 Okay. Peter, I have to be the side in front of the camera, right? That's, or roughly, doesn't matter. I can just go around. Okay. All right. Sounds good. Good morning, everyone. The title of my talk is... I'm sorry, okay. I'm not good with this. Right. The title of my talk is Entropy-Driven Assembly of Colloids and I'm very happy and honored to be giving this talk at the Hands-On Research in Complex Systems and as Petro had mentioned that I was one of the students in the first Hands-On School back in 2008 in India and this is Harry, myself and others looking at a bouncing jet. In addition to the school, you know, the school was a wonderful opportunity for me to learn the scope of the field and it really got me excited and continue with research in this area but it also made me really famous by becoming part of Figure 7 in this paper and it's a paper in annual reviews of fluid mechanics which talks about how to take fluid mechanics to the public. All right. Going back to the talk. So the outline of my talk is about... I'll start by discussing what colloidal dispersions are, what are colloidal particles and how do they interact with each other and how these interactions lead to assembly of ordered phases like crystals and partially ordered phases like liquid crystalline phases and then I will discuss how entropy can be utilized to assemble two-dimensional membranes from hard rods and then I will discuss how using chirality as a tool we can assemble really exquisite phases with colloidal particles. So colloidal dispersions are everywhere around us. We have these materials or dispersions that we use every day in our life starting with paints, inks and milk. Opal is really a colloidal crystal so it's a crystal made out of colloidal particles and we'll talk more about this as we go along. So essentially a colloidal dispersion is made out of micron-sized solid particles suspended in a solvent. So for example, ink has these colored pigments or nanoparticles put in water or something like that. And the micron scale is really special because at that scale Brownian motion becomes really important and thermal fluctuations ensure that all these particles are uniformly suspended in the solvent. So another theme in the area of colloidal research is to use these particles as model atoms. So chemists have become really good at making colloidal particles all of which have the same size. So that property is called mono-dispersity that means all the particles have the same diameter, same surface properties and so on. And if you put some of these in water and look at them under the microscope and that's really easy because the micron length scale can be simply visualized with an optical microscope. What you would find is that they jiggle around in water due to Brownian motion and the time scale of motion is in millisecond so you need really simple cameras to look at that. The advantage with colloidal particles is that one can change the interaction potential between them and have them mimic some of the interaction potentials that are relevant in atomic systems. The advantage here is because of larger length scales and slower time scales we can access the same similar physics what you would access in atomic systems but far more easily and with far more detail. So let's look at what are the interactions that exist between two given colloidal particles that universally exist. And the first one is van der Waals. I'm sure we've heard all of you must have encountered van der Waals at one point or the other. It's an attractive force that exists between any pair of atoms even if they are neutral and so the idea is that fluctuations induce dipoles in atoms so the positive nucleus and electron if they are separated that leads to a dipole and then two neighboring atoms act as a pair of dipoles and interact with each other through an attractive force which goes less minus one over r to the power six. So it's a really short range force because it's going as one over r to the power six and it's fairly weak if you are to think about van der Waals interactions between two atoms. But if you're worried about van der Waals between two macroscopic bodies what we need to do is to sum up the interactions between all pairs of atoms in each of the two bodies and then the interactions become significant and longer range. So what that means is that if you have two macroscopic plates at a separation of a few nanometers they experience force per unit area of 10,000 atmospheres. So at that scale thermal fluctuations are way too weak to overcome this attractive force and that's what exactly happens with colloidal particles if there are no other repulsive forces if the only force that exists between colloidal particles is van der Waals they will all stick to each other eventually and now they are big enough to sediment and that leads to what is called instability of the colloidal dispersion. So if we want a uniformly suspended colloidal dispersion we need to introduce some kind of repulsive interactions and one of the ways to do that is to use electrostatics. So the idea is that we graft charges on these colloidal particles and similar charges repel each other. So if I have only a single electron charge on a particle and they are separated by a micron it's too weak. The interaction energy for such colloidal particles is only about a KBT so thermal fluctuations would be good enough to overcome this repulsion and so what we need to do is to graft many more charges and then put them in non-polar solvents to enhance the electrostatic