18 Colloid Dynamics

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18 Colloid Dynamics
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30 (Lecture 2 missing)
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Lecture 18 - colloid dynamics, a topic rarely included in discussions of polymer dynamics. The forces are the same; the particle shapes are different. George Phillies lectures on polymer dynamics, based on his book "Phenomenology of Polymer Solution Dynamics".
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lecture 18 call Lloyd Dynamics based
on George Phillies book phenomenology of polymer solution dynamics Cambridge University Press 2011 ends today this
lecture E is lecture 18
call Lloyd dynamics I'm
Professor Phillies this is the next lecture and my series on Parliament From last lecture finished off with a discussion of optical prone you what I'm going to do today is to push us to entirely new topic chapter the new chapters can you how they of Chapter 10 colleges and politics solution if got through the review was founded in the early part of the book that reviews by people like to rail and launch and a whole variety of other books on holiday in the rulemaking interesting observation there are lots of discussions of polymer diffusion polymer viscosity almost none of the other sources you again discussed from diffusion in any way and there's absolutely no discussion of college dynamics of all our life might be interested in looking at how particles move let's remember what college correlated the result was faced with a objects in solution and objects in solution fears there quite small I have happened a tens or hundreds of demanding then surface treatment in some way In most cases and as a result I while you say this is a suspension particles the big articles but they can be density may have an even if they're not the charge to a program to give polymer coats on the service so that they sit in solution why would we be interested in these round hard objects the quite rigid I promise you that some of the hottest years the lives of weights or whatever why would we be interested in the eastern discussion of policy :colon why would be interested this discussion polymers Wyoming talk about the answer is using its solution and their 3 sorts of forces on a random thermal forces fluctuations that's what drives Brownian motion the heightened dynamic interactions talk about those daily as long particle wolves accessible wage in the surrounding solution like the weight of motorboat ,comma really exactly like some Watson and waited ranks neighboring particles along with and direct interactions of which the most important is voluntary exclusion that is designed objects are solid so they cannot pass through each other I'd also discussed polymer solution through here is what I always the important feature of the lifestyle of polymer solution is that the forces between the polymer boils thermal interactions Georgia Paul boils solvent a dynamic interactions between Paul oils and voluntary exclusion interactions between polymer boils those forces are precisely the same with the forces that between college so we have 2 systems we have the same set of forces acting were looking on the same time scales so the the same basic dynamic equations however there is 1 substantial differences between pall over dynamics and Holiday Inn and a substantial difference years shape or some people call a college fight apologies to colleges will point out that this linear that they're both simply connected volumes and discussion there the same about really are however according differences here that's something that's long and straight and you can certainly imagine this object having most of motion interactions they're not solidly scientists this fears for example if have to move to fall oils you can certainly imagine what Paula oils wrapping itself around the honorary life to rattlesnakes a rattlesnake serious however just sit there and can grant wraparound beaches and if you believe in the arguments that proposal and then with friends but the thing of all this year that would say the following oil plausibly and tangles of many pictures of 1 name the Sears certainly did not so tell I end up they show there is a fundamental difference in shape and in possible dynamics but the basic forces the same on the base saying she over motion as the wasn't equations on saying there's some similarities some differences 1 thing 1 might however proposal is the phenomenon of our common to call dynamic polymer dynamics cannot be explained on the grounds that polymers that wrapped up in knots followers can perform reputation snakelike motion like the boat constricted going through bamboo grove anything is common to these 2 2 systems of various certainly cannot be assigned apology so that is our perspective here and what we're going to do used to looking at a variety of discussions of how serious injury moves as opposed to how Paul we're going to look at college phenomenology and then tell us something about she feared of the all the short discussion about how is this area of the workers he is there is no comparison and regional manager of Paris is that if you look at other treatments polymer dynamic you will be very hard pressed to find another does a substantial discussion following note so let us start out we will say about the revenue From the peace
