Lecture 29 : Special Cases: Polymer-Based Nanomaterials

[Music] [Music] welcome to the lecture 29 and this is the last lecture i was supposed to do 30 lectures but then i understood because it's an online course i could finish with even one less idea was not that basically in online teaching your level of space is very high there is no question on succession going on at the same time so you always trying to teach more in every lecture than what is expected to be taught in an offline course so hence the this is the last lecture and i only can hope you have enjoyed the course you enjoyed the content of the course i i am very open for discussions or questions or anything which you have failed i may have made mistakes or i may have not covered or i have made given some reasons which are not maybe proper according to you so please do use this forum to tell me provide me the feedback so that i can improve in my future courses on this nptel forum so this lecture we are going to talk about polymer nanocomposites that we discussed about it right so we have discussed over these 28 lectures various aspects of nano materials we learned the effect of size for on the various properties and we have also one tried to understand the structure nanostructure issues of the nanostructure how they are correlated with the properties of the nanomaterials so other than size many other aspects of size comes into picture right like arrangements at the nanoscale and also how you put things together so that's the one of the important consensus issues in nanocomponents so the last lecture we did some discussions about carbon-based materials in the following i'm going to just give small recap and then i'll talk about you know some of the important aspects of polymer nanocomposites because this is something which is coming off very sharply and probably it will these composites will find use in the real time in times to come so what we discussed about the government nanomaterials we talked about how the carbon can you know cell plus symbol to produce different kind of nano structures we started with 360 buckyballs and we showed that by putting arrangements of hexagonal and pentagons of the carbon atoms basically we can generate this kind of buckyballs and we also understood or rather we also try to you know show you that the carbon nanotubes can be produced by using a single graphene by simply wrapping around a cylinder and graphene is the recent nanostructure carbon materials although i didn't talk about nanodiamonds they also are useful materials in the carbon family since nanodiamonds are used in other purposes like coatings high hardness is can easily obtained using nanodiamonds and diamonds can also act as lubricants in various applications so therefore the varieties of nanostructures can produce using carbon based nano materials but the basic thing is this graphite you know graphitic network is the underlying structure for almost all the nanostructures except for a diamond so you know that graphite is basically layer structure it has hexagonal network in each layer and within the layer you have van der waal bonds between the sheets of carbon atoms so we can always devise ways and means to cut off these fundamental bonds and produce single layer of the hexagonal network which is very you know easy to say but not easy to do in real experiments and that's why it took so much time even though graphite or discovered 1500 years 1500 bc so uh eddie sorry so that but the discovery of this nanostructure so very late maybe 20 to 30 years not more than that so that's the difference of the time scale when you want to produce a new material so you can use this sheet of graphene to produce different kind of non structures like you can drop around a ball and create zero dimensional nanostructure like buckyball which came in 1986 and you can also wrap around the cylinder produce nanotubes if you rub several cylinders you can put multiple nanotubes or you can even cut off each of the sheets you can produce 2d graphene or durian materials like graphene okay so this different kind of nanostructures can be easily produced for one single thing that is called graphite when you stack them together you produce this graphite so that's the connecting link for all these beasts okay i call it beast because they are very powerful materials they can be widely used in different kinds of applications that's what i call them as a beast so that means what the basic underlying structure although we know is is basically single layer of graphene but it took lot of time to understand that aspects now is the question of how we can apply it and all those things so this can be produced mostly by arc discharge method and you know in case of auger discharge of graphite graphites tend to melt and during melting most of the graphite will solidify as a glassy particles but some of them will undergo undercooled heavily and then reproduce this kind of nano mass structure materials like nano rods or nano sorry nano tubes actually or you can use even catalyst in a technique which is very popular you can put this graphitic material in a tabular furnace and you can always apply catalyst like iron or nickel and then you can start producing graphene at much lower temperature sorry nano two is not much lower number that is something about 1100 degree celsius temperature can be used to produce this kind of nanotubes ok so here ah in this case actually a gaseous mixture of methane and nitrogen or carbon or the organ is used and passed through this catalyst then you can produce nanotubes and the temperature is much lower it's almost 100 degree celsius temperature can be used well this is one such picture you can see this nickel catalyst is used to produce this nanotubes and you know nickel is visible at the end of the nanotube and this micrograph clearly confirms that this catalyst can be easily used to produce this kind of cnts well graphene can be produced in different routes one of the ways basically mechanical explorations in mechanical explorations you can have you can take a graphite and take it it will put it within