 In this type of lecture what we are going to do is basically we are going to work on some of the concepts that Andrew explained in the first lecture and apply them to the specific case of the small angle neutron scattering. So some of the ideas that Andrew explained for example scattering length, scattering length density and so on will be refreshed and then we will talk a bit more about how we use them in the small angle neutron scattering, okay? So just to start with almost one of the last messages from Andrew, we are going to talk about scattering length. So the scattering length is this parameter B that is used to quantify the interference between the neutrons and the atoms, okay? So basically we have here a neutron that is a point scatter, this also applies to x-rays but I'm going to specifically talk about neutrons now. So we have neutrons which is a point scatter and we have this incoming wave vector that it's basically the beam that we use and then we have some scattering at a given angle that is 2 pi, okay? So basically here we have some scattered neutrons at this scattering angle and what happens here is that the phase of the scattered wave, it depends on this interference factor but it's the scattering length of this given atom, okay? So basically here we can predict how this phase of the scattered wave will behave depending on what we have there in terms of materials, okay? So basically it's important to know that the scattering length for the different atoms varies in a random fashion for neutrons, whereas for x-rays, as x-rays interact with electrons, what happens is that the more electrons we have in a given atom, the stronger it's going to be in the interaction. So we have this linear relationship where the scattering length for x-rays is calculated as the atomic number multiplied by the classical radius of the electron, okay? So it's this value here, okay? So this difference is actually quite useful because for example for neutrons we also have this isotope dependence. So different isotopes will interact in a different way with the neutrons. So for example here we have the case of protium, deuterium and tritium and we can see that the scattering length is different for each of these isotopes, whereas the scattering length for hydrogen and for these three, for these three hydrogen isotopes is the same in x-rays. So this means that x-rays cannot differentiate between them. And that's not the only advantage of this different behavior in terms of the scattering length. So for example, if we want to study something that is very close in the periodic table, with x-rays it becomes challenging because we have very little contrast difference between these two. So the scattering length between two atoms that are close in the periodic table in x-rays will look very similar when we use x-ray scattering. But in neutrons we have this random variation and for example if we want to investigate something that is manganese and I don't remember what is after manganese, does anyone know? I think it's iron. So if we want to investigate something that has manganese and iron, we can use neutrons to get a super good contrast between these two elements. Whereas in x-rays they are 25 and 26, so they are just two, they are there, so actually the difference is scattering length is very small, therefore the contrast is going to be small and we will not have super good data if we use x-rays. Whereas neutrons will be good for this. So if we derive this concept of scattering length and scattering of a point scatterer from a point scatterer, for an ensemble of atoms we get this equation which is the differential scattering cross-section which Andrew have already presented. So basically here we have two main contributions to this scattering cross-section which basically will measure the number of neutrons we are having in a given scattering angle. So this is kind of like the scattering that we are going to measure is related to the scattering that we are going to measure. So what happens here is that we have two main contributions. So we have the interaction, it's basically is the, tell us how, using this scattering length, tell us how the different atoms will interact with the neutrons and then we have this factor here that accounts for the spatial distribution of the different atoms in the ensemble. Okay, so normally when we are doing a small angle electron scattering experiment or when we are doing a scattering experiment what we want to investigate, sorry, a diffraction scattering experiment what we want to investigate is the spatial distribution of the atoms because we're going to get this structural information from the system, okay? So when we are talking about a small angle electron scattering what often happens is that we are investigating the structures in the mesoscopic scale. So we are talking about something that ranges from a few nanometers to hundreds of nanometer and as you can imagine if we are going to treat this system from a metomestic point of view that's going to be very challenging because we are going to have loads of atoms there and it's very complicated. So the only thing that we have to do is to use a technique in this case small angle scattering that we lose the this atomistic resolution. So the resolution of our experiment is not going to be good enough to investigate atomic to get like atomistic information. This might not sound great but it's actually the principle by which small angle electron scattering works. So what happens here as Sandra explained before is that when we have this ensemble of atoms or these systems I'm going to use as 100 H2O for the example and we look at the scattering density profile what happens here is that at the beginning we have a high SOD because of oxygen and then it decreases because we have hydrogen and then it increases again because we get this conservation layer where we have oxygen again so there is some kind of structure because of the hydrogen boiling water and then it just goes down again because we have hydrogen but it's already less pronounced at the first oscillation and then we get to a point where we have this constant scattering length density okay. So we get