 In this lecture, we will learn about carbon nanostructures. Carbon is one of the most abundant elements on the earth and forms a basic form of life. So, there are many polymorphs of carbon which are available and eventually, they go into forming nanostructures. So, we will learn about certain of those nanostructures which belong to that of carbon in this lecture. But before we go into that, we are more interested in what is nanotechnology because carbon nanostructures, if we can somehow engineer them, we can tailor them to suit certain properties or certain application. We can make them as sensors or we can also make them as reinforcing entities. We can also eventually get some data out of it like we can make them as bridges between two entities and we can pass the current through them and we can again allow some properties to be measured from that aspect. So, that nanotechnology is emerged as a very strong tool because of these nanomaterials, but nanotechnology, it comes out as a combination of not only engineering, but also some other sciences such as chemistry, biology and physics. Initially, the sciences were very, very different. In the case, we will go only with say physics, biology or chemistry and engineering was supposed to be a different field of study like making things work. But right now, the paradigm is that everything is merging at a common podium. So, if I want to implant a chip in a body, I also need to see the physics of it, how those things will really make that happen. I also need to understand about how do I engineer it. It means how I can make that device work while it is in the body. Then, I also need to understand the biological aspects of it. If it is in contact with blood, what do I do with it? So, now, the paradigm of using this nanotechnology has merged all the disciplines whether it is science or engineering, we need a common platform for working on that. So, that is how the nanotechnology has brought all the disciplines of engineering. It is not only about the material, but also about the mechanical and the electrical aspects as well. So, if that chip is being implanted into the body, it has to sustain certain forces or certain stresses. So, I need to design it using mechanical engineering. I need to design a material. I need materials engineering. If I want to pass some current into it, I want to sense something. I also need to worry about the electronics of it, so that it does not degrade with time. In case I am also worried about releasing some drug using that particular device, it can be a material and I want to release some drug into the body. I need to have a very controlled degradation of that particular material. So, I also need to study about the biological part of it, that how much drug is to be released for a certain stipulated period of time. So, these are these aspects make things much more complicated, but now it has brought all the aspects to make this nanotechnology and interdisciplinary field of study. So, nanotechnology we are worried about materials which are very, very small sizes, order of less than 100 nanometers and that has made it an interdisciplinary field of research. If I am worried about certain catalyst to release a certain drug, I also need to worry about the surface area of that particular catalyst. I need to worry about the rate characteristics involved in that. So, I am also worried about the chemistry part of it. So, there are many, many aspects which make things very, very complicated and the subtleties are somehow ignored or sometimes if I want to engineer it to that extent, I will also need to worry about those certain aspects. So, that is how it has become a very complicated tool and when I am using a nano material, I need to also understand things at the nanoscale because right now the bulk, the bulk physics is very, very different than what you might expect at the nano level. So, again it is a very complex phenomena and to engineer that we always need to worry about the nanotechnology. And again coming back to how small is nano, nano is nothing but any entity which is less than around 100 nanometers and to see it, visualize it physically. A nanometer is billionth of a meter, but it is about 1 by 80,000th of the diameter of a human hair. Human hair is approximately 100 to 250 micrometers in diameter or this nanometer is approximately 10 times that of a diameter of a hydrogen atom. So, right now we are worried about 0.1 angstrom that is a hydrogen atom, the diameter of that and I am talking about scales 10 times than a hydrogen atom. So, that makes it around 1 nanometer. We can see a human being, a human is generally a couple of meters like 1.5 to 2 meters. So, that is a height of a human being around 1.7 meter and ant it is approximately 1 millimeter. The length of the length of an ant is approximately 1 to 2 to 3 millimeters. Then we have red blood cells which ring in the order of microns or 10 power minus 6 meters. And when we talk about a material we find that a material has certain polycrystalline grains into it and the grains also extend to the order of couple of micrometers. So, the grain size can vary from micron to submicron. And now we are worried about the microstructure of a material and that is approximate that approximates to the micrometer length scale. So, I am worried about micrometer length scale I am talking about couple of micrometers size of the grains. When I define the grains to submicrometer range less than 0.1 micrometer then I am talking about something at nanometer level. So, that is what the range is approximately here that I am worried about 1 nanometer or 10 power minus 9 meter or that is approximately 10 times the diameter of the hydrogen atom and that is what is nano. To give a physical sense if a ant if it starts holding a nano gear. So, if I have an ant which is approximately 1 to 2 to 3 