 Up for Laurence. OK, good I said that before. Our upcoming second part of the session is purely online. Speakers in the majority are first name is Lawrence or Lawrence. And I don't know if that actually is the sorting criteria area. OK, he's busy. Anyways, though, let us get started. And it's my pleasure to introduce his first speaker, Lawrence Marks, who's joining us, I guess, from Chicago or suburbs. And it's going to talk to us. Oh, another. We had actually a similar picture before this week about how flexing materials actually does introduce charges. And Laurie, give me one second to change the setup here again to a view where you are in the center of attention as soon as you're speaking. OK, Laurie, the stage is yours. Thank you, Roland. I wish I could actually be there, unfortunately. It's actually still turn time here. I have to give an exam next week. Otherwise, I'd be enjoying, as Roland said, the blue skies and the warm weather. I wouldn't be actually sitting in the room. I'd probably be swimming. So I'm going to be talking about something different. Really, this is the work of three very good students, Carl, who is actually sitting. He's actually in the audience today. He's done some of the most recent work. Chris, who did some of the earliest work and is now a postdoc at Los Alamos and Alex, who added some tribology inputs to a lot of the work and is now a postdoc at Brookhaven. And my name is as appropriate small. And this work, it's really four papers, although I'm only going to be talking about work related to three of them. The first one is a PRL from a few years ago, just pre-COVID. The second one, I'm not going to mention anything out about it, but it's got actually a lot of relevance. And there's two others, both in nanoletters, which literally came out within the last couple of weeks. So the first part of the work is related to going from the macro scale to the micro scale for tribo electricity. And then the last two papers relate to going down to the nanoscale. Overview, I'll talk a little bit about tribo you've already heard. I will talk about flexor electricity. If I was there in person, I would actually ask people to raise their hands if they'd heard of tribo electricity. It's one of these weird things not many people have. Tribo electricity or flexor electricity, not many people have. Tribo electricity, right, goes back 2,500 odd years. This is actually a picture from a statue of Thales. And the word electron comes from, in fact, the Greek word for amber, which is where it was first discovered. And the basic concept, and this is a very simple picture that you will see in many places, is you put two solids on top of each other. As everybody knows, of course, we all know better, but as everybody knows, also solids are flat surfaces. They slide, you get charges, and then you separate. Yes, I will come back and correct this later. There's many areas going from powering wearable electronics to dust storms, of course, lightning. What you may not know, and I found this one out relatively recently, is that there is a significant role for tribo electricity in actually how your body gets rid of bacteria. And something else which you may not know about is that there is one accident industrially a week associated with static electricity from tribo electricity. It's a massive thing, many different areas. And it's got a huge history. One of the most standard ones is the tribo electric series. And we already heard from Martin earlier on, this is known to be wrong, but it still exists, and you will still find papers. Tribo electricity is an amazing area where not that many people have read the older papers from the 60s and the 70s, or even going back to the turn of the 20th century. There are some very important papers there. They're basically forgotten. And people have sort of very simple ideas like differences in work functions, iron transfer, and what they call reactions. And I'm actually calling them transfer layers, because really, for any good tribologist, what you've got going on here is the formation of a transfer layer. Now, there are some big issues. First thing, charge transfer is known to be inhomogeneous. You can't simply say, I have A on B, and I get transfer from A to B. That just does not occur. Secondly, curvature matters. There's a beautiful paper back in 1910. It's a schoolteacher from Glasgow. Somebody else read it out. It actually appears in nature. And he showed that with a little bit of material, there's essentially a guitar pick. Depending on which side it was, which way it was bent, the charging was different. The tribal current scales is F to 1 third. And in this audience, if you know your contact mechanics, that should raise some big bells. Tribal charging is bipolar. In other words, when you come down, it's different from when you go up. Depends upon the pre-strain. One thing which is very curious, but you'll see later, it can change sign with pressure. Different sized particles. This is one of the things which is very important for the pharmaceutical industry, as well as other things like lightning. Small particles charge one way, large particles charge another. And then there's other things like work function, dielectric, constants, trap states, temperature, all matter. But there is one big issue. And this is where this whole thing started for me. You can't beat Gibbs. This is something which I tell my students all the time. If you try and do something which is thermodynamically uphill, then you're just being dumb. Why does it occur? The free energy change must be negative. That's a big thing. And the other question is, why is there rubbing required? It is not simply a contact. It is truly rubbing. So let's be a little bit more accurate. We all know this. Friction is truly plastic elastic sliding. John gave us a nice revision of this. The question we have to ask is, when you have asperities, can you get potentials? And the answer is actually yes. And it's