 Good morning, everyone. I'd like to thank the organizers for the opportunity, truly, to present this work here. It's really truly, for me, it's quite remarkable. So I'd like to talk about some work that we developed in the group of Professor Ernst Maia during the past years. And this work is actually a collaboration between many different research groups. And lots of people contributed very substantially. But these three stand out. I mean, for, well, not only in experiments, but also for the numerous discussions that we had to gather, Alexis and Ernst for teaching me how to bridge the simulations with these quite complex experiments that they're performing there. And yeah, so I have recently moved to the Universidad Autónoma de Madrid, where I have started, as a junior group leader, a five-year tenure. And so my talk will concern about the role of flexibility in different tribological aspects, particularly friction and adhesion. And I'm not so much worried in upscaling this. Instead, the interest here is focused in understanding how flexibility at single molecule level plays out in different dissipation processes. And, well, this taps into fundamental questions as we have heard from this beautiful talk this morning of Urwak on how rigid sliders now allow us realizing a wide range of superconducting interface, sorry, superlubric interfaces as the rigidity of the sliders prevents interlocking. And so one question that stands is if superlubricity and flexibility are compatible. And the other thing that it's perhaps more in the long run is from the tribology community to try to tackle some issues emerging in other fields, such as the burgeoning fields of molecular machines, where this single flexible molecules, where you have bonds rotating around a single CC bond, allow to produce work and transmit it into the media, and also to understand how molecules move over surfaces, which is super important for supermolecular devices, for example. And I realized how difficult it is when talking with Remy. And you might have heard about this first nano car race, where five world leading groups had to propel their molecules over surface for a finite amount of time. And only two out of these five groups were able to do it. And well, actually, they got the first prize for this. And well, so I'd like to discuss, then, the role of flexibility in different processes, in distortion, the friction, and then, say, in a more collective effect, so the motion of an ensemble of molecules. So these works have been published in various publications. You can find the references here. And I will leave at the end of the line the references. So the methods that we used were very closely interconnected experiments and simulations. I was responsible for the simulations part. And so the main workhorse is molecular dynamics simulations. The thing was that we're interested in this very delicate, say, a bending, a specific bending or a torsion. And whereas general force fields allow us to describe, say, even the dynamics of DNA, or proteins, or many other complex systems, here we really needed something with a bit more precision. So what we did is we compute the infrared spectra, so the vibration or the dynamic matrix of our molecule at the QM level. And then we fit it to a common form for which this is called the force field, or a common force field where you have, say, a stretching term, stretching, bending, torsions, and so forth. And then when you compare in red the quantum mechanical data of the different vibration frequencies of different normal modes with the classical data, you see that we have really good overlap. So this allows us to describe with the spectroscopic accuracy vibrations of molecules. But not only that, it also opens the possibility to tackle any other molecule we wish. So we're not bound by the available force fields. And then these are going together with cryophore spectroscopy experiments to manipulate the molecules as already described by Hemi. These experiments were performed by Hemi, and also Philip Dostofo, PhD student, that has just finished his PhD thesis. So the systems that I'm going to consider, the first bulk of the talk, will deal with the torsion and friction. And they, in both cases, will use the same molecule. And this is the one that Hemi already mentioned yesterday. And we could call it as a flexible graphene nano-reven. As we have, say, this polyurematic structure that is interlinked by a single carbon bond where you have this bending and this torsion. This, in the torsion alone, already has some effects. So for example, we see that the molecules, they absorb along bent conformations. And then another thing is that, contrary to graphene nano-revens that align along compact directions, we observed that these molecules oriented along non-compact directions. So first, the torsion, this will be very brief, as Hemi already mentioned, a substantial part. So we have a molecule that is deposited over the surface, as you can see here. And then we started lifting it up. You can measure the gradient of the normal force while you do so. And then when you look, which we call contact stiffness, and then when you look to the contact stiffness, you observe short and long detachment units. This is quite surprising, considering that it's a chain composed of identical units. And this repeats throughout the whole lifting process, and the simulations, and experiments. And to understand this, there are two basic ingredients. The first is symmetry breaking of the chain as you lift it. So you might remember the talk from Andrea Silva this Monday, where he lifted this graphene nano-revens, and you saw how they followed along, say, the line that they were originally oriented. Here it's not this case, because the molecules absorbed along a non-compact direction. And so in order to go forward, this was already discussed by Roberto Guerra and also Niccoli Manini that there is this compact directions, along which this graffitic structure nano-revens have much lower friction. And this also happens here for this flexible chain. So since he doesn't want to go along this high friction direction, it rotates, and this leads to spontaneous symmetry breaking. The other ingredient is the torsion between consecutive units. And this torsion, ultimately combined with this rotation, is what explains the two detachment lengths. So if one unit once detaches, it rotates anti-clockwise as this screen. It moves away from the sliding axis, whereas if it rotates clockwise, it moves towards the sliding axis. You can see this quite nicely. The green units are moving away. The purple ones are moving towards