used water and so the thought was that this extra current was actually coming from the electrolysis of water that you are basically breaking down the water and producing electrical energy in 2013 a group at Stanford decided well why don't we simulate this we have very powerful numerical simulations where we don't have to make any of the assumptions I made earlier to solve the Nernst-Planck equations let's just solve this thing with a very powerful computer and what they discovered this is the group of Alimani is something very beautiful so what they discovered that at first everything is fine the ions in the electrolyte are homogeneously distributed more or less in the bulk except for a very small layer the so-called quiescent electric double layer or the Dubai Huckle double layer some of you may know it that's affiliated to the surface that has a slight increase in positive charges because the surface is slightly negative in charge when you drive the system at potentials above the limiting current the prediction is that suddenly you start to create these roles these turbulent roles if you drive it even faster what they discovered is that these roles become chaotic and time dependent and in fact when you look at the chaos and the time dependence it looks very much like normal fluid mechanics so-called inertial turbulence but except this kind of turbulence is coming from the right hand side of the momentum balance equation it's coming from the coupling between the electric field and the charge distribution whereas the normal turbulence comes from the left hand side which is from the non-linear term the V grad V term in the momentum balance equation so this is an eye-opener that says that even in a system that is at flow fields well below what you would consider laminar it can become turbulent in an electric chemical setting I know the hydrodynamics folks are having fun and the rest of you are thinking what is he talking about so let's move on I have to say that that is fun so we decided simulations are simulations theories are theories is this really true so we decided to do an experiment very simple experiment where we took an electrolyte we put tracer particles in this electrolyte they're dyed blue this is why everything looks blue on the right and we developed a microscopy cell where we can just watch and see what happens to those tracer particles and we can then gradually ramp up the electric field to see if the simulations are right and so the next click should give you a video of what we see and there's nothing special here and so if you look near the wall you will see that all hell breaks loose in the fluid and in fact if you look at the structure of these roles you'll see that they're not dissimilar to what the theory says indicating that indeed this hydrodynamic instability predicted by simulations this role cell instability can produce convection and can produce highly localized convection which can lead to the instability in the high current case that I mentioned earlier so that was good now we can do more we can actually map out the velocity profile in the fluid near the wall and what we discovered is that if we now map out the velocity field based on the particles the velocity has two dominant components it has a component u that is parallel to the surface and a component v that's actually perpendicular to the surface so stuff comes in and goes out kind of like that okay and so this is u this is v no sorry I lied v u okay now what is even more interesting is that if you now monitor u as a function of distance from the wall so the wall is here right roughly at about 1200 or 1180 microns it initially rises with distance meaning this fluid is moving faster as you're going away from the wall but then it starts to fall and this point is what's called a boundary layer so there's a transition in the physics that are occurring as you go from the wall outwards such that if you were far away from the wall you might think that the fluid is actually slipping at this plane okay so this is a kind of interesting result so it's slipping near the plane and in the region near the wall the fluid is experiencing a very strong shear flow right very strong shear because the velocity is changing very quickly with distance what can a chemical engineer do alright well so so I convince a whole bunch of students that polymers are the answer okay and they've all gone on to do great things so it tells you they are partly the answer okay so the reason I thought polymers were the answer is that polymers allow us to do two very interesting things right so the first is illustrated in this cartoon we can create polymers in configurations that selectively stop the fluid from moving meaning they provide a net that stops the fluid from moving high viscosity net that stops the fluid from moving but if the spacing between the net is large enough the ions in the fluid can move as if the polymer is not there now why is that important we're trying to make a battery and at the end of the day if we stop the instability and also stop the ions we've gotten nowhere okay so polymers that are entangled with big entanglement spacings this is our kind of instinct would be a good idea because it can stop the hydrodynamic flow that produces the eddies without compromising the ability of ions to get to the interface which is what a battery needs to do and so I'm not a betting person so I decided that one hypothesis isn't enough you need two okay just so that you have a trap door in case the one does not work and so the second hypothesis is actually more interesting and it comes from the structure of the velocity profile of the particles we measured by experiment so the structure of the velocity profile told us that the fluid came down towards the surface and then moved outwards came down and outwards and remember earlier I said to you that the places where it came down were the places where the bumps bumps formed