 OK, I think we are ready to start. Good afternoon to everybody. Thank you for joining us. So have a very special colloquium today, because usually we have some talks which are very much in the formal and theoretical side. I understand today is on the applied side, which I think is very good. We have a professible person visiting. He's a good friend of ICDP for many years, if I understood. He gave the first talk in this room in 1979. So it has been several years since then, which is a. And moreover, he was a student of Professor Lundvist, who is one of the founding fathers of our group in condensed matter physics. He's a longtime collaborator of Eri Otozatti also, who is our local expert and a very important component of ICDP. So I can read something about Professor Persson. He's currently working at the Peter Grunberg Institute of the Research Center, Julix, part of the Germany's Henfels Association. Besides several years as a visiting scientist at IBM Research Labs in Yorktown, Hades, and in Zurich. He spent numerous periods as a visiting scientist in research laboratories in Israel, Japan, China, Italy, and elsewhere. After his initial research work in dynamical processes at surfaces, he turned around 1995 to theoretical tribology, friction, addition, contact mechanics. He has published more than 400 articles in international journals. And he's the author of Slighting Friction, Physical Principles and Applications at Springer-Werdlach in 1997, and co-author with the Volokion on Electromagnetic Fluctuations at the Nanoscale Theory and Applications. Besides the early book with Eri Atosati, it's called Physics of Slighting Friction in 1996, collecting papers of the very first ICDP research workshop on that subject. When I said that he's doing applied sciences in a minute because he had been working for the industry. And he is the founder and CEO of a multi-scale consulting, a company involved in consulting, theory and experiment on topics related to contact mechanics and friction. Most clients are from the tire industry. So we have a Formula One racing teams and medical companies. So I'm sure we have very interesting colloquium. So please join me to welcome Professor Persson. OK, thank you for the invitation to come here. So I'm going to tell you about the topic I find very fascinating, very beautiful. And the way I got into this topic, contact mechanics, was about 20 years ago, the Pirelli Tire Company asked me if I can help them to explain rubber friction, the friction between a tire and a road surface. And after a few weeks, I had basically developed my most important contribution to physics, I think. I will tell you a little about that later. And then I spent about 20 years working out the consequences of this theory. So here's the outline of my presentation. First, a little about tribology, because maybe most of you don't know so much about this topic, about surface roughness, which is involved in all the application I'm going to tell you about. And then, basically, my theory on multi-scale contact mechanics and some application to adhesion, bioadhesion, and electrode adhesion. This has a lot of other applications, like rubber friction or leakage of rubber seals and things like that. But I'm just going to tell you about this application to adhesion. So about tribology. Tribology has to do with friction, adhesion, contact mechanics, lubrication, wear. And the reason I find this topic very fascinating is that, basically, everything we do, like working on the floor or eating or whatever you want, involves tribology in some way. And in addition, it's very important in a lot of engineering applications. If you take a car, for example, I give you some application here involving tribology, lubrication of the engine and the gear, leakage in maybe 100 rubber seals, tire road friction and wear, friction and wear in the brakes, rubber wiper blades removing water. These are all tribology applications. And some people have estimated that just the neglect of making use of what we know today result in a lot of waste in money. Now, it's also a very old topic, at least one of the practical point of view. So this organism here, our relatives from more than 400,000 years ago, they already knew how to make fire using frictional heating. And since I'm in Italy, I have to show this. Oh, sorry. These are some drawings of Leonardo Vincci. He already did sliding friction experiments. At that time, the concept of force was not developed. But still, he could find out that what I would say today, that the force to move a block when it stands on the small side here is the same as a force to move a block when it's lying on the big side. And the reason for that is that in this case, the contact pressure is higher than over here. And the net result is because of surface roughness, the area of real contact is the same in both situations. And the friction really comes from the area of real contact. As I said, he didn't know about force, but he could use different masses here to pull this block with. And he came to this conclusion, which I stated here. So I myself have been involved in a lot of different applications. And here, I'll just give you some example. Removing water from windscreen on a car with a wiper blade, syringes. Here, we're interested in the friction between the rubber plug and the barrel. Sometimes it can get so big that when you try to inject something, it doesn't move. And suddenly, it starts to move much too quick. You can damage your blood vessels. And there's also leakage of fluid between the rubber plug and the barrel. Here is tire road friction. That's what I got me into this topic to begin with. This is an application to the joint. The bone is covered by a porous elastic material filled with a liquid. And when you squeeze together these bones here, this liquid moves out into the interface and helps to lubricate this contact. Here is interaction between contact lenses in the eye. It's also a very important problem to study. And I'm going to tell you a lot about bio