 I have an announcement for people in presence here. It is assumed that people that are here in presence would come for dinner tonight. You're all invited, care of the conference. It would be a good idea if those that do not intend to come could write an email or inform the secretaries that they cannot come, that they will not come. This is simpler to avoid a mismatch of numbers, okay? The second thing is, those that come would have to comply. They would have to get the menu that we agreed. It would be the same menu for everybody, and it is fish. Now, for those that might have problems with that, either due to dietary restrictions or medical restrictions or whatever, would you please inform, I mean, it is supposed that there wouldn't be a minority, just a few people that have these problems. Please inform the secretaries of these problems so that you get a different menu, just for yourself, for everybody else that should be quite a decent menu. The place is called, as I said, Monte Carlo. I hope they don't toss the dice too much as to what they are going to give us. Have a good day. Okay, thank you, Irio. So, it's my pleasure to open this morning session of this Tuesday. My name is Lars Pastefka from Freiburg, and I'll be chairing this session. And it's a great pleasure to announce Michael Urbach, who unfortunately can't be here. It would have been great to meet, but of course, he will deliver a great science to us in the next 30 minutes on fascinating frictional properties of layered materials. Michael, the floor is yours. Thank you, Lars. First of all, I would like to thank Irio, Ernst, and Andrea Vanossi for organizing this excellent conference and for inviting me. I am also very happy to see that Annalisa is here. Actually, Annalisa made pioneering contributions to our understanding of mechanical and frictional properties of layered materials, and I learned from her a lot. And I will tell you about our recent studies, which are still in progress of frictional properties with layered materials. Okay, why it doesn't work? It doesn't move for some reason. Okay, this work is done in collaboration with Odette Odd from Tel Aviv University, and we were lucky to have great postdoctoral students who did the work. David Mandeli, who is now working with Michele Perinelli, Wengen Ouyang, who is now a professor at Wuhan University, Shen Gao, who is still with us, and a significant part of this work has been done in collaboration with Yuan Shui-Zhen and Ming Ma from Ching Wei University. Okay, so this is the outline of my work. I'm not sure that I will be able to cover all of these topics, but I will say a few words why we are interested in layered materials. I will talk about robust superlubricity in layered materials, about the possibility to have negative friction coefficient. I will talk about friction in nano ribbons sliding on the surface of graphene. Yesterday, Shen Gao talked about friction on polycrystalline surfaces, so I will not talk about this. I only would like to say that we continue this work. Now we are working with an experimental group of Ernst Meyer, with Emingson, and I hope we will have great results soon. And I will talk also about finite size effect in friction in layered materials. Okay, in this, yesterday, there were already many talks about friction with layered materials, so I don't need introduction. I only would like to say that the common property of these materials is that they have strong covalent interlayer bonds and weak wonder-wise interlayer interaction. This actually allows for the excellent frictional properties of these materials. Another important point is that using these materials we can easily build, at least for me as a ferrication, it's easy, diverse structures, including homogeneous interfaces that are connected between the same materials and also heterogeneous interfaces. And I will tell you about this. Okay, as already was shown yesterday, contacts of layered materials allow to control and manipulate frictional properties, and this is certainly very important for many applications. One of the most exciting properties of these materials was their ultra-low friction ultra-low wear called super-lubricity, and this phenomenon was observed in graphite, HBN, MOS2, and other transition metal decalcogenites. Okay, I would like to say that super-lubricity is important not only for tribology. For instance, very recently, experimental group in Tel Aviv University, led by Moshe Ben Chalon, they found that ferroelectricity in layered materials can be switched on and off and tuned, exploring actually super-lubric motion of domains of different staking. So now these days, I would like only to say that super-lubricity becomes important not only for tribology, but also for electronics. Okay, super-lubricity actually was first discovered as pure theoretical phenomena by, okay, in the 80s, after that it was found at nanoscale in beautiful work of Martin Duhembell and just Franken, and these days many experiments are done at micro scales and I show you here some examples, okay, but I will not go into details. I only would like to say that in most experiments, people looked at the interfaces, at graphitic interfaces, interfaces between the same materials. And this has some drawbacks. What are the drawbacks? First of all, when these materials, when we have graphitic contact, it can come to commensurate contact when two surfaces are in registry, and in this case actually system will be locked because of very high friction. You can start sliding being in incommensurate state as it's shown here, but after some time torque experienced by your slider will move you to commensurate state with high friction. Now another drawback mentioned actually by Annalisa is that you can observe superlubricity, ultra low friction at low loads, but