the sliding axis. And in this motion, led by the torsion of these units, you have different forces to detach each unit. So this internal degree of freedom, this additional flexibility, allow to basically differentiate these two kinds of detachments. So the second part is friction. The same molecule absorbed over cold surface along these non-compact directions, we lift it up, and then we manipulate it. As we manipulate the molecule, we can measure the contact stiffness, which is, again, the gradient of the normal force. And this contact stiffness, you can see that it has some modulation. And this has been shown before that when it increases, it relates to a stick event. And when it decreases, it's related to slip event. So the same stick slip behavior is seen also in our simulations. But what's puzzling is the distances. So the distance between the stick slip events is not the lattice distance along this non-compact direction. So in experiments and simulations, we get something around 0.25 nanometers. As compared to 0.5 nanometers, which is the periodicity along the sliding direction, or 0.29, which is the distance between the gold atoms. And the reason what's happening here, behind this kind of sub lattice stick slip motion, is because as we manipulate the molecule, we have this non-trivial, sine-winding, zigzag motion of the molecule, which is essentially composed by three elements. And here it's quite important to note that this is observed for regardless of the chain length. For example, you can get it for chains as small as three units. So the first thing that happens is there is the tail rotation. Second is that each individual unit, instead of going from one lattice position to the next, it jumps into an intermediate position. So this allows the unit to always go along compact directions. You can see it goes from here to here. And therefore, you break a motion of 0.5 nanometers into two of 0.25. And another interesting thing is when you look at the trajectory of these units, for example, this unit 2, the first that is in contact. And in gray, we represent the gold atoms. And you can see how it zigzags. The center of mass goes from one gold atom to the other. But as you go along the chain, you see that not all motion is coordinated. You see, for example, this unit U5 is moving in anti-phase with respect to this U2. So as this one goes away from the sliding axis and then approaches, the other does exactly the opposite. And this gives rise to this undulation that we see on the chain. So the other thing is what happens to this dynamics as we lift slightly more the molecule. And so to make it short, it changes. So we go from a regular 0.25 nanometer stick slip behavior to longer jumps. And when you look at traces, you see that these jumps are almost one nanometer long. And this is also reproducing in our simulations. And actually, you can have, say, a more better understanding if you look to how this contact stiffness changes with the height. So here we have the displacement. And then in the y-axis, we have the height of the molecule. And in colored, we put the contact stiffness. Say black is the peak, so a stick event. White would be a slip event. And you can see that at low heights, we have this high periodicity of stick events. And as soon as we start lifting the molecule, they start to fade away and give rise to these longer slip events. So it's quite, and actually when you look to the trajectory, you also see that it changes very dramatically. Not only the contact stiffness. This only reflects that there's a different dynamics of the chain. And so it's quite remarkable that by changing, say, 0.1 nanometer in the chain height, you can change the dynamics of a nanometer long chain. And the reason for this is, once again, the torsion between the units. As the chain is absorbed, it remains flat. So the angle between consecutive units is 0. When you have this strong contact regime where the molecule is the one that is in contact is essentially flat, you will see that distortion visits values around plus minus 1 degrees. So you're essentially here at the maximum. However, as soon as you start lifting the molecule, even by a small amount, you enter into this purple region where the angle between consecutive units changes from 4 to 12 or 10 degrees. And most importantly, you have a substantial energy change in this case, which gives rise to a net torque to this front unit and then changes very much the dynamics of this molecule. So by lifting a little bit more, the molecule what you're doing is switching on or off the relevance of this degree of freedom. The other thing was how this zigzag motion endures a backwards scan. And you know that Shige Kika-Wai and Andre Benassi showed that this was possible to realize and graphene and revans. And this was associated with the superlubricity effect. And so we got curious if a flexible chain like this one could also sustain this. And the answer is yes. You can drag the molecule backwards. And it still continues to do in this zigzag motion. But now we're not at an angle, but essentially straight with respect to the sliding axis. But when you look at the trajectories of the individual units, so in black is the trajectory of this first unit in the forward manipulation and in blue in the backward. And you can see they are essentially overlapping. And moreover, you see it's very smooth transition from here to here. There's no stick and slip. Everything happens smoothly. And this actually relates to the fact that the forward and backward traces also seen experimentally have essentially no hysteresis, which we also saw in our simulations. And what's funny is when you contrast it with these results for the graphene and revans, where you saw much bigger hysteresis. And this kind of indicated that, well, these chains, they have really low friction so that you can actually manipulate them quite easily. And here we show the lateral sliding forces obtained from our simulations. And you can see that the static force is about 40 piconewtons for a ribbon of about 10 nanometers long, which is about the same value that Sigeiki and Andrea saw for these graphene and revans. And moreover, here we're sliding in a non-compact direction, in a higher friction direction. So this flexible design is possible to achieve this ultra-low superluricity. And then this was actually prompted by Alexis. We look at how this friction changed as we increased the chain length. And you can see here on the right-hand side, the lateral force for two different chains. One is about 13 nanometers, and the other is 21. So you can see it's almost double the size. However, the