applications. So I want to explain for you how it's possible for a LISAD to move on a vertical surface. And the common theme in all my discussion will be surface roughness. Because basically, all surfaces in nature have surface roughness produced by engineers or natural surfaces. So even if you take a ball in a ball bearing, which might, to the naked eye, look perfectly smooth, when you start to magnify some surface air, you will always observe surface roughness. And if you magnify this as purity, which looks smooth at this particular magnification, you observe new surface roughness at shorter length scale. And this can go on the whole way down to atomic distances. So in some application like a tire on a road surface, the asphalt road might have roughness starting at centimeter, going down to nanometer. That's seven decals in length scale. And if you want to solve this problem numerically, you need to take into account seven decals in length scale in the x direction, in the y direction, and also in the z direction. You get such a big problem that no computer in the world can solve that contact mechanics problem. So you need some analytic approach to understand contact mechanics involving so many degrees of freedom. This is just to give you some feeling about how big our contact area is. So if you take a steel block on a steel table, the block is 10 centimeters width here, and you try to estimate in a typical case, what is the area of sort of atomic contact between them, then it's of order 0.01 square millimeter. And even if you take elastically soft material like a tire, the contact area between a tire and the road surface might be only one square centimeter or even less, which means that if you do strong acceleration like here, you produce a lot of frictional heat, and it's localized to very small contact spots, you get very high temperature, and the rubric can start to disintegrate. So the theory I've developed, it depends on the surface roughness, depends only on the power spectrum. And let me define that for you. Suppose we measure the roughness on a surface with a sharp tip, which will move along the surface. The tip will move up and down, and you will measure some height profile like indicated here. Then we know for mathematics that we can decompose this almost random profile into some of sinus and cosine waves with different amplitudes and different wavelengths. And instead of speaking about wavelengths, I prefer to speak about wave numbers to pi over the wavelengths. And very typical, I will give you some example in a moment, very typical if you plot this, what I call the power spectrum as a function of wave number on a log log scale, you see a straight line like indicated here. So the power spectrum is basically just the square of this amplitude like indicated here. And the slope of this line, when you see a straight line like this, it's indication of a fractal surface, or we say, self-defined fractal surface. And the slope of this line determines the fractal dimension of the surface. And what I illustrate this concept here, we look at the surface at some magnification here. We see some roughness. Then we magnify this asperity here, which looks smooth at this magnification. But if we magnify it, we observe new surface roughness, which typically look very similar to before, but with larger amplitude typically. If it would have the same amplitude, then we say the surface as fractal dimension two. If it has larger amplitude, then the fractal dimension is larger than two. And typically, we find about 2.2, 2.3 for real surfaces. So here I give you some examples. This is power spectrum of an asphalt roll surface. This is of a grinded steel surface. This is of the human skin, this part of the skin here. This is you peel scotch tape. You can get a rough surface. And you can see in all cases, if you plot the logarithm of this power spectrum and function logarithm of the wave number, you get a straight line, except you have some roll off on the asphalt roll surface and maybe also here. And from the slope of the line, you can obtain the fractal dimension. And in all these cases, it is in the range of 2.2 to 2.3. So most people who try to make numerical simulation today, they assume the surface as a fractal dimension of 2.2, which is sort of very typical. Now I'm coming to contact mechanics and let me begin by showing the pioneer in this field, which was Hertz. Of course, Hertz was most famous for his work in electromagnetism. But for people working in tribology, he is maybe most famous for the contact between a sphere or the contact between two spheres. And other sphere could actually be a flat surface if you choose a radius of curvature, infinite, large. And he found that if you squeeze them together, the area of real contact depends non-linearly on the squeezing force. Like with exponent 2.3. It's a very famous equation used by all kind of engineering application. There's also some prefactor here, but I don't care about prefactors in this talk. So let us know at last, what is the contact between two objects when you bring them together? So like between this cup and the table here. And I already told you, you have always surface roughness on real surfaces. So the real contact could look like I indicated here. We assume the solids are just elastic for the moment. And the important question to ask is, what is the area of contact? And in general, we're always interested in this non-contact region. For example, if you're interested in the leakage of a rubber seal, fluid can move in empty channels at the interface. So these non-contact region are very important for predicting leakage of seal or looking at fluid motion at interfaces in general. So I developed the theory. The first one was 2001 and the second one, 2007, which basically predict contact area, predict this interfacial separation, predict the distribution of stresses acting at interface, and predict the probability distribution of such interfacial separations because they will vary along the surface. But if you