[00:00:16] >> Ok Thank you David for the great introduction and it's a real pleasure to be here I've been in Atlanta a few times for meetings but never at Georgia Tech. And so I'm going to talk about our work more we're simulating actually a lot of the experiments that one of your faculty members you know on jaw has done and so you'll hear his name a lot in this some an hour and we're really grateful for our Whoops I always do this. [00:01:21] For a sponsor and lots of computer time which I'll get to that I don't even have to talk and so our Roark is this project is on now to materials and my group and many of you here know they can be beneficial. Especially if we can control their sizes and shapes and there's many examples of this there's a few I'm going to highlight here and later in my talk and there's other ones but they can be active in selective catalysts and it turns out by changing the shape and these are copper nano particles so they could be cubes of wire plates or this is just not no. [00:02:04] Upper you can control. The selectivity of this Apoc sedation this is a pox side hydrogenation to the cysts or trans isomer selectively depending on the shape of this copper crystal that you choose there's a very prominent chemical engineer salutes the Nicky's at University of Michigan who's written a very nice review in nature materials actually I didn't update the slide but since the sea at the 2nd review talking about the benefits of nano crystals in photo. [00:02:46] For solar fuels and Inferno voltaic because of how particularly Silver and Gold Act interact with the visible range of the solar spectrum there are these people call them solar and tennis and they really can enhance the efficiency of the ruble Taya and this is a very nice paper some years ago but I don't know a few years after it was published it already had thousands of citations so I like this paper and a big point of our work is that processing conditions can make a big difference in in shapes and how you achieve them and it's not so well understood how processing conditions work and that's a big part of our research and this is just an example for titanium dioxide and anatase which is aggregated in a way called oriented attachment which is a fascinating topic that we've worked on I won't talk about it today as much higher electron transfer rates than if you get some uncontrolled aggregate and so it really can enhance the. [00:04:02] The property. Ok so a big part of my talk today will focus on the so-called one pot solution phase synthesis of metal nanocrystals and a very nice Will these are 2 very nice reviews in particular the 2nd one by your colleague you know and John has so many citations of an it's a very nice paper that's why and so here we have the pot we have the Earl and Meyer flask I had to remember my chemistry from so long ago and into that pot they put a few ingredients. [00:04:39] Some of it metal salt. Capping molecule and sometimes other additives and we'll talk about what those might be later and they heated up and then out of the pot depending on the relative concentration say of metal salt and capping molecules or metal salt another additives they can pull out all kinds of nano shapes and these are really just a few of the shapes that fit comfortably on my slide. [00:05:13] Here we have we have cubes we have octahedron we have Kubo octahedron these beautiful fivefold twin pentagonal nano wires which I hope to get to at the end of my talk plates and even more shapes than this and a big question so Ok until until maybe recent years this was very much of an art synthesizing these particles and and to make it a science you think is a chemical engineer you want a process and you want to scale up the process that you really should understand you know what goes on in the pot and so this is this is what drives our research so we were interested in what happens in the pot and of course in general terms people do understand. [00:06:04] What happens in the pot and they can all point to these very nice reviews. And so the synthesis I'll talk about in the 1st part of my talk involves the metal salt and silver nitrate the solvent is ethylene glycol the p.v.p. is the cutting molecule we have no other additives here and so what happens in the pot is you know you start with the salt and it's reduced somehow someway or maybe by the solvent and then you have a nucleation of you know a neutral and maybe charged over will aggregate and make small nuclei. [00:06:46] Which grow to make seeds and the seeds are you know statistically single nanometers or they could be bigger and then once you have a seed the shape of the seed together with this capping molecule will determine the final shape that people grow and so for example these these are shapes that people grow with p.v.p. So if you start with a c. that's single crystal Kubo octahedron all you'll get a cube if you're capping molecule was not p.v.p. but it was citric acid it would tend to grow in octahedron cluster if you start with this decade he drawled beautiful multiplying twin particle you'll end up with a you know a nano wire or a nano bar and if you start with nothing you end up with nothing Ok. [00:07:37] And so. The adage here. In that growth that's