repulsion energy. Typically if we have put in the colloidal particles in an aqua solvent another very important phenomena takes place which is that there are counter ions in water. So if the colloidal particles are negatively charged the positively charged ions in the water rushes towards these particles and arrange themselves in a layer like geometry and what this layer really does is that it effectively neutralizes the charges on the colloidal particle and so instead of having a 1 over r kind of potential what we end up having is e to the power minus r over lambda by r. So the potential experienced, the electrostatic potential from a given colloidal particle exponentially decays out with a screening length that is about 10 nanometers if you have a millimolar of sodium chloride in there. A second way to introduce repulsion between colloidal particles is to use polymers. Essentially here the idea is that we will graft polymer chains on the colloidal particles and this leads to some kind of steric stabilization. In the community people have used standard polymers like polymethylamethacrylate but also there is an interest in using novel polymers like DNA and the advantage with DNA is that you have these base pair complementarity that can be used to introduce effective attractions. So if you have a polymer brush grafted on these particles and these particles are suspended in what is called a good solvent. By a good solvent what I mean is that the chains of the polymer are extended in the solution. When two such particles come close enough what is happening in this area is that you have a very large concentration of polymer chains and therefore a higher osmotic pressure that introduces an effective repulsion between the colloidal particles. And if the polymer brush is in a bad solvent in which case the polymers would rather be among themselves than be with the solvent that leads to enthalpy attractive interactions. So having discussed these standard interaction potentials let us look at a model system which is called hard spheres. So a hard sphere interaction potential shown here is a very simple interaction potential. It is zero until the particles touch and it becomes infinitely large as the particles touch each other. This is the simplest interaction potential that one can cook up and analyze theoretically as well as experimentally. And this is how John Dalton had imagined atoms to be. So if I look at the free energy of such a system the free energy is given by internal energy minus T times entropy and here the internal energy is purely kinetic because the potential energy stays zero and the only energy scale in the system is KBT so U is given by number of particles time KBT and so the free energy, the temperature really scales out. So what this expression shows you is that if you want to lower the free energy of the system you have to maximize the entropy. So phase with the largest entropy has the lowest free energy and that's the phase that one would obtain in equilibrium. So there is this usual notion that entropy is a measure of disorder and so one would imagine that for a hard particle system ordered phases don't exist but that's not quite true and in fact that was a really big question do hard spheres crystallize in the 50s and at one of these conferences the very famous people participated to debate over this question and they go around saying oh yeah yeah you know it really goes against intuition because many simulation and computational people had indeed found a phase transition for hard spheres to go from a fluid phase to a crystalline phase beyond a certain volume fraction and so there was a lot of controversy about whether that is really an artifact of simulations or it really takes place and eventually after all of this debate they actually say that oh no this is really too hard so let's abandon the scientific method and just vote it out amongst themselves. So they just voted and the vote was 50-50 so half the people thought that it's an artifact of simulations and half the people thought that hard spheres can indeed crystallize. Well now it's very well understood we have very large computer power and we can do simulations to actually plot out the phase diagram so this is how the phase diagram looks so below a volume fraction of 50% the colloidal dispersion is in a fluid phase what that means is that the particles are arranged in a completely disordered manner and then above 50% the crystalline phase sets in where all the particles are arranged on a hexagonal lattice or an ordered lattice and this can be intuitively it's counterintuitive that crystal phase has higher entropy than fluid phase but you can get a sense of it by considering let's say a volume fraction of 64% so entropy is proportional to number of accessible states and so if I were to pack spheres in a completely disordered manner the highest packing fraction I can achieve is 64% but if I were to pack the same spheres in a crystalline arrangement I can have a packing fraction of 74% so that tells you that the number of accessible states for a crystal are way higher than for a disordered phase yes, T is temperature and temperature plays no role in this transition so the phase diagram stays the same all throughout so Y axis has no role really and so after this phase diagram was put out the question was that can we see this experimentally and in a beautiful experiment by Pusey and Etal they prepared hard sphere colloidal particles by grafting a very small polymer brush and so in this picture what