to this point where the density is not depending on the atomistic structure anymore so this is the concept of SOD and this is what we actually use in the small angle neutron scattering to simplify the systems that we are going to investigate okay. So basically beyond this distance I'll call r star the atomistic information is lost so the SOD for that particular ensemble of atoms can be considered constant if the resolution of our experiment is low enough okay. So this is the concept of the scattering length density so basically is the sum of all of the scattering lengths of the atomic ensemble divided by the volume of that ensemble okay. So basically the scattering length density is used to quantify the scattering power of that ensemble of atoms it's a very useful technique it's a very useful concept because it means that we don't have to basically account everything atom by atom and then and what happens here is that the scattering intensity that we get is proportionally it's proportional to the square of the differences in the SOD okay. So we have this difference in the SOD which is the if we have let's say a simple system so this is the most simplest scenario where we have for example a matrix which we can call solvent but we have some dispersed particles in the mesoscopic scale okay. So what happens here is that the intensity will be proportional to the square of the differences between these and this is what we call the scattering axis okay. So this is what we are going to use to get a scattering signal. So then again we can take this scattering cross section and calculate the macroscopic scattering cross section by normalizing the this system to the by integrating this to the entire scattering volume and what happens here is that this is the scattering length density distribution okay. So this is the differences that we have in the system the in homogeneities we have in the system that that produced this scattering intensity and this is actually what we want to investigate in a science experiment the the distributions of SOD okay. So as I said before the scattering length between the different particle between the different atoms is also isotope dependent and this get this give us the possibility of using isotopic labeling and contrast variation to study a complex system. So the the idea behind this is that for example if we replace hydrogen by deuterium the chemistry of the system very often which is not always the case but the chemistry of the system will have which show very little differences okay. So the chemistry of the system will be different or will not be different but the interaction with the neutrons will be different so basically it's like getting pictures of the same thing but from a different perspective okay and this is the idea behind the contrast variation approach. So what we're going to do is we're going to modify for example the SOD of the solvent and then we are going to get different scattering profiles but all of them come from the same morphology from the same structure. So we can use these to study a system with to gain like a structural information from from the system okay. So the first thing to keep in mind is that as the difference in the SOD so this scattering axis is square in our scattering equation what happens here is that if we have a two-phase system and the two samples have exactly the same structure and the only difference between these two systems is the distribution of SOD so it's opposite so basically here the SOD of particle one is the same as the SOD of the solvent or matrix two and for the particle two it's vice versa okay. So what happens here is that this value means that the scattering axis is going to be the same so because of this fact we cannot by taking one single measurement in a SANS experiment we actually cannot know what is the sign of this scattering length density distribution so because this is a square we don't know if this is negative and this is positive or vice versa because all of the phase information is lost when we square this when we when we square this SOD profile okay. So and if we go back to the scattering equation and we say that this so we say that the scattering the scattering cross-section and microscopic scattering cross-section is proportional to the form factor which will be introduced later and this form factor is equal to the square of the amplitude of the form factor okay so this means that we have our form our sorry we have the amplitude of our form factor here which is the blue one and then we take this square and that basically means that all of our negative values of the amplitude of the form factor lost in this squaring process so basically it means that if we want to gain this structural information that is contained in the amplitude of the form factor we need to reconstruct this scattering length density profile and that's the main goal when it comes to analyzing SANS data what you're actually doing is you are trying to find a way to reconstruct the scattering length density profile of the system and that's because we cannot just simply perform an inverse Fourier transform of this data because as Andrew explained before the this microscopic so this scattering cross-section is basically the Fourier transform of the scattering length density distribution of the of the of the system but but as it has this square factor all of these negative values are lost so we cannot just perform an inverse Fourier transform to gain this raw var again so we have to use the different data analysis approaches that we will explain tomorrow and an interesting thing about this is that one way to get around this thing which is called the bobbinette's principle sorry I forgot to mention one way to get around this this this problem of the information lost and this problem that the that the coherent scattering is the same for these two samples is to play with contrast variation approaches okay so contrast variation approaches as I introduced before it's basically we play with the contrast in the system by exchanging different by exchanging different parts of the system by at different isotopes okay so I have this is one of my favorite pictures when it comes