Entropy, information and order in soft matter

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Entropy, information and order in soft matter
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Entropy, information, and order are important concepts in many fields, relevant for materials to machines, for biology to econophysics. Entropy is typically associated with disorder; yet, the counterintuitive notion that a thermodynamic system of hard particles (colloids) might - due solely to entropy - spontaneously assemble from a fluid phase into an ordered crystal was first predicted in the mid-20th century. First demonstrated for rods, and then spheres, the ordering of colloids by entropy maximization upon crowding is now well established. In recent years, surprising discoveries of ordered entropic colloidal crystals of extraordinary structural complexity have been predicted by computer simulation and observed in the laboratory. These findings, presented in this talk, demonstrate that entropy alone can produce order and complexity beyond that previously imagined, and that, in situations where other interactions are also present, the role of entropy in producing order may be greatly underestimated. Glotzer discusses how new statistical mechanical principles learned from recent findings can be used to design shapes that promote long-range entropic order.
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we welcome everyone I know they'll be some other people streaming but they were nearly complete and no 1 and start off this last part of the whole meeting last Monday was part of the meeting on state to even have surprises coming up but 1st it gives me great pleasure to introduce during lots at today's closing linearity plenary speaker former colleague of mine from the University of Michigan actually we're remembering Monday nite over over drinks Chechen reminded me just how embarrassingly short period we did overlap there but I think it was literally days guess as what we met briefly but I took off days after she officially started just a coincidence of course because I'm a big fan of work because she's done a number of many number of key advances in soft Matter Science but I'll just mention to but very well rather recently issues really done beautiful pioneering work on so-called patching particles of collards and if that's unfamiliar to you in this emerging as sort a field of its own lots of beautiful way of controlling interactions and self-assembly of collards and in addition to that tho he also did some very fundamental work in glass formation and I want to emphasize that word fundamental because Of I'd I'd like to point out would like to point out that her official affiliation is actually in engineering department Michigan chemical engineering and materials science both actually on and that Sharon is a great example of something near and dear to my heart also topic of the current discussions with and phone and namely bridges between the final science physics and engineering and turns a living example of that kind of a bridge at the end of the background of course is not too surprisingly coming from a physics background I union both underground and graduate of ucla's and Boston University respectively and then she started the independent career at the National Institutes of Standard technology on and after a few years there than joint engineering at Michigan just as appointments and in physics and applied physics but I think she represents a very nice mix of fundamental and applied and not only taking fundamental insights and finding sitting applications but the other way around which I think is equally important emphasize very good fundamental problems on can arise from practical considerations I think wouldn't be hearing today about injury and you know what is more fundamental for instance the 2nd loss in anemic and you'll know that also has its origins in very practical problems so I share and use of has number so honors I won't go through the list but just point out that she's been very recently elected to the National Academy of Sciences also the Academy of Arts and Sciences and very recently and won the MRS cries of Materials Research Society and and others of just last fall foliage so without further ado and were happy to have you up disclosing that if the the value of the afternoon everyone I am really just thrilled and honored to be here and to be able to attend the meeting this week and the will to give this disclosing lecture I listened to a number of really wonderful all talks and and learned quite a bit as president to talk about entropy there's nothing more fundamental than that of behind me the CAR molecular-dynamics Monte-Carlo computer simulation of a
suspension of nanoparticles in solution that when it
when the colors are blue indicates that the system is in a fluid state minister to see yellow regions emerging the yellow is the color the particles yellow when the particles start to
organize locally infected to nucleated crystal that grows and takes over
the whole system is playing elliptical much if you a few times in this simulation is meant to honor model but a typical situation of nanoparticles
that the majority of nanoparticles today they're better grown in solution from medals of middle irons like quicksilver I will grow up with fast in a faceted way to to form a little Polly he joked crystals and here we have a little lot to he shape crystals
and under no circumstances is might very
simulation but there it with me so fascinating except for
the fact that there are no forces know intrinsic forces
between the particles in the simulation whatsoever
the only thing that there is in this system is
excluded volume the particles are hot particles
they're moving around by rounding Brownian motion rotating translating around as the
older in suspension and they simply cannot overlap 1 another and yet they're
going from a disordered fluid state spontaneously to a
crystal state and this is happening solely due to enter