the Scylla tended by the capping molecules at least when we started is that nanocrystals expressed the facets that most strongly bind capping agents and we began working on this project it wasn't even 10 years ago like not 89 years ago we started working on this project and. [00:08:03] We said Well that sounds really nice but there was not so much or maybe very little direct proof of this and so the 1st questions we asked can we predicted that could we figure out a way that people could control that because even today these these synthesis are not so selective as people would like them to be and then could we even go further and exploit our knowledge to make other structures. [00:08:30] Ok so now we're going to get into. The challenges people face if they simulate on the tour Ok so it's really a balancing act and here Ok quantum mechanics is a very accurate way to describe these systems but really only small systems and I'll show you about how small. [00:08:52] And then if you want to go to large systems which would be like trying to simulate the synthesis environment with so all the ended capping molecule and additive and metal and salt you need accurate statistical mechanics which you need a large system for that and so some years ago it's more than 10 years ago but I believe this extract elation to still be fairly accurate this is what we're showing here is the number of atoms you can probe as a function of year with different flavors of quantum mechanics and so people think quantum mechanics is just it's all it's the most accurate is the most accurate but the exact quantum mechanics the configuration interaction today you can't even do 10 atoms Ok and then we're going up to approximation so this is what many consider the standard couple cluster and you know you can't quite get to 100 out of this here and then we go to more approximations this is what most people use and it's what we use. [00:10:02] Density functional theory where we can get into thousands of Adams of most people don't but you could I think if you wanted to but you get into this gray area up here which Martin had Gordon who wrote this very nice. Paper because the region of molecular complexity and this region would apply to problems in biology I just put this this is our problem material synthesis and processing soft matter assembly. [00:10:35] Not only do you need to have a very large system but to have accurate statistical mechanics actual accurate sampling you know get all the confirmations of a protein you have to say ample of that like millions and millions of times to have you know an accurate ensemble our fruits and this is quite a quite beyond what you can do with quantum mechanics today. [00:11:02] And so you have to make an approximation of what many people do as they have something called a force field it's a classical function that describes many of the configurations that people see in quantum mechanics and you hope that for the ones that you didn't fit it to it's still accurate. [00:11:20] And so if you look at people's devil demons in this area if you're just doing quantum mechanics you can say alright I used a huge amount of computer time how relevant if I calculated one little energy barrier or one little configuration how relevant with this to the problem you know the big problem I was trying to solve or if you're on the other end and you you know you've You've extrapolated quantum mechanics using a force field you can say But I use so much computer time but that wasn't very accurate or how accurate was it how good was my extrapolation and so a big a big challenge that people face when they do material simulation is you know how do we have the long time actor in the last hour John sawmills that we can get accurate statistical mechanics with the accuracy of quantum mechanics and so I'll talk about that's a challenge we face and you can see how we solve that challenge Ok. [00:12:25] So back to. P.v.p. we started when we 1st started working on the system you know not even 10 years ago we said Ok this is what this is what you know you could put dot dot dot dot dot dot This is what the backbone of p.v.p. looks like it's and I'll kill chain with the. [00:12:46] Rings hanging off the side of it and they're there random probably the way they have them in experiments but I made it Cindy a tactic here and most people would agree that the active part the most strongly interacting with a silver surface would be this prolly don't ring and so the 1st thing we did here is we used density functional theory and for those of you who do it or I know David students or the 8 Medford his students maybe do this is you know we used a code called value which is a plane wave density functional theory calculation and we did Vandar walls corrections and we looked at the interaction of this tiny little ring of the polymer with a slab of silver and we did this. [00:13:44] For the 111 surface of silver and the 100000 what we can do with these calculations is we can have many different starting configuration of this ring and we optimize the geometry we find the minimum for the local minimum energy that we get from that and you can see here for silver 111 we found 5 can think you're ations and for silver 1000 this surface