is as follows with their peers calling it's small enough that we can approximate .period terms distance scales the moves through polymer polymer solution as it moves through a Polish solution it's at the end of the war there's work after being exerted on the solution and this causes the liquid to and so therefore feel are and if have here is the full field has velocity me the couple and their low frequencies will be in the the team's expenses provided the reason is that cancer is that we're starting off with the vector here we're ending up with the here here and the 2 matters are not parallel the mathematical structure is linear that we can use to transform 1 the 1 their during to the other is a street-by-street constantly posing as part his posture about Constance Young seemed sensor falls off as 1 over all where are as distance called .period particle whose forays into is fluid and intensive tendencies the identity and the loss of our products are at odds we are very happy to see to it that Weinstein from this year and place the fluid there's some constants which have can put putting differently depending on whether you describe your worst loss at this point of wary important features of the old that 1st of all the flow field is not simply parallel to the velocity of the original object that this motion the resources yet 2nd the unseen tenser falls offers 1 over par that's not a potential energy following office 1 over or if I'm having object trial hold still is the flow of the deal creates foresaw the object from 10 the forest we have force here creating force forces there the Forest Falls office 1 over R this is the longest-range nature remains worried that she is really infinitely long-range denial of point out constraints imposed seems an approximation the 1st constraint is the fire 5 forests here for a brief period of time you have to sign off the flow field that takes a lot and not until you have set off the flow of field completely there are more complicated set of equations boasts that described how the worst year for some short period of time creates a flow the flow field has to propagate outwards and momentum propagation of fluid possess the speed of sound so if you were looking at a a very long ranges were very short times this is not perfect we are very long ranges we had very short time there's another constraint is sometimes lost which is we're actually doing this the inside and the containers filled with solvent the Solomons we're talking about are mostly Korean as a result we find drawing upon the engineering mathematical certainty across the container at some point the total volume flow of fluid across that line has to to be easier if you wasn't with compressing the flow of this can be done in this new state therefore as we approach the walls of the container somehow there has to be back on which 1 of the principal calculated and the back flow has the effect that the total volume flow across the system is 0 . 1 after prolonged qualification in suppose Andrews mathematical model years In this case the mathematical is intercepting the solid object and we are having a flow Delta B of objects in this volume we must have a net -minus of solvent out of that exists In compressibility when you remember this object as follows this is a significant factor in real experiments at a certain reasonable levels approximation the whole thing is answer reference but frame directions the core issue of reference friend corrections used that the reference frame with stationary with respect to the on the walls of the tank that's obvious spiritual reference and the reference frame the stationary with respect to the Song of Solomon this are not the same and reference frame interactions are treated in great detail In a paper by John gamble for work and collaborators 1960 favor all the paper actually appears after her staff over Memorial volume and his work on his farm work all offers insisted the government works of which the legal so there is something called a reference frames correct however the ousting services said various interactions and 1 would think Oracle was forced on its neighbors on was that they were simply a bobbing along with salt and if the neighbors are bobbing along with solvent moving at the
speed of 3rd movement and his philosophy that velocity of talking that was the overseen cancer and now we're going to put down some of the health and the next comes out of the hardware as well as fluctuation dissipation .period fluctuation dissipation are potentially tricky and hazardous that is it is possible to to charges set of statements all of which seems reasonable and whom you can get surprised by what you predicted by the way you were correct be surprised his predictions on how well they stressed however in this case it's fairly clear what you're saying that experiment the 2nd statement is fly-half particle theory was based on rules were settled that it's inside article I applied magnetic field great and nearby particles in the area the law the correlation between the displacement or all and the displacement particles correlation is given by the IOC and that is it's something that falls offers 1 over are is this constant nature and everything simply the parallel the lesser fluctuation is stationary and what we say is that it is serious he came here Ford driven by emotion if you see this behavior for promotion and enduring a lot of the linear machine which we are will also see the use of "quotation mark therefore if you look at the random walk to particles and label their emotions are correlated as described by the OSI but let me say if you think back to to what you may have read about Brownian motion undergraduates from physics you may have thought Well on the motions on Brownian particles correlated and the answer is the way far apart or if you don't know what questions to ask there appeared to be a orally and in the end the whole study of Brownian motion for a very long time was that you could do all the statistical