so we're going to talk about entropy I know it's last popular days so I don't get too heavy with equations but when I started out with a few of relationships that I know will be familiar to you when we think about entropy we think about on this day kids entropy and the way gives formulated it was the that the entropy can be thought of as the but the product of the probability of a given microstate a instantiated system the example of a microstate in the previous example might be 1 snapshot of this collection of nanoparticles of 1 instant of time that's 1 possible arrangement of particles 1 possible Thurman adamantly allowed microstate the system it's the product of the microstate of the probability of a microstate your piece of times logarithm of probability summed over all of the microstate I'm in the system and and generally speaking in in in any system the probability of depends on the energy of that part of that microstate and so it depends on the temperature the
system now if you think in terms of of quantum quantity their inquiry chemical applications that we think in terms of the one-on-one interview where we think in terms of other identity matrix where you can you can write the entropy is the traces of this density matrix times slot where mother of the density matrix and this density matrix can be written in terms of the Thai conductors then we can write the entropy in uniform that's very similar to the form in which Boltzmann wrote in the form of the entropy and so we understand what entropy means in that case when entropy 0 you have a Apure state on and the and and then the measure of the entropy away from 0 is a measure of the departure of your client system from from a pure state and when we go to know information theory then we have Shannon's expression for for entropy on ended and the way you think about the entropy In this context is that entropy is basically the day equivalent to the minimum number of binary er yes no questions that you have to ask to fully determine system 2 years you're familiar with the game of all of 20 questions you know this game where I say I'm thinking of a famous person you have 20 questions that have to be only yes or no but questions on to guess who I'm when thinking of the knowledge that they were playing a bazillion questions instead 20 questions but I simply give a favor proclaims personal friend here but this finely honed inquisitive skills might might start asking them to try again when thinking of you might say is a Gandhi is a Brock Obama is lady Gaga is that Einstein and he keep going and eventually you might guess what I'm thinking of OMB and in particular the doesn't know anything about me and so all choices of famous people are equally likely on average meticulous very long time get the right the right the bright person that someone else and 1 of the more advanced students an audience for example of whose for approved statistical mechanics at the Ramis is very fresh in their minds might say the Bolivar or dead male or female right of under 40 while you would have to go except the words yes or no CDs asked mailed it you know so really quickly he would act would design your questions to eliminate huge parts of the huge numbers of possibilities were huge parts of the space so that you could hone in on the correct answer as quickly as possible and if you could optimize the number of questions to minimize the number of questions that you have to ask to get the answer that's how I think about what entropy means now if we think about Klostermann anemic system then all micro-states are equally likely in general in any system all my crisis with the same energy are equally likely but if we have a closed system they all have the same energy and all my procedure equally likely and so if we have a maker micro-states than probably anyone is just 1 over the toll number microstate many very quickly the gives expression for the entropy reduces to 0 to the Boltzmann entropy of the famous expression that we now OK With the lid Contador Frankie people's men for purposes of units times the lot of the of the number might receipts in the system a case Hawaii why is that important status a situation that we are thinking of only look at that stimulation from the beginning where hot particles spontaneously organized under no extrinsic and intrinsic Inter particle forces but solely due to educate the system and so the key point that I want you to take away from the lecture today is that entropy can order stuff if there are more ways for the system to be water than there are for it to be disorder that's counterintuitive to many people oftentimes we think of what entropy as being synonymous with disorder and often times that is the case on and on strictly speaking you could think of it as disorder and receipts the faces but in terms of I'm thinking that your spatial arrangements and thinking about the the order as we conceive of it in a typical way entropy isn't usually thought to order up but indeed can and also the knew this the 1940 underlined he showed us that if you have a system of hard rides on a new crowd them enough and if you have heart red added that additionally ski excluded their actions taken overlap nothing else and it aspect ratio the riders long enough and it some mining fraction those rods will I go from all of us completely disorder fluid state where there were pointed in any direction to and alliance there were on average the the rods are aligned with 1 another and here we should be aligned awarded state by Green amended disordered state on by right and it's it's it's in this way that a better system of hot rods will undergo and isotropic nomadic transition it occurs to entropy maximization the system gives up rotational degrees of freedom to gain translational degrees of freedom because there are more ways to arrange the particles if they line up there's more excluded volumes available per particle so there are more ways to reduce system more entropy and that's what stabilizes the state and the same is true and this is a little less obvious for hard spheres and this was 1st predicted by by Kirkwood