the double sided tap and then you can remove open this peel of the temp so once you peel off the tape the thin layer of graphite can come off and it can produce graphene this is how the graphene was discovered and you know you can see these thin layers under optical microscope and then you will find that layers which are dead thin they will be having almost 99 percent transmission of light that's all uh the game and muscle of discover graphene and avoid a nobel prize for this you can also use chemical explanations oxidative explorations electronic explorations or liquid phase explorations there are three different techniques possible oxidative exploration basically use oxidation of graphite and it can exfoliate and produce different layers of the refined graphite oxides and then you can reduce this graphite graphite oxide to graphene oxide or reduce what you call a reduced graphene oxide or argue you can always produce using electrochemical explorations simply by discharging between the two electrodes you can also produce graphene by liquid phase exploration also so there are many ways you can do that and third technique is spacing wastes cvd or chemical vapor depositions we discussed about it you can use methane gas passed on the nickel ah catalyst or nickel plate which is kept at eleven hundred twelve hundred celsius temperature and this methane will decompose into carbon and gaseous hydrogen or basically moisture it can react with atmospheric moisture and produce moisture and it means oxygen produces moisture it can produce such a kind of carbon can dissolve into nickel at the temperature when the super saturation will be reached for the nickel then this carbon will come out and form like a graphene so this is how it is used you can use this cntn nanotubes cnts and graphing properties or purposes like philippe transistors or hydrogen storage or super capacitor okay this is super compressor this is hydrogen storage graphene can be used for energy storage transistor or even web guides this is what we have seen in the last lecture and there are many other 2d materials most important are the mos 2 and double s 2 and they are also produced in a similar way you can see this is the ws to multi wall nano tubes or on the right side you can see here ah the multi wall fluorine ah obtained from the moss two okay so you can do that you can always produce steel sheets of moss two basic bison chemical route which you have discussed you know earlier part of this course so as you can see there are various 2d materials can be easily produced during this purpose so now let us come back to our discussion today this is polymer nanocomposites ok you know what are the nanocomposers we have only discussed about it they are actually class of materials in which one or more phases are in nanoscale dimensions it can be zero d one d or two three two d and this nanometal is embedded in a matrix called metallic ceramics or polymer general idea is that addition of the nanoscale second phase will create synergy between the various constitutions and normal properties can be achieved the properties of nanocomposites rely on a range of variables particularly the matrix materials which can exhibit nanoscale dimensions loading even degree of task dispersion size shape obviously and i mean additional orientations of these second phase so among the various nano composite types the polymer matrix composites have been the widely studied one because you can have different kinds of ah variations possible in polymer nitric composites so much like any traditional composite system polymer matrix and composite constant stop a matrix which is made of a polymer material and the second phase can be anything like nanotubes also graphene also or even ceramics metallic particles can be put up so this secondary matrix is what is which is in nanoscale dimensions so that is what is shown in the picture you can see this is a polymer matrix and then you have put this particle inside the matrix which is nanoscale so they are in spherical steps so we'll talk about the left side picture a little later as you know polymers undergo glass transitions most of the polymers actually are amorphous or semi-amplifiers type so this amorphous phase will undergo glass transition temp and then if you keep on heating further it will become rubbery at high temperature so that's why the application of this composites are limited to temperature below tg at the glass transition temperature and this is very ah common you know plot for the glassy materials which are widely used as an if any every glassy material sounds fast material you have a glass transitions temperature however the glass transition temperature material will become rubbery and liquid like so therefore it cannot be used at the temperature so major limitations of the polymer nanocomposites is the temperature issue you cannot use it at high temperature compared to the ceramic and the metallic nanocomposites that is one of the major limitations okay so you know uh the in addition to that due to this nanoparticles present in the reinforcement page the interface to volume ratio is significantly higher than in combinational composite as a result volume fraction of second place can be reduced without regression degradation of the desired properties polybiotic composite systems can be obviously different types thermoplastic thermostat or elastomer so let me talk about a little bit about that before that let me tell you this is also nano composites you know this is basically aluminium copper alloy you can see needle separate ah nanoscale precipitates in aluminium matrix and these particles are actually growing in this various orientations and this is routinely used in in the real material synthesis you know aluminum four person copper allows is called dural mean is used as a material for the aerospace industries and this is the microstructure and we this was discovered long long back before even the uh the concept of nanostructure material came up into actual use or actual practice so hence the ah this picture is taken from the again from the book of michael