we found 4 configurations and for each of these configurations what I'm showing is the binding energy the total binding energy. [00:14:22] And then we can think that we can partition this total energy into 2 components the short range interaction which is what is traditionally given you alluded by a quantum calculation and at the time we started the the field has moved very quickly since but there's the Vander wall component which was new when we started this calculation in fact we had a collaborator who modified the vast code so we could do these calculations. [00:14:55] And so you can see here the short range part this is direct bonding or electrostatics or Paoli repulsion. And you can see and then the balance is the Vander wall and you can see that most especially on the 111 surface this interaction is mostly dominated by vendor walls but there is a stronger on component of direct bonding on the one to surface. [00:15:19] And so you can also see that across the board. That the interaction on the one or 0 surface is stronger than on the 111 not by very much but it is stronger and this is consistent with what experimentalists saw that you know you put p.v.p. and solution as I showed earlier and you can get these 1000 faceted keeps Ok so at the time we said we can make a making reasonable approximations for the partition functions we can make an equilibrium constant for this molecule to be on 10 or 1110 just remember all we have is this ring we don't have a backbone we don't have sadly we don't give you the polymer but still we said Ok Will each of these rings contacts the surface there's this poor Aleisha number and we're looking at the difference at a temperature we care about. [00:16:16] And if we plot this as a function of the correlation number we see that you know the more segments we can get down in concert on the surface the stronger is the selectivity and we took as the characteristic length something called the coup length and polymer science and it turns out in the Saul than they care about here ethylene glycol that coon length is about 4 to 5. [00:16:45] And so for that we get a very high selectivity and at the time you know this isn't so long ago this was consistent with the experiment that p.d.p. promotes one who keeps And so we are very happy about the move and but then we thought Ok that isn't so satisfying right because as I said we don't have a polymer we don't of saw all that. [00:17:11] And it doesn't This only says it's consistent with what everybody said but how does it how does p.v.p. really work and so we asked more questions so how did capping molecules work well there's a lot of different things they might do most people agree that they cover the crystal and they protect it from random aggregation. [00:17:33] They might direct aggregation as I've shown here so if they selectively bind to these facets they might aggregate on the unprotected facets they could also alter the surface energies of these shapes and so the will shape in material science will just in general it's the shape that minimizes the surface energy of a crystal and. [00:17:58] By binding selectively to one facet or another these capping molecules could change the interface will free energy of these facets and change the wolf shape and that might be why you get a kid who are another thing they could do is alter the fastest growth rates and so as I have. [00:18:16] Shown here if these facets are protected than maybe atoms will add to these other facets and then you can get the so-called kinetic will shape and so to answer questions like this we really so density functional theory it's not in solution it's in vacuum it's a desire of Calvin and we need to get out of the vacuum to answer these questions and so the way we do this is we have fit our density functional theory results to a force field and this is the so-called metal organic many body force field. [00:18:53] You could call it Mom and actually this this 1st field debuted at a talk that I gave it a conference on Mother's Day And so then it was mom and some said it's mom. Like you know whatever. Someone at the conference said that's a better thing to call it but I won't talk about it if you will I mean I can in the questions but this is my students actually this was a post-doc and this is the paper describing it so the idea is we get a lot of configurations of these rings and we fit in empirical force field and one thing you want to do is this is the d.f.t. energy of different molecules of the force field you one tacked to fat on a line with the slope of one and no intercept. [00:19:42] And then you can really do large scale So we're we have silver we have capping molecule we have solved it and then we can do large scale and decent mill ations and hopefully learn more about the system so we did this. And the question we wanted to answer with this and there were others but this is the one is one posed by you know on John's group actually and what they did was they they grew a over Cuba 1000 faceted q. and they say. [00:20:16] Solo that if they put that cube in a high concentration of p.v.p. and grew it further it remained a cube but if they put it in a low concentration of p.v.p. and grew it further it over from a cue to a cue