[00:00:05] >> OK So this is my second time I've talked to attack and I believe last time I spoke here. I talked about something that we're working on and buy a response of materials so materials that change their properties in response to a small molecule or protein binding event the change gears completely and talk more about assemblies of carloads to assemblies of things that can be you know particular all the doubt I'll show you today is largely with Micron scale things but the physics scale pretty pretty nicely. [00:00:44] Because I'll probably run out of time at the end would be acknowledge the people who did this work. Talk about today is largely the work of actually St John and also John McGrath who recently graduated Courtney and Grant taking over some of these things and is working on a different much more complicated aspect and actually you know it. [00:01:09] Is a distinct disadvantage because the aspects of the work that he works on are so complicated I have yet to figure out how to fit them into a fifteen minute presentation. So I may never talk about his stuff in full and he point. Nonetheless. Let's think about nano science in college because you know when I when I was a Ph D. student I started off in one thousand nine hundred two. [00:01:32] I got my degree in one thousand nine hundred six when I started working I was working on colleagues. By about one thousand nine hundred. The change at that point really was that people were starting to understand in some great detail that that nano particles had different properties in many cases between the bulk and the molecular or the cluster type properties. [00:02:00] So if we think about nanoscience it really is something that it's. Grown from college science and in some cases if you want to be a cynic about it. People have repackaged college science to call it nano science but but. Whatever the case may be you can think see these kinds of things in the standpoint of quantum confinement. [00:02:18] So for example semiconductor nano particles from clusters really colloidal materials that were known far beyond people understood what quantum confinement was and in fact people were looking at quantum confinement in thin layer devices far earlier than they were looking at so nano particles are clonal media then became just a different place in which one could understand quantum confinement but now in three dimensional structures. [00:02:46] Metal nano particles have enabled kind of a new field of planets nonexpert plus Monex existed before nano particles people understood. Well people manipulated plots Mons and Fin metal films for quite a period of time before people understood that metal nano particles really had some impact on plants Monex. [00:03:08] And then carbon nanotubes are very popular now for things like carbon reinforced composites. It's really taking an old topic carbon reinforcement and just shrinking its dimensionality and and changing the structure of the carbon so that now. You have value added properties from the colloidal property but these are just collateral dispersions of carbon nanotubes. [00:03:30] So again clue to media and understanding how colleagues arrange understanding the forces between the coloreds is a prime importance if you're going to start using nano spheres or nano particles whatever their shape of building blocks for new types of material so we've understood this for a while and people therefore have spent a heck of a lot of time trying to understand how these closest versions work. [00:03:54] People try to understand these for a long time because they're important things like how a particular color properties. So this is a cleaved face of a gem. An opal from the lights dimmed a little bit in the front as possible looking me. Thank you. It wasn't really understood until the early one nine hundred eighty S. that that the colors from little people such as those taken from Australian Open mind such as this one came from diffraction came from a periodic assembly of silica nano Spears dispersed in a matrix of hydrated silica So the only difference between the particles and The Matrix there and is the amount of water associated with that silica that gives you enough refractive index contrast to give rise to a diffraction of Van which gives you the very nice color associated with ripples. [00:04:49] I like to tell people that that I got off the hook. I got engaged when I was still in college I was in a wealthy man. My wife prefers opens to diamonds. OK And that's a very nice thing because opals are far cheaper. Some people prefer color gemstones as well and what I tell them is that they're getting ripped off because color gemstones. [00:05:10] Are colored because of defects opals or colored because of perfection. OK perfection in the assembly and if you're buying an amethyst or Ruby you're buying a defect. OK. I'm not sure wives go for that. Here's another example of a clue to splurge and these are actually clonal gold people have seen these pictures and one hundred thousand times. [00:05:35] These are clinical preparations made by Michael Faraday in a short period of his academic career where he was interested in trying to understand why he took gold. OK. Made it into a salt soluble lot is that through to reducing agent also and he got something that wasn't gold at all. [00:05:53] It was ruby red in color. So Michael Faraday spent a fair amount of time trying to understand why these things were that color and at that time understood it had something to do with the way the light. Scattered off of those presumably nano sized pieces of gold. Those other things like you know milk. [00:06:13] I mean people have known so dairy farmers have known for quite a long time that how you treat milk how what cows it comes from what you feed