millimeter in length and if it is holding a nano gear that nano gear will be 300000 times smaller than that times smaller than the ant itself. So, we can see an ant is approximately 10 power minus 3 meter and we are going to nanometer that is approximately 10 power 6 times bigger than a nanometer. So, that is what the overall feel of this nano length scale. Now, coming to the nano structures. So, we can see the carbon as many polymorphs which are available with it. So, in this case we can see we have a diamond structure we have a graphite structure we have fullerene structure and then we have something called carbon aerotube. In the case of diamond we can see we have sp3 hybridization it means that each carbon atom is now attached to 4 other carbon atoms. So, we have 1 carbon atom which is now attached to 4 other carbon atoms and that is what it gives a very strong strength of very high hardness of very high stiffness to the diamond. So, this is the diamond structure. So, each carbon is sitting at the tetrahedral tetrahedral and it is now connected to the 4 carbons along there with. So, that is why we can see that carbon can exist a diamond which is which is one of the very hardest known material and that requires hybridization of sp3. Though we say that diamond is forever, but diamond is not the equilibrium form of a carbon it is a graphite which is actually the equilibrium or the thermodynamically stable form of carbon. And in graphite we can see we have only 1 carbon is now attached to only 3 other carbon atoms and 4th one is forming some a wonder valve bonding with the layer which is beneath itself or above itself. So, we can see in this case we have sp2 type of hybridization in a graphitic structure. So, we can expect that conductivity of strength will be much higher along this length scale. So, we can see that we have free electron available and that can basically hop and in this case we can achieve very high strength why because in this case we have a covalent bond whereas, along the vertical direction I have Wender wall attraction. So, in this case in a in a graphitic structure I can get very high strength along this horizontal axis and apparently this Wender wall forces are pretty weak in comparison to that of covalent bonds. So, I can easily slide these two layers and I can basically slip those graphitic planes over each other and that gives the overall lubricating property to the graphite. Whereas, that thing is not possible in the diamond structure because diamond structure it has all the bonds which are covalent. So, that is the problem in diamond, but we can get very good lubrication in this graphitic structure because we have a Wender wall force which is joining the two layers of graphite. So, that is that that is what defines the overall graphitic structure and then we have something called fullerine. This is also known as Buckminster fullerine which is on the name of Buckminster fuller which Buckminster fullerine fuller which has actually developed this structure of geodesic dome and based on his structure this structure was dedicated to him. Now, coming to C and T this is nothing but a single layer of when a single layer of graphite is rolled into kind of a tubular structure. So, we can see a tubular structure is made and that basically is forming a diameter which is approximately less much less than 100 nanometer. So, that is why we are calling it carbon nanotube. It is a hollow structure that is why it is a tube. So, I am taking a layer of graphite and I am rolling it in a manner that I get a tubular structure and that is called a carbon nanotube. So, carbon nanotube are nothing but long and thin cylinders of carbon. It was initially discovered by Sumio Ejima in 1991 that actually popularized the application of carbon nanotubes in the nanotechnology. So, we can see there are couple of nanostructures. We also have a structure of amorphous carbon. So, again that part we would not be covering out here, but again we have also have amorphous carbon which can also exist as one of the allotropes of carbon which are very widely used are diamond. So, diamond is sp3 hybridization we can see and it is one of the very hardest known material and very high thermal conductivity as well. Then we have graphitic structure it is very well used as a lubricant and it is sp2 hybridization where along this layer thickness along the layer we have covalent bonds whereas along the vertical direction the interaction between the two layers is through vendor all forces and these bonds are weak. So, they can easily glide over each other and when a certain stress is applied. So, it can be a very good lubricant. Then we have fullerene structures. So, that is composed of certain pentagons and hexagons that complete the soccer ball type of a structure. And then we have carbon nanotubes carbon nanotubes are nothing but very long and thin cylinders. So, we can get aspect ratios which is nothing but the length to the diameter ratios as high as 1000 or more than that and that was discovered by Sumiojima in 1991. So, that is what we can see the overall how the carbon nanostructures are being developed. The first thing is graphene which we learnt about graphite, but graphene is nothing but a single layer of graphite. So, we are talking about only a single layer which is present in the graphite and that constitutes the overall graphene and we can see the overall hexagonal structure which is predominant in the graphene layer. So, that is what we can see out here that we have this hexagonal structure which basically develops in the graphene. So, we can see that we have a single layer of graphite and that is called a graphene. The beauty of this one is that it has a very high thermal conductivity as well it has a very high strength. The fracture strength can be as high as around 200 giga pascals whereas, the modulus can