ball octahedron to an octahedron which is all 111 facet and we wanted to know why this was and so if you think about how these things grow there's there's 2 processes there's deposition and there's diffusion of the atoms around the surface and so you have thermodynamic control if the fusion is very fast on the time scale of deposition because then the atoms can arrange themselves on. [00:20:58] The minimum energy facets and if that's the $1000.00 and you get a cube you know that's great. Where you can imagine kinetic control and that is if deposition is faster than diffusion around the surfaces and then we get facets with a slow growth 3 that those are kinetic shapes and so the question we wanted to answer is which is it of these 2. [00:21:25] And so. We start actually we I'm presenting this backwards I think it just makes a better story we really started with genetics but Ok let's look about the thermodynamics so in thermodynamics we want to predict these roof shapes of crystals in solution and. So the thermal this is a very nice paper describing the wall of construction is very old the one by roof isn't actually in German so I recommend this one unless you speak German Maybe the need it and so basically the idea is Ok we have some shape and the distance along with this vector that goes from the center of mass normal to each of the facets normalized is equal to the normalized liquid solid in your facial free energy and they should all be equal for every facet in your crystal this is a shortened version and so if I have a crystal that could only have 2 facets run $11.10 I can make a wolf construction without doing any calculation and you can see in this range on this gamma 111 is smaller than gamma $100.00 or less I'll have the not the heater and. [00:22:47] What happened. My pointer died Ok and if I have I have a other pointer and so if I have the opposite case I'll get a q.. Here we go. Yeah Ok And and so then the idea is to calculate these inner facial free energies and predict the wolf shape. [00:23:16] The whole thing died Ok I'm going to have to just stand back here I got us. Ok And so we used a technique called thermodynamic integration to find these inner facial free energy. Ok so the idea is we still we have an initial state that's a liquid solid interface and we want to divide this into both liquid and bulk solid. [00:23:44] And the the and the difference between the free energies of these 2 states is the negative of the liquid solid in her facial free energy and so to calculate this we want to design a reversible path that takes us from the state to the state and this was done by a very talented grad student Sion she in my group. [00:24:10] And so we have a 6 step path whereby we and the idea of having 6 steps is really to achieve this transformation reversible plea Ok so if you go from the final to the initial or the you get the same answer with no history recess. And so whoops and so so we insert the wall we turn off the liquid solid interaction which is something you can do easily in a classical force field then we have basically a liquid with walls around it in a solid which doesn't need walls but it has them anyway and then with the liquid we we get rid of this extra space we take out the wall so we have bulk liquid we get the periodic boundary conditions back and here we put in this ghost solid and we slowly turn it off and we get solid and so the interface will fritters as the sun the free energies of all these steps divided by the surface area. [00:25:17] And so the result of this calculation showed Ok so what I'm showing here is are the interface will free energies of in Ok in vacuum of server 10 in silver one with just sold in ethylene glycol with half a layer coverage of p.v.p. and with a layer of coverage of p.v.p.. [00:25:41] And so when you can see in every single one of these cases is that yes savage p.v.p. lowers the in her facial free energies but we always get the same shape which is a truncated on ought to Hedron is that shape and so this was the negative result which told us that so far nanocrystals aren't they're not thermodynamic shapes and we've done further work with a colleague who doesn't spare moments they're not they're not kinetic she I mean they're not thermodynamic shapes. [00:26:16] And so the reason for the is. So if you look at the free energy change of each of these steps you can see that the solid vacuum surface free energy dominates the in her facial free energy this is the liquid solid which mitigates that and it is more selective to the $10.00 but it's not selective enough to change the stiffer incidentally appreciable way. [00:26:41] And in this paper we did ask the question was how strong does it have to be with just a phenomenological model of capping agents and what I'm showing here is the binding energy selective 821111000 and for each of these the scale gives this relative surface energy of one more $1.00 to 100 and what you see is you have to have a highly highly selective binding energy here to be able to get at a cube and. [00:27:13] Yeah it just and also just to say our model that some people's experiments. Ok And so you need a strong one so we went to Kinetix Ok And so now we worry about the kinetic shape and this is a