those cows contributes to how good it tastes and how good milk taste has to do with the fat content has to do with the protein structure has to do with the fat droplet size has to do with the protein agglomerate size so cool dispersions are important for things like food and in fact the cream in an Oreo cookie is a little dispersion too but dairy farmers haven't worried about that quite so long. [00:06:43] This is a clinical dispersion of air droplets inside of a fat and sugar matrix. That's appetizing. OK so. So hopefully from this of giving you a little bit of a hint that clues Persians been around for a long time. There's lots of good reasons to understand them both from a kind of practical standpoint and also from the standpoint of making things that are advanced optical materials. [00:07:10] How does one control banana structure. How does one control how those building blocks are assembled so that one can then control the eventual properties of the assembly. OK so to motivate that further we need to think a little bit about how close will assemblies behave. OK what are some some guideposts that we can use before we even do an experiment before you can put pen to paper to try to figure out what we can expect from a global assembly. [00:07:37] So who about colloidal energetics we can can make reference or make make some inferences from how atomic assemblies are we already know a fair amount about atomic and molecular solids we know about length scales we know about dynamics we know about energetics So how to Colonial assemblies differ. [00:07:54] Well one most notable differences in the number density. So typical colloidal crystal glass for example might have a number density of particles in the order of about ten to thirty. Centimeter and the thirteenth. Particles per cubic centimeter and atomic crystal on the other hand might have a much much higher number density of spherical entities. [00:08:16] OK So so this tells you right now that that the density of this materials is very different. How does that translate into stability Well strength. Assuming that the interaction potentials are roughly equal and if you think about a a charge stabilised crystal this is going to be true strength is roughly proportional to density so cool crystals can be expected to be on the order of about a billion times weaker than a corresponding atomic Crystal. [00:08:42] OK. I can take a crystal and by rubbing it between my hands I can shear it into form and destroy it. I cannot do that with most atomic crystals. OK so the strength is roughly proportional to the density and you get a great degree of weakness I think is this gives you an experimental advantage it gives an experimental advantage because now I can take a colloidal Assembly and I can do for me or perturb it using normal laboratory apparatus and then hope to watch how it responds to that stimulus. [00:09:15] OK for most atomic crystals were usually using light or acoustics to probe them and the displacements are small. OK and the relaxation times are fast. So the relaxation times. For atomic crystals are usually on the order of about ten to minds eleven seconds which means you need to use optical or acoustic methods to try to probe dynamics for colloidal materials you've got much much slower relaxation times. [00:09:42] So if I take a closer with somebody out of equilibrium. I can sit there and watch it at my own leisure. I can watch it. Reassemble or restructure and therefore I can get some different laboratory time frame in which to study the fundamental properties of collateral assemblies. OK so. [00:09:59] So for these main reasons people have been interested for a long time. So now going. Something like forty or fifty years people have been interested in trying to use colloidal systems as analogs or models for atomic systems because these two last points give you lots of advantages with respect to how you can make measurements and what tools you need to make measurements. [00:10:25] OK. So let's talk a little bit about hard and soft sphere phases. OK start off with hard spheres. Those are the simple ones and then we'll move into how soft spheres might be different and then I'll end up the talk with a simple short example of how we've taken advantage of soft sphere interactions to make something that has value added. [00:10:47] So this is a classic photograph from a paper by Peter Prue see and meet in a nature in one thousand nine hundred six where they basically demonstrated in photographic form the phase diagram of hard sphere colloidal suspensions. These are poly method with accurately spheres. Ok about a micron in diameter. [00:11:09] Maybe a little bit less suspended in a medium that is refractive index merely refractive index and nearly density matched to the particles. So on the timescale of the experiment the particles do not settlement. OK that's an important point to understand this figure on the time scale of preparing these bottles of close versions the particles themselves will not set in. [00:11:34] Because they are iso picnic with the medium. So what do we say let's start over here at the right hand side. OK. We see a vile that at this resolution looks like it's got nothing in it in terms of man a structure a micro structure. It is a liquid phase it has an approximate volume fraction of spheres OK so the volume occupied by spheres is about forty seven point eight percent. [00:12:00] OK That state is the particles are bait. Diffusing around the Brownian motion in that medium. OK And they have new long range order associated with their phase as you start increasing the concentration increasing the number density and therefore increasing the volume fraction occupied by spheres you start seeing the appearance of a crystal in phase. [00:12:24] OK that's what