 Okay, hi. Good morning. I'm a PhD student. As I said, CISA, nice to meet you. Nice. Show my smile. Good. So that's what I'm going to talk about. It's only one slide, basically. The Role of Non-Context. How it goes and how it behaves. So let's get into it. So the story begins with this nice experiment from Alessandro Cira's group in Paris that they had this AFM tip, which was injected to a gold substrate, and they oscillated to make nano-junctions. Once they made it, then they started oscillating it to read the rheology. So they applied this force, this oscillatory force, and they read the amplitude here. They read the amplitude, and then they divide these two factors by each other, and then they can get the g function, which is the dynamical response function. So this g has two components, which could be real or imaginary, depends if the response function is in phase with the oscillation. The real part is the elastic regime, and the dissipative part is the imaginary part. What they observe is basically they have the elastic regime here, and so the black curve is g prime, and red is g double prime. So at the beginning, for a small oscillation, they have purely g prime, and once they increase the oscillation, the g prime decreases, and then the g double prime, which is dissipation increases, which is the plastic regime. But the important thing here to mention is when they go to larger oscillations, they have that g prime, which is the elastic response, it goes to a negative value. So that was sort of puzzling, and it could be interpreted as liquid, but it was puzzling because it is at room temperature, so it could not be liquid. So to understand it, we conducted some MD simulations, and here we have this artificially made nano-contact between two slabs, the ordinary junction we use for this model, and we relaxed it at room temperature to make some realistic shape of nano-contact, which is the one at the right, you see. And we did this for different sizes, different junctions from the four vertical columns to even more, to 20, 30, we could do it for different thicknesses. And once we have this, we apply this vertical oscillation, and we read the force. And we only apply thermostat to the upper and lower layers, just to stay away from artifacts in the nano-net regimes. And if you're interested to talk about thermostat, you can do it later. Okay. So in this plot, I'm showing you the oscillation. So the top one is for the small oscillation amplitude, and the more you come down, you see the larger oscillation amplitudes. So this blue dashed line is the oscillation amplitude that we apply to the system. And these data are the ones that we read from the force between the two slabs. And you see that in the top one, which is the elastic one, if you fit a sinus function on that, that goes like in phase with the oscillation, which means we are in the elastic regime. But once we go lower, for the lower plot, when there is larger oscillations, you see that the fit gets a little out of phase, and that's exactly what we are looking for. And you see the fit is not also very perfect. So this data could look like random points or random fit. Even in the lower plot, you see there are some strong jumps between this cap of sinus, which is displayed upward and downward in wrong positions, which this is an important thing I will explain just in the next slide. Just to give you a reason why we use this, we can use the Fourier analysis for the force data. And we see for the small amplitude, the linear response works well. So here you have the frequencies in the horizontal axis, and for the omega 0, which is the frequency of the oscillation, you see you have the main fit. So linear response works very well for here. But if you increase the oscillation amplitude, the linear response doesn't really work. There are many nonlinear terms that it's not easy to get rid of it, but we use linear response because we don't have much choice and we want to compare it with the experiment. So let's get to it. So the result is here. The picture I'm showing you in right is experiment again. The black curve is G prime, which is lastly red is G double prime, which is the dissipative response. This is done on the nano neck of size 11. Size 11 means 11 chain of atoms in the section. We did it also for the more or less the same thickness, but we could not do for 30 kilohertz because with computer that's not possible. But because we are very brave people, so we tried the 10 gigahertz. So 10 gigahertz and without any adjustment on the numbers, any normalization, you see it just works. So it gives right results. But at the beginning I thought some wrong things should be threw it away. Then we tried lower frequencies. So we did also 1 gigahertz and still it works. And we did even lower. We did 100 megahertz and still there's good agreement with the experiment. We push it harder, we go 50 megahertz and even 10 megahertz. And because the referee pushed us, we did also 1 megahertz. But I didn't put it here. So the message here is this is frequency independent. This response looks frequency independent. And the positive thing is you have G prime negative even in the simulations. So something should be understood. So what's going on? I think all the mystery is hidden in this picture. The force of the versus oscillation amplitude. And to translate this plot maybe in your mind, this is like stress strain curve. So something that everybody knows I think. What we have here, you see in the middle there is this elastic regime. When the non-adjunction looks like that and then you oscillate it a little bit, you get the linear response. So that's expected. But once you elongate it hardly, then you see it gets very narrow. It's called the necking regime. And once you compress it, it goes very fat, which we call it bellying regime. But there's two interesting factors here. First is this fatting and narrowing in necking and bellying thing is not occurring slowly. So it's like very sharp transitions. It's a sticky slip that translates necking to bellying regime. And which we try to show with that gray zigzag thing on top of the data. And yeah, that's the important thing. And that's what it makes it frequency independent. The other important thing is the average of this plot is not zero. The average is always tensile. And that comes from this nice work of Eryotosatia in the year 2000, which was maybe a little key. And at that time they showed that this is the string tension. So this gold nanocontact, the nanowires, they always have this string tension. Well, what it means, it means when the nanocontact is very narrow, it tends to break. There is some tendency to break it. And when it's fat in the bellying regime, it tends to collapse it to slab and make it a whole buck. So that's the important thing. Yep, that's all we need to know. But how this would result to negative g prime. In order to do that, we use some