 Well, no, I think it's okay, this one is okay. Okay, so, hello, thanks, the organizers for this great conference and the opportunity to talk here. This work was done in Milan in collaboration with Melissa Gennetti and Roberto Guerra who are sitting here in the audience and Deva Nossi here from here to us and Michael Uberg from Tel Aviv who should have been here but they were here at least virtually. So, what about friction and velocity? We've heard that friction changes with velocity and usually most of the times, friction tends to decrease with velocity but in more complicated situations, actually we've seen also in previous talk for example that this might not be the case and so we try to figure out some model where this kind of non-conventional temperature dependence of friction can be explained and put in evidence quite in a transparent way. So, just a very quick summary of what we expect in say standard nano-friction experiments like within the quantumism model. The general idea is that the total potential energy contains a corrugation part and a spring part. So, this would be the total potential energy and the parameters that define this simple model, the lattice spacing of the corrugation, the advancement speed of the support and then say the corrugation is somehow related to load usually and the temperature would be modulated for example with a large event thermostat. So, at zero temperature, the situation is quite simple. There is essentially a single parameter which is the ratio of the amplitude of the corrugation to an effective energy related to the spring constant and when this parameter is bigger than one, basically there is a single minimum. The situation is not like this, the total potential is a single minimum and the sliding is smooth, everything is quite boring and basically friction will be proportional to the velocity just due to the damping term of the launch event thermostat. Instead, the situation becomes more interesting when this gamma is greater than one, so this corrugation is dominating and you have a number of minimal least two and in that case at zero temperature you have a stick slip regime and the slider will just jump from one minimum to the next at well defined times and then this will give you a situation where friction has less trivial dependence of speed, say that the simplest way to understand it is that friction is essentially independent of speed although there are of course some little details about this but say mainly friction happens just at the slip times and they don't depend much on speed, at least until speed is not too big. So for example, we will get some kind of a friction loop like this, this will be the quantumism model, this will be an actual experiment within AFM with a scan on over graphite. The quantumism model at t equals zero will give you a perfectly periodic sequence of jumps and stick slips in an experiment which is always carried out at finite temperature. These stick slips are not completely regular, they are also affected by noise and mainly temperature will have the effect of slightly anticipating slips due to thermal jumps across the barriers. This is another example of an experiment of this kind also on graphene and molybdenum disulfide with different number of layers and you always get this kind of friction loops with stick slip with some noise due to thermal fluctuations. Okay, so what are the different time scales here which play a role? There is a wash ball frequency which is the ratio of the advancing speed to the lattice spacing and it's inverse which is the time between one NINU and the next. Then there is a temperature related time scale which is the product of some attempt rate time this exponentially scaled ratio of the barrier energy, this delta U plus to the thermal quantum. So of course these thermal jumps will anticipate forward slips and the higher the temperature, the higher this jump rate at the point that even though one might be from this gamma point of view in a stick slip situation, if temperature is large enough, eventually the system just advances essentially smoothly and stick slip disappears when temperature is very large. So say the general say panorama would be somehow summarized in this slide. At zero temperature there is a high speed regime where sliding is smooth anyway because the system doesn't have time to stop in each minimum it just advances quickly. At low speed there is a stick slip and the friction changes with this sort of behavior in time but it's average value is essentially independent of temperature with a weak dependence of temperature. At final temperature instead one can isolate three sliding regimes because on top of this high speed, smooth sliding, fast sliding regime where we're featuring this proportion to velocity there is this stick slip which depends a little bit of temperature slowly due to this thermal excitations which do depend on temperature because the barrier does change with velocity slightly but then at very, very low velocities at a certain point one is going so slowly that diffusion takes over and the contact will just diffuse thermally across and this pulling ahead would be just a small perturbation and again friction will become linear with velocity. Okay, so anyway, so the general understanding is that for any given speed one tends to have a friction that decreases when you raise temperature. So this is what usually one expects at least when one is sliding over a rigid surface and