correlations but until larger fund is very clever replays on until only 1 chiffon did his work on Brownian motion it wasn't clear what questions to ask about Brownian motion and therefore you've got lots of answers were startlingly helpful and afterward everything work parliament so if there is a saying that well the funds that the have driven motor and then if you look at the fusion you get the same result notice however we said fact falls offers universes distance and the basic unit the size of the particle told over the distance from the dimensions of number here so particles are tiny and far apart as far apart the interaction falls off a lot nonetheless doesn't fall off 0 ended a series of experiments all Crocker very clever :colon and minor 10 20 and what they do he used to say Well let us look into the system let's say actually 1 way or another track motion parallel particle Harris articles we get the articles closer together and we can actually look at this use of emotion and we can ask how this diffuse motion work and the short form in cancer is you can actually do the experiment invited displacement 1 displaced 2 foreign correlated this year times because of his age crossed the answered crossed his venture describes the relative motion carries of particles and he crossed fusion cancer as created by population is Asian Asian-Americans is proportional to the all-seeing cancer falls off 1 over all of this those 109 in Montgomery on heightened dynamic interactions were inserted in the fall of the very early on by the regional 3 of her Would Rise of that thank reference Brent of vertical reading American Statistical machinations over 1st the centuries 4 of the last century 1st and rational and what it has said his Hall of and we can on former chairman of string friction and the friction would be are attached to each other by little this or perhaps the friction be instant monomers bonded again and if the chairman moves in solution well the change in some sense her best velocities if I can't find external wall field of Homer flips federal failed and chaos is coming out perpendicular war against a rotational velocity Omega and that individual needs the fluctuation velocities relative to the general drift motion you know these things are all attached to each other it's not like a very long state if it moves large distances and they'll have to to stay at a hatch and therefore this article is sort of like a bad beats with fluctuate I don't what they put in all this the issue it said these these released some of them are obliged to be
moving with respect to the flow field while I was brought home him in the center of mass velocity applied a velocity sheared influence of fluids going in opposite directions the polymers tumbling head over details that does this that's a lot here to be inscribed with the flu and down here at the strike fluid but if you think of recall is circular motion that means that here and that's a problem that has year the after the warning signs so at least some of the beats Song said after the movement with respect to the full if they want the sheer terror Paul part and these motions with respect to the flow of net result we have to be it's moving with respect to what it is stirring course on the fluid and solve these these with with respect to the he should create a lots these but the each create their own flow fields which act on all of other beats and then have to be a little firing man during some things to get a self-consistent solution and you do in this curry with rice model for Parliament I'm sure laughter and careful to contain this fall and you music street Harris Interactive polymer chains and when you put it in 3 areas of injury at home with chains which can be done you get out concentration dependence upon the self diffusion coefficient viscosity you have to work a bit word that but it's possible and that talk about 100 of reactions for most of the objects were talking about the direct interaction is basically excluded volume this year spirit here and we have this fear there they cannot actually make touch but they can't penetrate because the solids now there is a balance sheet at this point they didn't she at this point is the real serious you're talking about well they they might be charged because water and suspended by charging that might have very short polymer molecules here to the surface he them stick they may have under walls forces between them and the net result of all of those is the very short distances there's some extra interactions that are not exactly birds fear now approximately speaking if you're just talking about the dynamics this is not serious but the real hybrid interaction between 2 spheres is not exactly posting and is the real interaction the reality is that policy stances which is part of our analysis of 1 over on the anniversary of higher-order corrections higher corrections a short-range therefore on how likely it is you'll find object to these objects real close together and that the likelihood of being real close together is modulated by the short-range potentials for durable harder to determine great detail so life gets a little trickier than we would like but approximately speaking to me work the minutes of however we have real hard spheres managerial riches sure I can I can do computers annually the real owner exteriors have thermodynamic properties the thermodynamic properties is described by far the the volume and what is fighting fire is equal to the number of years and some scientists were ties odds here you over 3 following a single spheres the total volume of all these years divided by the total volume so we can plot