in the 50's and shown in in really the very 1st molecular-dynamics simulation of of particles that was done by the an older and and Wainwright in the late fifties and at the same time that 1 of the 1st ball Carlo simulations of particles done by wood and Jacobs said they both are set out using computer simulation to test prep Woods prediction that even hard spheres is crowded to a high enough concentrations might spontaneously and crystallized just to educate and in fact it does enter a 50 cent packing fraction of a completely thermodynamic equilibrium fluid of of hot particles hard colloidal spheres will spontaneously form an SEC crystal because there are more micro-states that recognizable as crystals ordered another in a regular periodic arrangement but then there are ways for the particles to remain on disorder so it's a purely it's a it's in it's an end topically driven phase transition toward ordering and nowhere are in entropy driven phase transitions on described more eloquently and more clearly than in this this really classic paper by Jon Frankel on and to the different phase transitions published in 1990 and is again a I but this is a special picture of of Donnie does like to show it because the crown is tilted he likes it when it straight but I but like good but dont isn't even really is the king of entropy driven phase transitions and and that those of us like myself who work in this field learned everything we know up from from Don Frankel who of course made his career here and now is the chair of chemistry and
ate at Cambridge University so we got started on this problem because not because I started up being so obsessed with entropy like I am now but we were trying to design a cat Telluride had someone I and and another type of semiconducting nanoparticles a colleague of mine Nikko tough makes a slap across the hall from from me and their little man meter size particles that happen to grow as little picture heater and they're coated with Lincoln said they they have all sorts of the vandals interactions between these particles and solutions the ligands can be hydrogen bonding with 1 another departed schools can be charge they can have intrinsic on dipole moments but in them and so we were trying to extort understand all these different kinds of structures that that he was staying in at some point the civil war if we stripped away because the simulators we can do this what if we stripped away all of the interactions and left only the shape of the particle and asked What would entropy do and we were really surprised to find it and should be would do a lot of them in effect entropy produced for us just in the same way as hard spheres spontaneously crystallized the crystal of hard catcher he shaped particles that was actually paid don't get gathered all 12 fold rotationally symmetric classic crystal on which is a crystal that has no long-range translational order there's no repeat unit like there isn't a face and a cubic crystal you can't find a part of the crystal and then repeated and get your crystal back but instead it has long-range rotational ordering to it like like like in Penrose house and this is this was and still is to my knowledge the single most complex structure no known or it produced is Lisa computer simulation to solid entropy just coming from a hard colloidal tied up particles it's so complicated that I you could see here that the the yellow there's yellow Mateus blue motifs and that the sulfide particles will come together in a pentagonal died pyramid and then there's 12 particles that will come together in a 12 member ring with attaches to go up down up down up down all the way around and then they stack up and tackle detrimental member remain detrimental memory and then those things form of former logs and those logs each other until the little better and all of this spontaneously occurs out of the disordered fluid just sitting there I'm infirmary make equilibrium and then just slowly compressing present general 50 cent packing fraction and then you wait for it and this just comes out robustly on every time if this would if you were to find the nearest periodic crystal approximate it's called it would have 82 particles in the in itself so I I just found that
amazing and this is what the the bond order diagram along the top and then along the bottom the diffraction pattern looks like on the side you see the diffraction pattern in the periodic direction to Doda cattle closet crystals are an example of the an axial a planar Plaza crystals which caused pursuant to dimensions when you you look down much Welfel axis but it's a periodic in the 3rd direction so that we see but if you look on the toppled access you these beautiful and high-resolution diffraction patterns from the simulations died that look as nice as the crystallography would ever want to get on in an experiment could clearly see all these 12 fold rings on going around
reflecting the slowing traditional symmetry so Kwanza crystals all were discovered back in the early eighties by by Dan Chapman and his colleagues had menaced by former home but that was way before my time although I did work on the hallway were dance John Collins works you could feel the excitement I'm and so down at the end of the 2nd won the Nobel Prize for some for discovering cause crystals 11 enough in 2000 but he won the Nobel Prize in in 2011 because it was not necessary because classic crystals were so technologically important yet but because it represents an entire paradigm shift in the way that we think about crystals to think that you could have on structures that violated typical symmetry conditions and could have this kind of long-range acquires a period the city now our particular Dudek out applies a crystal of picture he is actually structural to another chalcogenide Kweisi crystal comprised of tantalum and tellurium we take the talent tellurium diffraction patterns and superimposed our diffraction pattern we see that it matches the peak for peak so it is the centers of our little hard catcher he drove her sitting at the atomic positions of the talent and and tellurium Adams in the chalcogenide requires a crystal