these diffracted of flex are those are colloidal crystals. They sink to the bottom of the vile because they have a slightly higher average number density than the fluid. So they're denser OK The crystal is denser therefore the crystal sinks to the bottom and the fluid is on top. [00:12:46] OK so what you see here is the. The phase coexistence region of going in a first order transition from a fluid to a crystal. It's a liquid to Crystal phase transition that has a finite phase coexistence region. So that's what you observe here. The relative volumes occupied by the crystal in the fluid phase tell you where you are in the phase diagram. [00:13:12] You then go to a fully crystallised region and then finally you go to this glassy state. OK so at higher volume fractions you go to a glassy state the glassy state is a kinetically trapped state. You're basically packing the particles in very tightly to one next to one another there translational diffusion coefficients are too slow. [00:13:33] To give rise to be thermodynamically preferred product. OK so that's why you see a kinetically trap glass at higher volume fractions and so this was an important paper. That's why it was published in Nature. OK. And they they demonstrated very very nicely that what people have been predicting for some time and what people have been pretty observing someone anecdotally in a few different systems could be rigorously defined using simple experimentation. [00:14:04] So what's going on here is the particles basically are experiencing what we consider a pure hard sphere interaction. They come up to next to one another and until they bounce into each other they don't know about their neighbor. OK that's how we're going to define a hard sphere interaction potential. [00:14:20] OK. The reason particles crystallise. Because while there are increasing in concentration is due actually to entropy. OK So we typically call this tropic solicitation. So we say hard spheres self organize to maximize entropy. This is usually counterintuitive especially for first year graduate students in my group. I told them that the more perfect assembly is the one that has the highest entropy Well why is that move mostly. [00:14:51] Most of the time we think about ordered structures as being very low entropy structures in this case you can kind of demonstrate it with a simple cartoon on the right here we have a number of spheres packed into a box. OK And we put them in a disordered arrangement you can see their star overlapping in some cases and the total volume occupied by each sphere is kind of limited right so this guy can't really move very much. [00:15:20] But this guy has some room to move it turns out that if you maximize the distance between each of the neighbors and form a crystal the total entropy of the system is higher because now the particles actually have the ability to move around and these little cages. OK they can occupy and effectively larger volume. [00:15:39] Therefore the number of states associated with this is greater than the number of possible states associated with a disordered arrangement. Therefore this has the higher entropy. OK so close to Crystal is ation is entropic. And that's an important point. So because of an tropic assembly. We find that you can model simply based. [00:16:04] Entropic considerations you can model these kinds of phase diagram so this is makes basically just a different representation of what I showed you in photographic form a few slides ago fluid phase coexistence. Going to a crystal. OK. Note the dashed line. We actually observe that dash line on those photographs as well that was the medicine able or glassy branch. [00:16:26] Remember you packed these things to get up against one another if they don't have any way of squeezing past one another if there's too much friction between the particles they get stuck into a medicine able kinetically trapped glassy branch. So because of this med a stable branch what one finds experimentally and what was shown in those photographs is that it's very difficult from a practical standpoint to prepare Purif them or to make phases of highly close packed crystals. [00:16:55] OK you can do it by slow sedimentation so I can take a vial of particles and let them slowly sink onto a substrate or I can let the solution of battery over the surface of the substrate and I form a cool crystal but it's not necessarily the thermodynamically preferred phase because it was performed performed under non equilibrium conditions and also if I try to do this in a dispersion by simply compress continually adding more and more particles. [00:17:24] I will always end up in the Med a stable regime with hard spheres. OK so you have a conundrum. If I have an optical material that requires us to make a close pact structure. I can either do it under non equilibrium conditions or not at all. OK because the hard sphere phase diagram with this kinetically trapped branch appropriately model does not allow for us to get high. [00:17:50] Sconce interation assemblies very easily. So what about soft interactions. So off interactions give you a little bit more room to play with things. OK That's why there are soft soap interactions can be roughly modeled as a power potential. OK. One of or are to the end where the magnitude of N. tells you how soft the interaction is OK. [00:18:12] So if I've got a very very shallow interaction potential that means the particles can squeeze on each other they can interpenetrate and that softness basically means I can put the particles closer together. While still maintaining a lower energy assembly. OK. That suggests that I should be able to circumvent glassy phases or kinetically trout phases more easily if I use software. [00:18:35] OK. And indeed there's all kinds of analogues