 You have a three-minute warning for the question period. OK, so Jin Wang from. Hello, everyone. I'm Jin Wang from SITSA and ICTP. It's glad for me to participate in this conference and give a talk here. Today, my topic is the sliding and pinning sublubric 2D material interfaces. There are several points I want to cover today, the background of structural sublubricity, some cases about periodic boundary condition stardis and open boundary condition stardis, also some further generalizations. Sublubricity permits an archer-low sliding friction due to the incommensured contacts. And usually there, we could achieve incommensured contacts by lattice mismatchin and twisting. 2D materials like graphene, hexano-birton nitride, and molybdenum disulfide are good candidates for sublubricity, things that atomically smooth interfaces and a relatively high in plane stiffness. So start from several decades ago, people start to pursue the application of sublubricity in real world. And but before that, the friction behavior of sublubricity should be understood beyond the present state. So the first thing I want to talk about some simulation is about periodic boundary condition twisted by layer graphene, supported by layer graphene. Here is the simulation model. We drag the upper layer and the lower layer is the static stationary. And we highlight the central green region in case you cannot see it's moving because of periodic boundary condition. And some detailed simulation protocol are listed here. So here in the right figure is our simulation result. The blue starts the friction pattern as a function of the twist angle, misfit angle. And you could see the friction increase as we decrease the twist angle from 30 degree and saturate at about 10 degree. And actually, we derived some theory for this. And it agree with our MD simulation pretty well. These are analytical expression. C is a pre-factor and has expression here. M is the atomic mass. Eta is the damping coefficient characterized the energy dissipating rate. V0 is the sliding velocity. And the important parameter H here is the auto-playing corrugation of the more restructure. As you may find here, all other parameters does not really correlated with the twist angle theta, but this H. So we should talk more details about this H. Firstly, see some simulation result with different twist angle. We optimized the bi-layer structure. And there are three typical regimes. Here are the 0.4 degree, 6 degree, and 30 degree. The upper panel is the auto-playing corrugation height structure. And the middle panel is the structure profile. The lower panel is the maximum, minimum, the coordinate. And the average is the coordinate of different twist angle. And benefit from our analytical derivation, we have an analytical expression here for this corrugation height H. So for twist angle larger than 10 degree, the more resize lambda is so tiny. So in this denominator, the first term dominates. And it is related to the bending stiffness of graphene, this D. And if the twist angle decrease down to 10 degree, lambda, the more resize again, becomes larger. And now the second term wins again. And when twist angle keep decreasing, this lambda keep increase. So this term, OK, these two terms can actually be cancelled out. So this whole formula becomes constant. That is the reason for the saturation of the H at the small twist angle. And apart from these two regimes, actually there is an additional regime as you could see here for twist angle smaller than 3 degree. The structure profile looks like a flat tie. It's no more sinusoid like the larger twist angle. So it's a flat tie regime. Some people believe this flat tie regime, which correspond to the more reconstruction and give rise to larger AB and BA region, should be overpained. So to answer this question, we perform a quasi-static simulation to extract the maximum static friction. And you could see here in the left figure, no matter the twist angle is smaller or larger than 3 degree, the static friction is in the same order of magnitude and much smaller than the rotated AB stacking case. And for a specific case, 0.6 degree, we calculate the pressure dependence and extract the coefficient of friction in the order of 10 to the minus 7. So basically, we believe this flat tie regime is also supra-rigged. So far, we talked about the bilayer graphene with purely boundary condition. But in real nature, everything is finite-sized. So we switch to some finite-sized simulation. And the lower left curve plot is mimics the experiment setup. And the lower upper figure is our simulation setup. Now we use four-layer graphene, the lower two are infinitely large mimics of the substrate. The upper two are finite-sized, mimics the slider. And all of them have the directional spring to mimic the normal elastic modulars of graphite. And the slider is jacked by a pulling spring with spring constant kp. And it's sliding with constant velocity v. So to some extent, our simulation model is similar to Prampton-Tomplinson model. And in PT model, two regime are divided by a dimensionless parameter, quasi, which describes the competence between the sliding energy barrier, u0, and the lateral stiffness, kp. When quasi is smaller than one, smooth sliding and larger than one, stick slip. So borrow this idea into our simulation with a fixed lattice spacing and the sliding energy barrier. We could switch between these two regime by adjusting the lateral stiffness of this