0 how do I suppose you could say 1 thing can get to the point out like that 0 2 we inclinations of that year because this series of part all the distribution functions the statistical mechanical distribution functions don't depend on temperature there is either a configuration steers is allowed because those fears over overlap words for building because you've got 2 years trying to be in the same place at at the time and guess what aware what you do the temperatures allow or forbid the highest volume fraction can actually yeah you close that's a powerful rights war volume fraction I have to be a little more precise there are actually several close their configurations but they all have the feature you can get more the 0 . 7 4 as a historical side this result was believed but had not actually been proven when I was a graduates the issue which is a method is that it would be a good show you couldn't find any configurations were not to at this fall with the mathematicians 2 it was to prove there was no way he atmosphere here is this year so the serious 13 other spheres if you could do that which you could create that configurations that regular and all these other things and have densities higher hexagonal close-packed well at some point fairly recently mathematicians were able to prove this result because people believe we can now say that this is the overwhelming that solid spirit it because that that's all on the other hand manager's 1st years of life ball bearings to .period on so you take toy models for the ball bearings put them in soft sand in the shape the new really wanted cloth sack box because the water ordering from the walls of the Nice box propagates in summer so what happens if you put all own flowers were sold anything that's nice and regular unit of AG and shake it will 1st thing that happens if you shake it starts to settle and
if you shake the longer it sounds more and after a while you shake morally just don't make more progress and it is very hard to see things so that you get a volume fraction that this much involved all of points 6 Telmex mountains that results because if you keep shaking can find better kayaking but there's a little bit limit about here to watch regular captain will look like to the 2 are pieces produced stop to experiments firing the computer experiments go back almost half a century at this point and what they did was to study various years and the behavior of birds series different densities and what they demonstrated is that there is a boundary of powerful .period people call for although I think 4 terminal for is a little enthusiastic given the size of the system In coming up here to about old hold on fight the issues her experiences followed surprise I have last stands herds fears here and more desperate years their love these were smaller schools that could form Lakewood we would have us for example of gas here a liquid down here and there will be a free service that will be supported by the attractive interactions with the molecules so you have a well-defined label would and you have well-defined yes To our hard years have no attractive interactions that spider called forehead and therefore there is nothing to see the to maintain this boundary between 2 regions of different kinds of density nonetheless if you delete computer experiments what you discover it will have lot of phased out about 2 you have a regional in which have conveys his 5 days in the region and in the by facing region there is a lesson there unless there a zones and dense problems and then all of the above here going out here and help you have a single phase and once said is the lower density phase years a fluid gas basically and the other doesn't faces claims to be an expanded solid because its structure is less all like the density is too but if you think about things the argument ideas to life fears cannot be gas-liquid boundary works just as well for aghast solid Hungary and therefore would you presumably actually hear this must be the last thing at the end of this is actually really also be asked because of there's nothing to McCain there's no attractive potential the hold the things need assault and therefore we have here what would appear to be an example of the gas gas phase transition but 1 of the 2 guesses is really very much solid like it's solid crystal structure if you really get up "quotation mark closely packed amorphous structures and Jeter were gaps in my search literature says this issue has not been studied very recently and if you study things with much larger systems you might get more interesting result or more the novelist the important issue is if you packing birds fears about half of all you hear is expected to be a thermodynamic phase transition leading off at a density of . 5 5 2 was distinct phases in between their 2 phases present let's work he said right from the start OK show watched his people don't while people McDonnell college more unless all of the same experiments have been on polymer solution we have talked about all the following measurements yet will get to what sort of things can you will want they for a recall a solution single particle to sell or trade here you and if you do that is the example figures standpoint want you to measure the diffusion coefficient using any of a variety of methods and it's some functions of its exterior of concentration and the the falls you have a lot of interesting little bit which is sort of like Rob also with polymers that is you can measure the diffusion coefficient over very fairly short time periods and you can measure it is using light scattering spectroscopy and you can measure the diffusion rate over a very logical long time periods for example the fluorescence recovery after photo bleaching you know better than usual proliferation concentrated system and he a very large scattering infected with the best using co-workers and aerosols is taken measures to defuse the qualifications for us you can measure a short time before the Coast vision of this Yukon measure also a longtime user globalization and a longtime diffusion coefficient of drops off significantly more rapidly in the short term and the future of the states them for the shortest time diffusion elevation right the essence and 0 in what was sometimes short volume fraction and you can actually measure fail while as in the coal miners were manager number 1 morning laughter -minus school the weight of cities for of a home and there is a theoretical result which is about minus 1 . 