nice paper by Alex charnel and he is still alive today. [00:27:36] And so here we worry about linear fast growth rate so this is the pile up of out of on a facet and so a thing about crystal growth that you may not get at 1st is that say if out of this pile up on this facet they grow the neighboring folks so you won't be as confused if you remember that and. [00:27:58] So basically the kinetic roof construction it's just like the thermodynamic or roof construction except we replace the inner facial free energies with linear facets growth rates. And we predict the same progression of shapes with the kinetic with construction and linear facet growth rates as we did with with the with the thermodynamic Wolf construction and one thing that I found intriguing is like Ok so we then we equate in this work the the linear facet growth rate with the flux to the surface Ok the flux to 111 versus the 100 surface and what I found intriguing is you don't really have to have a very big difference in flux in order to get a q. And so then we calculated. [00:28:54] These fluxes using a technique for free energy sampling called Umbrella sampling and I can explain umbrella sampling to you in the time we have because I want to talk about other things. But let me just say this is the plain vanilla of free energy sampling. No it's not as fancy as some but a lot of people like vanilla. [00:29:18] And we like the no law. So Ok so what you can get with umbrellas sampling is something called the potential of mean force and this is the free energy profile of your system that's a silver out of goes from the solution. There is solve it here and show it through this p.t.p. capping layer on silver 10 in silver 111 down to the. [00:29:45] Down to the surface and when you can see are several features on here 1st of all way out here you see that on the 10 it goes down a little slower than 111. That's because Ok this is non-technical but the p.v.p. layer is a little bit fluffier on the 111 facet because it blinds less strongly and this actually these these tails hanging out into solution facilitate trapping of silver atoms out here. [00:30:18] And that favors structures with 100 facets we also see here we get trapped in the film and we have to get over this free energy barrier to get down here next to the surface and we carve out the whole opening barrier because a whole has to open up in the p.d.p. film for the atom to get down here and we can see that that barrier is just a little bit lower on 111 that it is on 1000 and then we see that you know the selective binding strong binding actually down here. [00:30:54] On I think I skipped them but it doesn't matter on the one who facet and. This tells us right away that kinetic should favor one over facets and just a kind of back this of this. There we go and so just just to back this up this these are the density profiles of segments of p.v.p. on 10 and 111 and you can see on 1000 we have a higher density close to the surface 111 a more extended film neuro density out here away from the surface and this protects the want to a facet and this facilitates trapping of silver atoms in solution. [00:31:39] And so to calculate the mean 1st passage time we saw this is a very nice review article on this we solve the smaller calloused actually don't solve the smaller callous you equation one would solve the smaller callous good question to get the mean 1st passage time and so basically the mean 1st passage time is if I start here what's the average time it would take need to get down through this film to the surface and bingo. [00:32:10] Now what can happen is you know instead of going so so the solution is for what's called an absorbing boundary here which takes the atom and a reflective boundary up here and so the atom could also go in dissolution and diffuse forever and come back and absorb and so we can set this this the height to mimic the concentration of silver or ohm Celt actually in solution and so when we get the mean 1st passage time the flux is inversely proportional to that and that's what we did and these are the results and so one thing a so what I'm showing is the mean 1st passage time on the 101111011 surface in just solvent and then p.v.p. of different lengths and at different coverage. [00:33:04] And one thing I thought was really kind of amazing is that in just soil that we expect slower growth that we do with capping agents of capping agent pools the atoms down to the surface that we did not expect. But then we go to the p.v.p. what we see is across the board no matter what length we have our coverage we all we always see a shorter time to get to the 111 surface than we do to the to the 100 surface and we've we've we've partitioned this into a diffusion time to get to the edge and then the reaction time to get to the from the edge of the film down to the surface a bit across the board it's on higher to 111. [00:33:55] And basically we can we can look at this ratio as a function of p.d.p. coverage no p.v.p. you know around half coverage full coverage for Forum 3 different sizes of p.v.p. and what we see is that if the p.d.p. is long enough and if the coverage is high enough we're predicting slightly truncated keeps. [00:34:19] And so this says that the