been known since the early 60s. These are the two seminal papers. It was in Russia. So of course at that time, nobody in the West saw it. And it really wasn't until the start of the 21st century that people started to pay attention to it. And essentially what you have is the polarization is coupled to the strain gradient. This here is one of the early pictures. This is a piece of strontium titanate and it is actually vibrating when the potential is put across it. Why is this occurring? Well, simple. Let's take a centrosymmetric and we have the red and the green as ions. It doesn't really matter too much how ionic they are. If I make a strain to this straightforward linear strain, then nothing happens, there is no field. If I have something where I have, do not have centrosymmetric, I have a piezoelectric material and I strain it, then I get a field. Fine. However, there are not that many piezoelectric materials and it was studied to death back in the 1930s that piezoelectricity does not explain triboelectricity in quotes. Flexoelectricity is when you have a symmetric material and you have a bending type of strain which is basically a strain gradient and you see that this breaks the central symmetry so it actually creates a field. This occurs in every insulator and it doesn't matter whether it is an oxide, a semiconductor, a biological material or a polymer. It occurs, hasn't necessarily been measured, but it occurs and I'll leave aside whether or not it'll ever occur in the metal. What you have is an energy density, you have more familiar terms, you may have come across like electrostriction and piezoelectricity and this flexoelectricity term. Where technically speaking, you have a gradient, both of the polarization and the displacement. One thing which is of some importance is because you have a gradient here, you always have an intrinsic one over R dependence. Which means that flexoelectricity becomes very large at the nano scale. At the macro scale, it is not important or it's very minorly important. But there's increasing evidence, many different areas that it is important and maybe even in some cases dominant at the nano scale. And I'm not gonna go into this in any great big detail but there's been somewhat of a struggle but nowadays you can just about calculate it and have an issue, it's higher order moments. So going back to the triboelectricity, key point, the asperities, when you have contact shear bending of an insulator or a polymer, that is gonna give you a strain gradient, strain gradients give you polarizations. That means that it's gonna be a energy gain to transfer charge and it doesn't really matter whether or not this is electrons, ions or charged molecular fragments, I'm not gonna get involved in that argument. Independent of this because if you have flexoelectricity, then Homer is gonna actually gonna be satisfied. You're obeying the laws of physics. Big question there, are the fields large enough to matter? And this is the first paper with Chris and Alex where we looked at the question of what are the potentials gonna be here? So it's what I call a spherical bicycle approximation. You make it as simple as possible. So you take a sphere on a flat, Hertzian approximation, look at the indentation case, look at the pull-off case, you can look up the deformation fields we hear use the Hertzian later on I'll correct that and then you get the flexoelectric fields from those. Simplify it. Now you don't have to do this, but as you might guess, this is a fourth order tensor here. So the math of this gets a little bit hairy. So it's nice to make some approximations. We said, okay, let's just do an isotropic material. And we forget about the question of the surface, well, there's no surface charge. The electromagnetism here is kind of nasty. The polarization is kind of nasty as well. Here, it's strain gradients, right? The notation that is used, we use and others have used, it's this first index here is the one that you're taking the derivative of. So this doesn't look like what you've seen before for Hertz, but this is the Z derivative of the XX. So XX would be in this plane, the Z would be in this plane. These are large. These are the shear ones. Generally, the shear terms are somewhat smaller. And in fact, the flexor coupling terms for the shears are probably very much smaller to almost negligible. Although that is a generalization which may not always be right. And you can calculate essentially the effective field. This one here is the simplest one. This is the real message for the start is that you've got fields of the order of volts per nanometer. They are large. So that means that typically around an disparity, you can have some votes of difference. And actually these two here, that one is for 10 volts for what's called the flexor coupling voltage. This one is for one volt. There are cases with polymers where this constant F, the flexor coupling voltage is actually got values measured of 100 volts. So these potentials can be very large. The pull-off case is somewhat simpler. Standard JKR theory, I won't go into any great big details because I've got so much I want to get through. Summary at least for the first part is the potential you're going to get is going to scale as a constant, which is a materials constant which can be just about calculated or measured. Your force, r squared, so that's your tip radius and Young's modulus. And for pull-off, it's rather similar except because you've got a gamma over top, over the top, it's over r. And this F value, as I say, is one to 10, but it could be 100. All right, so that's the spherical bicycle model. Does the bicycle work? Now, I could give you about 50 different slides going back to the original work I mentioned earlier of Jamison in 1910. I'm just going to give you a few for more recent work. One of the nice things about more recent work is that the measurements have been better. So here is something from Putnamen which shows that the