7 3 to the all those touring quite satisfactory agreement because part of the May 1 st depends on fairly short range interactions and any deviation of the series from perfectly parts fear you slightly different number here to naturally predicts this concentration of and not also do completely different set of experiments completely different experiments the Georgia the thing the notion that there is a new case years and because we have a
wonderful supplier we have steers the optically and isotropic inside as a result if I send this polarized light and looking scattered like some of the scary White is polarized the same way as the incident light and that basically just says as White sees fear and some of the light is the polarized slightly vertically polarized light light polarized perpendicular to the
scattering .period Idaho out looking at a time when prisoners here a year horizontally polarized light and that like the amount of that light is determined by the serious the and other 2 features of the VA skier 1st of all if here the polarizing sphere you rotate the Serie rotates the amount of VA scaring change the series :colon Browning and random rotation so the intensity of the VH scaring fluctuates in time and the timescale of the DH intensity fluctuations exactly tracks the time scale on which the sphere reorient so after a great deal of clever man I think use of scary measure rotational diffusion question is in there I want you do is to measure the time correlation function of skin like so we have the intensity of VA scared life time we know measure is the latest time he lost we do this repeat this for lots of lots of times the together the average behavior here and what is left is a is a function of how and how these are the times that separation and so it was means that if the light is bright and in 1 instance in time so I pH he's got this point said after a while for guests which way it's pointing an ICH relaxes back to something which fail the correlation function however this is 1 statement classes just does not I averaged 0 instead of the light is initially bright he remembers is bright stays bright for what if light is initially being you remember is at the end of this year and it stays there for a while and these products do not cancel out former so the 1st thing in the rotation of the 2nd issue is I have to say fears there the directions in which they point the stack correlation averages 2 0 there is this fear is old bumping into each other they will get closer than a certain distance but these an optical mice properties are hiding inside Sears and so was here does not know which way the voters fear is claimed as a result the VA scattering from this year and the the age staring from next year or on quarreling among which was the elastic light scattering we see the single particle correlation function we measure how fast single particles are moving and we don't see any effects due to the the position of this for article and that particle beams orally this is not the same as regular glossy elastic lights the area in which the deceased relative displacements of these particles contribute to the white skin so any that Georgia was able to do this and he was able in 1 experiment to measure both how DSC hands-on concentration and found a slope of -minus what was the 1st and he was also able to measure how the rotational diffusion coefficient depends on concentration and he found slope all of -minus so what was it about financial playing time so serious fear interactions are less effective than it has been affecting rotation than they are in effect being selfish he also was a very purges these errors that follows her about words that if you have something that is headed down the since Continental sort of like a guest worker policy thoughts what sort of other experiments can do well 1 thing you can news that I made itself diffusion coefficient fear hiding there was tacitly was irresistible bodices was on ventilator arrest and what the was to show that you have a longtime diffusion coefficient and large concentrations of it's more of his heart concentrated on the long time this velocity was approximately constant so you had assume so excited signed behavior is soon tho because the product isn't necessarily what was done solutions but there is a region in which self-defeating loads of you know the kind of is more or less independent concentration Monday so that those experiment yet another set of experiments and affirmed their mutual the mutual diffusion coefficient the use of their describes the relaxation of concentration greater value would correctly inferred that the single particle single particle diffusion particles each individual is moving around France also contributes in part to the relaxation of concentration gradient but if we have interacting objects and concentration gradient more Oracle's here were part of the plot the interactions between the particles contributed to the silver-haired and even then it's a decent cannot concentration was on course on and on implement measures Prime measure slow the Czech challenges here Of the 1st challenges the solvents very being the 2nd issue is you can't go out very large five-member 5 is always less than normal but you can't go out to 5 a half a 10th or whatever because if you do approximating This is a straight line isn't it foreign if you have