ashby and others let me acknowledge their them for this purpose other than that this picture can be available in various published paper ah from 1950s late 50s to 1970s you can find it as a kind of microstructure split nicely preferred from hr level aluminum copper alloys so that is basically the idea of nanocomposites as you can see so hence the basic idea is the compounds what are polymers compound consisting of long chain molecules made of about repetitive units are basically called polymers right so we will have a small discussions about polymer then we'll go for the composition discuss because some of you may have forgotten about polymers let us have a recap of that the polymers are basically low density high normal strength and they have reasonably good thermal electrical conductivity strength weight ratio is comparable with many alloy steels because they have a very low density and they are very prone to instability because of substantial clip and you know cold flow at all temperature zdt and fertic strain much lower than the metals and they are normally used below 350 degree celsius temperature not more than most importantly polymers forms living organisms and their vital processes of life we i always compare polymer like a bowl of spaghetti we all know spaghetti you know you can always see this is the network of different polymeric chains in a real material well you know polymers as i said they can be classified into three com parts three different types thermoplastics thermoset and elastomer thermoplastics are once thermal passing thermostats one which consists of plastics which you see in the real life and elastomers are basically rubbery material right so ah thermoplastics basically can be molded thermostats cannot be they have once they are produced you cannot remelt and reduce but thermal plastic can be used again and again that is why they are called thermoplastics so as you heat the temperature they will melt and again they can then form the plastics but thermosets are light once like bacalite which once you set you cannot get it back so this is basically uh the problem of polymeric material most of the polymeric materials hence thermoplastic materials are basically ah more widely used in thermosets elastomers you all we know uh from the literature elastomers are basically rubber or rubber bands and even tires also elastomers they are widely used in the materials in the community well so as you said as we said that thermoplastics are basically solid at room temperature viscous liquid at high temperature which allows uh the them to be shaped into products heating and cooling cycle can be repeated without degradations examples of basically nylons acrylics cellulose or pvc they consider almost 70 percent of the polymer produced as i said they are the widely used ones and you know they can be molded extruded roll on the other and thermosets are softened on the heated but hardened when they cool into an infusible solid you cannot melt it back again they get cured and the skewering is basically reversible reading can burns and charge the material example epoxy phenolics and even certain polyesters they're used as a knobs and handles of the pots and pans and the light switches rubbers that undergo elastic large elastic deformations when subject to forces or stresses they can retain original shape and size of the stress matrix removable naturally available synthetic can be produced also both and they can be additive pen lead to produce specific mechanical properties they are widely used in space application like corrosion abrasion protections vibrational shock absorption electrical insulations and non-skid surfaces the different products like tires food gears gaskets most of the gaskets seals and floorings are used ok so what are the fundamental things about the polymers as i said polymers are synthesized by joining many small molecules together into a very large molecule called macromolecule side so obviously the major process which is used to produce polymers as polymerizations right there can be two types of polymerization addition and ah you know step polymerization what is addition polymerization well addition polymerization is basically ah very simple here i am showing you the case of you know polyethylene you know you can take one molecule of ethylene and join the molecules as large many numbers possible they are called polyethylene and nylon is produced by step polymerization because it is has different groups like this is my mild groups or urea groups or ethyl groups so therefore they will be produced by other step kind of polymation techniques ok now you know addition polymerization is like this you can have monomers then monomers will join from diamonds dimers will then join and polymers ok so you can do that step elimination is like that once you have nmr you can add a monomer then you can put this n plus one mark n one mark can be then added to n to mark and then you can join these two is called step polymerizations okay that means different types of monomers can be joined and produce a polymer that is what is happens in step polymerization as you can clearly see that so fundamentally ah the different polymers can be produced by both these techniques are the additive addition polymerization or the state polymerizations and this is very commonly available routinely so chains in the polymers can be different types based on the how you produce there can be a simple linear chains as you see here or they can be also branch like this or this or this or this they can also cross links right you can clearly see they can be other cross links right they can also tidy crosslinks very very entirely costlings ok you can clearly see that how the cross link is very ah you know all the directions and that's why the three dimensional poly the structures can be built up once you have tightly costly structure you can build a three dimensional polymers so ah you know this is what normal routinely we find for the most of the polymeric products that they are linked in a different manners okay now you can also have copolymers or homo polymers