when you increase load, quite at not very high load, actually the friction will increase significantly. These are two important points which we have to take to keep in mind. Looking at this, we decided to study interfaces between heterogeneous interfaces, and one of the examples on which we are using is interface between graphene and geaxonal boron nitrate, HBM. Geaxonal boron nitrate is very similar to graphene, actually has very similar structure. The only difference, small difference in atomic spacing, very small difference, and this is enough to have incommensurate state for any alignment. Our work predicted that in this case, super low, very ultra low friction, super structural superlubricity should be observed for any twist angles between two surfaces. Okay, here you can see some references, and okay, okay, and this was actually found later in experiments, which I will show you later. Important point is that describing modeling properties of layered materials, we have to use dedicated potentials. Importantly, in this case, it's important to use potentials which depend not only on the distance between atoms, but also on the lateral distance between atoms. This is probably first what was understood in the paper by Kolmogorov-Kraspy, and we extended this approach, mainly ODEAD, extended this approach, and we found that in order to describe correctly interaction between surfaces, it is extremely important to use these registry-dependent potentials. Okay, now for all studies which I will show you today, there are two important points. One is moire pattern between two surfaces, and this moire pattern depends on the misfit angle, on the twist angle. For instance, when we have aligned HBN and graphene interface, the period of moire pattern is about 13 nanometers, and this period decreases very fast with increasing angle between two surfaces. And this is one thing. And second thing, that when we apply a load to our system, actually we strongly influence out-of-plane corrugation of this moire pattern. This is shown here. Applying load, you reduce out-of-plane corrugation, and this also has a dramatic effect on frictional properties. As I told you, robust super-robricity has been predicted by ODEAD and by us together in contacts between graphene and HBN, and in the group of Ming Ma from Chinko University, they did, Iming Song did beautiful experiments actually supporting these predictions. He found that there is some anisotropy, angle anisotropy of friction, which you can see here, dependency of friction on twist angle. But the difference between high and low friction state is only, let's say, about three times. If we will take graphene interface, interface between two graphite surfaces for this, for microscopic, for micrometer size flakes, the difference will be about 10,000 times or even maybe more. So in this case, for any twist angle, they observed robust super-lubricity, very low friction which almost independent on normal load. When we looked at this system from the point of view of simulations using our dedicated potential, we actually found that the most important channel of energy dissipation, this is dissipation into out-of-plane fluctuations, fluctuations of out-of-plane propagation, and actually this channel depends on the angle, and this channel of dissipation provides dependence of friction on misfit angle. But as I told you, this effect is not that strong, friction force changes only three, four times when you change twist angle between two surfaces. Why this occurs? As I told you, when we increase the twist angle between two surfaces, corrugation decreases very fast, and as a result of this frictional dissipation in this channel, in the out-of-plane corrugation, out-of-plane flotation also decreases, giving only free time, let's say, anisotropy of friction. Okay, after this observation, we continued to work on this system, and we found actually, following this observation, we found that in this system we should observe negative friction coefficient. What does it mean negative friction coefficient? It means that when you increase normal load, friction should decrease, and indeed, these simulations, these atomistic simulations demonstrated this, as you can see in this slide, both for room temperature and for zero kelvin, okay, friction first decreases again here, the main effect, this is reduction of out-of-plane corrugation by normal load, of course, when you continue further increase load, you come to the range of powder repulsion forces, and friction starts increase again. Again, as I told you here, the most important effect is the reduction of out-of-plane corrugation due to normal load. Okay, we found that additional control of friction can be provided in finite size system, and we started to look at friction between nano ribbons and surfaces. In this case, we consider graphene nano ribbons sliding on graphite and HBN surfaces. Again, I would like to stress here that both nano ribbons and substrates in this case are flexible, so we take into account internal degrees of freedom, elasticity of both systems. Again, beautiful experiments on sliding of graphene nano ribbons on both surfaces have been done by, in the group of Ernst Mayer, and simulations have been done by Andrea Binassie, whom I guess also in the audience, and also by Eriota Parthosati and Andrea Binassie. But we consider the different systems, of course, using experience of the previous works. So this is basically our setup. As in atomic force microscopy measurements, we drive nano ribbon from the edge, okay, we apply force through the spring, and when we look what is going on. Just I would like to show you one movie to show why we called these nano ribbons nano surfaces, okay. This is graphene nano ribbon, relatively short graphene nano ribbon on HBN surface, and