this is where the lightning rods form and that is called a stagnation point and so the thought is that if I can somehow have big enough polymers localized near the interface at that stagnation point they will be stretched out and when they are stretched out they should exert very large stresses on the fluid that essentially prevents stuff from accumulating at those stagnation points those were two theories now it turns out we can test them and I will tell you how we did so again more equations I am sorry but I had to do this alright so these are the same equations you saw before these are the same Nerdsplank equations except now what we want to do is model them in the presence of a polymer and when you write down equations for a fluid with a polymer you need what is called a constitutive law which essentially tells you how the velocity relates to the stresses alright nothing fancy so don't read every word okay and we decided to use this very special constitutive law called the Roli-Poli model right so it sounds cool right the Roli-Poli model is probably the best constitutive model for entangled polymers that is out there and so we knew that if the Roli-Poli model couldn't predict what we were observing nothing good because this is quite the best model right so that's what we did and then we did what's called linear stability analysis and so the idea is that we perturbed the surface we say what if bumps form what if bumps form well obviously if bumps form they change the boundary conditions the fluid experiences and that then propagates through all the equations all the variables and the question was if we then enforce the boundary conditions that the fluid the ions cannot the negative ions cannot penetrate through the interface and the positive ions deposit at the interface to produce a current we can then figure out what the growth rate is of these bumps that is a mouthful the answer is nicer cleaner so what we can do is actually plot that growth rate for a fixed polymer concentration 0.01 so that's 1% at a fixed potential so this potential is 10 times the critical potential where the current approaches the limiting value so we are well into this zone of bad stuff alright and the question we are asking is the growth rate negative or positive or 0 obviously if it's positive it means a bump once form will grow and the thing is unstable we will get dendrites if it's negative or 0 it means the bumps once form will not grow and that is a good thing and so what we decided to do is for a fixed polymer concentration to vary the molecular weight of the polymer and monitor the growth rate for different sizes of the initial bumps and this is called the wave number ok and even you can see what occurs right so when there is no polymer 0 the growth rate initially is close to 0 and then it diverges meaning the system is unstable as we increase to 100 same thing happens but when we get to about 500 or 2000 the thing is completely stable so it's telling us that my hypothesis at least has support from theory the theory tells me that my hypothesis that the polymer should be able to selectively stop the perturbations from growing the bumps from forming is reasonable alright so next I did it ok and this is a bit abbreviated so I did it I just put the polymers in and I chose polymers that had relatively high molecular weights so these are 8 million PEO and polymers that had relatively low concentrations to make big pores like I wanted so 0.5 weight percent 1 weight percent and I used that device that I showed you earlier to basically monitor how the velocity of fluid was going on near the wall and what you can see is that I changed the concentration of polymer the shape of this structure doesn't change a lot but the values change a lot right so for example if we look at the peak value in you we see that it goes down by something of order a factor of 4 to 5 ok in the presence of 0.5 weight percent polymer and when I go from 0.5 weight percent to 1 weight percent it goes down by another factor of 5 to 8 alright indicating that I'm suppressing this flow like crazy in the presence of this polymer what we also notice is that the distance at which the peak appears right so this is where the so-called boundary layer that I mentioned before appears begins to shrink so as we add polymer to the system the boundary layer begins to shrink meaning that any flow is being confined to a progressively tighter and tighter layer near the interface where it's less harmful alright so the experiments the visualization experiments tell us oh the polymer is appearing to suppress the electric convective flow but remember what started me along this line of attack was this experimental observation that says that in real systems when I push the system above the diffusion limit I get new flow I get new current and the question was if this is true that the polymer is able to slow down convection which is the source of the new current then it should be able to slow down the new current itself and so we measure that and that this turns out to be a much easier measurement to make so we basically measure the current J versus V in electrolytes that force had no polymer where initially linear and then they diverge in this case they don't even get to the limiting current the flow is so strong the convection is so strong but as we add polymer you see this kind of bending over of the curve so you shift it you shift this region of upturn this flow region out to much higher voltages indicating that you're able to stabilize the flow at any given voltage so that was kind of nice where I started though was can I stop the instability which produces the dendrites from occurring I'll skip that and the answer is my goodness yes so the student who did this was actually a very interesting student she wasn't interested to just do it for lithium where what we're doing again is plotting how the trace of particles move which I showed you earlier but