experiments are consistent with kinetics and I'm very happy to say that very recently my colleagues Morag Rio and he worked with my other colleagues Scott Milner. To actually measure equilibrium constants for for p.v.p. a direction on one all in 111 facets and they came to the same conclusion as us were very very happy about that. [00:34:51] Ok So to conclude this part of the talk I'm glad I still have time p.v.p. is an effective capping molecule because it controls kinetics and it does bind stronger to the one who will sit as you know said many years ago. But that effects the flux of of species to the surface. [00:35:14] By having a strong higher density near the 100 than the 111 and having these trains hanging out in the solution and maybe a 2nd thing is Ok while this was a negative result on thermodynamics we do have a new tool for calculating liquid solid in her facial free energy and it also showed that you really have to have a very selective. [00:35:41] Affinity for a particular facet to get a thermodynamic shape Ok so I'd like to change gears actually still we're talking mostly about silver in this part of the talk on by the like to talk about 5 twinned. Nanowires which is another shape that people make out of silver and they make it with p.v.p. in ethylene glycol but they're And so this is what they look like they had this pentagonal cross-section with long one almost side facets 111 and facets. [00:36:14] And the f.c.c. geometry of these models is not space filling if you put these 5 sections together so the you have strain to make these spit so the wires are under tension or and I should say under tension there under strain it's a very complicated strain profile. And so that fact has led people to look at their reactivity for cattell says and there's at least one review article that I know of one on that topic and this strain and their and their shape also gives nanowires 3 other properties that are very interesting for applications one of them is that they're flexible so this is I think this is this is copper of these experiments and you can see how these are bent they didn't grow like you can you can really flex them like that. [00:37:12] And this makes Well that's one thing that makes them. Attractive for touch screens and also their optically transparent at this diameter which also makes them attractive for touch screens and the other thing is so and actually in today's technology server not all wires are used and touch screens for smartphones and so the 3rd thing is that they have high conduct of the Silver does but if you want to invest your money people say that the future isn't copper because it's cheaper and it's more Earth abundant than silver So there's a lot of research and the copper and zone Ok so these are fascinating talk objects I think so because we work on them anyway I just think they are. [00:38:01] And so they grow them in the same way like this one pot poly all solvent metal salt capping molecule other additives. And this is a paper by you non shock we're the world growing so over wires so here solvent ethylene glycol the metal salt silver nitrate. Capping molecule p.t.p. and other additive is in this case bromine or bromide and depending on here the ratio of p.v.p. to the salt water the ratio of salt to bromide you can see that you can either get with a no pro-life kind of fat or wires with lower aspect ratio single crystals were finally out here very long nanowires with high aspect ratio which have better property this is what people want. [00:38:59] And so my talk this part of the talk. Will mostly focus on the case of no bromine but I will have one plus slide on this topic. Ok So again people your colleague you know on had an idea about how this should happen and basically the idea was that p.v.p. should selectively cover the 100 facets so that I have a flux of atoms goes to the ends and that will grow along nano wire and so we believe that this is the case and so this is my of one slide up here. [00:39:41] When you're growing Ok now the solace copper you're out include ride and the capping molecules hexadecimal of the. And so this is recent work we did with Ben Wiley's group at Duke and this is a density functional theory with veils and what I'm showing here is the copper 1000 surface and 111 I have point $25.00 monolayer and so point $25.00 coverage of chlorine and what I'm showing here is hexadecimal mean so it's just an alkie all tail with like a and a mean at the end. [00:40:19] And each to group and you can see that the I mean form self assembled Monna layers and here I'm showing a top down view the green of. The green is chlorine and I'm just showing the nitrogen of the anine here just to give you an idea of where it is and so you know what low coverage of chlorine we see that we have self assemble layer on both surfaces. [00:40:47] If we up that coverage to point 33 layer we see that here on 1000 We still have a soft assembled layer but here on 111 I made this light blue to signify that the a mean has left the surface some the layer has left the surface. And as I mentioned earlier d.f.t. calculations are done at 0 Kelvin and in vacuum and so these can float off in solution but what we think happens in solution that non-zero Caliban