bell the other soft matter Plaza crystals but they make up a tiny fraction of all the classic crystals that that known OMB since the discovery of acquires crystals in the eighties there have been more than 10 thousand publications on classic missiles but only got a couple dozen in the field of soft matter and only those only started in on my 2003 2004 with reports of of soft matter Plaza crystals formed from danger molecules which are judge amount molecules are our branch molecules that have a starting point at the court may come out with branches and then from each branch to come more branches more branches slow factor logic you could make them no more more more generations and you have this is big ,comma squishy thing with a heart rigid quarantine at all and those things take the place if you will of Adams the like showing Adams and although my cells such as dangerous a block a polymer my cells or surfactant my cells are known to self assemble into in a cubicle body centered cubic on and even a 15 other typefaces on it said it was never seen before that they could form classic crystal unlike faces into these issues some examples of where 12 fold and even 18 fold on petitioner's snatch acquires crystals were found before the most part they're all 12 full
symmetric and what they all have in common is that they're all formed of these of these mice cells and 1 myself form in block a polymer but it's surfactant systems even systems of little nanoparticles will polymer tethers on them once those myself form they're they're sort of like closed objects there they they itself a symbol on their serve terminal objects and those objects have a much weaker interaction with each other than then the molecules within that making up the myself do so you could end end and they're typically spherical on and you could you could almost think of the self-assembly of these myself like this self-assembly of hard hard spheres or soft spheres squishy spheres I and then in effect it's possible to understand but the self-assembly of these is being analogous to what happens in metallic system so what is typically described in metals be via paralyze interactions between metal Adams as being responsible for long-range closet crystal in order is achieved here in my cellar systems due solely to entropy OK so how far can we go with entropy was this cause a crystal finding of hard-to-treat just as just 1 example with many more to come is it is the tip of the iceberg or or did we just get lucky but we definitely got lucky but was that it was there not much more to be found in OMB and so we embarked upon this this study would be doing up several years of every ship under the sun and trying to understand what is the role of shape and the entropy due shape in organizing and arming itself assembling our systems and in particular for a hot particle systems where you could actually mattered screening out the interactions than you really wanna know injuries Kennedy but even in systems were you still have other kinds than walls electrostatic static and other interactions between 2 particles knowing the role of entropy that's coming just from the shape load is very important in the design of nanoparticles systems for and for particularly targeted structures I there are there's there's a lot of other groups in the community working on these kinds of problems and 1
of the most prolific groups is right here but in the Netherlands and Maryland are Dexter's group of course however is what is 1 of the leading groups in the world in simulating the and tropical driven phase transitions as a function of of shaping comparing those with with the with dense patterns of states and trying to understand and how these kinds of cases a stabilized on in in in all sorts of different shapes systems now what we did
in years we we started the assistant with you started with a to which will have a robust is that what happened to the touches draw perfect right would we synthesize them in the the Tejeda really perfected the tips might be high energy at the fees might get get blunted and then they could be slightly Politis person size the so we said Let's do a study where we take our tragedy you we start sniffing the corners now the a perfect touch region enough you get to a perfect option he drank and so we starlets study although shapes in between and what I'm showing you hear is on detector he on you on your left arm which is what gives us that the classic assume you can actually see him that all wide and still get that was crystal the form very robustly minutes some someplace you it too much and now instead of the "quotation mark crystal self-assembly out of fluid phase I diamond crystals of the symbols of the fluid phase were now the particle detector Tejeda particles of flipped the staggered way every other 1 in much the same way that you would see carbon atoms in diamond a staggered ethane configuration if we keep staffing slipping even more not quite adapted future and then we see this very complicated bipartite structure was 16 particles in the Union itself that ISA structural to a high pressure lithium face where the centers of our particles would be like lithium atoms under under high pressure Mainichi step even more eventually get to a to a bcc phase it's known for her and for opted future and so on In looking at that which had an Istanbul why is governing what structure forms as a function of the shape of the particle the thing that really screamed out to us was that the particles I mean we know that the particles are trying to maximize entropy to minimize free energy because there is nothing else to maximize entropy means you want to maximize the mayor free volume in the system and what we could see here that the particles all momentum to maximize the alignment of the biggest faces of the particles because by doing so it's like it's like on saga on steroids so instead of rights coming together having line to get more translate give a petition for