ok ah this is homo homo means similar type this is sorry there is a mistake here ok this so homo polymers means ah you can have one type like ethylene groups or you can see c2h3cl groups copolymer means there are two types of ones called ethyl groups others can ah you know poly methyl ethyl okay so you can have different types of groups and they can be have different values of n and m then you can also have alternative things for the copolymers you can see that or you have a random you can have a block coal polymer or you can have a grafted copolymer you can have you can do grafting also like hair grafting in your head so all kinds of situations are possible to produce different kinds of the polymeric substances ok now you can polymers as i said they are mostly amorphous but they are not fully amorphous there will be always some crystallinity presence in this ok and this crystalline structures are basically ah randomly present in the material as you can see here i am showing this this is there is a crystalline structure there is a amorphous structure or you can have such a kind of folded regions also possible so what is the meaning of this you can have a bit of crystallinity in the polymers and this actually affects some properties of the polymers extensively when i had this nano materials like metallic ceramics or you know carbon based into the polymers this kind of things can happen actually but among us polymer can get crystallized into some part of it as a crystalline polymers this is what something is very uh nice picture taken from i can mass as this book you can clearly see these are the regions of crystalline are order regions such as crystalline regions okay and this is the region of polymer the random oriented whenever a template total disorder this is what is glamorous polymer completely amorphous you can see is they are you know random completely so this is how actually different kinds of polymers ah can present and you can have ah in a nano composites you can have either of these phases can be either crystalline or this phase can be the otherwise you know amongst us also you can always put carbon black into the ah you know an amorphous polymer produce polymer nano composites that is also possible well how polymer nama composites are produced ah you know some of these things i am showing you they are done research in my lab by my students okay so i will be using that those pictures also as you see this is a polymer non-composite p person using cnts first you do that you put the centers into acetone and then sonicate it for long and you do it because you know both the sentient epoxylation to the tickets there's not much agglumeration happens in the actual picture then you can stir at a very high rpm for 60 degrees celsius about one hour this is the second step you can see here this will be followed by pouring of this you know cnt acetone mixture in the epoxy okay and once you do that then you can again stir it at 65 degree for one hour for better mixing and then you can sonicate it again for large watts and after that you can do vacuum degassing so that all the water everything goes off after that you can mix ah the hardener of the epoxy actually epoxy as a ah hardener also and then it will be hardened and then you can hot press a 60 degree celsius temperature by application of some pressure for about 20 to 30 minutes then you can get easily nanofiller based laminates you can one by one you can produce laminates and after that you can cut the laminates and you can do different kinds of testing so basically the important aspect of this preparation fabrication route is that this is a widely used fabrication route ah you know that you have to mix them very well once you mix them properly then you can put pour in a container and degas accumulated gas that is widely used technique okay vacuum degassing this is not a very difficult thing to understand you can remove of by vacuum requesting all the water and other species which are easily removable and you can it will leave behind the solid composites ok so that's something which is very routinely practice in the real world or material world ok you know this composes can show different kinds of properties here you see the polymide composites with nano silicon dioxide having different kinds of transmittance zero percent polymide ten percent so zero percent silicon dioxide ten percent to about 30 percent so the transmission levels changes by different loading this is the property which is you know sometimes required for having you know different level of transmission to light it can be only normal light or uv so that is ah something can be easily obtained you know nanoscale reinforcing phase ah in a material what we discuss here like silicon dioxide or carbon can be grouped into three categories they can be nano particles like zero dimensionals they can nano tubes they can be nano pets or they can even nano grain materials in case of nano comp particles particle surgery distribution are of great importance and depending on the type of nanoparticles added the mechanical electrical electronics optical properties or thermal products will change in the field of mechanical properties change in the modulus and strength depends on the strongly on the degree of the interaction between the particle and the polymer uh in ah polymer line methyl collate or pmma like polymer nanocomposites reinforced with alumina modulus decreases due to weak interaction between the aluminum and the pmma whereas cpu is polystyrene nanocomposites reinforced with silica then modulus increased due to strong bonding so bonding between this second phase the polymer is very vital another advantage of using nanoparticles reinforcement is that the size is smaller than the as a critical crack length typically found in the polymers ah so the celestial nanoparticle provides the improved toughness very high toughness and strength however agglomeration of nanoparticles is a big problem in all these things that's why the strong styling everything is used so hence agglomeration is a big problem and several investigations have