simple, very simple model. The toy model we do here, which we call the zigzag model, which we apply this sinusoid oscillatory thing, which is a strain, so oscillatory strain. And we do this as a stress. We read this as a stress. So the first term is the linear term. The first term is the linear, which always should be there. The second and third term, we added for this bellying jump and the necking jump with JB and JN, which they only enter to the game when the oscillation amplitude is big enough to do so. And the last term is the string tension, which is some average value to elevate this, the average of the plot, which I show you it was not there. So at the end, this is the function of the stress, which is a strain, a zigzag. If J is zero, you have the perfect line. And if J is not zero, you get these jumps at this necking and bellying regime. Okay. So here I use J the same for necking and bellying. I use the same value just for simplicity. So what we want is G prime, which for this system would be the ratio between Fourier transform of stress relative to strain. And we do this Fourier transform and we calculate G prime. And we see that for this very simple model, if J is long enough, G prime goes negative, as simple as that. So I think these two elements that I just told you is all you need to have G prime negative. And I think that explains the story. But you should remember the jump should be big enough to touch the zero level. So that means there should be a strong jump that relieves the stress when it goes to bellying and necking regime. So it's like there is a stress, but there is this sudden jump, sudden slips, which are usually FCC, HCP, sleeping layers because they are closing energy. And it relieves the stress for a moment, and that's all is needed. Even it can be understood from the slope of that plot, you see. I don't know if it's clear, this G prime thing. If you put away some very rushed average on the slope, you see it turns slowly negative once you include these jumps. That's all the story. But so we said frequency independent, but how long this is frequency independent? If you go with one hertz, is it still doing this? So to understand that, we estimate these crossover frequencies. Using transition state theory, from the simulation, we estimated this energy barrier for these jumps. And we took the system when it was in bellying regime. We didn't oscillate it, we just fixed the height of these two slabs and then what? Yes, then we simulated for a long time. Then there are some attempts to unbellying the system. What we did, we used Fourier transform to analyze the signal in this unbellying regime. And we got a frequency, some attempt frequency like 10 megahertz. Using this attempt frequency, we can get very rough estimation for this crossover frequency, which is like 600 hertz. This is interesting for experimenters here, if they can try. They will see in some frequency close to that we predict that there would be some viscose sliding, which may be linear with frequency. This is interesting to see. So the last slide I show here, the motivation for this is the other day some of the professor here asked some questions. If there is liquid, is it even possible to have liquid between the non-adjunctions? So we failed to do it in simulation. We couldn't see a liquid between junction and simulations. It's really tricky and hard to maintain. But we could do instead, we could increase the temperature to increase the mobility and somehow mimic some very mobile material in between. So in this plot I'm showing you here is a non-unique lifetime versus temperature. You see if you, so that's our simulation limit. You see around one microsecond. When you go to the lower temperature, then the lifetime of a non-unique of course increases. We predict that room temperature, they can exist like one second or something. But this is a strong argument that in experiment it's, so what has been observed or what could be, it's not liquid. Because liquid would really break before experimental feedback time. So the shadow I'm showing you is the experimental feedback time that they use to read the force signal. And then they adjust the piezo to do, I don't know, some experimental stuff to adjust the strain and the stress and things. But the lifetime of a liquid non-unique we predict is shorter than the feedback time scale. So I think it's not really doable to have liquid. But still would be interesting if any experimenters can show that. Yep, so that's all, that's all the story in one picture. Questions? We already discussed a bit at the post session, but it's still just me not understanding enough. So what is the negative oscillation amplitude? Because if it's just like what I think it is, I would expect a symmetric response, for example in slide seven. Very good question. So the negative response is the tendency of the nanocontact to be oscillated. And the reason of that I think is the strength tension. Because once you go to this story when you pass this crucial value of the oscillation amplitude, you make a neck and the nanocontact wants to break. Then you get the belly the nanocontact wants. Ah, I do not have that. What? Ah, the negative oscillation here means compression, sorry. Compression and positive means expansion. At each point we have oscillation amplitude. It is a displacement. Okay, good. Yes, it is a displacement. Okay, more questions. In the meantime, I try to show you movies. I still have 10 seconds. For the talk, actually if you keep increasing the amplitude then you are going to get back to positive model, right? I'm sorry? If you keep increasing the amplitude then in your sixth I think you are going to have to go back to a positive response on your... Very good, very good question. The nanocontact would break before that. But I think you might be right. The misconception is trying to apply linear rheology to something that is nonlinear, right? No, I mean... Okay, I understand the linear response is not enough for this story. But still you will have the force negating your oscillation, right? So I have no idea what would happen if you use nonlinear response. But I mean the thing that you see is a physical thing. It's not that if you use some nonlinear response... It's my point that is puzzling on having a negative g-prime is just that you are going too far. I mean for understanding the experiment if you go too far maybe it doesn't make a lot of sense. I think, yeah, maybe some new module should be developed for this story. So that is true. Yes, we measure the noise, yes. And we do the... Which is nonlinear, and I think I showed it here. Yes, this plot. This is the noise. We do the Fourier transform of the noise. And you see here for a small amplitude you have the peak at the frequency of oscillation. But for large amplitude you get peak at almost, I don't know, for 10-12 harmonics. But still, thank you. I think we come back 11-20, huh?