be as high as 1 tera pascal. So, that is what we are talking about graphene apparently graphene has very high transparency to the order of 97 percent which can be utilized for making transparent screens out of it can absorb as much as 2.3 percent of the incident radiation and that is what makes it very very special because if you are depositing this graphene via single graphene layer we can really see the change in the opacity and if we have two layers that will be much more opaque. So, even we can detect this opacity via our naked eye. If we go about characterizing it because to see a nano layer we need very sophisticated tools such as TEM or something like that at the order of electron microscopy. So, but if you just deposit a single layer of graphene we can just observe it using this our naked eye. So, that is the beauty of this graphene structure. So, it can be utilized for blocking the radiation whenever it is required at the same time providing a very good conductivity. So, that is what because the single layer of graphene is very highly conductive as well and its conductivity can go as high as may be more than 100 around 100 times that of a 10 to 100 times that of a silver or copper. So, it can be highly conductive as well. So, that is the beauty of this graphene layer. Apparently a group in the Maryland at college park they have isolated a single layer of graphene and then what they have done it is approximately 1 micrometer wide and they have sprayed them in a vacuum chamber and they were they held it in mid air by using some electric fields. So, once it is being held in the electric field in vacuum it is kind of floating and after this floating they have applied magnetic fields and then from that they have seen the rotation of this or rotation of this graphene and it can rotate as high as 60 millions rpm that is highest ever observed. So, it means that graphene that graphene layer or that graphene particular layer is rotating at a speed of 60 million rpm. So, it is rotating in that speed apparently if I try to rotate anything even at say 30,000 rpm or 40,000 rpm or even 1 lakh rpm it will start heating up like anything. Whereas, this graphene layer does not heat up it is still stable at 60 million rpm and it is it is actually been proposed that this is not the top speed of this graphene layer. So, we can make very wonderful things out of graphene without letting it disintegrate. So, that is the these are the recent applications which are coming in this particular arena. So, graphene is one of the very fascinating materials and if you want to rotate it like using some magnetic fields you can make certain rotors or motors out of it and from that we can generate very high power as well and they can go speeds of order of 60 millions rpm without even disintegrating. So, that is what is one of the applications of these graphene layers. Now, coming to fullerines, fullerine again it is nothing but a geodesic dome type of a structure where you can see that you have a truncated ecosahedron. So, it appears more like a soccer ball. So, you have a structure which is a kind of a soccer ball and it has it has around 20 hexagons and 12 pentagons which gives the overall curvature because if you have only hexagon and you rotate it it will form some sort of a tube not really a ball kind of a structure or a sphere kind of a entity. So, you need to have pentagons to give it a curvature and that is what is happening here and all these pentagons are not really joined with each other they do not shear the edge, but it is being shear through the hexagon. So, we can see we have hexagons out here and that thing is being joined by a pentagon. So, that is what we can see out here hexagon then again we have a pentagon. So, we have pentagon hexagon pentagon hexagon kind of a structure and that is how it is being joined to give it a curvature. So, that is the beauty of this particular fullerine structure and it is been named on the birth minister fuller and who had popularized the geodesic dome structure. So, fullerine is again one of the one of the polymorphs of the carbon it has a structure which is a truncated Ecosahedron. So, it appears more like a soccer ball and it has around 20 hexagons it has 20 hexagons and 12 pentagons to give it this kind of a spherical structure. There are other entities also possible like C 20, C 70 and so on, but this is the one which was initially been discovered and it was basically named on Buckminster fullerine it is also called a bucky ball structure and to shorten the form it is called as a to shorten the form of Buckminster fullerine it is called as a fullerine only. As I said earlier that the carbon nanotubes were discovered in 1991 by Sumio Ijima, but these CNTs or the carbon nanotubes were discovered being they have been actually named as carbon filaments even as early as 1952 that is what we can see here. So, the transmission electron microscopy of these carbon nanotubes were mentioned as early as in 1952 may be like 40 years before in general of physical chemistry of Russia, but these findings did not come to limelight during that time because there was a cold war going on between Russia and America and also there was a problem of access to the Russian scientific publications and also the language of Russian was not that predominant during that time. So, that is the reason that this finding did not emerge even till very late. So, this paper was written by Raduskovich and Lukyanovich in 1952 and they mentioned them as carbon filaments and not as carbon nanotubes. So, that was the earliest finding of carbon nanotube even later on the filamentous growth of carbon was again being mentioned by Oberlin and Endo and Koyama in general of crystal growth in as early as 1976 and they had told that they can form this filamentous carbon by parallelism of benzene and they were more worried