look at it historically, you might say this was beginning with Hertz. He approximated all these asperities with spherical bumps, and he squeezed it against elastic solid. In that case, you can apply Hertz's contact theory for each point here, each sphere, and you will conclude contact area dependent on linear layer on the force. But this disagree with all the kind of experiments. For example, you know Coulomb's friction law. Coulomb's friction law tells you that friction force is proportional to the normal force. And usually that's explained because contact area is proportional to normal force. So this result is not valid for randomly rough surfaces. Then there was very important work by Greenwood and Williams, and they took the same model again, but they put some random Gaussian fluctuation in the height of these balls or these asperities. Then they could show the contact area is almost proportional to the force. But this result turned out to be valid only for very small applied normal forces where the contact area is extremely small. So in the paper I wrote on this topic, I showed that contact is proportional to force up to about 30% of complete contact, assuming just elastic contact mechanics. And this agree both with experiment and with numerical simulations. I also, as I told you, I also obtained information about this interfacial separation, but I'm not going to discuss it in this presentation. I want to just tell you one thing. Why is this model here not good? Why is it bad? And it has to do with the fact that they treat each contact independent of each other here, like a Hertzian contact. While in reality, if you have a higher spirity, it will push up the elastic solid, not just at the location of the spirity, but also farther away. So if this spirity is very high, it will reduce the contact over here and here. And that's neglected in this model. And that has a very big influence on the contact mechanics. Here I'll give you an example. This is an exact numerical study of the contact between a fractal surface, self-defined fractal surface, and an elastic half-space. The blue area is the true contact area, and the white area is no contact. If you neglect this long range elastic coupling, then you get instead this incorrect result over here. And you can see the topography of the contact area is completely different. And for example, if you're interested in the leakage of a rubber seal, you have high-pressure fluid here, low-pressure fluid here. In this situation, there is no leakage because you will always hit into a wall when you try to go from this side to this side. In this case, you have big channels where you can get leakage. So trying to calculate leakage of seals using this Greenwood-Williamsons theory will give you completely wrong results. So now I'm going to tell you about the most important discovery I have done in physics, at least from the point of view of practical application. And that's the contact mechanics theory for random-leraff surfaces. And it involves in looking at the interface at different magnification. So engineering surfaces typically are very smooth. To the naked eye, they look perfectly smooth. And most engineers would approximate these surfaces being perfectly smooth. So at the naked eye level, you squeeze one elastic block against another block. It appears like you make contact everywhere. And if you apply uniform stress up here, at least if you neglect friction on this interface, you expect the same uniform stress at the interface. That means that if you plot the probability of stresses at the interface, you will have zero everywhere, except when you reach this applied stress. There you have what we call a direct delta function. That's a function which is infinitesimal sin and infinite high in such a way that the area under this function is one. That's sort of definition of this direct delta function. Now we increase the magnification. We start to see surface roughness. And now we notice that we don't make contact everywhere. We have only contact on top of bigger spirals. And if you looked at the stress distribution now, it will not be uniform anymore. You will have the highest stress on top of a bigger spirality. And you will have zero stress where you don't make contact. So if you look how this probability distribution changed. Now when you increase magnification is that you get a direct delta function growing up at the origin, the area under that is determined by the non-contact area here. And then this direct delta function will start to get broadened into something which looks roughly like a Gaussian with a tail extending to higher stresses than the applied stress you see here. Now we increase the magnification even more and we observe even shorter wavelength roughness and then we'll observe even higher stresses on top of these smaller asperities. So everything gets broadened and in general the non-contact area will also increase. So this theory I've developed focus on the probability distribution of stresses at a given magnification. And I've shown that this probability distribution obey something which looks like a diffusion equation where time is replaced by magnification and spatial coordinate is replaced by the stress and then there is a diffusion coefficient which depends on the elastic properties of the material and depends on this power spectrum which I told you about before. And Q is just two pi over the wavelengths. And when you solve this equation you need to use some boundary condition. And one boundary condition you can see from this figure here, there can be no negative stresses if you neglect adhesion. It can only be compressive stresses. So this probability distribution must vanish on the left negative stress axis here. What one can show is that this continuous part here vanish continuously when you go towards the origin. So one boundary condition is given by this at zero stress for any magnification you have zero probability to find any such contact condition. This only tells you that there is no infinite