spring. And here are two typical friction traces for two regimes. For subrubric regime, the lateral force evolves sinusoidally. But for stick slip regime, it's an apparent saw-tooth function, so stick slip sliding. And correspondingly, for area dependence of the kinetic friction, the superrubric regime gives a linear dependence. But for edge-controlled stick slip regime, it's a sublinear dependence. And for velocity dependence, again, superrubric regime, blue one, gives a linear dependence. And the stick slip regime, at the beginning, at low velocity, it's an apparent sublinear. And then return to linear. The crossover velocity could be determined by this equation. And could we use our simulation without understanding some existing experiment? Here in the right plot are two typical experiment results, starting the friction dependence on velocity. And it is the logarithmic dependence. So friction scales linearly as log v. Firstly, we replot this experiment data and then extrapolate it with the logarithmic function up to the high velocity range and compare it with our MD simulation result of stick slip regime. You could see that not only the magnitude of friction, but also the slope, the vibration tendency, agree with this experiment extrapolation pretty well. And compared to superrubric regime and our simulation, you could see if we choose the same velocity range, then the experiment friction should be orders of magnitude much larger than our superrubric regime result. This result indicates that the real experiment should be belong to stick slip regime. And in terms of that, it should be. Because in real experiment with typical lateral stiffness of FM tip, 10 Newton per meter, analysis spacing, and the sliding energy barrier extracted from these papers, they give the parameter side larger than one. So belong to stick slip regime. And finally, the temperature dependence. In our MD simulation with stick slip regime, friction decrease exponentially as temperature increase. And in superrubric regime, it increase linearly. And again in experiment, existing experiment, all of them friction decrease exponentially as the temperature increase. OK, so far people may ask, you talk about some nanoscale friction, but you want to use this knowledge to understand the microscale experiment. How is that possible? Yeah, it's reasonable. Because the smallest experiment now is still much larger than the maximum size of the simulation. But benefit from the supercomputer and the latest high efficient algorithm, we for the first time perform all atom MD simulation to field in this gap. And in the right plot is our result. These red circles are our simulation result with different size from nanometer to micrometer, billion atoms, and compared with some of the existing experiment and most from everyone here. As the first thing you could see, OK, the size scaling is, again, linear dependence between friction and contact area, which agree with our nanoscale simulation. And our simulation are nearly parallel to the existing experiment values, but are a little bit smaller. The reason could be, OK, we fixed with 30 degree twisted. So should give the smallest kinetic dissipation. And also in our simulation, there is no defects, no contaminants, no adsorbents. So everything is perfect, which could be the reason to give a smaller friction compared to the existing experiment. But the linear scaling seems to be same. OK, so far we talked about period boundary condition with different twisted angle. And there are three regimes containing the interesting flat-tie regime and open boundary condition. Two regime, stick slip, and a super break. So the next question will naturally be, what about open boundary condition, but flat-tie regime, smallest angle? So here we perform some simulation with two degree, which should be the flat-tie. And we start the static and kinetic friction of two degree and compare it with 30 degree results. From the left figure, you could see no matter if static or kinetic, two degree result it always larger than 30 degree. And if we focus on this two degree result, you could find some fluctuation behavior. It turns out that this fluctuation periodicity is correspond to the Moray size. For two degree, it's 7 nanometers. And what is the reason for this fluctuation behavior? So it turns out that the ABBA region that expels to the edge become the pinning point, which give rise to large kinetic friction. We pick two different sizes. Here, the local maximum, 10 nanometer, red one, and the local minimum friction, 14 nanometers. You could see for this 10 nanometer red one, the boundary cross directly through the sixth ABBA region. But for 14 nanometers, all AB and BA regions are hidden inside the boundary, which should be reasonable. And now, things we could already hewn this boundary pinning effect by changing the size. We no longer need to change this KP. So we fix the KP. But the tuning the size, thus tuning the sliding energy barrier and switch between stick slip regime and super brick regime. So for 10 nanometer case, again, the friction trace is show a stick slip behavior. And for 14 nanometers, it's a smooth sliding. And our velocity scaling result verified this. So for 2 degree 14 nanometers, this blue one, scales linearly. And for 10 nanometers, it scales apparently sub-linearly. And apart from the twisting, so we always talk about twisting. So apart from that, we could also change the incrementability more rescaling