you're looking at are vials which have these hard sphere colloidal particles put in at different volume fractions and then after equilibration what you find is the following so these vials are backlit with white light and what you're getting in the 50% volume fraction is some kind of iridescence and what's going on is that you have crystals made out of micron sized objects and so the wavelength of visible light which is about half a micron is undergoing Bragg diffraction which is giving you these beautiful colors so having looked at hard spheres what I would like to now show you is that that the geometry of the colloidal particle plays an important role in the kind of phases that we can assemble and so the farthest away you can go from spheres is the most an isotropic object a rod and unlike hard spheres where the chemists know how to synthesize highly mono dispersed particles the situation with rods is quite grim in the sense that we don't know how to synthesize rods which have identical lens and diameter and so physicists resorted to using viruses and in particular tobacco mosaic viruses these viruses are engineered by nature and mono dispersed because all viruses are identical to each other and they have very high aspect ratio so the aspect ratio of the rod governs the phase behavior and they have uniform surface properties so in a beautiful experiment by Bernal what he did was he took a very dilute TMV solution about 0.1% TMV in a fish tank and examined the fish tank in cross polarizers and so basically he has this goldfish that is swimming in a dilute TMV solution and what you find is that away from the fish in the cross polarizer regime you don't have any signal so if you have an isotropic a uniform refractive index material and you observe it between cross polarizers you are expected to observe dark signal but what this fish is doing is actually through its flow fields is aligning these rods and once you have an area where the rods are completely aligned it's optically an isotropic so the refractive indices along the axis of the rod becomes different from the perpendicular to the axis of rod and that makes it bifringent and gives you signal even under cross polarizers and what really is exciting about hard rods is that as you increase the wall infraction of rods from 0.1% to say a few percent what you observe is two phase coexistence so in a while which has to begin with 1% of hard rods they phase separate into two phases which if you examine under cross polarizers the top part is lighter in density and has no signal and the bottom part is heavier in density and gives you strong bifringence and so the top phase is what is called an isotropic phase where the rods are both positionally and orientationally disordered on the other hand the bottom phase is called the pneumatic phase where still there is no positional order there is orientational order meaning all the rods are roughly pointing along the same direction whereas in the isotropic phase the rods can point in any direction so also I really got interested in this problem as to how isotropic to pneumatic phase transition takes place in hard rods and in a way it's a much simpler problem to analyze because the phase transition is happening with a volume fraction of few percent unlike spheres where the phase transition took place at 50% so what Ansarva did was he expanded the free energy in terms of as a virial expansion in density and he has two terms first is entropy of mixing which is basically translational entropy and then he has the second term which encodes the orientational entropy and so what's really happening is that by forming a phase where you have lost orientational entropy or orientational disorder but you have gained a lot of translational entropy so at the expense of orientational entropy we have gained translational entropy and therefore the pneumatic phase becomes stable and this transition is sensitive to the aspect ratio L over D because if you look at the excluded volume in the pneumatic phase it scales as D squared L whereas in the isotropic phase is D L squared and so if I take the ratio of that that tells me which one will be more favorable so TMV is a cool virus to work with but is also very difficult to synthesize so it's a plant virus where you have to grow the plants for four months and then hope to purify TMV out of it a new system that I have been working I and others have been working for a long time now is what is called an FD virus it's a bacteriophage so it infects bacteria and so you can just grow up E. coli and purify within a day or so so that's a huge help that we can get virus in a day's time rather than over a month's time scales it's a completely non-pathogenic virus it infects laboratory strains of E. coli and it is chemically homogenous it's highly mono dispersed and also it has much higher aspect ratio than TMV TMV has an aspect ratio of 16 FD has an aspect ratio of 150 and so it's a virus which is one micron in length and few nanometers in diameter and in a beautiful paper by Fredin what they did is they figured out the isotropic pneumatic coexistence as a function of ionic strength and the experimental data had a beautiful overlap with the Onsager's theory of hard rods so these rods are truly hard rods so it has quantitative agreements with Onsager's theory so when you increase the volume fraction of rods even beyond the pneumatic phase what you end up getting is a symmetric phase where you have layers of rod-like particles and the rods are arranged as shown and this phase