 I will continue with the examples which some studies first what has been done in Dhruva but I'll also use examples from other sources. In these examples I tried to mix length scales as well as materials because both of them are of interest to various people. One is that from started from microscopic structure we are now moving on to mesoscopic structure and then mesoscopic structure in various materials are of interest to various group of researchers and also various industries. Last lecture I discussed with you some examples from micelles forming using surfactant molecules. I'll continue a little bit with that. I'll also talk about polymers and I'll also talk about and very interesting subject known as vortex plus lattice. So in these lectures I will mix up length scales, length scales and materials because sun's technique is of interest interest for materials and this lecture I'll try to cover a range of materials so that you will get a flavor of what can be done using sun's techniques. I will repeat with this figure small angle neutron scattering as I told you earlier with a little derivation that in the low Q range you have guinea f log p to the power minus q square rg square by 3 i0 that is intensity so log of intensity versus q square should be a straight line of course this depends if it is an rg square if it is not they can deviate from straight line but such low Q plots can give me the values of rg. This is in the guinea region and in the porous region when you go to slightly larger Q then the intensity is given by some constant I will not know divided by q to the power n depending on the fractal dimension of the material that you are using and it is surface structure and here it is q to the power 4 for perfectly perfectly spherical smooth surfaces but it can be other parts of q if you are using fractal materials and I will show you as an example what fractal material that we get and I've also talked to about fractals earlier that fractals are materials which have non integral dimensions instead of one two three like one dimensional two dimensional and three dimensional object fractal objects can have dimensions between one and two or two and three and why because the way they're embedded in space as I showed you as you reduce the length scales the number of scales required don't go as a power node and I took the example as one dimensional fractals and the coastline of India and showed you that as you go to shorter and shorter length scale your lengths become longer and longer faster than a power an integral power also small angle scattering in higher angles of the small angle scattering you can get structure from structure of the nano nano size in inhomogeneity that you are studying so interatomic structure will give similar to Brad Pitt or more precisely similar to what we saw and liquid and amorphous system you will get p that will tell you an average inter inhomogeneity distance and of course in all of these the x-axis is q vector all our structural works are q vectors and I must mention at this point before I miss it that in all this structural work we are considering coherent scattering cross-section and not incoherent scattering because incoherent scattering cross-section does not help me to get g of r or inter particle correlations but incoherent scattering cross-section can help in dynamics I'll come to that later but when I'm talking about all this structure was I will be talking about coherent coherent scattering length please remember this and I also showed you that in case of small angle neutron scattering you can make mixtures of d2o which has got six point something 10 to the power 10 per centimeter square which is the scattering length density and h2o has minus minus 0.57 into 10 to the power 10 per centimeter square and mixing the two d2o and h2o we can make a contrast with respect to the particle that was studied to our desirable values and we can sort of lighten up different parts of a particle so this gives the broad range of q values and the broad stuff kind of information that we get from this values now I have chosen a few examples I showed you micella structures earlier now I'll be talking about first about something called gemini surfactants very interesting as this simple sketch shows that micelles where as I talked to earlier micelles were having a head group which can be a cation anion or a neutral head group and a large tail group hydrocarbon hydrocarbon carbons so this large head group is generally positive or negative if it is then they will like to be actually like to face the water whereas the tail group which is making a made of hydrocarbon chains they will be hydrophobic and then I discussed with you then the simplest case they'll form a sphere with the heads looking outward and the tails looking inward and micelles are very important component in various chemical industries so made forming of science surfactants now I'm talking about one step ahead from this kind of single head group surfactants so these were designed by a specialist group at ISC Bangalore the experiments were done at Tuba so these are called gemini surfactants which has got two head groups two head groups connected by a chain so this is a my myself with multiple head groups and multiple tails so in this case there's a spacer layer and there are two head groups now question is the question was asked that how do they combine to form a material in the in an electric in a solvent something like a micelle so and there is a competition and that the studies used either a flexible chain so here the flexible chain is a chain of CH2 CH2 CH2 depending on the name is the number of chain length these flexible because you can bend it this chain can bend and here there's a benzoic ring which is stiff one you cannot bend it so basically these are flexible these are flexible head group sorry flexible spacer group is a rigid spacer group we form micelles using surfactants with two kinds of spaces and see the difference in the small-angle data here you can see that when we have d sigma by d omega these by 1 by q square fitting for when the space group is free when the spacer group has four chains then it is 1 by q whenever five chains it is zero slope at the low q this is because the confirmation of the surfactant when it forms micelles is changing because it can bend so this gives us a lot of flexibility in forming structures