and solution is that these would happily drift off into solution and join a myself. [00:41:24] So there is this regime where we cover 1000 we don't cover 111 and then you get high enough coverage you don't cover either surface and this match very nicely with Ben Wiley's experiments where at very low coverage on you they get these you know not well shape copper particles in this regime they get wires and in the in the high coverage regime they start getting wires but after some point they grow thicker. [00:41:57] And that this is the subject of our excuse me most recent work and so not only did they do these growth experiments but they did electro chemical experiments and maybe to just distilled this so this is the current density at the mix potential and so down here there's there's no read ox chemistry going on at the surface and up here there is and what you can see is that on the one a low surface is passive aged for just a higher range of chlorine concentration than 111 and this matches actually nicely we could correlate this with our Like the distance of. [00:42:40] Of the nitrogen from the copper surface and so. Up here where they're activated h.d. is fizzes or been away from the surface and down here or there possibly that it's chemist or been making it very difficult. And we can do something called ab initio thermodynamics and get as a function of the solution phase chemical potential of h.d. including regimes where both facets have h.d. a design worked selectively does the work on 111 and a derived on both and you can see there is this region of selective desertion and we think this is very important because this is the Cooper us on that they think is coming down on to that surface it's very very big and so it can come down affectively as we showed in this paper if there is nothing on the surface but if you're passive aided with a self assembled layer that's very difficult. [00:43:44] Ok So that was my one slide now I move on to the case with the 9 and we went back to you know on Jaws original idea that it's our kinetics and then the 1st part of my talk I did discuss. The flux 21001111 surfaces and in that rock we showed Yeah that flux is sufficient to give us cubes but if you translate that So this is the kinetic move shapes you can get as a function of that floor for wires and you can see this flux ratio will just give you a stumpy little wire and so. [00:44:25] It doesn't it doesn't predict the wires the flux and so we look for a solution involving out I'm diffusion that's the other thing we have. So so much for that. Now we go to chemical engineering like your 1st Kenny class right material an energy ballots fasten a ballot the linear fastened growth rate is the accumulation of atoms or 111. [00:44:53] They accumulate by deposition and when atoms come from the one or facet to the 111 and it and it takes down the accumulation when they diffuse from one 211210 the same for the other facet. And about these terms from experiment we can because they measure d.l. over d.t. of this wire we can estimate the deposition rate. [00:45:21] 10 to the minus 4 seconds per deposition and so then we want to know about indoor facet growth rates and I think I'm going to have to accelerate here a little bit. And so we do this by 1st figuring out where what grows here is the seed and this is what everyone would tell you the seed looks like something called an no deck a Hedron So we took 300 embedded out a method it's a it's a way to describe silver Adams 300000 we're new with it and we got something that looks like this and this is what's called a marks that he drew. [00:46:03] And we're happy that this looks like people's experimental Kras So so this looks more like this than that right you can see that. And if you look very closely you know we have this 100111 notch here at the edge and not only that but we have a series of steps and we try to figure out what kind of facet that is and the lowest energy gave us this $11.00 of facet. [00:46:36] And so this is what I hope to describe because I teach this in my graduate kinetics class it's part of the broader impacts on my National Science Foundation grant and so the theory of observing Markov chains at least the Penn State everyone likes them they all get it within 2 lectures. [00:46:54] And so you can save the master equation to get the needed 1st passage time but an ad deposited on any one of these sites so this is an example to get our 10002111 so any of these sites to equal probability will the average time it would take it to diffuse to the 111 facet and here we define transience states which are like life you know you go from state to state to state and eventually you end up in an absorbing state which is like Def you go in I don't know what who knows what happened really no people think they know what happens but you don't come out not not like in a transience state and so I don't think I have time but we use the theory of absorbing Markov chains and we can calculate this mean 1st passage time and not only that we can calculate where it should go to on the 111 facet and some of you know about kinetic money Carlow This gives the exact same answer as kinetic money Carlow for the same rate input but it's much faster and we've discussed