stresses at the interface of soil. And this is like an initial condition that at the lowest magnification we don't see any surface roughness and there we have what is shown in the first picture here. The stress distribution is thus the direct delta function. I put this equation in red here because when you include adhesion which I will do in a moment, then this is no longer true. When you have adhesion you can have tensile stresses at interface and pi can be non-vanishing also for negative stresses. So for when adhesion is included we need to modify this boundary condition but everything else reminds the same. This is just a figure showing when I compare this theory which I told you about with an exact numerical study which you can do for very small systems. And in this case you've got the blue line here and the red line is what this theory predicts which I told you about. This is the relative contact area A over A zero so one means complete contact. And here is applied pressure in units of the Young's modulus and this is the root mean square roughness of this surface. So here enters the surface roughness basically. And the analytical equation which comes out from this theory is that the relative contact area is given by the arrow function with this argument here. And I think many of you know that arrow function for small argument depends linearly on the argument. So if you look at small pressures here you get a linear increase in the contact area and you can see from the figure here that up to about 30% of complete contact you have a linear relation. This rest of the talk will be about adhesive contact mechanics. And when you include adhesion situation gets much more complicated. Here I illustrated with a rubber ball squeezed against a flat surface. In that case you have repulsive stresses in the center by close to the edges here because of the adhesion you get tensile stresses. So clearly this boundary condition I told you about before is no longer valid and it has to be replaced by another boundary condition namely that there is a maximum tensile stress which I denote with sigma A here in magnitude. And one can relate this maximum tensile stress to the interfacial binding energy. If you take two flat surface of these materials you bring them together, they will bind to each other with an energy gamma per unit area. And so this expression comes from theory of cracks but I will not go into more details. But this illustrates how you can extend the theory to include adhesion. Now I will show you how does adhesion influence the contact mechanics. So in reality the atoms here and here they interact with each other and the forces they interact with each other are very large. Even the attractive force is very large but still I don't feel any adhesion and I will come back to that in a moment. But so this situation where when I pull up more and more the contact goes to zero when the normal force, normal applied force goes to zero. So this figure here I show the relative contact function of the pressure again. I show it for three situations. No adhesion, that's a red line. Weak adhesion, that's a green line. And strong adhesion, that's a blue line. So what I have added is this interfacial binding energy as you can see here. And you can see that if adhesion is not too strong the contact I will still vanish linearly with the pressure when you reduce the pressure. So you will still have coulomb's friction law obeyed because the contact I still increasing linearly with the pressure here. So in this case here I still expect coulomb's friction law to be valid. But if the adhesion is strong enough like if you take Scotch tape for example you push Scotch tape against the contact here of course you need an additional force to remove the Scotch tape. That's the blue line here basically. So if the adhesion is strong enough you end up at the finite contact area also at zero applied normal pressure. This figure here illustrates how the contact area change when you change the magnification. So at low magnification you don't see any surface roughness. You start at, it looks like you have my contact everywhere you start at one here. The red line is without adhesion. The contact area decreases continuously when you increase the magnification. In fact one can show that if there is no cut off in reality you have always atomic cut off. If there is no cut off but you have roughness extending to arbitrarily small length scale the contact area becomes zero and you have infinite high stresses in this zero contact area in such a way that it gives you the external load. What happened when you include adhesion now is that in the beginning, if you look at the green line now in the beginning you see no difference between with or without adhesion. But then you see some difference and here you can see the contact area get constant. So what that means that is that when you start to look with a microscope at the interface when you reach some critical magnification sort of then the contact spots does not decrease anymore. They stay constant when you increase the magnification. That's what I illustrated down in this figure here. This is how the contact might look like in functional magnification. This is at low magnification. At large magnification you see long wavelength roughness. You see no contact region. At even higher magnification you see contact on top of bigger spirited only. And at even higher magnification they break up into smaller contact spots because of the new roughness you observe. If you do the same when you have adhesion like in the green case here in the beginning everything looks the same. But then you come to some point and basically that's this point over here. The contact spots look the same the whole time. So even if you increase resolution down to atomic resolution sort of it looks still the same as it would look at maybe micrometer resolution. That's sort of the basic picture behind this. So here is one of the first comparison we did between my theory prediction and experiment. This