by playing with the length of the head group and that is evident from the low q data at the same time whenever rigid spacer group we do have a structure which is vesicular a vesicle is basically a micelle but forming the bilayers so there can be bilayers or there can be more layer number of layers so in a case of bilayers actually it can be like this the head groups that micelle comes here head group in the present case because there are multiple head groups so two of them will be there let me just be a little more clear about it so you have bilayers means this is one layer this is the inner layer so these will have the micelles stacked up and this is called a vesicle and here in this vesicle you have two head groups coming here also you have two head groups coming and in between you have got back gap where the solvent goes in this called a vesicle and in case of rigid spacer layer we find that it's a vesicular structure this is the structure which is preferred unlike a flexible chain connecting the two and this vesicle structure is more clear if you see this what I was talking to you about they shown as the part over here at the head groups these are the head groups from the surface layers here and here and in between the tails are in this vesicle and there is an inter particle distance because this the circle inside circle inside circle you have got a first layer second layer third layer and you have got a coherent small peak so we have multi laminar vesicle where it is one sphere inside another inside another and you can make out the shell thickness from this small peak that we see around 0.1 to 0.5 angstrom inverse in this sounds data so this is one example this is a very fine work where the gemini surfactants are made and their structure in the micelles were studied using small angle neutron scattering the similar studies are possible if you are interested in the structure of this kind of in homogenities in a solution then I can talk about multi-headed surfactants the previous examples were two surfactants connected by a chain but here a single tail and there are multiple chains multiple head groups the tail is like here it is C14 H29 so it's a long tail but you have got now two head groups so here there are three head groups so we can make such surfactant molecules where the hydrophobic tail is one hydrophobic tail is one but connect to multiple head groups I'm simplifying it for your understanding so there are multiple head groups I can have one head group I can have two head groups or I can even have three head groups and let us see what we get when he tried to form micella structure with this head groups so this is a schematic of the structure that it will it might form of course it is shown in two dimension in reality it will be in three dimensions so when you have h equal to one the tails are stretched and you can see depending on the tail length that means approximately twice the tail length you have got a circular structure actually in case of three dimension it will be a spherical structure but when you have h equal to two I am showing myself with two head groups you can see the two head groups they're repelling each other because the head groups have same charge and they're repelling each other so when they repel each other then this association is difficult to be made because they'll try to be away from each other and the tails will have a hydrophobic interaction which will tell them to be close to each other so the head groups try to go away and the tail groups try to come in together and same thing so they start bending the tail start bending so if these two head groups have to be away but the tail is there and there is one more one one head group and two head groups they have one tail there is one more has got tails now these tails they try to come to close to each other so they like to bend and get entangled in the in this place inside the inside the myself inside the myself and this entanglement increases as you increase the number of head groups so the coordination number decreases and the entanglement increases because they have to fill up this space not allow any water to come in at the same time the repulsion between the head groups have to be respected and then the data I show you here you see so this is the small-angle neutroscating data so it has got two parts one is the form factor per one is the structure factor per the structure factor is that gives which that which gives us the interparticle distance and the peak comes from there now you can see as a peak is moving out that means the size is becoming smaller so that means with increasing number of head groups the myself becomes smaller that is one indication because the peak is moving outside outward also by fitting this slope we can find out that number of coordination of such a suffix turns in a myself excuse me under the assumption this is a proleth spheroid we find that for one the coordination number is 244 for two the coordination number is 48 as I mentioned to you earlier and for three the coordination number is 20 and also you can see the A and B values actually this is a semi major axis and B equal to say the semi minor axis so it's a proleth spheroid B equal to C A so you can see under the assumption that the myself it takes a proleth spheroid shape we find the parameters for the proleth spheroid these are all in angstroms so I want to point it out to you that you see I'm dealing with length scales which are much larger than crystallographic length scales but I'm able to predict interparticle distance like I did in case of atomic liquids and molecular liquids for liquid and amorphous diffraction I'm able to find out the interparticle distances from there I can find out the particle size by finding a fitting the models for a spheroid so this is a finding in sans where I can find out the shape of the particles and also they are interparticle distance in a sans experiment this was also an example from what we did at Dhruva now I will go ahead with the example of sorry surfactant and protein interaction now again I just very quickly mentioned that pq is the structure form factor and sq is the structure factor why you have the dimension D of the fractal dimension so you cannot don't pay too much attention in this expression except that you have a form factor and a structure factor part here the form factor I have derived it earlier for