concentrated spheres solvent unless you're very careful this series and the solvents are not perfect burned nearly perfectly indexes and you get multiple scattering which the from from bounces off several spheres work against your character you can describe the diffusion measurement is a Doppler shift starts straight line most of speed and the smaller Doppler shifts make the particles to use pure interviews faster there really not last the collaborators using founder but coincidences that trusted you want to know what is agreed to pay 2 papers a 1st met technique than demonstrated that works I think month doing there were able to measure case someone in there is however another complication which is not trivial which is you would like to know what the volume fraction of Sears's the problem with the several problems with this daily on if you will actually has a series of souls of the named by the insolvent if you drop drop seriously into vacuum and measure the radius and with an electron microscope but she along with various electron microscope directly the artifacts that change the shape of the Association of the volume fraction we don't quite know perfect novel west face of it with something like Myerscough .period green or minus school .period the approximately is that a large share of our will and you realize that if you look at the top of the list of the year's time yeah Over the observed range of 5 diesel family changes by a modest number cent the slow there to be accurate requires that you have a measurement accuracy which is small relative to the modest number said you know that's pretty difficult these are wonderful regiments and this is in reasonable agreement with period these read Italy's Prada to leverage on Monday Britain's various forms of energy the predicted values a little smaller than there may be minus 0 . 9 but the number is certainly the right people apart from the if you increase the concentration of you go light scattering Specter trusted the from uniform system for you could know like scary inspection process the from a system in which a small loan over the years our different from the rest of you only get light scattering from refused to the 1st experiment gives you the mutual diffusion of the 2nd experiment actually give himself you feel for argued of both of these measures of 2nd grade finding small lined mold relaxation well we plot intensity at 1 time and intensity of the other plot correlation function yeah right through breeze pursuant Brownian motion this straight line of support for these experiments what you find is initially and then you get a 2nd phase which is also West exponential even then pull out of approximately speaking to diffusion coefficients 1 diffusion coefficient describes short-term motion In 1 diffusion coefficients describes long loans so a long time to get on the field of the shortest time both processes presently active and the CEA average relaxation which is typically pretty close to the short time let's say they were too clever that high accuracy measurements were fading and pull out to
confusion and now we come to admire the results of security the and what's Graham Pewsey did to do this experiment and they did this experiment and a series of different scattering the incident like being scattered light goes out to the side of this measure where you better ties to and there is guarantee the fate of the spider invention he finds a way I describe and changed later you change the distance over which you are measuring particle there is an low failure looking at very long distance motion ensured the distance the comes up short as he's seen this before well at conceptual part cost 1st probably saw the first one for approximation yes really had description scattering in solids in all of these years back the gathering something with wave after coming in cases filed by and scattered light comes out of some paying on X-rays and very close to to saying Place the initial phase final the final line they usually do find a scattering their well human is not measured particle motions over a single distance and said See how long it takes your looking at spatial 48 components the density and in this case because liquid the spatial story components relaxed time goes the relaxation of agrarian Pewsey found was final the only thing they found it was the decision the intensity of scaring the kids you fly policy and in particular they found that some scary vector a maximum in and the maximum and corresponds to typical face we have fears the attacking constraints behind between fears concentration area all the time and therefore there is a typical distance between his and he human corresponds to what all this distance you get a lot of scary because there are a lot of errors spheres separated by the White oversimplified that's the general idea In any event the the 1st thing they found was the decision to hear the short and the long yes to both of these diffusion coefficients depend on you know you have a ratio of 0 so the ratio was approximately human and the other thing they found here is a way back through the use of which as you back stuff I say as he was there that he is a relatively easy to make fluctuations in their way factors and therefore that waiver vector the food in some senses relatively soft because it's easier to make fluctuations that wave what they found is to verify the 0 with the funeral of a major the cost of going the end the 1st is that its sales as mediators 0 Universal Data this Europe concentration this is part race here the viscosity does determine the diffusion coefficient but also the the specific way factors namely the wave that eating population are how can you explain that well wealth as he was in Mexico where it's relatively easy to make fluctuations of food soft and if you apply a sheer the flew the fluid 10 steeled by yielding where is the softest namely here some sense of the next stuff so all this is my 1st stop was more precisely