also looking at how the interface grows in the top this is the absence of polymer in the bottom is when we add the polymer so in the top what you notice is that first of all the bumps grow in a random way so they begin to become dendritic and as I deposit more the bumps grow even more if I look at the trace of particle lines I can see that in fact the theory is right that the trace of particles appear to point towards the bump indicating that the fluid flows are in fact feeding the growth of the bump as we speculated at the beginning in the case of electrolytes with polymers you notice something very different the growth is not completely flat but more uniform than in the case without polymers and what we also notice if we monitor the trace of particles there's this gentle rain they just come down uniformly across the surface indicating that the polymer is able to provide uniformity in the deposition now I said the student was special that she was really surprised by this result even though we predicted it and so she decided to do it for sodium aluminum copper pretty much anything she could get her hand on and as reported in this paper it works in every case indicating that this phenomena is really not about chemistry of the metal it's more fundamental and it's more physical and it is an indication that by stopping the hydrodynamic instability we can stop this so-called morphological growth that produces dendritic deposition so that was fun now I guess more math so we wanted to know how the polymer worked right so I kind of showed you that it worked I kind of show you that it's working had consequences for the limiting current I kind of show you that that had consequences for the deposition but we wanted to know in detail what is it the polymer did okay and so we decided to do more simulations right again it's the same equations just that they're written in a nicer way again but instead of using that roly-poly polymer model we use a polymer model called the Fini-CR model that is actually more amenable to very straightforward numerical simulations and what is nice here is that we can now simulate the whole system including the polymer stresses to basically see what's going on when it's happening so we can learn what the mechanism is by which the polymer is producing stability and so perhaps you can understand why it's so effective across different types of chemistry alright so the results are kind of cool so the left is essentially a video showing you what occurs this number Debra number is actually a surrogate for the polymer effect so a big Debra number means a big polymer effect it's kind of like a large polymer concentration and if you stare at this thing you will notice that as the fluid lines come down the polymers this thing becomes red so the polymers are highly stretched just like I predicted earlier but then what is occurring is that even before the fluid stops coming down the polymer relaxes and then moves again with the end result that the polymer causes a kind of chaotic flow in its own self near the interface producing and it's more apparent in the case of high polymer concentration producing a kind of back flow that homogenizes the down flow of ions towards the interface and in so doing we believe homogenizes the deposition of the metal at the interface so it's not that the polymer is stopping anything the polymer is actually making it more chaotic by providing elastic stresses that are time dependent that are driving this sort of chaotic motion of the fluid in the vicinity of the surface and that chaotic motion is causing the current if we measure it with a function of position to become generally flatter in the case of a polymer where the Debra number is non-zero so more bumpy in the case of a polymer where there are hot spots in the case of no polymer where the Debra number is zero all right so the lessons from this part of the talk are actually pretty simple but pretty important the first lesson is indicated here that over limiting conductance this upturn in the IV curve is in fact produced by convection and what is important is that we can extend the diffusion limited regime by using polymers that provide visculasticity into liquid electrolyte and perhaps more important is that if we arrest that convective instability we can arrest the dendritic deposition of the metal with the idea that we introduce unsteadiness in the flow that makes it more uniform in deposition so that is that is part A part B is a little shorter but just as exciting alright so this is the high current case the low current case is hard because it starts with chemistry and the question that I struggled with was like how do you make lithium not behave like itself which is want to react to everything how do you make chemistry of lithium look like the chemistry of copper for example and I know how to do that now but at the time we did this work I didn't and so I did what chemical engineers do I cheated alright so I said well I can't do this with you know enough confidence so I'm going to pretend the lightning rods are formed and I'm going to ask in physics win over chemistry that's what I'm going to ask in other words I'm going to do yeah this is fun but I'm going to come back please maybe in the questions okay so I asked this question right so the question I asked is just as in the last part of the talk what if bumps are formed can I learn something from the Nernst Planck the stability of the Nernst Planck equations now at low currents not at high currents which is the case I did first at low currents that gives me hope that gives me hope okay so so we did the same thing as before so we write down again the conservation of mass equations and this is the flux the flux has basically three terms so there's a diffusion term there's an electro migration term that goes like the potential difference and there's a so-called pressure diffusion term which was not known before this work and the way