about the carbon fibers which also incidentally contained a hollow tube. So, now, we have gone from carbon filaments to filamentous growth which is also showing a hollow tube with a diameter approximately of 2 to 50 nanometer along the fiber axis and again they have also formed an annual ring of structure of tree. So, that is what we are they also mentioned that by the parallelism of benzene at around 1100 degree centigrade they can form carbon fibers which with the presence of some hollow tube which is which is a diameter of around 20 to 500 angstrom that means 2 to 50 nanometers along the fiber axis, but again these findings also did not come to limelight as such. Why that thing happened that now the discovery of carbon nanotube was dedicated to 1991 to Sumo Ejima because first thing was in 1952 the Russian general were not that accessible the Cold War was going on and those Russian publications were not available to everyone and again the Russian language was also not so popular. In 1976 again they talked about this filamentous growth of carbon, but the problem is that time they were studying about avoiding this formation of this filamentous carbon in certain areas certain regions it was some mineralization was some process was going on and they wanted to remove the formation of this filamentous carbon and they were more worried about how this growth is occurring and all that. At that time the nano wave had not come so that is one of the biggest thing which really came into that and all this investigation was based on some growth mechanism and that was not so interesting for the physicist. Even the maturity of science was not there and they were not able to think nano during that time because nano was popularized much later in 1980s and 1985. So, that nano wave had not caught in the people and since they are worried about the growth of this filamentous carbon where they want to avoid this formation this did not really interest the physicist whereas in 1991 this paper was published by Sumo Ejima in nature and that is read by all kinds of scientists you know academicians which will which will involve basic research and fundamentals and physicists read them very easily they are very widely read by physicist. So, now that nano wave had caught now people are more aware of what is happening around the world it is it was written in English and it was read by all the physicist nano wave was catching up and the term he had coined it was carbon nanotube now it had caught the wave because it was published in nature written in English physicist it is accessible to all the physicist and it is being read by matured scientist because the science has developed to that extent and that basically popularized the discovery of carbon nanotubes. Though we can see that a filamentous carbon had was forming in as early as 1952 later on it was again reported in 1976 that they are observing growth of hollow tube kind of a structure and apparently all these two journals 1952, 1976 they also have reported TM images transmission electron microscopy images showing the filamentous carbon, but still it got popularized only in 1992 by Evesen and Ajay to point the term carbon nanotube in their nature paper. So, that actually created the way and that popularized the application of carbon nanotubes of basic research as well as for further application apparently the carbon nanotubes they have hexagonal lattice. So, the lattice goes like this. So, it is symmetric hexagonal lattice and then so we can see that kind of lattice which is forming in the hexagonal that is nothing, but the graphitic layer of carbon nanotube and the distance between carbon to carbon atom is approximately 1.421 angstrom in graphite, but because of curvature there is a increase in this particular bond distance between carbon-carbon and that comes around to around 1.44 angstrom that is a better approximation what researcher generally use this can go even higher when the curvature depending on the curvature. So, that is what is being that is what is basically being accepted as a value for this bond line between carbon-carbon in a CNT structure. So, we have CNT it is a hollow R-tube. So, higher the curvature higher is the stretching between the bonds. So, once you have a flat layer if you can cut them up it will be in equilibrium, but once you start putting the curvature the bond line between the carbon-carbon will start increasing. So, if you can define a Karel vector and we can also compare it with the Cartesian coordinate it can go like this that Karel vector we have something like this going along this direction and second entity which is going along this direction. So, we can see that we have a 1 along this direction a 2 along this direction and then we also want to define it using a Cartesian coordinate. So, if I take this one as a origin and I want to define it as a Cartesian coordinate I will take let me just change the color of the pen. So, I can. So, if I take this as origin I will take it as x and I will take this as a Karel vector or Karel vector is defined as the direction along which if tube is rolled that becomes its circumference. So, the Karel t can be given as n times a 1 plus m times a 2 where a 1 and a 2 they are nothing but the vectors of the hexagonal lattice. So, they are around 2 vectors with around 120 degrees of opening. So, that is what is a 1 and a 2. So, we can see that a 1 and a 2 will go along this direction. So, they will have around 120 degree of opening with them and using a Cartesian coordinate I can define a 1 is equal to 3 by 2 times a c c where a c c is the bond length of carbon root 3 by 2 a c and then your a 2 can be given as 3 by 2 a c c minus root 3 by 2 a c c. So, we can see if it has to traverse. So, I need for a 1 I need to traverse along x I need to travel 3 by 2 times of the bond length and along y I need to