tribo-current scales is F to the 1 third. There's a couple of different cases. And of course, that is exactly what you expect from the model that I showed you. And he's actually, I really shouldn't be calling this a model because the flexor-electric effect is a known phenomena. If you want to call the flexor-electric a model, you're calling indentation a model phenomena. This is some work from Ali-Odema, which shows bipolar. So in other words, here is your friction. He was actually sliding with a load and you get charge injection and then charge transfer. And you may notice these go in different directions which is exactly what you expect because there is a sign change going in versus coming out. And that just drops out. Something from ZL Wang. This is a case where you have two pieces of the same material, A and B, you bend it this way. Without contact, when you contact and then separation, you get potential like this. If you bend it the other way, you may see these reverse. That is automatically in because the flexor-electric term is a curvature dependent. So you are changing the sign here. And then some work originally from BetaKin et al in science, but the bow did a very nice analysis of this showing that the charge is inhomogeneous, which is exactly what you would expect for having rough contacts. And the last one I believe of this, if you take two materials where there's no strain, you get a charging distribution like this. And if you strain one, it shifts. And of course, if you have a rough surface and you apply a strain, then you are actually getting flexor-electric terms at these asperities. And also, just for fun, almost certainly this connects up to the X-ray emission. And also there's a whole area of what is called triboluminescence and fractoluminescence, where you're getting large potentials and large electric charges with cracks and so on. In fact, the case for cracks is known already to be related to flexor-electricity. So we've got some of the issues handled, but there's still three which we don't have. So the next step is actually not just these two, but to go one further and to actually do properly the band bending. And I'm going to skip an awful lot of this for reasons of time. If I had another hour, I could do it. Actually, I probably couldn't do it. We need to have Chris here. I can talk with people about this later on, maybe over the post-sessions. Essentially, you have to calculate the potential from the polarization properly. The strain terms, something of the meaning of potential, which is really rather important, and you have to go beyond the Hertz type of solutions. So this is an example. This is a sphere of the same material on the flat. You actually get an asymmetry. You can see here, I've got positive potential. Here, I have negative. There is an asymmetry between the two sides, most noticeably here. So this corresponds to, this one is 0.89, which is about here. This one is slightly on the other side where it's opened up, but you break the symmetry if you go beyond Hertz. Something that everybody may know, I would just mention it, the Hertz solutions are artificially symmetric. And just as a nice example, although this is known from many other work, this is some beautiful experiments by Heinrich Jäger, where with one set of particles, which are smaller, or one set of particles, which are larger, you see a linear charging of the two sides. Two different cases, but the opposite sides. This is one of the things which is dropping out, at least at the qualitative level. Some of these things, I'm pretty certain that we have this quantitative, we haven't had a chance to put it together for publication as of yet. Another one which is really rather important is the band bending between two different materials can actually go from a simple case here, where you have the valence bands, sorry, the valence bands and the conduction bands separated to a case where now, actually here, they start to overlap, and now you will have what is called Xenotunneling. So there will be a reversal of the charge transfer between that case and that case. And this has been known as well for some time. There's a nice example here from Jan Lee's group, where maybe this one is the simplest case as a function of the load, the potential changes. So weak load, tip to the substrate, high load, substrate to the tip. Xenotunneling. The last part, and I'll just do this in the last five-ish or so minutes, is can we actually quantitatively do this? And this is mainly Karl's work. Conductive AFM experiments on niobium-doped strontium titanate, that's the tip. After we've deformed it was actually stable at that size approximately, of course it starts to get off sharper. And as everybody knows, who's ever looked at a TEM image of a tip, they never look as nice as in the pretty pictures such as this. You have a flexoelectric shocky diode. So in this direction, the electrons are going over this barrier. So it's thermoionic emission with standard temperature dependence. In this direction is thermally assisted tunneling. When you apply a force, you're actually changing the band bending. This is the experimental data. So this is the lowest force here, the red on this side. As you have more force, these shifting. So in the forward direction is the lower voltage similarly in the reverse direction. You can take this data here and you would fit it by a thermoionic model with a parameter N, which is sort of a standard semiconductor fudge factor and an effective shocky barrier. And this is just a fitting for that effective shocky barrier. The dots of the results, that's an F to the one third. For the reverse case, where you've got tunneling, we just took very small current above the noise ceiling. You then have to include the mean inner potential, the flexoelectric potential and also the depletion potential. Quite a lot of work. In fact, I think Carl almost went nuts doing this, but he managed to do an excellent job on it in