was a rubber block with a rough surface which was squeezed against a glass plate and the dark region is contact. And here I show how the contact change when you increase the normal force. And then the same thing is plotted in this figure here. The red data spots are from this kind of experiment. This is a relative contact area. This is applied normal squeezing pressure. The blue line is my calculation without adhesion and the green line is with adhesion. And there's basically no fitting parameters here. We know the roughness from separate measurement. We know the elastic properties and we know this binding energy for flat surfaces. So there is still some mysteries. For example, if you take a finger and you squeeze it against a glass surface you typically get a pattern like indicated here. In this case, theory would predict that the relative contact area should be only like 10 to minus five. So the white area here should only occupy 10 to minus five of the nominal contact area. And clearly this is completely nonsense. You get much more than 10 to minus five. And what we think is happening is that, that or one thing which is happening is that even if you clean your finger when you push it against the glass you get fluids from the finger entering into the foot, into the footprint between the finger and the glass plate. And this fluid will sort of make the contact appear bigger than it really is. So this number is I believe very accurate because we know the elastic properties. We know the topography of the surface. So this is still something which we are working on because it's important in some other application I will come back to. Okay, now let me come back to the adhesion again and tell you that even the weakest force of interest in condensed metaphysics or one of the weakest forces which is the van der Waals interaction you can easily estimate that if you have just one square centimeter cross section and these two material here interact only with the van der Waals interaction if the interface is perfectly smooth one square centimeter cross section can keep the weight of a car. This assumes that you break all the bonds that interface simultaneously when you try to separate them. And clearly you can never observe this in reality. And the main reason is due to surface roughness. This is called the adhesion paradox. And actually even without surface roughness these will not work but for reason I'm not going to spend more time on. So one of the first measurement on influence of roughness on adhesion was due to Fuller and Tabor. Tabor is one of the pioneer in tribology. They did measurement on rubber balls squeezed against sandblasted plexiglass surfaces. And here they used rubber with two different elastic modules. This is a soft rubber, this is a stiffer rubber. This is similar to tire rubber maybe and this is like on Scotch tape or a little stiffer maybe. But you can see that with this stiffer rubber just a few micrometers roughness kill adhesion. And with a softer rubber you need more roughness to kill adhesion but still you kill the adhesion. So the question is how can you get strong adhesion when you have roughness on surfaces? When even for rubber which is very soft material you have basically no adhesion in most practical situations. And there's two ways. One is you have to use elastic material which are in some way very soft and I will explain how you can get soft material from stiff material in a moment because that's what nature are done. Nature start with stiff material and is able to convert it into effectively soft material. It's a very fascinating story, I will tell you that in a moment. But there is another way and that is you can, if you have rubber here for example you can freeze in the deformation field at the interface. If you can freeze in this deformation field when you remove the ball you need a very big force to remove the ball. So let me come back to this picture shown here. The reason for small adhesion in general is that in order to make atomic contact here you need to deform the rubber at the interface in order to make contact. When you deform it at the interface you store up elastic energy here. And these act like compressed springs. When you remove the ball all the elastic energy in these compressed springs are given back and help you to break the atomic bonds between the materials. This is the main reason for why you don't have why I don't observe adhesion in a situation like this. Even for soft material. In addition of course the contact area becomes smaller but that's less important. The elastic energy is the most important. So if you can get rid of this elastic energy when you break the bond you will get strong adhesion. We did some experiment on that which was important for different application. Here is a rubber cylinder we squeeze it against sandpaper. When you do this and then we pull off. If you do that at room temperature it goes off by itself. You need no external force at all. It just pop off. If you take this squeeze them together at room temperature then you cool down to low temperature below the glass transition of this rubber. Then you freeze in this deformation field. So when you remove the contact this deformation does not act as elastic springs anymore and helping you to break the bonds. And now you need such a big force to separate them that it's almost impossible to separate them by hand. So I think this is a rather interesting application which has some technological applications too. Now I will spend some time on explaining some bio adhesion problems. So I want to explain for you how it's possible for LISAR to move on surfaces. Not just on a smooth glass surface but even on a stone wall. You can see that outside here on the stone walls outside the interest everywhere is running LISARs. And how is it possible? Because the material the LISAR has on the fingers here is keratin fibers. It's similar to our hair here. If I put my hair against something it will not stick. So there clearly some difference between the