in terms of the arrangement of biological macromolecules and biological entities in nature. Almost all of that stuff is based on soft interactions. OK. Nature has this ability to self-heal and soft interactions that give you the ability to self-heal parts for faces are not as defect tolerant. [00:18:59] OK So the questions we started asking in my group we started studying soft little assembly was how does particle softness manifest itself in the fundamental phase behavior the optical properties of for making an optical material sake little crystal or an artificial Opal in Defect healing. OK or self healing properties and the dynamics of the assembly and also what are the appropriate tools to study those phenomena. [00:19:27] I tried to convince you earlier in the talk that we had more tools or disposal because of of the length scale because of the slow dynamics because of this the small energetic parameters but what are the appropriate tools. So other people have looked at this. And here's just a couple of examples. [00:19:47] There's experimental evidence that shows that. Thermodynamic close packed faces can really be prepared by soft spheres. This is what you would expect particles are a little bit softer they can squeeze by each other their translational diffusion coefficient doesn't precipitously go down. As quickly as you start packing tightly. [00:20:07] So. Showed that you could make truth limited damage phases. He also showed that the softness gave rise to a higher temperature a higher volume fraction at which you obtained crystal that is you need to push the particles closer together and order for that in tropic crystallization to kick in. [00:20:27] And he also showed that there was a narrower range over which you saw phase Kostitsyn it was very difficult to actually observe phase coexistence in these experiments. So there's lots of experiments that point to those kinds of things now and there's also people like this group in Germany in Duesseldorf that has shown that if you model with a variety of different modeling tools. [00:20:52] Soft fear phases sometimes you can come up with really bizarre phase diagrams. So here's one that's interesting that a lot of people point to in literature because using soft spheres that are truly spiritual at certain packing fractions you get diamond like faces diamond like phases are important because they have very unique optical properties and quarter length scales relative to face hundred cubic type lattices which is what I was showing you before. [00:21:19] OK So there's some motivation from the switch respect to the definite uniqueness of how close all phases behave. And there's some motivation from the standpoint of the fair Titian's who keep on feeding us these little teasers and say hey if you guys could make this particle and you could do the experiment right because experimentalists always screw up the experiments when it went theoreticians are involved. [00:21:40] If you guys can for once get the experiment right. You would be able to make that. OK. We still haven't done it so we're still not doing things right. OK so. So we've got these motivations to this study. So all spheres the soft fears that we look at in my group are something called micro gels so micro gels are an appropriate model system for software. [00:22:04] Micro gels or simply small spheres of Hydra gel hydrogen is a super absorbent polymer OK It's the stuff that's in baby diapers. Our materials are a little bit more inspired synthetically than the stuff that's a baby diapers but the but they're close. So you've got this water swollen network which means that it's very very soft material. [00:22:27] OK Jell-O. is a very soft material and that's also hydrogen. We work with response of hot or just so these are hydrogels now that have some stimulus that imparts upon them a change in volume. OK so this volume phase transition allows us to make colloidal particles that in the cases in the case for this talk we increase the temperature and they shrink. [00:22:50] OK. It's going to be very important for how we're studying the chordal assemblies. But that's the point here. We're making firm response of particles very modern dispersed little dispersions as you heat the solvent the particles expel water and shrink. OK so let's see how we're going to use that. [00:23:10] We can understand why that is vs very simple osmotic pressure argument the volume occupied by a gel. If you take a piece of gel and put it in water the volume occupied by that is dictated by simple osmotic pressure equilibration the osmotic pressure inside of the gel has to be the same as the osmotic pressure outside of the gel. [00:23:34] That's what will define a swelling equilibrium. That's dictated basically by two terms you have this osmotic pressure associated with the last to city that is there's only so far I can stretch those chains before it becomes tropically unfavored to stretch those chains more. And then there's this free energy of mixing your osmotic pressure associated with soluble ization of the polymer the polymers hydrophilic it wants waters of salvation. [00:24:01] So that's going to drive an asthmatic pressure. Did with. So balancing those terms gives you the equilibrium swelling volume anything that you do to the polymer that changes one of these terms changing the cross-link density changing the salt will felicity of the network. What have you will change the equilibrium volume. [00:24:25] So that's how thermo sensitive polymers work thermo sensitive polymers work by changing how good a solvent the water is for the polymer OK they drive a hydrophobic aggregation of side change and I'll show you the chemical structure and second and that drives a DE SILVA nation. Interesting thing is since this equation basically