we start to drive it. Stress is accumulated at the leading edge, and you see it behaves later like snake. It tries to find most stable from an energetical point of view, commensurate situation, and this basically defines the motion of this nano ribbon. Okay. The most important from our point of observation, which we found in this system, this is dependence of friction force on the length of nano ribbon. Here you can see results in black for static friction, in red for magnetic friction, for both nano ribbon sliding on graphite and HBN. Important point here that above some size, about 15 nanometers, actually friction becomes practically independent on the length. What in both systems, okay, with some fluctuations, what is the reason of this origin of this phenomena? Actually it's very simple. When we drive our nano ribbon from the edge, stress is accumulated at the leading edge, as you can see here, it's accumulated, accumulated, it reaches some threshold value, and then sliding starts. The length, characteristic length of this range, range of length of stress accumulation depends on intrinsic properties of the nano ribbons, on stiffness of this nano ribbon at its interaction with the surface, and for these nano ribbons, on graphene nano ribbons on graphite surfaces, this is above about four nanometers. When the length of the nano ribbon becomes longer than this characteristic length, actually friction becomes independent because in any case, the stress can be accumulated only in this limited range of nano ribbon. Similar effect, a little bit more smeared, is observed for graphene nano ribbon on HBN surfaces. So friction becomes practically independent above the length of the order of 15 nanometers. This research was, frankly I have to say that this research was driven by purely scientific, okay, interest, okay, same, and but two years ago, a guy, Joanne, she from university, Jiaotang University from Shanghai approached us and asked to help in understanding the experiments. What are they doing? They are growing micrometer-long nano ribbons, narrow nano ribbons with the width of about three nanometers, directly on HBN surfaces, using metallic catalysts. You can see schematic picture here, and the results of experiments here. These experiments actually, and you can see the image of these nano ribbons, really beautiful nano ribbons, three nanometer width. Okay, as you know, HBN is isolating substrate, and I hope these growing nano ribbons directly, very well defined nano ribbons with narrow width directly on isolating substrate, can lead to important applications in the field of nano and microelectronics. So doing their measurements, they found that actually majority, here you can see, okay, distribution of corrality of nano ribbons grown in this way during catalytic growth. Majority of nano ribbons are armchair nano ribbons, and their length is limited, let's say, by four, five micrometers. It was not clear what is the origin of this phenomenon. So we started to look at these, and what is the relation between growth of nano ribbons and friction. When you grow nano ribbon at catalysts, when you would like to introduce additional unit at your catalyst, actually you have to overcome barrier for kinetic reaction. And this barrier depends on friction force opposing the growth of nano ribbons. Okay, so as I showed you before, our friction force is almost independent. It grows a little bit, but almost independent on the length of nano ribbon. And this actually allows to grow very long micrometer long nano ribbons. Okay, so velocity of growth can be described by this very simple equation, kinetic equation, where you have, okay, rate of growth of adding one unit to the nano ribbon, and also rate of the composition of nano ribbons. And as you can see, there is exponential dependence on friction force. We found that for a little long short nano ribbons, the difference in friction between armchair and zigzag nano ribbons is about 0.5 nano newtons. You can say this is a small number for this, but when you calculate the ratio between velocity of growth of these nano ribbons, the rate, these friction sits in exponent. So it gives you more than 100 times difference. And this is actually explanation why this, our explanation why in these experiments they observed mainly armchair nano ribbons, just friction for zigzag nano ribbons is larger. In this diagram also, I show you the, basically that friction limits the length of nano ribbons. At some point, at some length is about of, about a few micrometers, friction becomes larger than the driving force from the catalytic growth and nano ribbons cannot continue to grow. So I think it's an interesting example, as a pure scientific curiosity can lead to interesting and I hope important, also important implications. Okay, now I would like to share with you our results, which are still in progress. We are trying to understand all experimental system, of course, finance system. You have finite size flake, which you drive around along the surface. And now we would like to understand what is the origin of friction in this system. In majority of graphitic systems, the experiment results are summarized here. Friction grows more or less linearly with the size of graphitic flame. Of course, there is very big scatter of the results because for many reasons, but still all experiment results, which I'm aware of, okay, show more or less linear growth of the friction with the size of the system. Many people sitting at this conference participating in this conference, Martin Meusser, a lat-corin, Astrid, Andre Schermaisen, Mingma, Jin Wang, he gave a talk yesterday, Yuan Shijun, started the effect of dependence of friction on the size of the flame. And we're also using our experience and description of friction in layered materials