traverse root 3 by 2 of bond length of carbon. So, that is how I can go from here to here. So, I have to traverse along x I traverse some distance along y I traverse some distance. So, this is x this is y and that gives me x and y in the Cartesian coordinate. Apparently if I take its chiral vector. So, chiral vector is nothing but n times a 1 plus m times a 2 and that comes out to be. So, c h that is a chiral vector that comes out to be root 3 bond length of carbon n square plus m square plus n m. So, we can see that the c l is a circumference of this tube or which is defined as the chiral vector for this particular carbon nanotube. So, that is how it is coming out for the carbon nanotube. Apparently we can define carbon nanotubes in two certain forms. So, once I once I come to that I will also discuss how we can really form it. So, let me first go back to this carbon nanotube structure and then let me explain it further. Let me say it that for arm chair we have n equal to m and for zigzag my m is equal to 0. So, for arm chair my chiral vector becomes when m is equal to 0 sorry n equal to m I can get root 3 a c c n square plus n square plus n square that becomes root 3 again. So, root 3 n square I get 3 a c c n. So, that is what my chiral vector is for arm chair chiral vector is 3 times n multiplied by a c c for zigzag structure my m is equal to 0. So, chiral vector becomes root 3 a c c multiplied by n because m is 0 and m is also becomes 0. For zigzag my chiral vector is root 3 a c c multiplied by n whereas, for arm chair my chiral vector is 3 a c c multiplied by n. So, there is only difference of root 3. So, now if I can see how is zigzag structure will look like. So, for zigzag m is equal to 0 for arm chair m is equal to n. So, if I get this lattice of carbon nanotube layer. So, something like this. So, what I am getting is let me just again change the color. So, I can give it a better feel. So, let me start with here. So, if I am traversing along this side I am getting 1 0 2 0 3 0 4 0 and so on. If I am traversing at the 30 degrees what I am getting is I am getting to this point this becomes my 1 1 I go from here to here becomes my 2 2 and so on. So, if I am traversing along this side what I am finding is this is if I am traversing along this side my m is equal to 0 it is forming my zigzag c and t. If I am traversing along here this is my 0 0 I am traversing along here I am getting a arm chair kind of a thing. So, in zigzag I can see I can get this sort of a traverse where is in arm chair I am traversing like this and I see this sort of a structure. So, that is what I am getting that I am traversing here I am seeing something something and then again I am coming back to this. So, I have a repetition of from here I have a repetition of something like this is forming my arm chair and this one is forming my zigzag. So, we learned that the carol vector for a zigzag it was root 3 n a c c for arm chair the carol vector was 3 times n a c c. So, depending on the n that is the vector which has been traversed along on a particular side. So, n is along direction x and along a 1 and m is along a 2. So, that part we can see here and from that we can all and carol vector is nothing but it is kind of a length which has been traversed that forms some sort of a diameter or sorry the circumference diameter metal plate by the pi that forms the circumference. So, that carol vector is something like a circumference of that particular tube. So, when I have this type of structure I can always find what is approximate diameter of the tube because that diameter multiplied by pi will give me the carol vector. So, that diameter is equal to 3 times n a c c divided by pi for arm chair and d is equal to root 3 n a c c by pi for zigzag. So, from this from the carol vector I can always identify what is the diameter of that particular entity. So, if I want to find a zigzag I just need to roll them along this particular direction. So, depends I will just show you the examples of zigzag and the arm chair configuration. Apparently I can also find the theta that what theta I am rolling this particular entity. So, for arm chair theta is equal to tan inverse of root 3 m by m plus 2 n and this case m is equal to n. So, what I get is 1 by root 3 tan inverse of 1 by root 3 that is equal to 30 degree for arm chair for zigzag my m is equal to 0. So, I get theta also equal to 0. So, just couple of things that in zigzag I get this kind of a morphology that I go up go down go up go down that is forming a zigzag and carol vector is given by root 3 n a c c. Whereas, arm chair I see I traverse I go up traverse come down and that is forming a arm chair because that is more like sitting on a chair with a rest arm rest on that that is why it is called arm chair and carol vector is nothing but some sort of a circumference which is being achieved in the structure. So, I get a carol vector I can relate it to the diameter of that particular carbon nanotube and from that I can get the overall diameter apparently the theta at the angle at which I am rolling it to get this particular nanotube that can also be achieved using this particular relation and for arm chair it is 30 degree. So, the theta value I am talking about is the theta is 30 degree with respect to the Cartesian coordinate and that thing is 0 for the zigzag whereas, it is around 30 degree for the arm chair. So, now, let me show you how these structures look like. So, we can see that once we have a graphic plane the way we roll it we can achieve either arm chair, carol or zigzag type of a carbon nanotube. So, in case when we have a arm chair we have theta of 30 degree. So, we have 30 degree theta when we have arm chair and in zigzag we have theta of 0 degree. So, depending on that it just matters on way we define it. So, we have 0 degree out in zigzag and arm chair is around 30 degree. So, we