by changing lattice mismatch. So here, we actually use a simple way to change the biaxial's joint to apply a uniformly distributed biaxial's joint to the substrate, thus to introduce some more rescaling into a system. And again, here, show some similar fluctuation behavior. And this local maximum, 1, 3, 5, gives this stick slip friction trace. And the local minimum gives the super brick friction traces. And for specific cases, graphene sliding over hexano-bronitride with inherent lattice mismatch in about 2%, we also find this similar fluctuation behavior. The periodicity correspond to the more resized. Thus, for a 30 degree-tested misaligned case, there's no such fluctuation because the more re-subtiny. So basically, that's all of my talk today and brief summary. Firstly, different structural regime due to competition from interlayer and interlayer interaction and a smaller than 3 degree interesting flat-tie regime. All of these cases are super brick. And two different friction regime due to the edge-pinning effect. Super brick and stick slip regime, they have different area, velocity, and temperature scaling. And finally, recovering and extending many results in existing experiment. The overall picture of 10 years apply to general super brick interfaces. So that's my talk today. Thanks for your attention. Question? OK, questions? There's one over here. Oh, our speaker, our microphone assistant has been kidnapped. So, but I've got a backup plan. So here's your speaker. Thanks very much for a very nice talk. My question is about sort of elasticity. Am I assuming correct that all the simulations were rigid, essentially? So you are sliding? Flexible, or layers are flexible? OK, OK, did you ever see sort of interlocking? So that you have, because of elastic interaction, you can have local regions that interlock and that destroy, can destroy super lubricity. Depends a bit on the stiffness. Yes, and you mean at very large scale and then the elastic could destroy everything? And we estimate that size. That should be millimeter sized. So the shell stress and the shell modulars of the material, which give the very large size should be in order of millimeters. OK, that's for graphite and HBN and so forth. OK, so if you go to softer materials, it may actually move to the maximum. Yeah, might reduce to micrometer or even smaller. OK, thanks. Thank you. I see that there is a question in the chat. Are you able to open that up? Maybe I can read the two atoms. Could you read the question into the microphone? Thank you. OK, so how you estimated the contact area between atoms? Is the estimated contact area loaded dependent? If yes, how it looks like dependent? OK, it's actually a good question because for 2D materials, we already assume it's atomic flea smooth. So it's fully contacted. And so we believe no matter how large the normal pressure area applied, it should be the contact area should not change too much. And actually, we have some result about the normal pressure dependence and where that. So actually, when we apply this pressure to this open boundary cases, we could extract the friction coefficient of kinetic friction in order of 10 to the minus 4 from negative to positive. So basically, we think the contact area remains a constant. OK, thank you. Yes, thanks for the question. And I have a question. In your setup, can you say which layers are flexible and which layers are rigid? All layers here, four layers are flexible. They're all flexible. So there's no substrate, correct? Strictly speaking, yeah, no substrate. By the bottom and top layer are tethered to some of these proteins. OK. So what I'm wondering is, in a practical application, you are likely to have the graphene supported on a substrate. And it's very difficult, of course, to make that truly atomically flat. People have seen even the atomic scale roughness of silicon oxide, for example. It still can have some effect. So have you thought about or would you expect that there to be some influence if you had some roughness of the substrate, of a substrate? Yeah, actually, that's true. And in real nature, the atomic smooths could not really be achieved. And we started that in our previous work. And if the corrugation reaches three atoms, so one another atomic layer, then the superglue could behavior could be, to some extent, destroyed. So friction increases several orders of magnitude. OK, so roughness can have a strong effect. A strong and bad effect. Yeah. OK, very good. Thank you. Any last questions? One over here. Yeah, thanks. That's probably very nice. But just to see, I understand. You said there is no substrate. How can you apply pressure on your system where it doesn't just fall apart? You hold it on a theta at the low level? Your first graphene plane, if you apply pressure, and there is nothing behind it, you should just go down. OK, you mean, again, this model? So actually, we apply some z-directional spring to reject the outer plane movement of the bottom layer. So it cannot really move. So it's soft on the plane, but it's hard on the plane. Yeah, it's soft in plane and also out of plane. But the outer plane, the z-directional movement, are actually rejected by some non-exist spring. So to mimic the normal elasticity of the material. Thanks for the question. Very good. OK, let's thank the speaker again. And our next speaker will be Roland Benowitz from the Liebnitz Institute for New Materials in Tsarbruk in Germany. So two talks from Tsarbruk.