to contrast variation so basically what happens here is that there is a monster visiting these two old guys and as you can see the old lady is sitting in the sofa and wearing exactly the same pattern that surrounds her so basically the monster came and the monster comes and he he cannot see her but the old guy is wearing a different pajamas and basically he will be the board because of course the monster could detect him so this is the main idea between its contrast variation approaches that we want to selectively enhance or hide the contribution to the scattering from different parts of the system so this is a quite common approach in science experiments as I said before one would have to resolve a complex structure it comes for a contrary handy because it can see you we can use this to simplify the system as I will introduce now and and the way to do this is by playing with the isotopic composition of the system so in soft matter which is my field the most common approach is to do a hydrogen deuterium exchange but actually you can use different types of isotopic labeling so it's not only limited to hydrogen and deuterium so basically this will help us to study specific parts of the system by highlighting some particular features or hiding some others and we can use these to investigate complex systems so for example when we have a mixture of nanoparticles of different composition and we want to investigate them so let's just imagine that we have different nanoparticles that I was going to have in the next example and we can we can resolve the shape of those nanoparticles in individually as I will show you now and there are other complex systems for example a mixture of polymers or protein detergent complexes that can benefit from the from investigations that involve contrast variation approaches so there are different neutron construct contrast conditions okay so this is the most simple contrast conditions that you can have in the small-angle scattering and normally what happens in when you're investigating a system that is relatively complex is that you have a mixture of some of these okay so you have provided contrast one there is one difference between one scattering axis so we have one set of particles and in a matrix these particles have a different SLD than the matrix so basically we have this final contrast condition so zero contrast is when even if you don't believe it there are some particles in here but basically what we have learned is that we have much the SLD of the matrix of the matrix to the SLD of of the particles and this means that neutrons will not be able to see them as we cannot see them there now and the intensity arising from the system the coherence scattering arising from the system will be actually zero when we subtract about one contribution okay then we can have system where we have multiple contrasts and this is for example what I said before about when we have a mixture of different nanoparticles so we have one nanoparticle that has one weaving composition and therefore one SLD and then we have a second population of nanoparticles that have this second SLD okay so if we have this in a in a given matrix we can have this situation where we have two different scattering nexus coming from the particle matrix correlations so we have the difference between the SLD of these particles and the difference of the SLD of the solvent and the difference between the SLD of these particles and the SLD of the solvents okay and this is just speaking about particle solvent correlations because there will also be obviously a correlation between the SLD of these two particles so what happens here as you can imagine is that the analysis of a system like this becomes far more complex than the analysis of a system like this so the contrast variation approach what it allows you to do is to convert this system in a simple system like this and and we can do that by just playing with the deterioration in this case of the with the isotopic lab in this case of the matrix so basically we just disperse these particles in a matrix where that has that fulfills the condition that the SLD of the matrix it's equal to the SLD of one of these particles in this case the blue and what happens here is that we will effectively see this scattering from this red particle so even if there are blue particles floating around we will only see the red particles the scattering coming from the red particles and that's the concept between this contrast match condition that we can reach to this using this contrast variation approaches okay so this is probably the most commonly used approach when it comes to investigating complex systems using a small angle neutron scattering by varying the isotopic composition of the solvent so one of the common approaches is that when you have water as the continuous phase is by exchanging some of the water by D2O so you have like light water H2O and D2O and we can play with the ratio of H2O and D2O without hopefully changing too much the chemistry of the system that's that is also something that I will mention later but it's something that we have to keep in mind okay so by changing the isotopic composition of the system we assume that there is no major changes in the in the chemistry of the system but this is not always the case so we have to be careful about that and I will mention it later but this is something that we have to check okay because for example the isoelectric point the isoelectric point of proteins change it's different when we have it H2O and D2O so the charges in the protein will be different and so on so there are some things that we have to keep in mind when it comes to isotopic exchange okay so basically what happens here is that we have exactly the same structure so it's this core shell particle that we have here and this is just like a quick simulation I've done using SAS view what happens here is that we have this solvent that I said that is something close to D2O so as this SLD it's a 6 times 10 to the minus 6 axons to the minus 2 and then we have this core shell particle that has a internal density distribution so the shell has a different SLD to the core okay so if we calculate