tells you how swollen that polymer wants to beat equilibrium. [00:24:51] It essentially tells you what the shape of this curve should be OK. So if I'm pushing on the particles they want to push back because I'm trying to make them squeeze into a tighter space and they want to be given that particular state. So how hard I have to push or how much energy. [00:25:13] The system builds up internally based on how tightly I squeeze those structures tells me about the shape of this curve. OK and that female come back in a few minutes. So here's the polymer. And it's all not present in polymer science right now. Polly and I suppose. It's the classic for more sensitive material in the swollen state you've got good hydrogen bonding interactions between the polymer and water as you raise the temperature above about thirty one degrees centigrade you change the solvent quality. [00:25:47] That's what I ask you if you change the solvent quality and you enforce hydrophobic aggregation thermodynamically this is the same thing as a cold nature ration of bent in proteins. So if you go to open your biochemistry textbook and look up cold nature ation the thermodynamics I. OK. [00:26:05] People been looking at these things for a long time. Haskins and good that showed in one thousand nine hundred sixty eight that this worked for a high molecular weight polymer and solution to NOCCA showed that it worked in gels ten years later the same year that this Heston's paper came out Caldew shek proposed that these thermodynamics would happen in gels but he proposed it for a very unfortunate system that was for polystyrene micro gels in organic media where the thermodynamics are much much trickier. [00:26:36] OK. It turns out that water is very special here and that's why it doesn't work for polystyrene collards. So here's how you make these things. It's really simple. I'm a physical chemist by training which means that synthesis must be simple in my group. OK. Monomer you've got a residue here too. [00:26:55] To. Cross-linking monomer ammonium So if it is sir fact and you work at seventy degrees centigrade. Note that we're doing the synthesis at a temperature far above the phase transition temperature of the polymer I'll show you why that is in a second from that you get a cross linked network of polymer. [00:27:17] If you do Dynamic Light Scattering on these kinds of structures you find that in this case we've got about one hundred fifty nanometer radius particles. At the temperature that we predicted they undergo a large magnitude the schooling transition. So the particles go from being very very swollen solvents well and in this case about ninety five percent water by volume and go down to only about twenty percent water by volume above this temperature. [00:27:43] And this that the way you synthesize these things. OK this is the same synthesis slide but now with the trick of how you actually make them colloidal OK. You're working at this temperature because that's a temperature at which water is not a solvent for the polymer the monomer So what's. [00:28:04] Alveda the polymer will not be solved once it's formed. So what happens is you get this propagating a little radical at about a degree of plumbers ation about ten monomer units the polymer decides it doesn't want to be solve it any more. It would rather aggregate upon itself once it does that it forms a precursor particle which nucleus the growth of micro chills this process. [00:28:26] If you do it correctly. OK if you do it with very very good control over the nucleation event. You can get very very modern dispersed particles less than ten percent coefficient of variation in terms of size. OK So what happens with these things. So here's an experiment. OK I'm really showing you an experiment still Now here's a couple of extinction spectra associated with colloidal sludge that we got at the bottom of a centrifuge tube. [00:28:56] From two hundred ten and a meter diameter poly Spears and also two hundred ten and two hundred eighty nanometer diameter poly night Pam co-occur like acid Spears you see that you get this kind of ugly extinction spectrum. OK now particularly interesting. If you look at the centrifuge Tube It looks like kind of just a turbo white somewhat opalescent But but really nothing to write home about. [00:29:24] So we present prepared here is a glossy phase. OK we did what I told you would happen. You take the particles you slam them together into a high concentration and you get a kinetically trap structure. It has no long range order because it hasn't. We haven't given it time to find its thermodynamic minimum. [00:29:43] If you take advantage of thermal responsiblity However you can a needle the defects out of the material. So now we take that material we heat it above the volume phase transition temperature the particles shrink they expel their water and now they can diffuse as much as they want because they've got all this room in their neighborhood they cool. [00:30:02] They swell and if the cooling rate is. Commensurate with the nucleation and growth of. You get a little crystals. OK you can see that here. These are close dispersion sandwiched between two cover slips with. Orange gasket. I have to explain that explicitly because I was giving this talk for at a mainly undergraduate institution a couple of years ago showing similar data and at the end of the talk someone raised their hand and said Why are all of your crystals orange. [00:30:31] OK this is not the crystal this is the gasket. This is the crystal in here. You can see if you look at the transmission spectrum. You can see beautiful brag peaks associated with diffraction off of the one one one faces of this face energy that crystal. OK how do we know that is facing a cubic what we can do three dimensional