shown that small level of agglomeration can decrease the strain to failure by small tensor percentage and additional mechanism that occurs in for well dispersed nanoparticles which weekly bonded to the matrix ah is the phenomenon of gravitations okay in other words nanoparticles can act as a void sexually they can create voids which will initiate the yielding and increase the volume of material going through the deformations nanoparticle can also significantly affect as is you know discussed already the tg or the cascades and temperature typically this occurs because nanoparticle influence the mobility of the polymer exchange due to bonding between the particles and the polymer and even the breezing to the polymer ok so hence in terms in some cases depression in the tg is observed which is not good news however in many cases the temperature digi temperature increases a lot electrical optical properties of polymer matrix can be also improved by additional nanoparticle respect to the electrical properties of you know matrix and this is can be done by various arrangements of the nanoparticles in the matrix and type of nanoparticle low density polyethylene nanocomposites filled with zero nanoparticle source you know extensive improvement in properties as we have shown you here let me just go back yes this is the one you can see this is a picture of zero nanoparticles in a poly low density polyethylene nanocomposites it can improve electrical properties a lot so in terms of optical properties there is a large development large interest in the transparent nanocomposites ok ah transparent nanocombos are very widely used this is what i discussed just couple of minutes back and ah the with enhanced mechanical electrical properties to achieve transparency uh the what is called the scattering must be minimized which means the nanoparticles should be as small as possible while the index of refractive refraction should remain as similar as as small as possible of the the matrix for example addition of nano particles of silica dioxide to the you know silicon dioxide or these things can control the transmissions of the nanocomposites furthermore the addition of nanoscale alumina to gelatin has improved total transmittance by as much as hundred percent next ah you know let us talk about little bit of carbon nanotubes as you know the one dimensional nanomaterials in particular cnts can act can be used as a reinforcements for the nano composites a couple compensative discussions on this you know cannot be done because of the uh you know shortage of the time but one can read the different books and find out the use of cnts in the composites has received wide scale you know attention due to their external physical and mechanical properties however you take full advantage ah of the scientists and components applications several critical issues must be addressed first is the uniform dispersion which is very difficult to achieve second is this alignment of scientists and in the composites this is very challenging to disperse nicely these scientists in the matrix particularly as comparison polymer poly you know that procedure i just discussed just now because cnd exhibits smooth surfaces and intrinsic van der waals interactions which can promote clustering when in a polymer mattress so at least this problem many people have basically modified the sandy surfaces ok by putting some you know some kind of a layer on the ceiling somehow functionalize them so that can be done or you can have shear mixing in the during mixing process or you can have surface and edited assisted processing also the different kinds of techniques can be used this is a typical picture of agreements from carbon nanotubes uh you know this is taken from the work of pj ferrari and at all for mit i am just using this picture from michael ashby's book so i acknowledge both of them for the use of this picture for the class well now let us see some of the examples of which we can these are the works done by my students and this is the polymer nanocomposites epoxy base basically using multi-wall cnts you can clearly see that the cnts are present here there here a lot of cnts are present and this scene is basically in many cases got agglomerated it is very difficult about the agglomeration of the scientist but scent is provide many many interesting ah you know many many improved properties of this nano material this is where you can see these are actually cnt's some of the cases you can see they pull out of the senties also it is possible to observe that ok ah you know they are well dispersed many cases so this is something which is routinely found and now polymer is also used for functionalization and solid stabilization cnts and you know you can also stabilize the cnts to produce different kinds of structures okay like here we can see the different kinds of structures you can clearly see that these are the different radicals actually which can be used for this purpose ah so in order to in in fact in addition to uniform dispersion of the polymetrics a crucial aspect of providing optimum respond polymer is ah orientation with cnts because of the very high aspect ratio cnt's process highly anisotropic mechanical properties took advantage of their load carrying efficiency along the axial direction is essential that cnts are well aligned within the matrix several method have been used to do that okay so polystyrene nanocomposites are basically filled with multicell ah conts have been produced compared to the piston sample modulus of a line ah composites increase almost by 50 percent ok so that is something which is widely uh used in many purposes narration alliance entities or polystyrene companies were also shown to exhibit increased ill strength and ultimate tense ultimate ah uts also for compared to the pristine ones due to the fact that cnt's exhibits high electrical conductions uh you know applications of the magnetic field or electric field also been used to produce saint alignments it is observed that elastic modulus measured in the direction parallel to the magnetic field was far greater than the