was first predicted in computer simulations by Franco and then experimentally observed in FD viruses and the advantage here is that the rod is one micron in length scale and so we can also do single particle studies in these phases so so far what I have shown you is that we can make three-dimensional structures both with hard spheres and hard rods but if you were interested in making two-dimensional structures the situation is a little bit non-trivial and so most people think about membranes when they think about two-dimensional structure and one of the ways, standard ways that our body and you know chemists alike use to make self-assembled membranes is to use amplifiers or magnet-like molecules which have a hydrophobic head and a hydrophilic tail and if you have many such particles they would in water they would spontaneously assemble in these sheet-like geometries so that the hydrophobic tails are shielded from the unfavorable solvent and so now what I am going to show you is how we can assemble two-dimensional membranes starting with homogeneous hard rods instead of heterogeneous surfactant-like molecules and to do that I am going to use what is called depletion attraction and essentially the reason I need to use depletion attraction is that the viruses by themselves are electrostatically repulsive so they do not really form ordered phases at low concentrations and so what we really do here is to mix these rods with polymeric coils and the idea is that each such polymer coil is excluded from a zone around the rod and if two rods come closer than a coil diameter apart then some free volume is available for the polymer coils which increases the entropy of the polymer coils and here the number of polymer coils are way larger than the number of rods so it is the entropy of the polymer that really matters and therefore favors alignment of rods so the excluded volume zone overlap is maximum when the rods are aligned along their axes and it is a generic mode of attraction where the polymer concentration sets the strength of the attraction and the polymer size sets the range of the attraction and so what is going to happen is that if I have two rods and I add polymers they come together and get aligned along their axes and then more rods will join to form these disk like structures right so basically the rods are joining the initial cluster of two rods and now these disks themselves will undergo depletion attraction to stack up on top of each other and give you a phase which looks like a bulk symmetric however at low polymer concentration what is going to happen is that the rods will now fluctuate up and down from the disk and therefore if I bring in two such disks at low polymer concentration these protrusion fluctuations will be suppressed and lead to an effective repulsion between the disks if I am at the high polymer concentration the protrusion fluctuations are not allowed so I have really very two smooth disks that undergo depletion attraction and stack up on top of each other so at low enough polymer concentrations this is how the assembly kinetics works out so as I mix rods and polymers together I make many such disks of aligned rods and this is how they look under the microscope so from the top they appear as a circle and from the sides they appear as an ellipse and if I have two such disks they coalesce and make a larger disk so in the end I can end up with really large disks tens of microns in diameter one rod length thick and on a good day on a good sample this is how it looks like on the cover slip lots of these sheets and here I will switch to fluorescence where one out of 10,000 rods are labeled and the rods are pointing at us so they appear as dots and they freely diffuse within these sheets so these sheets or membranes are very similar to lipid bilayer in the sense that the constituent rods or molecules are free to diffuse within the sheet and they have long wavelength elastic properties that are similar to those of lipid bilayers so far I have shown you that we can hud spheres and hud rods assemble in fluid and crystalline phases and I can use depletion attraction to assemble two dimensional membranes with hud rods and now I am going to give you examples of how I can use the chirality of the viruses to control the line tension of these sheets and assemble what are called colloidal rats so I am left with like 10 minutes for 45 minutes barrier and so let's go quickly so if I were to and I will explain by chirality exactly what do we mean but first let's look at the edge of the membrane so there are two possibilities at the edge the rods could be perfectly aligned and that would give me a square edge and that is quite implausible in nature there is nature never really likes sharp edges and what really happens is that we have a rounded edge where the rods are tilted and the reason we have a rounded edge is because of surface tension with the surrounding polymer solution yes yes yes yes I will show so this is a fluorescence micrograph where one out of 10,000 rods are labeled so in the center the rods are pointing at us in their dots and at the edges the rods are lying along the XY plane so you can see the entire rod this is about a micron and so essentially what's happening is that this membrane itself is optically birefringent so within the bulk of the membrane the refractive index is the same in the X and the Y direction but the edges it's not true and so if you were to look at it schematically this is what is happening the rods are standing straight in the bulk