the scattering for this particle we get this grain curve okay and we see that has some features and so on so if we want to investigate this using a contrast variation approach the most simple way of doing this will be just by exchanging the composition of the solvent so basically what we do here is that by knowing the composition of the of the shell we can calculate what is the SLD of that shell and then just prepare an H2O D2O mixture that has exactly that SLD so basically when we put this in the neutron beam we get the scattering from the core that will look like this and the shell will be will be contrast matched so effectively the shell will be invisible to the neutrons and we can do this same thing in the other way around so basically here we have the core that is contrast matched to the matrix or the solvent and we are seeing the shell and as we can see here the scattering curves that we get from these three different systems are different but they all come from the same structure so this is as I said one of the ways that we can use to obtain structural information from complex system by simplifying them using contrast variation approaches okay I did not really write it down here but I just remember that it is something important that we have to keep in mind here which is the incoherent cross section of H2O is much higher than the incoherent cross section of D2O and as Sandra explained before the incoherent contribution in the small angle of the scattering experiment mainly contributes to the background so we have this four pi scattering so it's not angle dependent it just goes everywhere it should be flat but the H2O has a really really strong contribution so if we are gonna play with a contrast variation approach where we exchange the H2O to D2O ratio we have to keep in mind that by increasing the level of H2O we are going to also increase the incoherent contribution so we're gonna also increase the incoherent background we have to keep this in mind because if we have something that is a weak scatterer so for example let's say that this shell is a very very very tiny contribution and here we have it in in an H2O matrix we might be in the situation that basically we have no effective scattering coming from the shell because the incoherent background is so high that just basically marks masks out all of the all of the coherent signal from the shell so we have to keep in mind that when we play with the H2O to D2O ratio or when we play with the H2O in a sample we will only not affect the coherent signal but we also affect the incoherent signal so we have to be careful with the amount of incoherent scattering okay so just keep in mind that with more H2O will probably mean worse data for you because the incoherent signal will be higher so another approach to do this contrast mask experiments is by playing with the deterioration of in this case the particles so not only with the H2O and D2O so here for example I've just put some calculator in SLDs for different components so we have H2O and D2O and then we have this iron oxide and lysosine here okay so I'm just putting these as examples but basically what I want to show here is I mean it's a few details that for example what happens when you have proteins in solution is that you will have some H2O exchange in deterioration conditions so if you put this protein in D2O what will happen is that we will have an exchange of these exchangeable hydrogens and they will this protein this protein atoms will go away and will be replaced by deuterium some of them okay so we have to keep in mind that when we put a protein in solution for example there will be some exchange and it happens with all with other type of compounds not only with not only with proteins but you have to keep in mind that the SLD of your system might change when you put it in D2O the SLD of your particle sorry so for example here you can see that as we increase the level of D2O in the system we will also slightly increase the SLD of the protein and if you have DNA and other stuff it might also happen that you see a change in the apartment SLD of your particle okay and then here what I wanted to show you here is that for example if we have some surfactant that has some tail that is like a hydrocarbon tail what happens is that we can also play with the deuteration of this system okay so basically we can replace that by using some smart chemistry we can this is not as straightforward as just making a mixture of H2O and D2O but by using some deuteration chemistry you can change the SLD of what will be hopefully your particle by replacing the proteins in this tail by deuterium and this will effectively change the SLD of your system okay so another important aspect when you are doing a contrast match experiment or a contrast variation experiment is to find the contrast match point okay so we can say that contrast variation is just the general term of playing with different contrast to get different information and the contrast match point is that we want to get this zero contrast condition where there is no effective scattering from this from a specific part of the system so for example here I don't really okay they are measuring silicon oxide particles and they wanted to determine the contrast match condition so they wanted to determine at which level of solvent deuteration the incoherence scattering is zero okay so they wanted to actually determine where when these nudox particles were invisible to the neutrons and to do that common approach is that you basically take your particles and you disperse them in different H2O to D2O ratios so they I mean they did this using all of these great points it's like a million points they got using a microfluidic system but you can also use you can also do this by using some discrete H2O to D2O measures which is the this circles here okay so what happens here is that then you put your particles in different H2O to D2O ratios so for example here somewhere around 20% something around 40 something 60 blah blah so what happens here is that in each of these H2O to D2O ratios will have a different coherent signal and that's because we are changing even if the particle is the same