laser scanning con focal my cross could be on dyed assemblies So these are Flora seen dyed particles are about eight hundred ten nanometers in diameter and we're taking Z. sections through them and I've labeled each of the prominent faces. [00:31:07] OK As we go through the Z. to mention the crystal you get packing. So it's a face in or cubic Crystal. OK we have access to thermodynamically preferred state in a very high volume fraction assembly. By this thermal and kneeling process you could not do this straight from a dispersion by sedimentation because again segmentation is a non equilibrium process. [00:31:35] OK so that we've got these building blocks we can start asking these two questions one of the appropriate tools and also how do we quantitatively measure these things. The two problems are going to pose to you. The first one is determination of the volume fraction all of the phase diagrams I showed you were based on changing the volume fraction of the spheres and then looking at how the assembly changed but how do you do this when you don't even know what. [00:32:04] Density of the particles are. I've got these polymer networks are like ninety five percent water by volume. They're really hairy on their surface. I don't really know the size very accurately Dynamic Light Scattering does not give me a precise size. I don't know the density very accurately we know it a little bit from various light scattering methods but we don't know it precisely. [00:32:26] We certainly don't know what the structure typology the particle is to a great degree of accuracy. And we therefore don't know the number density accurately So how do we define the a volume fraction of a collection of sponges. Turns out you can do this by using an old trick that is just looking at the relativists gossipy of low concentration dispersions. [00:32:52] This is The Bachelor equation which is a modification of an equation Einstein came up with that basically says that the shear viscosity is propose. Equal to or proportional to the effective volume fraction of hard spheres the beautiful thing about soft micro particles is if they're far enough from one another and when they diffuse and hit each other they're not under some external pressure they behave essentially as hard spheres. [00:33:19] So at low concentrations. OK at relatively low weight weight concentrations you can treat them as hard spheres. You can get the effective volume fraction from a low concentration dispersion and extrapolate to high concentration. So that's what we're doing that gives us basically a way of relating the effective line fraction to some concentration away percent by some constant that comes from a fit to this line. [00:33:43] OK. So this is been worked out. It's very nice. It allows us to just take a bunch of different kinds of particles look at their effect evolving fractions we can look at their effect of buoying fractions of the function of temperature as well and that allows us to map things like this. [00:33:57] So here in the open circles. I'm showing you the hydrodynamic radius of the closest particles in a global dispersion as a function. Temperature and overlaid with that this cafe the shift factor that tells us how to relate with eight percent to volume percent. And as you can see these two lines track each other very nicely an important thing here is that we're only looking at stuff lower then the temperature at which we see that large magnitude dip in the volume. [00:34:29] OK. The reason for that is once you cross over this the particles become very hydrophobic the second varial coefficient becomes non-zero. And that means that your interaction potential changes dramatically. We take advantage of the fact that these particles have a very shallow change in volume below zero. You get to be below that. [00:34:48] Fraction of that temperature of volume transition and that allows you to use this region in here to now tunes the volume fraction dispersion So here's a mock up of how this phase diagram for Hearts fears looks and look at all we can do if we've got a dispersion that's pretty that's prepared up here and we heat it. [00:35:09] The particle shrink. So the effective volume fraction of spheres will go to the fluid regime that's how we did this in kneeling before member I showed you that glassy assembly. I heated at the particle shrank I'm basically using temperature to drive it into the fluid region of the phase diagrams and that gives rise to a change in the face behavior. [00:35:28] OK So this is the tool we're going to use now. We figured out how to define volume fraction and now we have a temperature knob to turn that lets us to the volume fraction of any assembly. That's our perturbation we can use that perturbation to then look at how the system responds to that perturbation. [00:35:51] OK so now with this ability to define volume fraction in hand we can look at things like how tightly can we pack in assembly and here's kind of an impressive result from a few years a group go my group of six part was done by a woman named same. [00:36:04] Bill De border still aboard who now works in Houston Texas for a company called Baker Hughes. So she's supporting Halliburton Baker Hughes basically make stuff for Halliburton. And so this is a long way from fundamental physics but she basically showed that if you are careful in how you and Neal look a little dispersion. [00:36:25] You can make something that is essentially one hundred ninety six percent effective volume fraction. OK What I mean by that I mean if I define the effective volume fraction at seventy four percent being that volume fraction associated with. Unperturbed particles or particles that are the same volume that they are different diffusing around in solution. [00:36:45] Then as I squeeze