interface, because this also decided to look at this phenomenon. And we found results, actually, from our point of view, unexpected results. Okay, so this is our system, and this is joint work between our group at Tel Aviv University and the group at Wuhan University, okay, where our former postdoc, Wengen Yang, Wengen Ouyang, is professor now. So this is our system. We consider finite flame, graphite flame sliding on graphite or HBN. In our simulations, the system includes three layers, okay, two layers, both substrate and slider include three layers, two layers, interfaces are flexible layers, okay, bottom layer and top layer are rigid layers, just to mimic effect of substrate. And we drive our system from the top. And we consider different geometries, okay, square flake, triangular flake, hexagonal flake, and circular flake. I will start showing you results for the relatively simple simulations where our system is rigid, both flake and graphite are rigid. In this case, friction just is completely determined by the interfacial sliding potential landscape, which is basically determined by moire pattern. So what do we see here? We see that this is dependence of friction on the size square of the area in units of the moire period. In this case, we are driving system along armchair direction, graphite, and moire period is about five nanometers. So you see here results for circular flake, for triangular, square, and hexagonal flake. So what do we see here? Right circles show your results of our simulations, okay, and black lines actually results of very simple model which just takes into account the interfacial sliding profile determined by moire pattern. And there is perfect agreement between both. Okay, what do we see? First of all, we see that in the case of circular flake, basically friction grows, envelope of friction grows as a square root of the radius of the flake. This is well-known results. I don't remember who first discovered this. For sure, a lot of the current discussed this phenomenon. But surprisingly, we found, and again, I forgot to tell you, these are results for five degree twist angle between two surfaces. So there in commensurate situation. Okay, when you look at other flake, triangular, square, and hexagonal flake, actually we see two different periods. One period, this is just small period. This is just moire pattern. It's observed also for circular flake. But second period is much larger. In this case, it's about 20 times longer. So I will say it's about almost 100 nanometers. And it can be described. Our analytical equations show that it depends on moire length divided by sign or twist angle, half of twist angle between two systems. So first of all, you see that for triangular, square, rectangular, hexagonal flake, friction does not grow with the size. It shows oscillations. Okay. And actually, you've seen that you have large period and almost zero friction force for this large period is explained by the situation that incomplete moire, for this size incomplete moire at one side of the slider is complimented by the incomplete moire at another side of the slider. At whole, you have basically complete moire and almost zero force. So you can see here that friction does not grow with size of the system. And I think as at least up to my knowledge, nobody found this. But actually, nobody did simulation for such big system. Size of the system here is, let's say, 25 moire size, moire is five nanometers. So it's more than 100 nanometers. Okay. And we also did simulation for larger sizes. So these are very large systems. This friction does not grow. Of course, you can ask me, okay, you showed in previous slides that experiments friction grows. Why your simulation shows that friction doesn't grow with the size. You know, I can give you many different reasons. Maybe one first obvious is that these simulations are simulations for rigid system and maybe for flexible system behavior is different. But our preliminary results shows that this is not the case. Another possibility, of course, that at the edges of the flake, you have contaminants and this will lead to linear dependence on the size. Okay. Here I would like to show you how this effect depends on the angle. Okay. So the first plot, let's say this is five degree twist angle between system and with increase of twist angle between two systems, period, large period, decreases. Okay. Decreases, but it's well described by the simple model taking into account sliding potential due to moire structure. Now we looked at friction again with rigid system for inhomogeneous interface, okay, interface between graphene and HBN. We have graphene flake, rigid graphene flake, sliding on HBN. And the results are interesting. Again, I show you first in left column results for aligned system. In this case, even aligned system isn't commensurate. And again, for circular flake, as before, we have dependence on the square of the radius. For square flake, the friction envelope of friction grows as length of the system. Again, I'm saying, telling you, this is incommensurate system. Previously, for twisted incommensurate system, I showed you that friction does not grow. But here for aligned, but incommensurate system, friction grows as a size of the system. Again, small period here, this is period of moire. But when we twist our system, for small angle, about one degree between graphene and HBN, we start to see the same situation as for homogeneous contact, graphitic contact. For circular flake situation is more or less the same. But for square flake, we observe two periods, small period, moire period and large period, which depends on the angle, twist angle between these two systems. So again, we do not, for all geometries, except circular, we do not observe friction with increase of size. But again, I