way he used the hair on the fingers compared to my hair for example. I will also tell you a little about the tree frog in a second. So not only the LISAR can bind to surfaces but if you take LISAR which is maybe only 40 gram heavy. People have done experiment not this way but people have done experiment where you can hang four kilogram in the LISAR and he's still not falling down. So they can bind much stronger than they really need if you have a very flat surface. Experiment was actually done like this. You have attached one, two on this glass plate. You put a rucksack on him and you load the rucksack until it falls down. And these LISARs are other aggressives. I had to put a scotch tape around his nose. Yeah, so how can they bind to surfaces? I already told you to get strong bonding. You need to have something which is elastically very soft. And they make use of kind of a hierarchy construction to get a very soft material on all length scale. So it's illustrated here. The fingers on the LISAR is covered by thin hairs about four micrometer in diameter, 100 micrometer long. You can easily bend those hairs because almost no energy at all to make contact with some surface roughness here. But if this hair would end with a smooth round tip because of the high elastic modulus of this hair, it's about a gigapascal, 1,000 times more than typical rubber. Because of these high elastic modulus, you will get no bond at all here. So what is happening is that because you have surface roughness at shorter length scale here. So what happened is that each of these hair branch out into 100 or 1,000 much thinner hairs, maybe only 0.1 micrometer. And now you can bend those hairs to make contact with roughness at the shorter length scale due to the shorter wavelength roughness you have here. And this might happen even one more time. And even this will not be enough. So what is in the end is that each of these fibers has a very thin plate which in some places is only a few nanometers thick. And you can easily bend this thin plate to make contact down to the atomic distance. So by having this hierarchy kind of structure, you have a material which becomes elastically soft on all length scale. But you might ask, why not have just one length scale? You have hairs which are very thin, maybe just a few nanometers, but long enough. The problem is that if you make them too thin and too long, they will bind together like indicated here. And they will come together in big bunches and the whole adhesive system will fail. The same with this plate, if you make it too big in too thin, it can self-bind like indicated here. And I'd like to show this picture. This was the first people who tried to produce artificial adhesive according to this gecko mechanism. They produced asperities like this cylinder fibers and then they make contact, but immediately they start to bind to each other and after this has happened, the whole structure fails. This was actually a guy who got Nobel Prize later for his work on graphene. So before he worked on graphene, he worked on this topic. In nature, there's some tricks in order to avoid this self-binding. For example, you can put some structure on these fibers which point out. And on the plate, you can also put some structure which make it hard for them to overlap and bind to each other. Let me also show this picture, which is also about contact mechanics in some sense. If you look at Elisa when he walked, he has his hands pointing away from the body, not under the body like a crocodile, but pointing away. And the reason for that is you can easily understand just take a scotch tape. You have a flat surface here, you attach scotch tape. If you have a very small angle here, you need a very big force in order to pull off the scotch tape. If you have a small angle, like if the legs would be under the body, then already a small force can peel off this scotch tape. So this is simply to do with mechanics in some sense. This figure like also, this shows that these fibers and plates, the more heavy the animal, the smaller the fibers and plates become. So this is some beetle. It has very big plates. This is a fly, relative big plates and big fibers. This is spiders. Spiders can be almost as heavy as a gecko here. And they have also this hierarchy construction with thin fibers and thin plates. And here they have this hierarchy construction. You can see how they branch out into thinner ones. So the more heavy, the more optimized is this adhesive system. Yeah, this is just a picture how it look like. And if you scale up this to human size, the gecko adhesive is strong, is good enough to have this being reality. You need a smooth counter surface, like a glass or something like that. But in principle, it would work out if you just scale it up. Just a few words about another adhesive mechanism. This, what I told you about now, the fibers basically bind to the counter surface with just fundamental interaction. But some other insects and organisms, they bind by capillary bridges. If you have two surface like this and you put a small amount of liquid in between, if the liquid wet surfaces, you can get very high negative pressure inside. If this distance here is small, you get negative pressure, which is basically given by the surface tension divided by the radius of curvature of these meniscus here. And if you have radius of curvature of 10 nanometer, for example, if you take water, you can get negative pressure of minus seven megapascals. That's 70 atmosphere negative pressure. So some insects, they attach to surfaces by putting small droplets of liquid between these plates I showed you and the counter surface. This is true for the fly, for example. This is foot of a fly. You can see the fibers here and he bind to this flat surface by injecting a small amount of liquid between the plate and the substrate in each case here. And this is the beetle and you can see the same thing, plates binding to the substrate. Okay, my last topic. Oh, it's almost finished. I need to finish quarter, quarter