something with not particularly complicated structure. And for this there is a huge literature of which many of the distinguished audience are the authors and so many of you know this thing much better than me. There are a lot of other aspects like logarithmic velocity dependencies, this thermal assisted obesity, thermal obesity low temperature. This is also related to to Jardzinski inequalities and this kind of physics is very interesting and very well known. However, this is not always the case. In experiments sometimes one finds that friction does also increase with velocities. For example, this has been discussed in this set of experiments with different rigid substrates which has been done in Schismann's group and interpreted with modeling by Mikhail Urbeck in terms of multi-asperity context. So you see that there is a friction peak at the function of temperature and there are some regions where friction decreases with temperature but also ranges where it does increase. And also talking with Carlos Thurmond, I realized that also in the SFA experiments one finds situations where friction has some non-trivial dependence on temperature. For example, in this work, in this SFA experiment, they used this squalane lubricant and they put it in between the mica contact surfaces which are say mesoscale in size. And you see that they find some stick slip at low velocity. You see this is a micrometer scale stick slip so it's not atomic at all, it's a microscale. And increasing velocities, this stick slip amplitude and the frequency get reduced. And eventually at large enough velocity, all stick slip disappears and friction decreases and one goes to smooth sliding. So how does this relate to temperature? Well, you see here we have some critical velocity separating the stick slip at low velocity and smooth sliding at high velocity. And when they measure this critical velocity as a function, for example, of load at different temperatures, you see that there is a clear difference between different temperatures. And when the temperature is smaller, the stick slip regime is pushed down and it stands up when you raise temperature. So you have a consistent increase of friction by increasing temperature, by a lot. Okay, so we wanted some model for somehow modeling this possibility that friction increases with velocity in certain cases. And so we actually got inspired by some experiments we were got aware of based on some zwitterionic molecule, which have some polar part with a positively negative charged residue and some part which is non-polar, some long alkylic chains which basically help them to self-assemble into vesicles. So that the alkylic chains stay away from water and from these vesicles. They are also trapped, for example, inside an SFA setup. And the evidence is that the sliding basically occurs between those polar heads in this region while the vesicles stick to the SFA surfaces. Okay, so we tried to model this. We didn't want to model the whole vesicles. We just wanted to focus on this part. So basically we model these complicated molecules with just some united atom way with just a chain of seven residues with six describing this polar part and just this last part which is just a summary for the whole chain, for the non-polar chains which don't take an essential part in the friction physics. And then we assembled these molecules using some substrate layers like this. So these are the parameters of these molecules. They have some spring constants, some equilibrium spacing. They have some angular dependence of the energy. So that this part then wants to stay straight and this angle here wants to stay 111 degrees. So they tend to stay at this tilt geometry which is similar to what this molecule does experimentally. And these are the masses that we use for these residues. Then these molecules interact with each other. By default they interact with some more interaction which is a soft version of safe undervales with a weak attraction. And each range interacts with all ranges of other molecules with this kind of interaction plus the Coulomb interactions which charged residues have together. To create the layers, we arrange these molecules in actually ordered lattice. We come from solid state physics so we know that these vesicles are not ordered. They would be liquid but they have some average spacing in between the molecules. And so we decided, okay, let's make it simple. Let's make a lattice, triangle a lattice of these molecules. And to keep it in place, we planted into some rigid layers, two rigid layers, this pink and this violet rigid layers. This one is static and this one can be moving but rigidly and being pulled by this stage like in a quantumism fashion. The molecules interact with these rigid layers more potential so they get planted there. I don't, they just, they can vibrate but they cannot leave their position. Okay, to prevent there is some trivial crystalline locking the two crystals are rotated one with respect to each other so there is a twist angle of 20 degrees. So this one is rotated plus 20 degrees. The other layer which is not depicted here for clarity is rotated by minus 10 degrees. So it is a result that they don't interlock easily. So we simulate a supercell of about 100 square nanometers with 206 molecules per layer. Okay, so this is the initial position. After this initial position, all these interactions is Coulombic and what the vast interactions on, they tend to relax the chains and they tend to