this pressure diffusion term works is actually pretty simple so it works as follows so imagine that this is the battery and this thing is the separator so remember the plastic thing that is between the electrodes so our thinking was that when a bump forms it slightly compresses the separator because there's no place for it to go when it compresses the separator what it does is basically reduces the volume that is available for fluid so it increases the pressure slightly on the fluid and so our thinking was that region where the pressure is slightly higher it means the chemical potential of the fluid is slightly higher so the fluid has a tendency to want to move away from that part to go elsewhere on the electrode so this so-called pressure migration term actually acts against the bump so if the bump grows the localized pressure is higher so you push things out more so it kind of stops itself from growing so that was just a thought now just as again with that complicated roly-poly model we can pretend that this thing follows linear stability theory we can perturb all the equations and we can solve for the growth rate what we discovered is something remarkable for the field that no one as far as we know at a time expected so we came up with what's called a stability map which are again our regions where sigma the growth rate are positive negative or zero the way you should understand this map the regions that are in white sigma is negative meaning that you will get stable deposition if you can operate even a system that you have no control of its chemistry in the regions in gray are regions where the lightning rod just takes off and the odds are one that it becomes unstable now what was surprising to us is that by plotting the length scale of the bumps against the modulus of the separator which again enters through this pressure term we found that you can get stability at any pressure at any modulus and the field used to think that this is only possible for solid state electrolytes where the modulus of the electrolytes is bigger than the modulus of the metal in other words if the modulus of your separator or electrolyte is larger than the modulus of the metal it means the bumps just can't go through it what we are saying here not true we are saying that if you design the system right in such a way that lambda the length scale of the bumps are smaller than a certain critical value any modulus should be able to stop the dendrites from brewing controversial the stuff that you should be thrown out of a room like this for saying but we said it and then we did it so the question was how in the world can you do this well you can predict what that length scale needs to be by looking at what the normal parameters are in a typical electrolyte and it turns out for a typical one molar LIPF6 EC DMC popular electrolyte that number is 250 nanometers so it says if you can keep those spacings if you can keep those bumps below 250 nanometers you can stop dendrites from brewing in any electrolyte and so the way we did it is to create what are called nanoporous electrolytes in two different configurations so one are electrolytes created by cross-linking nanoparticles so these things are like porous media where you control the pore size that 250 nanometer number by basically the length of the ligands that connects the particles so that's relatively easy to do chemistry from chemistry so the end result is that you make plastic like sheets where these sheets have a secret that they're porous and this is what the secret looks like so the black spots are the particles so ions can't move through them the gray spots are the empty spaces that ions can move through and again by controlling the number density of the black spots I can control the gray space size so I can control this length scale lambda okay the other system is cleaner and actually more amenable to fundamental studies so what we decided to do is to create using anodized alumina which makes very beautiful porous structures where you can control the size of the pores by the voltage at which you create the porous structures to create things that have pore sizes at range I will show you in a minute all the way from a few tens of nanometers to hundreds of nanometers and these are straight pores so we can test the predictions somewhat more rigorously so to cut a long story short we used two different methods to evaluate efficacy so one method is called the galvanostatic plate strip experiment so we apply a constant current and take lithium or any metal for that matter from one object in this case a foil oxidize it to the ions and deposit on the second element again a metal foil and we do the constant current so we take lithium from one place strip it plate it on the next one once we do that for a certain period of time we reverse it and we basically measure the voltage if the system was behaving in a simple Ohm's law like way we would get a response like this an oscillatory response where the amplitude of the current remains more or less the same okay what we observe in general is that this kind of Ohm's law like response sustains for some number of cycles in this example for about 55 plate strip cycles but then it reaches a point where something gives and we have a sudden drop in the voltage meaning that there's a lower resistance pathway somewhere this is a dendrite this is a short indicating that you can quantify very easily the effectiveness of this membrane either based on the amount of charge past CD at a time the dendrites are formed or by the number of cycles at which they're formed now we like this number better because CD would be infinite in the case of something that stops the dendrites entirely such that it's reciprocal would be zero so this gives us a really simple figure to know whether this theory is right and whether the materials we've developed are effective and so so here are the results and so you look at them for yourselves