two or? Okay, my last topic is electro adhesion, which is something becoming a very hot, very hot topic. It's illustrated, there's two aspect of it. Here we have two materials with some conductivity. We apply a voltage. We induce charges plus and minus here and they will of course attract each other. And this will be some kind of long range attraction between the bodies. And there's a second variant of this. There you have the two conducting bodies inside one insulating material here. You apply some voltage, you will get some electric field lines. They will penetrate. If these conducting regions are close to surface, they will penetrate outside and polarizes other material here and it will also give you attraction. This is actually what people try to use for robotic application. And this is what is used for touch screen application. First, a few words about touch screen application. So if you have a normal touch screen, like on your mobile phone, the surface, if you close your eyes and move your finger, there is no structure of course. You need to optically see something in order to do something. What people try to do now, and in fact there is already produced devices like this, is that by putting a conducting sheet under the glass, close to the top of the glass surface here, and applying a voltage between that and the finger in this case, you can induce charges like indicated here and you get an attraction. And if you modulate this voltage as you scan your finger over the surface, you can build in pattern of the surface because the friction between the finger and the touch screen will depend on the normal force. And the normal force will increase when you add this electro adhesion here. So in that way you can build in pattern on surfaces and this is already close to production by some companies. Which means for example that blind people can, from even though the screen is perfectly flat, the blind people can feel a pattern on the surface and get message coming out. So in order to understand exactly what is going on, you need to have some picture for this and the skin, it is covered by about 10 micrometer, very insulating material called stratium corneum, that's the green stuff here, and below is something much more conducting. So when you apply a voltage, you expect charges to pile up on one side of this insulating material and negative charges in the conducting layer below the screen here. And if you try to calculate the electro adhesion force now, you need to determine the electric field in this air gap here because this electric field, they are Maxwell's stress tensor. You can use that to calculate the attractive stress which act on the two bodies here. And it's very easy to estimate this electric field, it's basically the applied voltage. We know the distances here, we know the field strength. So we get immediately this relation here. And from simple electrostatic, we know that the electric function times the normal electric field is continuous at all the interfaces. And if you make use of that condition, you end up with this expression for the electric field. And I told you that from Maxwell's stress tensor, you expect the attraction to be proportional to the square of the electric field. So you end up with this equation here. And the way I've solved this problem now because this is a complicated problem because the interfacial separation change here. It's not constant, it change along the surface. So I have solved this problem in a mean field way. So I say that there is a force which push them together, which is given by the external applied pressure here, plus this force coming from this electrostatic interaction. And that one you can calculate using this equation here, but you need to integrate it over the distribution of interfacial separations, which depends on the pressure which push them together. And I have a theory which I did not discuss. Part of my contact mechanism theory is expressing for this quantity here, for this probability distribution. So I can, if you solve, you can solve these two equations together here and basically calculate the electrician force or electrician stress. And from that you can calculate the change in the friction force, if you know the friction coefficient. And yeah, there's some complications. So just a few minutes. There's some complication that is that this is not a perfect insulator. It's almost an insulator, but not a perfect insulator. So if you apply a static voltage, finally the charges would leak down to the bottom surface here. And if you wait even longer, they would leak out on the glass plate. And then you lose all the attraction. So in reality, people are oscillating this voltage, typically with 100 hertz, in order to avoid this leakage to happening. If you go to DC limit and wait long time enough, you have no electrician at all. This is some experiment I was involved with doing. Here's a finger on a glass plate, which can, the hand or finger can move back and forth like that, and we can measure the friction force. Let me only show you this figure here. This is a friction coefficient as function of the normal force you apply to the finger. When you squeeze it against the glass, this is the friction coefficient without applying a voltage. This is a friction coefficient after applying a voltage. And the lines here is my theory prediction. And again, we have measured everything which enters into this theory. And you can see the friction coefficient actually diverge here. That's because of the attraction. It will give you a diverging friction coefficient. The last thing, two minutes and then I'm finished. The last thing is the same thing but for robotic application. That's also a very hot topic now. Here we are interested in putting electrodes close to the surface of this material here, plus and minus voltage, alternating, which will give rise to electric field lines outside here, which can polarize this material here and give rise to attraction. And this is an example of one experimental realization of