it in these 2 papers. [00:48:10] And so they calculate there are still a couple more assumptions one is that. We only partially account for the a fact of the effects of coverage. So certainly if there lie and grows to that diet with the diameter of the seed there's no there's a dilute coverage on the 100 facet but it's accumulating on on 111 and so we have an approximation for that and the bigger approximation is that we ignore the effect of the solution on the kinetics and Sir now no wires are grown in vapor Ok here's a picture of one this is grown in the vapor phase of they don't have solution and not only that they're grown in various savants and were Dr Ensign species in the solution and what this suggested to me anyway is that it's really the structure of the seed that affects the growth morphology and not any particular thing someone has added to solution can going to skip this and so to be able to do the Markov chain we have to calculate barriers and there's 3 main features one is due to strain we have out of the traps on the 111 facet. [00:49:27] That's a notch this 111 notch at the edge the diffusion barrier on this is much lower than on the one of Facet So the the notch acts like a superhighway that funnels out of this to the edge and went to go from the one over 111 this is the path of least resistance really going through this notch down the steps into the 111. [00:49:53] Ok and so each of these we calculated a bunch of different rates of with the Arrhenius form and basically what we find I'm just going to try to cut to the chase is that so this is the mean 1st passage time as a function of because it depends on how long your wire is in the one or the direction this is our run $11.00 time which is fixed for a fixed I am better and this is our deposition time and what this tells us is that the rate to go from 100 to 111 is about equal to the deposition is much greater than the rate to go from 111 to 100 and what that means for our equations is that we can get rid of this 111-2100 time basically the growth rate of the 100 facet is 0 and that all of the atoms are funneled to the end via surface to fusion. [00:50:54] And so how long do the liars go this is my last slide on the site last scientific they grow until the deposition rate becomes comparable to the rate that they go from 10002111 then they pick it and so we use that a quality to estimate the aspect ratio and we say all right you don't exactly have to have one atom you could have a few atoms especially as they grow longer and in what we estimate is the dilute limit we can predict nanowires with aspect ratios between 30 and like 150. [00:51:32] Which is completely consistent with what they see an experiment. And so to finish up seeds grow until the mean 1st path it's time matches the deposition rate then they grow thicker and this matches experiment we believe it also explains the growth of copper in high coverage of chlorine. [00:51:55] And hell lives hail rides can also affect fashion facet deposition rates and that also can lead to high on aspect ratios I just like to these are the papers on that we have that contribute to this talk and I would like to call out one student who's on a lot of these papers on Dr Ch'ien she who is just a stellar grad student she's in a post-op now at University of Washington with Jim Fenton are. [00:52:29] And so these are the other students who have contributed to this work these are along no I. This these are students currently on this project are a collaborator with some all c e and Ben Wiley that Dooku is a former Ph d. student of you know on jaw thank you and I'd be glad to answer any questions. [00:53:03] If you. Will. Actually we have we have a paper like we're writing a paper on this right now it's a very fascinating subject because it turns out on the 100 surface 7 letters the diffusion barrier and so it goes faster than it would in vacuum in which you wouldn't there is this effect of discovery crossing of the transition state and 7 facilitates that but the barrier is so low that it it goes faster on 111 it goes the opposite way so it goes slower in insead and then it goes and so it really is very sensitive to these details but we believe that. [00:53:56] Well when we find should not change what should not change qualitatively by Sol that but maybe quantitatively like maybe we'd predict a more of an aspect ratio or less of an something like that but not qualitatively you know. Yeah yeah. For those. Young. Or why. It's. So you know I think it I mean that's not the I mean they can get down without without p.v.p. But yeah p.v.p. love silver I mean according to what we find. [00:54:48] The oxygen and p.v.p. and to some extent the nitrogen. I wish it was. One. Yes. Ok so this is a material science thing so a twin is like a stocking fall so f.c.c. models they're stacking goes a b. c. a b. c. And so a twin is awake it's the stacking is the there's misses it goes a.b.c. a.b.a. the a.b.c. and it turns out a nice structures like the $520.00 Irish Lions between the sections those are the twins. [00:55:35] So yeah it's just it's 20. Yes Yes There's twinning balance reason each of those faucets. It's kind of a smaller detail but that's what people call them 512 and you. Of course.