the end. You find that there's, it's not really obvious, but over here roughly there is a saddle point. The potential is going up here, it goes down here. There is a saddle point and to go from the tip, the tip would be here out to the main material. You have to go across the saddle point, which is shown schematically here. This is actually contours of the real case. So thermoionic is going over this effective barrier that's changing with the force. And then similarly the tunneling. And when you do the calculation somewhat nicely, that's the blue results of the calculation in the reverse, in the forward case, which works really rather nice. In the reverse case, it's perhaps not quite so good. I mean, this is tunneling, it's a little bit more picky to your sample. And almost certainly here, there is breakdown. It should go up here, but it doesn't want to continue. So there's much more still to be done. I mean, that is the, I think the first truly quantitative agreement between in this area, there's been a lot of work on flexor electricity and making calculations. Not everybody has included all the terms. There's still many things to be done. I mean, I'm just putting down a few of these. All right, got to go beyond Hertzian and JKR to include the shear types. Plowing, transfer layers. All right, there's a question I have in my mind. These large potentials of the order of volts, banana meter, what is the tribochemistry that those are doing? John Pethiker will probably give me some comments about the plastic flexor electric contributions. Gradient elasticity. Actually, this is almost certainly absolutely important. We can't live with standard elasticity. Dynamics of choice transfer. This, I'm not really sure anybody's ever measured this, but it should be something. And then of course, you have to do experiments and theory on this. And a little bit of a teaser. This is some preliminary results from Karl. Sphere versus cone with a sharp angle versus cone with a wide angle versus cylinder. The cylinder solution is almost certainly a little bit dodgy. You need gradient elasticity, but as you can see, the black is where you have a negative. The white is where you have positive. Very significant effect from the tip shape. Not necessarily a great surprise. And if you go sheer versus just straight forward, you have significant effects. So this is the barrier around here, whereas here, the barrier is larger. And in fact, there's significant reduction in the barrier when you start to include sheer terms. Although I will say that this is preliminary. So I'm going to say that it doesn't explain everything, but it explains a really significant number of things. Reversal of transfer with force, identical materials, cure and roughness, temperature, balance, et cetera. And I really do want to stress this point at the bottom because I've had one or two people not really being clear about this. We're not proposing a model with ad hoc parameters. We are doing a calculation based upon known physics where all the different terms can actually be measured independently. And on that name, that note, I've left a few minutes for questions, so I'll pass it back to Roland. Thank you very much, Laurie, indeed, for working hard on this notoriously difficult to reproduce phenomenon. Are there questions? So let me start with Lars. I think, thanks a lot for a fascinating talk. I've got one comment, one question. One comment is you said that Appinicio calculations are almost there to calculate flexor electricity. As far as I know, Massimiliano Stengel has worked quite extensively on all sorts of codes and methods to do this in Appinicio. I'm not sure if you're aware of his work, otherwise. Oh, he's actually cited. That was the comment that my question is, so there's lots of reports in the literature on microstructuring surfaces that that enhances tribal electricity. What is your take on that? Why does that happen? It seems that nobody has an explanation for it, or at least not the people that do the microstructuring. Okay, I think you have to remember that there are relatively few tribologists who have actually worked seriously on tribal electricity. And with my apologies to Roland, I actually tried to get him involved at one stage and he was a little bit scared of the irreproducibility. Incidentally, there's Massimiliano Stengel's, right, he's actually one of the people referenced. You change the surface roughness, you are changing disparities fairly straightforward, at least at the qualitative level. Okay, I think, yeah, let's move to a question from Alejandro online. Can you unmute yourself? Okay. Yes, could you hear me? Yep. So what do you have to say in your picture about how the tribal electrification scales with the speed of the sliding between the materials in contact? Well, there's the very old Volta Helmholtz approach, which is at least partly true. And they said that the speed dependence was because you are hitting more asperities per second. That's not necessarily the only thing, because of course it's the same as the speed dependence of friction and the elastic deformation, right? So I would, we haven't done the calculation as of yet but I think you would take the standard models, I'm sure that there are, for the velocity dependence of deformation during friction and calculate the flexor-electric terms. Okay, so we have questions from three of our notorious question askers, Martin, Rob and Ariel. And, but in the interest of time, we have to move on because we killed poster sessions before and we will not kill the poster session today. And so thank you very much, Laurie and I hope that more experimentalists will sort of follow up on your questions. Various people, we can talk later. I think we have the virtual poster session that various people want to talk with me. Okay, thank you very much. So that we will move to our next talk in this session, which is actually on liquid solid artificial energies and the highlighting of