if the form factor is the same what is happening here is that we are effectively changing the scattering axis of the system of each of them okay so what happens here is that the scattering axis of the system is going to be different to the scattering axis of this and so on and the only difference whereas the form factor of the particle will be the same so then they started to measure all of these samples and what happens is that as you can see here that the intensity it gets to a point that it gets close to the signal of the solvent so when we subtract the solvent contribution is effectively zero and then we get this contrast match point which tell us that around 60% of D2O in an H2O to D2O mixture the contribution of these particles to the scattering will be effectively zero okay and as I said before this comes handy when we want to when we want to investigate a system that is complex for example as I said before this mixture of nanoparticles so we have some other nanoparticles that have a different SLD and we put both nanoparticles in a 60% D2O solvent what will happen is that the contribution from these Lugox particles will be zero and we will have only the scattering from the other nanoparticles okay so this is one of the approaches that we can use for determining the zero contrast condition and as I briefly mentioned before there are different ways to actually play around with the scattering excess and with this contrast variation approach and a slightly more complex approach is to use a deterioration chemistry to play with the deterioration of different parts of the system so here again you are expecting that by using the Ethereum label chemicals you will have a minimal impact on the chemistry of the sample but this is something that you have to check it's not as simple as you're saying like yeah this is going to be this is not going to change the chemistry of the sample so you have to check and there are different approaches to do it I will not go into detail but if someone wants to know more I can always give them some further information so what happens here is that we can for example here we have a lipid this is DPPC it's a common lipid that is used as commonly used as a model for biologic membranes so what happens here is that we have this proteated lipid so basically it has a proteated tail proteated head group but then we can also get this lipid synthesized using deuterium so we have these deuterated tails that are attached to deuterated heads so this is like a per deuterated lipid but then we can also have some more complex deterioration schemes so we can have for example these tails only deuterated whereas the head is proteated or vice versa so we can have these proteated tails with a deuterated head so when we want to for example determine the internal structure of a lipid bilayer this is very useful because this approach will help us to gain more information on the system or structural information on the system because we can for example only contrast match the head group or we can only contrast match the tail group and things like that and this will help us to resolve complex structures so there are two ways of getting these deuterated materials one way is to buy them but there is limited availability of compounds so you can get maybe DPPC but if you are actually working with some more complex lipids then it will be very unlikely that you can find them commercially so the best way to get them is actually to talk to the neutron facilities because they are often willing to collaborate and synthesize these deuterated compounds for you if they are not commercially available and for example at the ESS they have the DMAX labs that basically what they do is they synthesize deuterated compounds for users so it works on a proposal basis so basically you submit your proposal and you say I want to do this nutrient experiment on this and this deuterated molecules so basically they will say they will there will be like a panel to evaluate the scientific interest and feasibility of your experiment and they will decide if they can make these compounds for you okay so this will help you to elaborate some more complex deuteration and contrast variation schemes so there are like a variety of them but one of the I'm just gonna use one here as an example which is a zero the zero average contrast condition okay so the zero average contrast condition is for example when you have particles in a matrix you have two different populations of particles and basically you you you go to a system where you fulfill this condition so basically the solvent of your SL the SLD of your solvent will be in between the SLD of these two particles so let's say that one of these is proteated and the other one is deuterated and basically if we are in this condition what happens is that the interaction like the interaction term cancels out so the structure factor cancels out and and this comes from the interaction between these particles and the single form factor of the particles can be calculated okay for this example I'm sorry I didn't realize but for this example of the circles you have the same okay so this is the most simple zero average contrast condition experiment which is when we have particles that are identical and we just play with the deuteration level of those or with the SLD of those so we have some particles that are just use your imagination equal in terms of shape but they are different in terms of SLD so what happens here is that for example for this polymer case we have this upturn and low-q that comes from the attractive potential between these polymers but if we so basically that means that it's difficult to that remind the form factor of the polymers different difficult to that remind the the structure of of this individual polymer chains because of these structure factors so what you do is then you prepare a sample in the zero average contrast condition and we get rid of this of this interaction term and then we have the form factor that we can just keep using some some form factor models and get information on the structure of this polymer okay so this is the most simple case of a zero average contrast condition experiment