you for a sphere and our P is the radius of variation for a particle and this expression it gives me the structure factor as a power of q d where D is the dimension it can be a factor dimension for the object so these are the two things we must pay attention to in this expression so I'm talking about surfactant induced protein unfolding now proteins proteins are important for all the fun for most of the functions in our body and proteins are actually they made of amino acids the list is limited amino acids amino acids but with various combination of amino acids the proteins they form helixes and beta sheets beta sheets and helixes and they fold up the protein folding is an important aspect of proteins activity so the protein are made of alpha helixes and beta sheets so you have parts of the protein which will be like this possibly like this and also there are helixes and sheets that they fold up in its environment in whichever environment you are putting them so depending on the environment protein folding changes and proteins activity also changes because it has lots of charge size now in this example the interaction between protein and surfactants have been studied in a solution so I just give an example this is bovine serum albumin is a protein and SDS is a micelle and the interaction between the two and you can see that when we add this SDS to the solution the protein this this background chain is protein this background chain is protein and there are these small spots where inside which because of the charge and the protein we have this kind of micelles for me so very interesting system interesting biologically and also chemically that the proteins are interacting with the micelle that has been formed using SDS surfactants and with the percentage of BSA and SDS we can see that the this from this results that the structure of the micelle changes and again in this experiment the protein we call it a necklace and the bead arrangement so as if the protein falls the background the chain of the necklace and this micelles they're forming beads on them on a very very simplistic model and you can see that these experiments with and their contrast match so you can see the protein or you can see the micelle found with the SDS SDS surfactants and by contrast matching the background which is an H2O and D2O mixture and also we can use hydrogenated SDS and D2O hydrogenated SDS so what we find here that with the SDS concentration it's in millimolar solution millimole you can see that the structure of the micelle changes not too large but they're almost similar but marginally different but we can find out and when this unfolds that means the protein can unfolds along with the micelles then there's a drastic drop in the radius of gyration but with unfolding the radius of gyration increases so this is one interesting aspect of protein and surfactant interaction in a solution and it's a study using small angle neutroscate so small angle neutroscating I have used examples from organic chemistry I have used example from biology so it can really integrate studies in this whole range when you are okay with the length scale that you can study this is 70 angstrom 70 angstrom 70 angstrom you can see these are 70 to 80 to 90 angstrom size semi-major axis semi-minor axis around 20 angstrom then unfolding unfolded structure this is folded structure when it is folded then what is it and when it is unfolding you get a radius of gyration that means the micellar arrangement is becoming larger that's what this part indicates that the radius of gyration for the micelle is increasing when you unfold the protein structure and unfolding depends on the strength of the SDS surfactant so up to 20 millimolar concentration the structure remains folded the protein remains folded and beyond that the protein starts unfolding from this point onwards and we have found out the radius of gyration of the micelles in this unfolded protein structure and we have done the experiments with 1 weight percent of BSA protein which is bromine serum albumin and with the hydrogenated and deuterated SDS micelle this is also a struggle done on the slit and velocity selector based small angle neutroscating machine in Dhruva and this is a statement of the beat necklace structure protein and the surfactant and the fractal dimensions now this SDS micelles as they go to higher and higher concentration as the chain becomes more and more linear you can see the fractal dimension actually the fractal dimension should have been three if it is a three-dimensional structure three-dimensional but it is never so because you can see the starting from 20 millimolar the fractal dimensions 2.27 so this structure it as it becomes more and more linear you can see the fractal dimension goes towards one but it is not one it is 1.71 so fractal dimension is 2.27 it is just a from three-dimensional structure to it goes to a linear value and of course the micelle radius remains almost fixed for the this is the radii this is the radii of micelle radii which is sitting in pockets in the unfolded chain but the unfolding is like the coastline of India that I discussed to you discussed with you so this protein can be unfolding like this like this and then from there it might go to more and more linear chains and when it goes to more and more linear values then you can the fractal dimension because now the how the surfactants attach to the background protein structure dictates how the fractal dimension will be coming out and also the number of micelles and the aggregation number that you can see so here I complete my discussion on what we did on surfactants to protein unfolding now question is that we can expand the length scale using m-sans which is medium resolution m-sans is medium resolution sans that is m-sans and we can also add up sans with small angle x-ray scattering or sacks machine this is the very interesting observation that you can have data from sans you can also data from sacks if your sample allows not that all the samples will allow you to get small angle x-ray scattering data for example the example that I use so far are deteriorated or hydrogenated samples and they cannot use cannot be used for small angle x-ray scattering so I will be using some examples where m-sans and small angle x-ray scattering can be added and we can get data over larger curing in the next module or next part of the talk