can see that the nature or the electrical nature of this one can be very different like in zigzag it can be highly metallic and carol it is a semi metal and arm chair it is a semi conducting. So, depending on that the way we are rolling it we can achieve different type of conductivity is in the carbon nanotube. So, that is what we can see out here generally arm chair we have everything is semi conducting carol it can range from semi conducting to metal. So, once we have this relation when 2 n plus m is an integer multiplied by 3 then we get something which is metallic and other cases it is generally semi metallic. So, if we can roll it. So, the rolling is like this. So, this particular part will be metallic whereas, this part will be semi metallic semi conducting to metallic. So, along this side it will be metallic and that basically corresponds to the zigzag structure or the 0 0 direction and in this corresponds to the arm chair type of a fabrication which is nothing but semi conducting to metallic. And carbon nanotube the exhibit well defined perfect crystal which is a covalent carbon to carbon bond and again this graphite is now rolled into various ways. So, I can roll it like this I can roll them like this to get this arm chair type of configuration. In that manner I can roll it to get a zigzag structure when I roll them along 0 direction and then again I can. So, basically I am joining this end with this end to get to get this to get this arm chair if I can roll them like this. So, I can see that this things will come at the end the extremants will come at the end and if I am rolling it like this I am getting zigzag and if I am rolling them in any other direction then I am getting this chiral type of a structure and this properties they are very different basically along different directions. So, apart from the conductivity so I conductivity can be very very different along arm chair or zigzag whereas, other properties like if I want to reinforce them that also will depend on the covalent bond strength of the covalent bond. So, that will depend again which is essentially the same in all the three cases because I again have covalent bonds along the length of the tube. So, I can get pretty much very uniform properties along this side and also they are much uniform along the cross section of that as well. So, depending on where I am loading it if I am loading it loading it along this side I might get very very high properties whereas, in other case transfer direction it might be different. So, why do we want to use carbon nanotubes? Its current density can be 1000 times higher than that of copper because there are no problems associated with the electro migration as in case of copper, but this does not mean that the carbon nanotube also have lower resistivity than that of copper. We can see that the carbon nanotube has resistivity to the order of 10 to 50 micro ohms meter whereas, that for copper it is 0.01 micro ohms meter. Even if I conducting silver it is approximately around 100 times than that of a silver. It can be utilized in microelectronics such as cathode ray lighting elements CRT, flat panel displays, nanotube transistors. The idea is that what we achieve in a LCD is we have some sort of pixelated picture and each pixel has certain dimension. So, because each pixel will give a certain color and that will eventually produce some picture which we are looking at with different colors. If we can replace all these pixels by CNT. So, the diameter of CNT is nothing but couple of nanometers. So, if we can replace them by a CNT I can get more number of pixels in the similar area. So, eventually what I am getting I am enhancing the resolution of the screen. So, it will appear more like I am watching face to face anything and I am it will appear very much it want the picture will not appear pixelated, but it will appear like I am watching someone face to face and that will produce the clarity in a picture or in a particular display panel. So, that is the idea behind using carbon nanotube. Also carbon nanotubes are also being utilized for energy storage because it has a hollow structure. It can store hydrogen very easily and then it can be utilized for the application in fuel cells. Also for nano probes and sensors if the sensor is the smallest possible entity then I can detect that much. So, that particular sensor will be that much sensitive to grabbing or detecting a particular species. If my sensor itself is very very big it will require very high concentration of that species to be able to detect. So, this carbon nanotubes are very very small entity. So, they can be used as a nano probe and they can also sense it very easily. So, I can achieve very high resolution that is the advantage again with using CNT which are nanometer they have nanometer diameter nanometer length diameter. They can also be utilized for very high strength applications. So, if I can somehow reinforce a material such as polymer or a metal matrix with carbon nanotubes I can achieve very high strength as well. So, again CNTs have very wide applications like an electronic novel electronic applications because of their high conductivity and microelectronics again in energy storage it can be utilized. I can also utilize them as nano probes and sensors to collect a particular signal from a particular species. It can also be utilized for enhancing the strength of the composite again it can also be utilized for some biological application. So, the application of CNTs are just plenty in number. So, application of CNT are basically utilized for enhancing the strength and polymer matrix enhancing the modulus again in the in the metal matrix, but in ceramic matrix the modulus is pretty high already, but what the lack is nothing but the toughness. So, in polymer I want to utilize CNT for enhancing the fracture strength, enhancing