on them. I'm affectively increasing the volume fraction so it's an artificial nomenclature OK and it doesn't have any great meaning we don't really have we haven't like creative space here but she packs this thing tremendously tightly eleven weight percent polymer as a huge weight percent for these kinds of dispersions and she sees colloidal assembly. [00:37:09] These are our one micron scale bars by the way I'm sorry. And she observes that for this particular simple course grained experiment you get melting at about fifty percent effective volume fraction where you would expect for hard Spears. OK. The point of this data though is that you can really overpacked these things tremendously. [00:37:31] So one stole left and after she had shown those and original demonstrations. We started thinking about. Well let's be a little bit more quantitative about this. Let's just not take some pictures. Let's figure out how to accurately determine what things were in and accurately determine what the dynamics of that phase are OK. [00:37:50] So the question was Is there a method besides visual inspection that permit quantitative analysis of the assembly motif. I don't think there's anyone in the audience who would argue with me if I said that this was essential a crystal. OK against a one one one face of face in a cubicle out of. [00:38:04] It's taken by optical Mike Ross to be transmission microscopy. What phase is this what phase is this. Can't really tell by a static structure. Turns out that this is a glass. The particles are not moving. If I were to show you a movie of this one you'd see that it's a fluid. [00:38:25] OK The particles are diffusing around almost in a purely diffuse a fashion. OK so the structure doesn't tell you very much. When you start getting to disordered media. So you need to have more quantitative tools. The solution is very simple image analysis tools will take a microscopic image will filter it almost make it binary and it will take a great still scale dilation and basically these steps. [00:38:48] Tell us how we can define what a particle is on that image. Once we know what a particle is on that image we can take a movie of the dispersion and follow the particles in real time. OK we can feed those images into the computer and have the computer tell us where those particles are going thousands of particles at a time that allows us to do things like calculate mean square displacements. [00:39:15] So if I define the mean displacement for all particles in the medium. I can see that I could have Cage structures structures that don't diffuse beyond the confinement of the cage so this is what you would see for close to glass. I'm sorry for a little crystal or you can have things that are approximately diffusive on this scale. [00:39:34] OK At long time the limiting magnitude of this tells us how much room what how big that that room is for that particle to move around. So this now lets us look at basically the fusion of the particles and that tells us how these things are behaving in that assembly and what that assembly really should be called. [00:39:57] We also get trajectories out of this so these are trajectories for individual particles in the field of view over the course. About a fifteen second movie. You can see the particles in the crystal have very tight confined trajectories because they're bouncing off their neighbors. The particles in the fluid regime. [00:40:13] This is a growing crystal the crystals propagating in that direction. The particles in the fluid regime have much more diffuse trajectories as you would expect. OK So here's the sample format that we used to do these experiments these are rectangular Caterpillar tubes about one hundred microns in diameter and going into the board. [00:40:36] OK So hundred microns in thickness so we get about about about one hundred lot of claims of particles in that thickness. This is the glassy face you can see there's almost no color heat it to a fluid and you see it's target because there's lots of scattering from the disorder in the structure and now if you cool it you get this beautiful crystal so you can see the color associated with Brad diffraction. [00:41:00] These are actually higher order diffraction peaks because the fundamental the first order fraction peak for this crystal is in the infrared region of the spectrum. We can also visualize it by looking at the real space image and the trajectories here are those data I showed you before. Here's the glass type confined trajectories Here's the fluid diffuse trajectories Here's the crystal taken time to directories OK so this allows us now to really look at what the particles are doing on an individual basis and then also on an ensemble basis. [00:41:33] Here's an example of how we can actually monitor Crystal melting using this mathematical treatment. Here's an initial Crystal a twenty two degree centigrade. It basically the particles are moving they're totally stuck they're totally frozen I start heating they shrink as they shrink they get more room to move the particles become more diffusive until boom they snap into the fluid regime between twenty eight degrees and twenty eight. [00:41:58] I have to greese in this particular data set. We see a melting transition. OK. Basically a first order made melting transition. OK So we collect lots and lots of data. So actually St John in my group does a lot of this and she showed pretty cool experiments early on that suggested that the volume fraction of packing mattered. [00:42:22] Naively this makes sense if I pack the type particles tighter together. Then I'm going to have to go to a higher temperature to make them squeeze down enough in order to fuse right. If I'm packing them really really tight together. I got to go to a higher temperature