force is essentially the same. And this leads to this vanishing friction per contact area. When you plot the static force or the average force, whatever component you wish to pay, you will see that as you increase the chain length, this decreases. And this is quite surprising because the molecule, as you can see here, it's improving its registry in every slip event. So it's not structural superluricity because you're improving your registry as you go along. So we call it this flexible superluricity. However, they emanate from the very same source. And that is the incommensurability between the chain and the gold. So you know that the distance between this, say, hollow sides of graphene are 0.24 nanometers compared to 0.29 and gold. And what this makes is this induces a bending in the chain. And you can see here this bending angle between consecutive units in black as we slide the molecule. You can see how it oscillates. And in gray, we show this bending angle for another unit further down the chain. And you can see that as you enter into this, when you begin the onset of the slip event here, indicated by this dashed line, you see how this angle drops to zero in both cases. So the chain is bent, and then when it begins to slip, it straightens, and then it recovers a new bent configuration. And so in this way, this mechanical energy is being transferred and released from the chain into the slip and vice versa. And you could think that, well, if you, this doesn't scale, because if you have sufficiently long chain, then you need to synchronize this bending event, and this will cost more and more energy. The funny thing is that they are never synchronized. Here you show this angle for the different units, for, we take, I think, 10, and you can see that they are never perfectly synchronized because this incommensurability between the graphite, this poly-aromatic carbons and the gold leads to this asynchronous excitation of this internal degree of freedom. So in a way, you have this incommensurability between these two systems that permeates into a spatially incoherent bending. Kind of similar to this structural superlubricity, but in a more dynamic fashion. Here I was comparing, I compare some results for a rigid and flexible chain, and the results are quite obvious. The first thing in blue is the rigid, and in blacks the flexible is that you can see that the flexible can obviously split an event, a slip event of zero, five nanometers in two, and that the energy barrier or the static friction for us is lower for this behavior for the reasons already mentioned and also because you need to impede a smaller amount of atoms. So now I will very briefly mention on this assembly. Mostly because it's quite entertaining, I think. So you have this hard aromatic core. This was work done by Sebastian Scherb, Antoine Nino, and also Chemie Pavlac, and they had this aromatic core, and they were wondering what was the role of this flexible chains. If you add this flexible chains to this rigid core, what would happen? And in particular they were interested in molecular assemblies. Here you can see the molecular assembly at 5K. These bright dots correspond to the center of each molecule, so you can measure the distance between the bright dots and you get the distance between the molecules. You do it at five Kelvin and at 300 Kelvin and you can get a thermal expansion coefficient, which is 1,000 larger than conventional materials and 10,000 larger than any other material. So this already tells us there is a major anharmonic effect playing a role here. And well, that is actually the flexibility of the chains. When you're at low temperature, the system compacts to increase the interaction between the molecules. However, when you increase the temperature, this changes. So this is the molecular 300 Kelvin and you can see that although you have energy to move the chains, you still cannot diffuse the molecule. However, the assembly, when you're together these fluctuations, they lead to this thermal expansion of the chain, this anharmonic fluctuations of this flexible side chains allow us to reach this giant thermal expansion. So to come at the end, so we've shown how this flexibility allows us to tune the absorption, how it gives rise to this flexible superlubricity and how we can use it to create materials with giant thermal expansion. I'd like to thank all the people involved in this work, the group of Ernst and thank you for all the funding agents and thank you all for your attention. The question is for Robert. Thank you very interesting results. I was wondering whether you have some benchmark about the role of the interaction potential that you use between the molecule and the sub straight because I expected so that the subtle detail that you find might be influenced by particular by this potential. So have you tried the robustness of these results against this? Thank you. It's a very good point. I did try this. In particular, the one that I'm using for these simulations is the potential from Stefan O'Courtney, the scope force field. And I tried with others like this interface and other linear drones parameterization. I just saw your recent publication New Gold Force Field. And this one, the scope force field was the one that was able to reproduce better the distortion energies of these individual units. And well, as you can see, it captures very nicely the dynamics also of the chain. And so, yeah, so I did test it. And I found out that the scope, it's quite, or it served quite well this purpose, especially for aromatic compounds. Thanks. Very intriguing phenomenon issue. I was wondering, these chains are oriented along against a specific direction of the gold substrate along the reconstruction of the ribbon. Do you know what is the relative size of the moire pattern in this direction and the unit cell of your chain? Like, are these the unit of your chain like sub moire space, sub moire tile? A good question. So I did look at this because this is one analysis that Roberto and Nikola and Andrea, I think they also did for the ribbons. But in this case, the molecule is really so thin that, I mean, and then it bends to commensurate. And so I don't know by hand what would be the size of the moire. It's along the non-compact direction. So I cannot recall. But it would be interesting to see how it scales with the area of this. If you can link like a unit of different area and connect them with these bridges, how it will scale with the area of those. But yeah, we can discuss later. Okay, thank you. So I think we should move on to the next talk, which will be given by Olivier Nouvelle.