which is when we use a mixture of deuterated and proteated particles but they have the same form factor but this can be extended to more complex systems and then we gain some different types of information so I'm gonna just gonna very briefly go through this example but if someone is particularly interested in this type of approaches we can you can email me or you can contact me and I will try to redirect you to the right to the right information so let's say now that you have a system that is forming type of complex so now this particles when we put them in solution they will form this complex let's say it's a one-to-one or it can be I don't know like a six-to-one or whatever but what is happening is that they form in the complex so we can use this contrast condition approach to determine the state of the particle so we can determine particle complexation for example and here it becomes slightly more complex this equation but the idea behind this is exactly the same so we want to determine the the different contributions to the scattering by getting rid of the interaction term okay so what happens here is that when this particle forms you have to keep in mind that the SLD of the solvent is in between these two so it's at exactly one point that is equal to the to the scattering and the density of these two together okay so there is this contrast match condition that it's fulfilled so what happens here is that we form a complex so if we look at the SLD of the complex it will be effectively the same as the SLD of the matrix so it means that the lower angle signal will be zero so the scattering at i of zero will be zero because effectively the complex itself so the entire complex is invisible to neutrons but what happens here is that the internal structure of the system has a density correlation so there is going to be some scattering from this and I have here some data that I analyzed just to show you how this works okay so we have four different contrasts and what happens here is that the red is the entire particle so it's entire complex the black is the red particle for example and the blue is the blue particle so we can play with the deterioration of the solvent to get the structure of these three different parts of the system and then this green is actually the zero average contrast condition so if this complex is formed what happens here is that the i of zero will be equal to zero which is what we see here so this is basically just noise and this is because the SLD of this complex when we see it like when we see the entire complex is equal to the SLD of the matrix but what happens is that as there is some density correlation inside this complex then we will see this bump and high Q that will correlate to the structure inside a complex so basically we can use this is just a very brief explanation of what we how we can use this zero average contrast condition also to resolve complex structures for example the formation of lipid domains complexation between nanoparticles and this was the case of some proteins refactoring interactions but we can use this to investigate different complex morphologies okay now I'm gonna move a bit away from SANS I'm gonna talk about SANS in connection to SANS so basically SANS and SANS are very very very powerful techniques when they are put together and that's because we can investigate the structure of a given system by playing with the contrast without the need of for example using deuteration okay so as Andrew I think Andrew talk about this too but x-rays are also introduced before x-rays interact with electron clouds and neutrons interact with the nuclei of the atoms in the scattering volume so we will get a different type of interaction okay but both of them are looking at the same length of scale so they are looking at the same structural information let's say so this makes these two techniques complementary and actually the corrifinement of SANS and SANS data has become a powerful technique to study different systems so this is just an example for neutron imaging on how an SLR camera looks on when we use neutrons but x-rays so for example here we have here the film which is gonna be highly I mean we'll have it's basically plastic so there will be lots of hydrogen in there whereas the rest of the camera is some kind of metal and this means that we and with neutrons we are gonna get like a good information about this part of the system that is that has a high hydrogen content whereas the we feel x-rays we will see the metal but we will basically have no information on the plastic part on the one that is light okay so the concept between using this the concept of using these two methods in combination of combining these two methods is basically gaining information of different parts of the system so effectively getting different contrast okay and I have here one example to clarify this which is some I think it's gold nanopilot course dispersed in an organic solvent and they are colloidally stable because someone put some I think it's some lipids but I don't remember really well so someone put some lipids around the around the none of the I know it's not a lipid I think it's a I think it's yeah some kind of surfactant or the philip molecule so what happens here is that the head group of the surfactant will attach to the nanoparticle and the tails will be floating around and this will be will stabilize the nanoparticles and prevent coalescence okay so then so then these people took some signs and such measurements and this is how the data looks like okay and if we look at the scattering length density to distribution of the scattering length density profile we see that they are very different okay so this is the scattering length density to distribution for x-rays and this is the one for neutrons so what happens here is that if we look at the SLD values and calculate the scattering excess we see that for example the scattering excess between the particle and the solvent is huge in comparison to the scattering excess between this shell around the particle when we compare that to to water or to sorry not water to the to this organic solvent that is the dispersant so what happens here is