to make them shrink enough to diffuse and you can see that here. [00:42:39] Here's a eighty nine or ninety percent effective volume fraction. It's got a melting temperature at about twenty seven degrees. This one melts at about twenty five degrees. OK And this is only about seventy one percent effective libration. But then she did a clever experiment and these data kind of opened our eyes she said OK I know that by controlling number density and temperature. [00:43:04] I can make any collection of dispersions in this case three different samples have in principle the same exact effect of volume fraction. This starts off at five point seven one percent six point three percent percent polymer six point eight percent polymer she's adjusted the temperature of these structures so that they all have the same effect of volume fraction of about sixty five percent. [00:43:28] This one's a crystal. This one is a phase coexistence this one is a pure fluid again. The surprising thing here is within our ability to determine. The vector volume fraction of these to dispersions these all should occupy the same volume the spheres in those dispersion should all be occupying the same volume but this one's a fluid and this one is a crystal. [00:43:56] This is the less dense material in terms of polymer concentration. OK so that initially. It was bizarre. What this tells us is that if we make the assembly denser. It becomes easier to melt. OK if I make the assembly denser in the face of what I was telling you before. [00:44:18] What I was telling before is that density roughly scales with strength of an assembly here making a denser assembly and it becomes apparently weaker why. You can actually do this. For a whole bunch of different assemblies here on plotting this is kind of a confusing plot or at least that's what the reviewers of this paper said the effective volume fraction of freezing. [00:44:40] So this is the effective volume fraction at which the sample freezes or melts it's the same thing right. Freezing and melting it's actually the same thing. Just depends on which direction you're going. Vs how tightly we're packing the assembly to begin with. So really really tightly packed assemblies basically melt at a higher effective volume fraction you don't have to strength the particles as much to get that assembly to be destroyed stronger assemblies are denser assemblies are weaker. [00:45:11] OK. If you look at this as a function of the softness of the particle you find that the stiffer the particle three percent here two percent here one percent here. If you make the particle stiffer this effect becomes stronger. OK So particles that are research more difficult to press on that got a higher modulus three percent cross-link or you find that you get a weaker assembly faster. [00:45:39] OK you know weaker assembly faster. It's kind of strange we can come back to this and this is the punchline. Remember that this is what tells us about how easy it is to push in these particles. OK so if I'm squeezing in a particle what am I doing. [00:45:56] I'm depriving those chains of water that they want to solve eight and I'm making the change a closer confirmation then. They really wanted to. OK. So the particle of the sensually has a higher internal energy it has a higher internal asthmatic pressure than it would have in free solution. [00:46:15] OK. That means that the shape of this curve is going to have an impact on the total energy of the system. And that gives rise to this. Well how if I pack the particles very tightly together. Sure they're stuck together more tightly. But my internal energy of my Somebody is higher right. [00:46:38] The things are basically pushing back on each other. OK they're going to try to occupy more volume because they've got this internal elastic osmotic pressure that's pushing back. So the actual temperature the effective temperature of the assembly is Katie whatever room temperature is. Plus the internal osmotic pressure. [00:46:58] The tighter you pack the assembly. The more internal osmotic pressure you have therefore the effective temperature is higher. OK So hopefully I've convinced you that things get weird when you start pushing on these things. OK you make different types of assemblies that you could not make with hard sphere assemblies and you also resolve different physics that you would not observe. [00:47:22] I've run out of time so I'm not going to talk about the last thing I'll just show you pretty pictures. Here's some particles that we can make that are hard core with soft shell the military asked us to make colloidal dispersions that were paintable we need a hard interior for structural stability. [00:47:41] We need a soft exterior for defect healing. If you're going to treat something roughly like a paint needs to be able to a needle. So we steal a trick from the emotion polymers world we make shells that are soft and in your penetrable you can make inks now that dry into beautiful uniform photonic crystals under ambient conditions they have beautiful three dimensional architectures. [00:48:04] Associated with softness of the interaction. Plus a hard sphere cord that gives this three dimensional stability and we characterize the optical properties as a function of the swelling and drawing and show that what happens is they go from a soft repulsive to a soft attractive polymer entanglement motif to a hard repulsive motif as a function of drying OK So in conclusion. [00:48:29] Hopefully I convince you that there's some interesting physics here. There's also some interesting optical properties that one can obtain by taking clues from soft spheres and applying them to hard spheres in a rational fashion. Thanks for your attention thanks again for the invitation. I'll take any questions. Thank you.