perpendicular to the magnetic field so in fact this suggests that alignment of cnts contributes significantly to the increase in the mechanical properties of these polymer nanocompose finally the interfacial bonding between the cnts and the polymer is very important it is believed that efficiency of the low task while nanocomposite depends on the interfacial uh characteristics of the reinforcement phase in the matrix so in case of in case of polymer matrix and composite reinforced by cnts the main mechanism of load transfer is mechanically interlocking between the cnt and the matrix so that is the main mechanism other than that you have a chemical bonding or nano bonded interaction between the c to the matrix addition it is believed that key factor in forming a strong bond is the polymer matrix and the client lies in polymer morphology especially the ability to form large diameter helixes around these individual cnts strength of the interface is then due to molecular level and triangle bands of the cnts are the matrix in inclusion of scientific polymer matrix nano composites can also be used to improve thermal conductivity of this nano composite the centers create percolation network in the ah nano composites ok to conduct the heat and conductivity up to 3.5 times higher than the what is observed in piston polymers however thermal conductive nano compass still far from lower than the theoretical value and this is something which is a big concern the major reason for discrepancy is the large thermal resistance that exists between the polymer matrix and the cnt surface because cnt process high surface to volume ratio when cnt says disperse in a polymer matrix large you know interfacial area creates a significant resistance and this effect has been attributed to the difference in the pronoun dispersion of phonon frequency between the cnt and the polymatics some solutions has been suggested in the literature to decrease this thermal resistance and it is proposed to covariantly bond the same pieces of polymer to improve this pronoun pronounced scattering but it has also been suggested that multi one center is use of multiple centuries instead of singular scientists because former or the multiple scientists can ah you know have smaller aspect ratios therefore less interfacial area the use of scientists in nanocomposition has also improved the thermal stability of the polymeric composites it has been found that scientists can improve that well there are many other aspects which ah you know can be discussed about that you know the last one is basically 2d second phase particles and composites in a polymer diagram there are plate like layers materials with the thickness of the order of one millimeter we got aspect ratio of twenty five above can be used most common ones are layered silica structures ok which is widely used this is the one you can see the sick layer silica structures silica can be used that and once if you use you can improve several properties of polymer nanocomposites ok so this is a layer silicon structure and which can be produced which can be used as one of the reinforcing materials and it can lead to improve up resistance improve strength gas permeability get a dimensional stability many other properties can be improved okay so among the layered silica mica and asthmatically mycans medically can also be used okay micah is easily available and can you have seen probably they can be used also for this purpose they are layer structures mica consists of large sheets of silicate with strong bond among the layers on the other hand and basically they can be used for this purposes also on the other hand contrary semantic lays exhibit weak bonds between the layers ah the semantic layers consist of three layer sandwich structure composed of two outer layer containing silicon and oxygen bonded to the inner aluminium magnesium or any other atoms presence there or the hydroxyl groups due to the substitution of the divalent magnesium to tribal and aluminum negative charge can be produced and this can lead to uh in this chart has to be compensated by the absorption of the cations like sodium potassium calcium and lithium layer structures is you know okay it's shown here in the 2d you can see this aluminium iron manganese is produced to charge for the create this charge imbalance and which later on can be used for better bonding between the polymer matrix so to work on this problem uh you know sometimes exchange reactions usually varied or carried out variety of organic uh cations openly open the clay structure well so polymer style composite can be it can be used the two types conventional composites intercalated nano composition exfoliated nano composite ok so nano scale layer silicate set pro moment to be ah provide much better insight into the properties so there are many such immunities can be used i'm just telling you only few of the ingenuities which are there so with this i'll close this class and close this course hope you have enjoyed uh over the last you know three months this course and you have enjoyed various you know parts of the course and they're always deficiency when you develop a course it is not possible to cover every subject of the course in a very systematic manner because of time constant because of the available literature and this this field is basically evolving this is not a field which is already mature enough this field is evolving so the subject matters are also available many cases in the published literature not in books but that is another big problem challenge we face when you talk about these courses and so but most importantly you should study books and try to understand the basic part of the course so that you can use such concepts for your own research or technology developments or preparation of different kinds of new materials so thank you for your attentions thank you for your you know participations in large numbers i know many of you have joined with with a lot of expectations i hope i have lived up with expectations and did injustice to the course thank you again for the attentions [Music] [Music] you