translation of the century feature coming together or or the trunk Institute coming together and they're aligning on their faces to create more wiggle room more free volume on in the system and that's what's governing what's going on so that we got really um eager for some and we we embarked upon a much bigger study of my student Pablo shotgun Damascene I decided to take a shotgun approach at this he went mathematical and supports of what 1st 145 shapes and Mathematica so he he studied all of the all of the other Platonic solids all of the Argentinian solids and their duels the Catalan sellers there 92 Johnson solid Devinney picked the bunch as only he dropped presence in presents for good measure and each 1 of those we did a study like we did of the teacher uterine cancer OK as we increase the density would we get would look at two-year phase transition if we do a kind of structure we see there and just a giving examples so out of 145 particles 101 of them self assembled into a recognizable all structure Peter justify a few of them we get things they're like your typical SEC BCC simple Cu structures we also get along at the bottom of the liquid crystal type structures where the particles aligned in either and some over on the Mac phase ,comma pointing in 1 direction or some suspect equated phase or even discarded typefaces on but there some of them and I went out of 1 a highlight those spell blown up here I'm from Joe Dickey he dry and truncated augmented DOE data he drowned bear-like structure that formed the beginning any structure with 20 particles in the unit-cell or gamma brass with 52 particles in the unit itself I mean I'm just amazed at these things figure out of form crystals with such large unit sells due solely to entropy it's not them something that I would have anticipated by you know years ago before it before starting from this project on any particular structures that typically you need of multiple types of Adams like like gamma brass up to see we even got to a deck Capital Plaza crystal the deck at the Plaza Crystal was always on -minus able to face a cubic so we have a liquid which I would come this beautiful structure and in the lower right out of a decade so we watch out for a while and it would spontaneously Chris Lysaght Kinnock because that's the lower free energy or higher entropy state but the
system now some of them crystal structures that we found have been validated have been found by various groups object Americans group arm has found a number of the simpler structures are trying to get some of the more complicated structures even without Chad's DNA programmable simply just throwing hot particles are in solution also paid on gangs group has has reported this on high-pressure lithium phase in up to Huger but using depletion interactions which is another entropic force that will will talk about and I'm in just a couple minutes into the search is on for some of these more complicated structures were trying to see how complex can we can we go with that having all this data allowed us to start to see trends I am so we could grip things together so we grouped in together into all the liquid crystals and all of the and all of proper crystals that we saw and in the end the upper right-hand corner you see on 66 different I'm crystals that we call plastic is there there's a rotator faces meaning that the particles self assemble into crystals were the centers of the particles are sitting very in an organized way on the bottom line of sites of some of the some crystal symmetry but the particles are free to rotate around and that that rotational entropy appears to stabilize these crystals in other words if you would stop them from rotating in some cases the crystals fall apart into the rotational that that gravitational too generously is critical in stabilizing these these kinds of these kinds of crystal crystal structures so at 1 of the things that I found most surprising about all this is that when we looked at we took all of our crystals so 101 of those form crystals but that means that 44 of them they just did not form crystals no matter what we did it doesn't mean that they can't just kinetically they just they just didn't but if we took all the ones that form crystals and we looked at in the crystal phases said OK what's the coordination number Of the latter that's like asking what surveillance of the particle and then lease we plotted that and then we said OK now if we go back into the fluid or any diffraction pattern which show you nothing on bonded diagram shows you nothing no correlations it's just a fluid and I you ask what's the coordination number or valence there replied that we found a nearly 1 2 1 correlation between the valence the effect of plants in the fluid and the crystal meaning that already in the fluid that putt that the there's of a type of emergency valence due to shape that's already dictating what that what Chrysalis going on to
form and so if we look further we could see that there different classes of shapes there are shapes where the acts a lot like metallic bonding systems is the ones that make a really complex big large unit sells like beta manganese and all of those are rotation are a rotator crystals but we see ones where there at their like covalently bonded systems and instead of being in that having 1 of you many many facets they have some really distinct large facets that control the coordination number and see others that like molecular liquid crystals arm and form these kind of molecular liquid-crystal smacked a nomadic and and and Kolomna faces I and so what we want from this is that shape entropy creates a valence them off for magically minutes at their atomic and molecular counterparts upon crowding so how do we quantified this I don't don't know what the right way to think about what's going on here is that if you were to grab any nearest neighbor pair particles in the system they're all moving around by Brownian motion on and that there's a sea of other particles around them and sea of other particles around them is imposing an