and tilted at the edges and if I measure the polarization of such a system using what is called a pole scope so in this picture the intensity is proportional to the local tilt of the rod so I have huge tilt at the edges and no tilt in the center of the membrane and one can write simple Frank Free Energy models to analyze this phenomena and this phenomena of expulsion of twist to the edges is has one-on-one analogy with how a superconductor expels magnetic field and so the twist penetration depth is about half a micron and the penetration depth does not change with assembly conditions and if you notice the dynamics of the edges so here I have zoomed on to the edge of a colloidal membrane what we find is that the edges are fluctuating and they're fluctuating just like any other liquid droplet would fluctuate so it has a certain surface tension associated with it because I'm taking a 1D cut it's a line tension and one can analyze these fluctuations to measure the line tension so essentially what you do is you break up the height of this contour in a Fourier series and then the mean square fluctuations of the Fourier modes are inversely proportional to the line tension and what we can do is we can control this line tension by tuning the chirality of the rod so by chirality what I mean is that the two rods don't want to be perfectly parallel with respect to each other but instead prefer angle with respect to each other so instead of making a perfect pneumatic these rods make what is called a twisted pneumatic where the directed continuously turns and so if I plot the preferred tilt angle versus the temperature what I find is that these rods become achiral as I increase the temperature and so if I plot the line tension as a function of temperature what I find is that it drops off as I lower the temperature so in this movie what we are doing is that we have a membrane and we are changing the chirality of the rods by lowering the temperature and what's going to happen is that the line tension continues to decrease and so the fluctuations increase and eventually there is a polymorphic transition into ribbons and the reason one gets twisted ribbons is the fact that that rods would really like to be tilted with respect to each other and they're free to twist at the edges and so basically we want to generate as much edge as possible so what's going to happen is it's fluctuating more and more and then eventually it would turn into twisted ribbons and so twisted ribbons is basically small membranes that are now connected to each other through these bridges and with such high surface area structure the rods have as much twist as they could ever ask for and it's completely reversible, we can go back and forth from the membranes to ribbons so so far the data that I've shown you was from my postdoctoral lab Professors Juan Medojec at Brandeis University and this is the data that I acquired while I was a postdoc in his lab so the problem that I was interested in is related to lipid rafts sorry so in a cell membrane is made up of hundreds of different types of lipids and proteins and it is known that certain lipids and proteins associate within the membrane to make what are called lipid rafts and these are highly controversial because the length scale of these rafts is few nanometers they fluctuate a lot and it's not clear why they are stable and so to mimic this problem in the colloidal membrane system we decided to add a second rod which is slightly shorter than the rest of the rods and so there are two possibilities the two kinds of rods can be uniformly mixed or they can be completely demixed and that's understandable purely on the basis of depletion attraction because in this case the excluded volume is as nice as much as possible and here I'm actually dominated by entropy of mixing so when we did this experiment we did it with rods which are different in length by about 26% they were oppositely handed and slightly different in flexibility so I will come to each one of them why oppositely handed is required and so on and so forth but when we did this experiment we found the uniformly mixed ways so from now onwards all fluorescence movies only shorter rods are labeled and longer rods are not labeled so you have two kinds of rods but in the fluorescence images you can only visualize one kind of rods and so here you have uniformly mixed rods and then at higher polymer concentration the shorter rods have completely face separated within a background of longer rods and in the fluorescence only the shorter rods glow up so what was really interesting is what happens in between these two limits and what happens is the following that we observe these clusters of shorter rods in a membrane of longer rods these clusters have a very well defined size of about two microns and you can wait a day a week or months the two clusters will not merge they repel each other strongly and they are self limited so schematically what you are looking at is a sheet which has these two dimples made out of shorter rods so these samples were made by mixing the two kinds of rods first and then adding the depletant so a question that a natural question that arises is it the true ground state of the system or is it a kinetically arrested metastable state meaning the two clusters cannot merge because the repulsive forces are really large or is it that the system would really prefer to have many many clusters and so to answer that question we did the following experiment where I took a sheet made out of purely shorter rods