this. Each of the line here is an electrode and the voltage oscillates between plus and minus V. So alternating, this side is applied to plus or minus and this opposite side. And they did some experiment on this. They was hanging this electro adhesive device on a glass plate and they put load on it here until it starts to move. And from that they can calculate the electrician force or electrician stress. And that's plotted in this figure here as function of contact time. And the green line is what I predict where the T were taken into account, the roughness, the blue symbols are experiment. This is for perfectly smooth surface, no roughness. You see there's a strong reduction coming because of the roughness. And you can see there's a time dependence. The time dependence comes because glass is not a perfect insulator. It has also an electric conductivity. So slowly ions will move towards the surface and become much closer to these opposite charges here. And that will tend to increase electric field strength and increase the attractive force. That's basically the origin of this time dependence you see here. Okay, I finish. Thank you very much both for such an entertaining talk. Questions? Yes? Sir, I have very simple two questions. The first thing that you said that we know that there was a diffusion equation there. So how can we know that the equation that is gonna be satisfied is a diffusion equation? That I know what? You know, how do we know that it is gonna be a diffusion equation for this particular problem? You know it because I have derived it. There is a mathematical derivation behind this equation. Okay, so is there any paper which I can do? Yes. In order to, I don't know. My most cited paper is the paper where I derived this equation. Okay. The mathematical physics from 2001. Okay, thanks. And the second thing is that I'm not working at this field so I don't know that. Can we make a prototype of the human finger so we can get rid of the fluids which are getting off the finger and we can do the experiment to get that actual area? Yeah, there is liquids you can put on the finger in order to reduce sweating and things like that. And people have done that. So this picture I showed you was really after waiting some time. There's other pictures which shows a function of time how the contact area appears to increase. Which we think is because liquid moves out from the finger and into the contact region. So this was sort of, this picture was an extreme case which was, yeah. Good for questions, sir? To change the adhesion in an dynamical way because sometimes it gets thick, sometimes it moves. First I think this ad, when he moves, I think he knows, he has a feeling about how much force he need to keep him up sort of. So he probably not apply the maximum adhesion he need which would mean squeezing your fingers strong enough against the glass. On the force applies, not something. On the normal, yes, it depends on the normal force. Also, the way he breaks the contact is very interesting. His finger, he can roll them up. It's like peeling a Scotch tape. You want to peel it at large angle, then it's easy to pull it off. If you move it 180 degree over and peel it, then it's easy. This side is able to rotate. He doesn't have these stiff bones like we have. He is able to rotate the finger starting at the tip backwards. That's how he break the contact. This was seen only some years ago with very high speed cameras because it goes very, very quick. More questions? Something myself, at the beginning you were showing this fractal dimensions 2.2 to 2.3. Is there an understanding why is that number? I have a paper on that too. If you have higher fractal dimension, the surface tends to get, the root mean square slope tends to be very high. Those surface are very delicate, very fractal. If you do anything mechanical to them, you will smoothen them, you will break this. You can have surface with higher fractal dimension. If you draw them in a well controlled condition in electrolytic cell or something like that, you can get like fractal pattern very open standing up. But if you produce it like most real surface are produced by sandpaper or sandblasting or something like that, then you will never reach very high, too high root mean square slope because it becomes too sensitive to, and then that's my argument sort of why the fractal dimension always is not too large. It's only more hand-waving argument. But you get more or less this estimate to be 2.2? I estimate not maximum 2.3 or something like that under normal condition. Interesting. And something else, where is the use of quantum mechanics here? Quantum mechanics? Yes. This is all classical mechanics. Quantum mechanics, I do have together, that's a different project, quantum mechanics. So that's all? No, there is aspect, for example, we are looking at vacuum friction and things like that. That involves pure quantum mechanics. But this thing, soft matter, contact mechanics is, you don't need quantum. Of course, the force field in principle comes from quantum mechanics. If you're interested in the force field, you want to do molecular dynamics or something like that, you might want to do quantum mechanics to calculate the forces between the atoms. But I think quantum mechanics doesn't matter on the level, which I'm discussing here. Just to finish, can you tell us, how is it that you work with Formula One? I'm curious. I get a rubber sample from them and I mess with the properties of this. We mess with topography of the racing tracks and I have a theory of rubber friction, which predicts what the friction should be. So I calculate rubber friction curves and things like that. These I do also with normal tire components, but with Formula One, it's more complicated because they use these strange compounds with strange properties. But in principle, that's what I'm doing. Very good. It's making a difference, too. Look, these companies tell you very little because it's all top secret. Very good, very good. Okay, so let's thank you again.