would like to stress that this is for rigid system. What is going on for flexible system? How much time do I have? Okay, I will just show you a few. You have two more minutes, but that's including questions. I should come to an end if that's possible. Okay, I'm coming to the end. So basically here, I show you results for flexible system. In this case, this is flexible graphene on HBN. This is again aligned system. This is kinetic friction. This is static friction. This is periodicity. Periodicity depends on moire size. And actually for static friction, we found that simulations with flexible systems, when we look at maximal force, which we observe calculating force traces, these maximal forces agrees excellent, agree excellent with simulation with rigid system. So basically, rigid system gives us very good estimation of maximal forces. You can consider this as a static friction. I will show you again, just one, this slide. This is energy dissipation map in this system. And you can see that most dissipation occurs at the edges and at the corners. Contribution of corners is extremely important, especially for square and triangular flake. And when we look at the scaling of this friction in this flexible system, this is what you see here. You see scaling for different geometry, rectangular, square, triangular geometry. And actually you see that for kinetic friction, this is the friction obtained by averaging friction traces. The scaling, these are results for aligned system. Friction scales, envelope for friction scales as a size of the system. But also there is very important, very significant contribution of the corners, which is independent of the size. This contribution, especially high for triangular flake, but also is very high for square and rectangular flakes. Okay. And this is my last slide, natural question which arise. At what size actually the contribution of edges and corners will become smaller than contribution of the surface area? And our simulations show that this contribution of area will start dominate only above few micrometers. It depends on the system, above few or maybe tens of micrometers. I will stop at this point and I will put my conclusion. Thank you for your attention. Thank you, Michael. Already a little bit behind, so maybe two quick questions for Michael. Thank you, Michael. You showed that for graph flakes on graphite or graphene, what are graphite, graphite, graphene, graphene, the scaling in the experiments was pretty much linear with area. And you do see linear scaling with area with your graph on an HBN. But if I followed you said for graphene, graphene, it's not linear. It's shape dependent. So how do you, I'm wondering what your ideas are to reconcile the experimental trends you showed with the simulation results? Again, first of all, I would like to stress that linear dependence for graphite or HBN, we found only for aligned system, for misaligned system. Also for graphite or HBN, there is no increase of friction with size of the system for both rigid and flexible. And again, I think in our simulations, we went to the largest systems with flexible, flexible system of the size of 100 millimeters. Now, how do I explain this difference between the simulations and experiments? My guess is that there are, all these experiments have been done in air. And my guess is that there are contaminations at the edges. Okay. Martin, we saw the question last one. Yes, yes. Thanks, Michael. I just wish to comment that I'm not so surprised at the scaling because all the scaling arguments about the contact area assume randomness. So I think if your circle is not a perfect circle, but you add randomness to how you cut the circle out, you will get a square root dependence with the circumference of the friction force. And otherwise, you get pretty much systematic annihilation within the contact area because it simply integrate out sine and cosines and that averages to zero. And then as you move along the circumference, you pretty much integrate over a frequency modulated pattern. And so what I see is frequency modulation as it is used in radio broadcasting, right? And I think this is really at the origin of your signals. Or would you contradict to that statement? Martin, thank you. I completely agree with you. This is what we observe here. But I think this is first, let's say, first time when in simulations or in theory, people suggest this behavior. All previous, again, all previous results which I am aware of show different kind of scaling with, but increase with size of this increase. But I think it was emphasized in the literature that you need randomness along the outer rim to come up with all these scaling arguments. And if you don't have that, and I think as to discuss that too, if you have a perfect alignment of your circumference with a crystallographic axis, you get a different friction force than if you don't have such a thing. So I agree with you that maybe the first time that it has been evaluated. But I think the principal ideas have been out in the papers by Astved and myself. Yes, I agree with you. You noted, and of course, you know, you noted that randomness is extremely important. I completely agree with you. Again, I would like to say that probably scattered of scattering of the result, experiment result is related to this randomness in preparation of samples. Right. Of samples used in this experiment have more or less, I will say, well defined square rectangle or triangle shape. Of course, with some randomness, I agree. It's interesting point which you raised, how randomness and how strong should be randomness to destroy this modulation, which I showed. It's interesting. I agree. Okay. Thank you. Thank you. I think we should move on. So thanks, Michael, for a very nice talk. The next one up is Renato Putzio.