and a sheet made out of purely longer rods under the same polymer concentration and have them merge this way I would start out with a bulk interface and this is what happens so indeed now I have a clear interface between the shorter and the longer rods and it looks like that nothing much is happening although I would not be showing you this movie if nothing much was going to happen so let's see what happens next and this is what happens the interface destabilizes into these clusters which are connected by thin liquid bridges which then break due to thermal fluctuations and the system equilibrates itself into these clusters that are stable and hang out in the membrane so this really shows that the micro phase separative state is the preferred ground state of the system and it's interesting to note that each of this cluster which is about two microns in diameter has about 24,000 rods and it's highly mono dispersed and so what we have done here is we have taken 24,000 colloidal particles put them together in a cluster of well defined shape with an error bar of maybe 500 rods and that's really a very sophisticated self-assembly given the contrast in the colloidal sphere regime where it's a matter of great pride if we can put together four spherical particles in a tetrahedral cluster and so this is a large membrane where I'm showing you these clusters of shorter rods and we can see that they clearly interact with each other through repulsive interactions and we can measure these interactions so in order to know the origin of the interaction I need to first measure it and we measure it using what are called optical traps so the red dots are essentially focused laser beams which push on these clusters like snow plows and so what I'm going to do is I'm going to bring these two clusters closer than what thermal fluctuations would allow me to do and then I would let the traps go so this is what is happening I'm coming in with focused laser beams and then I'm pushing them together and then I would let go and once the traps are off the particles feel strong repulsive forces and they drift apart and by repeating this experiment many many times there is a way to back calculate what is the true interaction potential and this is how it looks it's really an exponential fits really well to this it has a characteristic length scale of half a micron and it's strongly repulsive so on contact with hundreds of KBT and so what sets the size of these clusters and what's the origin of repulsive interactions has to do with the fact that these rods are chiral and so the half a micron length scale comes from the twist penetration depth so if I look at the polarization image of these bidesperse colloidal membranes what I find is that at the edges of the cluster I have a preferential tilt of the rods by forming these clusters I'm allowing the twist to penetrate the membrane interior and lower the chiral free energy of the rods and that's why it is favorable for these clusters to form and they interact repulsively because as I try to bring two clusters closer than the twist penetration depth then the rods at the edges have to untwist and that costs a lot of energy and leads to effective repulsion and if this hypothesis and so we can add what we also observe is that shorter smaller clusters have less twist associated with them then larger clusters and we can quantitatively measure measure that to find that the peak retardance or the maximum tilt angle as a function of the size of the cluster goes up and the twist penetration depth stays the same so if this understanding is correct then I should measure the interaction potential between clusters of different sizes and and we do that and we find that indeed larger clusters repel more strongly than smaller clusters and I can collapse the data with an experimental error by scaling with the experimentally measured tilt angle and now I can use these repulsive interactions to hierarchically assemble larger larger crystals and so essentially sorry so at low volume fraction the clusters are in a disordered configuration as I increase the number density of smaller clusters some short range order starts to set in and then at the highest volume fraction I get these beautiful cluster crystals so in appearance they look like colloidal crystals but they are actually very different because here each cluster is also self assembled unlike colloidal crystals that are made out of let's say polystyrene beads and so what I have done is that I have shown you that we take hard rods we add polymers to get membrane like structures to which we add a second rod or second component to form analogs of 2D micelles which I can then further self-organize to come back to colloidal crystals so I have completed the circle in a way and this is just to emphasize that it's not that I took 2 rods that were highly designed to see all the phase behavior so colloidal rafts are quite ubiquitous we have changed the relevant parameters such as the length difference the chirality to get a zoo of phases that I hope to explore in future and I would now conclude that I have shown you a number of phase transitions that are driven by entropy and we can engineer the colloidal interactions by changing the geometry of the particle the chirality and the flexibility and what colloidal length scales really allow us to do is to directly visualize and manipulate with simple tools and the system of hard draws, chirality and attraction has a complex unexplored phase behavior so with this I will thank you for your time