arms might pressure on those 2 particles and there's a competition these 2 particles on their own 1 have as much wiggle room as much free volume as they Katsav overlook it like a pair of the truncated purple to appeared orange kids they won't have is not much wiggle room as possible on the other hand the closer they get together the more free volume there is for everybody else in the system and those to competing in terms can be quantified by writing on basically a potential Amin forced toward this is the standard some kind of constant that's that's used in in in colloidal arms systems where typically you write it down you have to bear interaction term arm in which all year intrinsic interactions between the particles would be would would be put the here we don't have any word saying these are just hot particles we got rid of all that their intrinsic interactions we just have steric interactions and then you can you have this other These are the combatants the competition between these other 2 terms accounts the number of ways that appear particles can be range relative to each other and for each 1 of those all the ways in which you can arrange all the other particles in the system and the reason why I think by writing this down is useful is it gives us for the 1st time a tool to quantify just how strong is and is 1 of these entropic bonds in the system I'm so here is an example from taken from this truncated Tetra he system that's truncated still enough to form but none of 4 diamonds still wants a former closet crystal but we were counted so so it's 1 of these very dense fluid states and in stands fluid state we we just take a pair 1 pair that's next to each other we see what's the difference in free energy of the system between the pair being aligned along their faces were pointing like best and that's what's shown here the difference in free energy is 3 Katie that's big that puts this emergent and Tropic action and this is all this is still in the fluid phase this puts this piece and Tropic bonds if you will of the same importance numerically as hydrogen bonds or vandals interactions or even some screen electrostatic interactions of system so even in the presence of other interactions it's important to be able to quantify the role of entropy in contributing to order in your system rather than disorder in your system now
when we look at our systems worked were we were typically thinking in terms of we have a bunch of particles and therein some solution which we just imagine is imparting Brownian motion to the particles I would just confining them more and more to make it dented cancer but there is another and tropical force that is closely related which is typically thought of as a depletion interaction and that's where you have colloidal particles in solution and in addition you have the 3rd component which is a much much smaller particle or a little polymer molecules something that maybe for a 1 micron-sized political article might be 15 animators and something in diameter and the more Of these little depleted particles of depleted molecules throat you throw in there and those are the more likely you are to see to get an effective attraction between the big colloidal particles and the way they think about it is it is in this way every 1 of these the big colloidal particles has an excluded volume region to it and it it then and that takes up some some volume where and where you don't other particles can go and then you have think about all the microstate available To although depleted molecules in the system there's a gazillion of them but if the colloidal particles come together then all this and it frees up a little bit of local free volume that is now available to be much much tinier particles give you many more Mike estates for the particles making it very entropic be favorable and so that is what's behind the depletion interaction and it produces an effective as pressure of the deplete molecules on the particles than the big particles holding them together so that's another example of entropy ordering things this system so we're talking about are related to that on it said that we don't have to pleadings but imagine that the little deplete and are now the original not the particles themselves in question had many many fewer of them to the factual depletion interactions can be much much stronger but still the ones that were seeing a very very strong and and can produce ordering in the
systems and you can find everything you ever wanted to know but were free to ask about college and the depletion action in this textbook of course from I think like a Kroger and on Tonya which I'm not saying that properly all of which is a beautiful you know treaties on collagen and the depletion
interaction and so will we try to do is pull together what is known about the entropic forces from depletion interactions in Tropic forces from these purely hot particle systems from what uncertain from Socorro cell and put it all within this 1 generalize framework that makes it possible to think of these things on in a similar and in a similar way and allows us to connect a lot of the workers from all of these wonderful Dutch physicist some of which are here with us today I'm like whereas the relevant runways admitting mentioned yet and and Alfonse warm-blooded and in the woods studied various other examples of on entropic forces in some in colloidal systems due to depleting arm and and other types of problems and so on friend mentioned that without my group has worked a lot on on patchy particles in the idea behind it is trying to understand how can we designer nanoparticles of coal Lloyds which interactions such that we could get them to self assemble into structures that we've decided that we want a priori what we can do now with shape is that we can now understand how even in the absence of any sticky patches explicit sticky patches we can put shaped into particles and get effective sticky patches that can help too get the kind of order that you might want come in your system