that if we do some sacks as we can see from the from the scattering excess most of the intensity in this experiment will come from the scattering excess between the nanoparticle and the solvent so because they will dominate them basically this will be invisible I mean about 100% of the signal will come from the from the from the nanoparticle but if we do some neutrons we and we play with the deterioration so we have some deteriorated continuous phase and we have some proteated shell what happens here is that the the nanoparticle scattering is much lower than that of this shell so then in the neutron case the the the scattering from the shell will dominate the signal so basically we can combine these two methods to get information to get like detailed information on both the core which is the nanoparticle and the shell which is this ligand or surfactants that we are using to stabilize the nanoparticles okay so what you have to do here and I will go tomorrow in more detail into this is to use a simultaneous training approach so basically we're going to take all of this data together we're going to take all of these neutron contrast and we're going to take also this x-ray contrast and we are going to build the structural model where the only difference between these these contrasts will be the scattering length density and and I think that this picture of this drawing of the I guess some cats it's a good demonstration of that okay so basically we have one system here where we see the two cats then we have one system here when we see only one cat then we have a system here where we see the cats budding a different way to the first case and then we see the other cat in this last one here so the cats are the same in every picture so what we have to do is to find one structural model that satisfies all of these contrast conditions and that will give us a very robust answer in terms of the structure of the system so basically the use of several contrasts will give us a more accurate validation of the model and what we have to do the way that we do this is either by correfining different contrasts or introducing some constraints that we get from other systems so for example if from other contrasts so for example if we know that this is the shape of this cat then we can say for this okay we know the shape of this cat so basically the signal from this will be the total signal minus the signal of this cat okay so basically we can use this type of constraints to simplify this cat in data another advantage of using contrast variation approaches I introduced before is that we get rid of this phase problem so as we have more contrasts we can be at the more robust model that will get rid of this phase problem where we could where it was more difficult to find the the original scarring length and distribution and something that I've really mentioned before is this isotope effect so sometimes when we play with isotopes we might have a strong impact in in the system and for example if we talk about proteins and we put them in in a in a buffer maybe if the buffer is de-traded the proteins might precipitate because the the the isoelectric point of the protein is different in S2O and D2O so we might be at the point where the proteins precipitate so we have to keep in mind that there might be some isotopic effects that might also affect the structure of the system so a good way to do this to check for this is to take all of your contrasts and put them in an x-ray machine so measure sacks of all of your different isotopic mixtures if they all look the same in sacks it means that the isotope effect has no effect on on this particular system because the scattering from x rays is going to be the same and as I said before there is not isotope dependence when it comes to x-rays scattering okay so if they all look the same it means that we will not have isotope effect that affects the structure and this is just an example of a of a SMERB which is like some kind of a lipid nanodisc where we can have so basically what happens here is that we have like a region of a lipid membrane that it's like entrapped in some kind of a nanodisc that might be polymer or protein or different types of system but I want to show you here is that this is a relatively complex structure and if we only use one scattering curve here there is going to be so many parameters to fit that basically we won't be able to get a reliable answer unless we use a contrast variation approach so basically what happens here is that these people what they did was measure the system in different contrast conditions and then they found one structure that satisfied all of them okay so basically here what happens is that they're going to probably measure in different parts of the system and highlighting them as well as as it happens with these caps just to briefly mention here that the agreement between these is not perfect and that's actually often the case because there might be some polydisparsity there might be some differences in the concentration between the different contrast and there might be some differences due to isotope isotopic fats so it's difficult to get like a perfect fit but I will say that this is extremely good fit when it comes to corefinement of different contrast and I'm just gonna briefly go back here and this is the same case for this okay you can see that if we look at the models individually there might not be perfect but if you put the picture together and you say that these models satisfy the four neutral contrast I will say that that's a really good answer okay so this is everything that I have to say today and basically I'm just gonna briefly go through some of the things that I've mentioned and I think that it's very important that you know your system you know what kind of information do you want to get and the first question that you have to ask is do I need neutrons or can I do this using some lighter scattering or x-ray scattering which will be faster cheaper and easier but if you need the use of neutrons the first question that you have to ask yourself is how we can investigate the system in an effect in an efficient way in a way that we can get the most of