the modulus in metal matrix I have enough toughening available, but I want to enhance the modulus or fracture strength and in ceramic matrix I want to enhance the toughness, but the problem with CNT is that they have very low surface energy because there are no bonds available for it to bond with anything. So, we want to somehow break the bonds of this carbon to carbon and then make some bonds available for reacting with the nearby species that is nothing but polymer or metal. So, once we are breaking the bonds of carbon and we are attaching some additional molecules we call it functionalization. Functionalization it means we are breaking the bonds of carbon those graphitic bonds we are allowing one bond to basically tangle out and then give out a additional bond which is available for bonding with the interfacing species it can be polymer or metal and that is what we are interested in, but that if we are damaging this carbon bond then there will be some damage to the carbon nanotube itself. So, I can have single layer of carbon nanotube single layer of graphene and then I can roll it to form a single walled carbon nanotube. If I have damage in the structure basically I am deteriorating the properties. So, I may want to go for a double walled or multi walled carbon nanotube it means I am taking a multiple layers of graphene and then I am rolling it to form carbon nanotube. So, even when I damage the top layer I still have some layers available beneath that to take care of the additional load or to deliver the stress. So, that is what is certain design criteria which are which need to be considered for designing the carbon nanotube based composites. So, they can be utilised in polymer matrix, metal matrix or ceramic matrix and the utilisation of CNT is very different in all the three cases because in polymer I am more interested in reducing the density as well and also enhancing the fracture and the modulus and metal matrix I again want to enhance the modulus and fracture strain and ceramic I want to enhance the toughness. So, how do I basically enhance the strengthening? I can utilise the higher elastic modulus of carbon nanotube that is to the order of 1.4 tera pascals which is very very high fracture strength can be as high as 200 giga pascals also very good bending strength, but advantage is that carbon nanotube they can bend completely. So, I have carbon nanotube and if I apply certain stress to it certain load to it it will basically bend completely without breaking. So, it can just bend completely without breaking and that is the advantage of it because of its high strength at the same time it won't fracture. So, it won't fracture. So, it can absorb very high energy in terms of bending. So, its stiffness also is being utilised and its modulus also is being utilised in delivering the bending strength to a particular composite. At the same time it is very high specific strength because of its low density. So, because of low density of C and T if I dispersing them in a particular matrix it can also yield very high specific strength or the overall strength it can be fracture strength yield strength it can be basically be enhanced because of presence of carbon. Apart from that we can also achieve toughening specifically in ceramics I can achieve toughening by carbon nanotubes by crack deflection. So, if a crack is progressing I can always have some C and T's to disallow the propagation of crack along this direction and it will have to change its direction and once the crack direction is changed it requires additional energy to propagate. So, because now it has to go again in this direction. So, the energy required to change its direction is pretty high. So, C and T's they act as obstacles and they help in absorbing extra energy that gives rise to crack deflection and crack will not only propagate through them because of their high modulus and high strength. So, it would not be able to fracture carbon nanotubes right now. So, in that case we can achieve crack deflection. So, instead of crack propagating straight it has now contoured path and that results in the enhancement of the fracture toughness enhance fracture toughness. Second criteria is crack bridging. In crack bridging what is happening if a crack is trying to propagate and I supply crack is trying to propagate along this side, but then I have a carbon nanotube which is present between particle A and particle B. So, it can it would not allow the crack to propagate further because I have a bridge kind of entity which is out there. So, for crack to propagate these two entities have to go apart, but because of C and T it is holding the two particles together or the two structures together the two surfaces together. So, crack will find very hard to propagate further because it does not have the space it cannot make these two things go apart. So, in the process this is called crack bridging. So, I have crack which is being bridged by the carbon nanotubes. There is second way of toughening it is called crack bridging and third thing is crack C and T pull out. So, in this case once it goes to an extreme I can also get C and T fractured. So, if I had a crack like this when some excessive load is being applied these might start fracturing. So, I have carbon nanotube and applying loading like this. So, it can eventually it can fracture some of the carbon nanotube, but C and T's have very high strength they are very high fracture strength. So, it is now absorbing extra energy ideally that energy would have gone to enhance the crack length, but now that is gone in fracturing the carbon nanotube. So, eventually the crack length is much shorter than what it would have been in absence of carbon nanotubes. So, in presence of carbon nanotube it is just restricting the flow of crack in that particular direction. So, we can see carbon nanotubes can