so the red is the electrolyte without the nanostructured membrane and so what you see is that after roughly about 50 hours it's random it goes to zero then it cranks up back and then it goes to zero again and that's what we did this is what happens with a 20 nanometer porous structure it goes on for hundreds, thousands tens of thousands of hours and then the challenge becomes how does a student graduate if you just keep going so I wanted to make this thing fail because we had to know when it fails so we increase the current we increase the current the values that are not even normal in lithium cells and you can see it just goes on and on indicating that we've completely eliminated the propagation and proliferation of the dendritic bumps in these systems so the question was okay 20 nanometers is a lot bigger than 250 what happens is you begin to approach the limit specified by theory so we started to look at bigger and bigger AAL structures so 20, 50, 100, 200 300 at the highest current density and I think what you will notice here is that somewhere between 200 and 300 things went awry which is just remarkably consistent with the theory in fact I don't believe this to be true just so you know but it is true at least in this instance that it's almost right on the money telling us that the cutoff length scale is consistent with what we predicted theoretically there are lots of other things we did but I'm not going to bore you because I noticed that in trying to set the slides up I overstayed my welcome so I'm just going to end with this kind of summary slide that essentially says my group kind of went wild after this occurred and some of you who know my polymers were keep asking me when are you going to do more polymers were and the reason I can't is that students have been just excited by this result and we've been trying pretty much everything they can get their hands on from cross link polymers to this structure that I showed you to that structure very recently we have this very nice paper that showed up in science that looks at epitaxial control of the deposition and the framework is beautiful in that it really gives us a way of once we understand the stability of the interface it turns out that with the structure the stability of deposition so that's kind of what I told you in the second section the main result is that we're kind of excited that in a variety of configurations we can design electrolytes that appear to overcome this problem of battery failure or metal battery failure by dendrite formation on proliferation it's not over there are other things to work out and I'm happy to answer questions about some of those other things but I want to just spend a moment just saying thanks to the students who did all the great work so these are all just fabulous students one of the things we have at Cornell are just exceptional students like your professor Chang Li Yuan who many of you know who just go beyond beyond in terms of how they execute work and the elegance at which they do things and I do a lot of collaborative work with Don Koch who's a really nice person to work with and Jeff Coates who's probably one of the best polymer chemist I know and a lot of our work was actually funded not by the DOE as you might imagine but by the NSF who kind of saw this as a way of understanding how polymer structure might influence energy systems of the future alright so thank you for your attention and I'm happy to take any questions you've got we will start with we will start with a fourth of a question from students we will start with questions from students one transport question yes does the counter flow originate from the movement of the counter ion and if so does the transference number have an effect on the turbulence that's a great question so the answer is the flow actually results from the coupling between the concentration of the active ion and the electric potential the counter ion enters because electroneutrality would want the concentration of the counter ion to be everywhere equal to that of the active ion which in this case is a metal ion once you get a separation between those two as required to create a gradient in the concentration of the active ion you have an electric field penalty for that separation and so it sort of feeds on itself so that gradient creates a high electric field and is a product of that gradient and the electric field that drives the instability alright so it's so if you had a single ion conductor which is I think what you're alluding to something that literally prevents the gradient from occurring in theory we would expect to not have this instability at all and we have some work that shows that as you approach so-called transference numbers of one where you're not allowed to separate the ions because you're tethered together you do in fact have a suppressing effect that's bigger than what you see in the case of a neutral polymer one more question thank you I was wondering about the first part of your presentation regarding your really pulley model so I was wondering were you testing like polymers like for example I noticed you had done something with PEO so I was wondering if you had done some testing or knew if there was a difference between testing with the linear PEO polymer versus a like a graphed PEO polymer like PEGMA or something like that so that's something that's in our future and it's my way back to polymer science right it's an important question because there's a pretty large literature that tells us that the way a polymer stress is developed in response to share depends a lot on its architecture in particular polymers at our branch tend to stretch more and offer much larger elastic resistances than polymers that are linear and so a graphed polymer would be something that would be of a lot of interest but that would be definitely a possibility so what we will do is bring this part of the day to a close so let's thank our speaker