information by for example using contrast variations so you have to keep in mind if there are like internal density correlations if we have a multi-component system and so on and try to think on how we can benefit from a contrast variation approach then you have to consider the isotope effect you have to consider if there is gonna be some effects that come from from the exchange of H2O and D2O from the change of hydrogen and deuterium or any other isotopes I've seen people doing contrast variation by exchanging for example between different isotopes of lithium and so on so it's not only limited to HD but sorry if I go back to HD all the time but that's because it's my I guess because it's what I use more often and another important aspect is where will you get your deuterium chemicals okay not everyone has I have here no everyone has per deuterium codon candy in the lab and what I want to say with this is that deuterium chemicals are by no means as as common as proteated chemicals or naturally abundant chemicals so you have to keep this in mind where do you gonna get them you're gonna request them to a deterioration facility you're gonna buy them they're gonna be expensive you're gonna need extra funding and so on so you have to keep all of that in mind and then for more information on the different aspects of contrast and contrast variation in sounds you can check and this book that is freely available at the next website and it's called the sun's toolbox I think it's something like six or 700 pages but there are some interesting I mean it's basically everything about the small angle neutron scattering so you maybe you could check it out if you have some specific questions about this and after this I'm done with my lecture and if there's any questions now it's time to ask them since I don't know there are no questions yes I have a question actually it's about the R star that you showed for a scattering density of the oxygen and hydrogen that after a certain are it becomes constant yes so this R star is it a specific to the every material system and how we can calculate it and this is like a general let's say it's a general conditions for the science experiment because when you are looking at the cure range that we are investigated with sons we have no optimistic information because the resolution of our experiment is low enough let's say that this are it's hard to become more important when we go let's say about 0.5 or 1 inverse answer so if you go above that Q value we get into these let's say wide angle scattering so it's not a small angle anymore so when it comes to science you don't really have to worry about this R star it's more about when you go to this more complex yeah or not more complex if necessary but when you're going to this wide angle to scattering and what you have to do there is you have to use a model that contains that type of optimistic information so you will have to use simulations or you will have to use some other approaches to gain information on this system but when it comes to science you don't have to worry about this R star because basically the reason why science works as it does is because the resolution is not let's say good enough to get information on optimistic okay thank you you're welcome any more questions something to chat yes of course so Anton is asking if there are support labs in neutral facilities what iteration is possible yes so I will say that even now there is some kind of like common effort between the different facilities to kind of like be able to supply to provide all of the all of the detrait chemicals required by by users so what you have to actually look at is what do you need from for your experiments so if you need lipids or if you need proteins or if you need some other polymers and things like that and and then what happens is that the different deterioration facilities at the different at the different neutron scattering facilities will be let's say specialized in some different types of materials okay so you can you can check what would you be interested on but for example yeah I think that a demax here at the SS they can prepare quite a lot of small molecules and things like that but they also do I think maybe wrong but a deteriorated proteins the one at the island they have like a really broad knowledge and the deterioration of proteins isis have been good at preparing different small molecules and surfactants and things like that in Germany they prepare deteriorated polymers so I think that there is like the different facilities have different expertise but there is a common effort so if you're gonna do an experiment that requires something maybe you can talk to someone that even if it is a different facility to prepare that deteriorate material for you so if you want more information about this or any other thing I'm gonna write my email in the in the chat so every so anyone can contact me any more questions yeah I have a question yes the the resolutions for these x-ray produced and the neutron produced the images can be different so when we combine these images to produce a single one how we balance these to you know produce a fair combined image okay that's actually a very good question and I will go more into detail tomorrow and as you very correctly said that the resolutions might be different between the techniques it becomes really challenging to actually take your data and say okay if let's say like the convoluted the resolution so what you normally do is you use some resolution models that applied to your structural model and for example if you have an x-ray signal and x-ray curve you say okay this has a resolution of this value when you are gonna try to fit a model to that and then you take this other model and just say to the neutrons okay there is this other resolution so basically the structural model that you're gonna get is gonna be as mirrored by the resolution of each of the pictures you take let's say and then tomorrow we'll talk about a bit more about about the resolution and how we implement it in the different models but that's a very good question thank you thank you any other question okay so I think that this is then all for the day