so I want a close just a couple of examples of how far we think we can go with and should be just justice to use very recent things
and so so you might think well if you want a target crystal structure why not take the crystal structure and find out what it's born sell it right so you can take any crisis section find out what what is the the the water celebrated some crystal structures will have multiple warm ourselves there's multiple Wyckoff positions to consider arm and so then imagine you know with the warmest sellers who you know already by construction in the limit of infinite pressure they have to fit that together like a puzzle to give you space structure natural lattices started with so what if you could make particles in the shape of on ourselves and throw those in water can find them in the face self assemble and what we find is that sometimes that works what we find also is sometimes that doesn't work and sometimes you get a totally different days and it seems to be related to the cemetery like the highest amateur particles work in the lowest symmetric particles don't work but 1 of the things that jumped out at me that I just was up just amazed by listen some of systems where you have 2 types of ordinary particles and you know that they have to be offered in the final structure you take those 2 types of water particles used from a box and outcomes like in this case the target structure that started with but there's occupational DeGeneres C In the positions of former particles so that the word somehow entropy maximization and the shape of the particles are enough to give you the structure you started with but without everybody in the right position so that's something interesting that were still looking to figure out what we're really excited to see this recent paper from off ensemble utterance group where they figured out really clever way to start with spherical particles and grow them in a crystal in such a way that they formed the Voronoi should be adopted Warner shapes of the of the crystal structure that date that they started with that they want to have and so we think it is light particle shape approach might be something that's viable In the
future my friend Mike my friend and colleague Makoto often Michigan and I have done a lot of work where we study his low-caste Tyree cats so my particle sometimes mixing together with proteins come and over the past couple years we've been setting a specific system of highly Polly dispersed nanoparticles that self assemble and their charged all like charged particles also Havana was interactions and instead of forming the crystals a larger wanted structures they come together for myself many many many myself in each 1 of my cells is basically exactly the same size with several hundred nanoparticles in them they adopted Kaushal structure With with the war by size in the nanoparticles and once they got to certain times they stopped and put another nanoparticle merit doesn't wanna touch the forces completely balanced because of a charge renormalization that goes on during jury duty during self-assembly due to the screening of the of the interaction by sold in the solution and what's amazing is that the structure of those supra particles that form is so good that those big spheres out crystallize into an FCC arm Cuba crystal and that's shown in the in the tedium micrograph but behind the cartoon images of from the simulations on business nice order crystal so we can and and and at that point the those big spheres are organizing by entropy you know just like it myself from surfactants systems original other interactions uphold those those fears come together
into spheres just in this month's the issue of Nature Materials from there's a beautiful series of papers there's of that there's a especially beautiful paper by Alfonse bombarded on and off and airline Dykstra showing what happens if you you have to take a hard spheres they're going to crystallize FCC like we saw what they showed is that if you can't find it so that it you inhibit the spheres from adopting the FCC crystal and promote the natural tendency towards local Polly Tejeda a local icon the Hugel ordering of this fears that you can actually grow and and I cast a huge Hugel crystal look at it periodic crystal that cost symmetry and passing out too about thousands of particles which is much bigger than anyone thought you could do before and that's due solely from duty due solely to entropy and on the close with an example of
something that we haven't gotten yet from entropy but which were hunting for that I'd leave it as a challenge to the students oppose such an audience of to think about how you might do this is I mentioned that that's for most of the day no 1 Plaza crystals are icons dueled full three-dimensional I'm quite a crystal so their quasiperiodic in all 3 directions to get all the soft better 1 so far are playing so in the same issue of Nature Materials reported on the 1st computer simulation of a concierge requires a crystal which we got not ships entropy but by .period particles interacting with a short range totally isotropic potential and 1 component stocks already we're increasing unexpected that you don't have the multiple components you'd only long-range interactions and that you don't need multi by many body terms which might give you angular correlations angular interactions and but what we are we but the but that so far back that is a classic crystal that is energetically stabilized to OMB and requires an explicit intrinsic interaction and so were thinking about what kind of shape you might be able to make that could self assemble into structure of this incredible level of complexity where this structure the nearest classics the the nearest crystal periodic approximate OMB we can rule out with 5 10 thousand particles in the Indian it's also something we have to be bigger than that so I think that is a puzzle to you and I am now and there and thank you very much of the opportunity and for sticking around so late in the day thank you Hi


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