form some kind of older layer like this because they are planted regularly they attract each other so the chains get lower down and they get to some quite ordered layer positions. So the interlayer interactions tend to, to be those responsible for friction and they include on top of this van der Waals most interaction also the Coulombic repartions because charges are positive and negative charges are in both layers so they are both kind of interaction playing a role. So when we start to pull this molecule, this molecular model through the spring, we see that I also call this particle by different color so that we can see it advance. If we do it at reasonably low temperature like 150K, this advances smoothly. You see that there's very little stick slip. It's essentially advances smoothly. This is the first trace and we get a very, very small friction due to those layers being quite flat and ordered. Instead, if we do the same simulation at 300K, the situation is quite different. You see that we have stick slip, now it's sticking and at a certain point now it gives away and it slips forward and this is the first trace, the friction is much bigger and you see that increase in temperature we found a situation where we promote stick slip from smooth sliding low friction at low temperature. So we have this reversed friction behavior compared to the standard wisdom. So this is summarizing what one finds when simulating all different temperatures. You see that at, you just look at the green curves. You see that at the small temperature we have this smooth sliding very small friction then as you raise temperature stick slips to take place and the friction increases. Those error bars just represent the fluctuations of instantaneous friction when they are small, this is smooth sliding when they are bigger that means that there is stick slip. So you see stick slip coming up from the smooth sliding increasing friction, increasing temperature. You also see here in the sub-distance that there is a thermal expansion. Of course, when you raise temperature chains starts to pop up and so the two layers get pushed away from each other. And indeed, it's precisely this mechanism of chains fluctuating up and down which is the reason for this friction increase because as you can see at low temperature these layers remain quite flat. As you increase temperature, there are some chains coming down from the upper layer or up from the lower layer. They get intertangled and this intertanglement is responsible for the stick situation. So we also computed some of this hooking, the percentage of those molecules that get entangled from one layer to the next and indeed there is a clear correlation of the stick slip friction force which is the green curve with the percentage of molecules that get hooked. By the way, we wondered how much these charges are important, how much it is important to have positive and negative discharge residues on these molecules. So we already did the whole simulations with no charges, which is the red curve here. And you see that there is still some increase of friction with temperature, at low temperature, but the phenomena is much less clear. There is already stick slip at very low temperature and the reason is that without the charges those layers don't order so efficiently. So it charges quite helpful in ordering those layers and keeping them flat at low temperature. And so you always get stick slip and then eventually the standard thermolubric effect at high temperature. Okay, then we wanted to characterize the superlubric regime, that is the low friction regime. So we wanted to see, say at 50K what happens as a function of sliding speed. Indeed, as a function of sliding speed, this superlubric regime has the regular velocity proportional friction that you expect for this low friction state. And on the contrary, when you go to the stick slip as a function of velocity, you see there is a transition at low velocity to stick slip exactly like in Drumann's experiments. You see that then friction does not depend on depends very weakly on sliding velocity as one expects. So clearly in simulations, we cannot explore all possible velocities. In principle, it would be interesting to track this critical velocity between stick slip and smooth sliding as a function of temperature, but that's beyond what we can do in simulations because we are limited to velocities of the order of a few meters per second. It's quite hard to go into the micrometers per second as it's done in experiment, but certainly we have this same phenomenology that as you lower temperature, this transition gets down to lower speeds. Then I just wanted to note that of course, in our model, we do have dissipation, we have a long-term thermostat, we put a damping rate of one picosecond to the minus one and indeed we checked that the results don't change much as a function of that parameter. What about load? All the simulations that I showed were done all at 10 megapascal load. We tried to investigate other loads typical of the SFA setup, so quite moderate loads. And you see that friction depends quite weakly on load. Perhaps there is even a slightly negative friction coefficient, but anyway, essentially close to zero. Load doesn't affect friction very much and the fact is that when you apply load, you are somehow acting against temperature. You are pushing the chains down, making them flatter and the result friction tends to be reduced while of course you're also