enhance the crack deflection they can cause crack bridging it can also cause C and T pull out. So, by all these three processes it can render a toughening to the ceramic. So, in crack deflection the crack has to change its direction. So, it would not be able to propagate in crack bridging we still have some carbon nanotube left between the two surfaces. So, it would not allow it to go further apart in C and T pull out we are using some energy to fracture carbon nanotube and says carbon nanotube is a very high fracture strength of fracture strength or ideal strength or even the bending strength that energy is now being utilized in fracturing C and T rather than fracturing the composite. So, what is happening that overall crack length is not a very short it has now a very shorter length in comparison to what it would have been in absence of carbon nanotube. So, that is how we can get different sort of toughening by the presence of carbon nanotube. Second thing is the wetting of carbon nanotube if I want to wet carbon nanotube because all the surface it is very low surface energy because there are no free bonds available for anything to sit on this particular material. And if I have ceramic material and I want to make it a stronger bond or a metal with a stronger bond with it I need to melt that particular metal. So, that creates a difficulty in modelling because to melt a metal or to melt a ceramic I need to go to the melting point plus some additional temperature to cause the wetting of the carbon nanotube surface. So, I have a melt of say ceramic. So, that becomes very difficult. So, I need to take this melt at very high temperature so that it can cover the carbon nanotube. Again the role of roughness so it the seniorities can also impart roughness to the structure and in that case it will affect the overall wetting. What is happening is I have carbon nanotube on the surface and if I put some droplet of water it might just stay over those carbon nanotubes because it because of because they can support the water droplet because there are plenty in number without letting the water to get into the grooves because it will require very high pressure for the grooves to be filled in. A datum of around 3 or 3 to 10 meters is might be required to fill in the cavity which is approximately 1 micrometer apart. So, that is what it tells that role of roughness can be very critical. I can change the overall surface properties I can change the wettability I can make it highly super hydrophobic. Second thing I can also enhance the overall catalytic property in terms of adsorbing or detecting a certain species. So, that is how I can really alter the overall specification of the surface characteristic by adding roughness to the composite. So, those are all things which can happen in this case of carbon nanotube. Again CNTs are again they are being discussed as toxic as well as biocompatible. Why because toxicity is of a concern when I am using carbon nanotube in a particular biomaterial there are two schools of thoughts. First thing is that anything in the nano form because I am talking about carbon nanotube. So, anything in the nano form it is anyway dangerous because if those particles get into the lungs it will be very hard for them to come out cannot come out. So, they might cause some problems of the lungs and it can like it is more like silicosis that silicon gets deposited into the lungs and it cannot really come out. But, on the other hand there is second school of thoughts which says that carbon is the basic form of life. So, anything which is carbon should not harm the functionality because carbon is the basic form of life and once this carbon nanotube is being reinforced or being trapped in a matrix it is no more available as a free form. So, then it cannot be toxic. So, it is non-toxic, but people still do not know what will happen if CNTs are available in free form they might get deposited into either the lungs, kidney, liver or heart or they might even go to the brain and cause some damage. So, CNTs in free form might be dangerous, but once they are being trapped in a matrix then they might be much more biocompatible and apparently there are some researchers who have also shown that once we have a CNT carbon nanotube it can also allow the precipitation of appetite. Appetite is nothing but the mineral part of the bone. So, people have seen that researchers have seen that the appetite can really grow on the carbon nanotube as well. So, carbon nanotube surface can also it has a surface for precipitation of appetite crystals. So, that is again which are certain consumption associated with the carbon nanotube in terms of their toxicity or their assistance in precipitation of appetite. So, again this has to be handled with extreme care when a biocomposite or biomaterial is being developed. So, in summary we can see that nanotechnology is basically interdisciplinary field of research which involves science as well as engineering. Then we learnt about this carbon nanostructures polymorphs specifically the graphene layer, the graphite, fullerene and nanotubes and we concentrated on basically the nanotubes in terms of strengthening and toughening the matrix and also learning about how the wetting can occur in carbon nanotube and why it is very essential because I can impart a different functionality to the biocomposite or that particular composite. And then I am also worried about the biocompatibility because I want to utilize their strength for enhancing the toughness of a ceramic that is the appetite. So, whether it can be utilized as a biocompatible material that is again it requires much more research before anything can come to a conclusion. But definitely once there have been incorporated in a matrix they can be used as a reinforcing or strengthening agents. So, with this I close my lecture. Thank you.