trying to increase corrugation effectively. So the two results basically compensate each other. So we have charged molecules and we were thinking perhaps an electric field might affect the dipolar molecules. So if we add an electric field like a transverse electric field like we have here, perhaps this might affect those chains and this can change friction. Indeed, if one puts rather sizable fields of the other or several giga volts per meter, so volts per nanometer if you prefer, then we see that the lower chains, the chains in the lower layer can get popped up while those in the upper layer get flattened over and as a result, this does affect friction. Some cations come out from the plane and they interact with the anions in the upper layer and we do see an increase of friction in for increasing electric field. An increase which is quite more substantial and at zero Kelvin where one starts from a smooth sliding and one activates stick slip, but also at 300K one sees an increase of friction by a factor of about three and enhancement of stick slip, at least for moderate fields. Then when field becomes extremely large, all dipos basically stand up and at that point, everything becomes somehow more trivial and temperature does not affect things too much and eventually friction decreases because molecules get frozen in the upright position. Okay, I'm basically done. So we know that in standard rigid set ups, friction tends to decrease with temperature and we invented a molecule where things can go differently. Thermal fluctuation can promote these chains to pop up and intersect more and create some sticking situation and therefore increase friction. So basically one forms thermally fluctuating, sticking configuration which increased effective coagulation and therefore promote a stick slip against the smooth sliding. In our model it seems that the charges on these withdrawing molecules are important. We tested what happens without them and this effect is gets reduced quite a lot. However, we are aware of those experiments where squalane was used which is a non-polar molecule and a similar effect was also observed. So perhaps the situation is more general than our model of course. And also now we are trying to see what an electric field could do although of course the electric fields that we need to put in for any effect to be seen are quite big compared to what is practically possible to do in experiments. Okay, thank you for your attention. Thank you very much. Questions, yes. Thank you for a nice talk. I was wondering about the field example that you showed there. You are actually playing a DC field, right? Yeah, DC field. Can you think about putting an AC field to actually try to reduce this hook in between the surface when you are sliding? Yeah, it's a good suggestion. Of course an AC field will have some frequency and one will tend to try and resonate it to some natural frequency of those chains. But yeah, yeah, certainly. I mean in practice experimentally it would be hard to make a frequency that goes so high that it resonates with the natural frequencies of those chains. So in practice one will have an essentially DC field with slowly changes in time compared to two. Right, so you mean one could make the field resonant to the washboard frequency to something like the washboard frequency related to the advancing speed. I mean I don't want to resonate your molecules. I guess if I got you well, you said you are hooking the two surfaces somehow and you have some friction due to breaking those hooks. So what you want to do is to break those hooks faster than what you do with the lateral translation of your plate. Yeah, yes, yes, it's a good suggestion. We will try that. Thank you. Can I ask about the hooks? How do you define the hooking? Its molecules are too short to entangle, right? So if you... Yeah, I mean how do we define precisely this hooking quantity? When is it hooked when are two molecules? So we will take the plane of the average position of the cations of the lower level, the lower level, so we have the chains coming up with the cations with which I have a certain average height and we count how many of the cations of the upper level come below this average level of the cations of the lower plane and we do the same on the other way. So how many of the chains go up above the average level of the cations of the upper level of the lower level? Solvent there, in particular I think about water but also salty water because then you can maybe form iron bridges or something like that. And yeah, in principle of course we have considered it because in experiments they do have a solvent. We wanted to make a minimal model at the beginning and so we did it without any solvent but certainly the next step is to include the specific solvent and also include, say, salts as you say and see how that will change things. In our, say, modeling without solvent just to make it somehow quicker and easier, we somehow tuned the interaction between the ratios so that they take this interaction range takes into account the possibility that there are molecules in between. So it is bigger than atomic interaction. It's like 0.4 nanometers instead of 0.1. More questions, maybe online there's nothing in the chat but not, then I think it's lunchtime and we'll meet again at 1.20, right? 2.20, sorry, not 1.20, yeah. That would be about 2.20, okay. So thanks a lot to all the speakers of this morning's session and I'll see everyone in the afternoon.