cannot be I should however also noted no results fell 70 the United States and if we put in the seller have the fastest it get slow Euratom relaxation rates and you increase the poll comes great fastball relaxes more rapidly than the small relaxed more slowly but the licenses interesting well if you use experiment on polymer solution you said you see a festival swallowed and concentration pendants crack each if you from probes into the the polymer solution you get all results and will consider this in much more detail later on course so that is using multiple roles and the concentration Monday and I will show them that we discussed light-scattering license gives some details here used to talk about the this is no we will not dispute that had been talked about for a trip and the issue is In looking at the video camera like video camera which reported only fancier and you can actually a microscope seemed articles and he can watch and therefore you can pull out full details of the statistics motion now the couple disadvantages this experiment that our way obvious the 1st is you're limited by by the video scandal in cannot be revealed scattering current technology ,comma microsecond timescale the 2nd thing is you're only looking at a small number of particles once so you have to spend a lot of time to do a lot of computation if you want to pull out considerable results the timescale problem is not as serious as it sounds that is instead of meeting Karimov what you can do is say we will increase the viscosity of liquids a place for water water was and presumably all of the same things will happen but they will have a lot of time scale described by the viscosity which wanted to read 3 words made want and there therefore were weaknesses instead of speeding up the camera slowing of the city all parent nicer experiments cast and what was done was to watch this motion is to change the policy increased ,comma concentration and the 1st thing that was found with her like that and the next said he used to find the called the motion becomes sold stories sold solvation movement by jumping across the cricket spends much of his time by sold so what happens is this year's received here the move the saying here that the move was not actual picture and sold emotional and if you grant the concentration of eventually get to the point where there is relatively little emotion tears or attract the current location of now you might like to interpret this all With this motion just measurement that matters here you can also cause elastic light-scattering respect trust me and that measures of that data fusion rate comparatively what was done it was interpret the light scattering spectra to salt is not always correct warned about this war is the finest where tests where there therefore you get out means the emotion that depends on how far apart the timing was our best according to this equation which is only true research you can also measure means we're displacement microscopically yes and volume fraction of powerful states these 2 great a smaller concentrations they didn't however at the volume fraction of old .period 6 the light-scattering inspector was a single exponential as we know from Lucero this result is not true in this fashion is not a simple less than if spectrum is a single lacks of do serious says this result is true and so when do serious said we were in good shape with this equation going through 1 volume fraction the indirect and direct measurements studies particle displacements agreed with each other you can however because you're doing video attracting new measurements you cannot pull out of Bosnia last place here for example movement of particle place that times the policy home and particle displays that when he joined brawl between the false house and he lost the use of both worlds and this was actually done by it feels like and what they demonstrated approximately speaking Was that all of you here 1st of all you could
call it a substantial knowledge this way 1 for the next time you have tended to have some recoil this article more often than not drift you but also in a series of people honest look at how part of neighboring particles move what happens if you look at this year's and demoted what you find is that there are groups of skiers perform somewhat word clusters of being precise about and then move moral lessons to destroy all Marietta slowly you find other groups of particles in the other groups to lie on revisions to the that was rapidly I may say OK why is this happening what going on and I can give 1 piece of an explanation namely the also large-scale on computer simulations of glass formation and there are a number of people were urged to use Michigan that have done this so work and they find experimental they fire simulation only that it's you approach last you get through normal while articles in groups of last fall while particles the last little while Perkins said alliance walls more mobile particles can rely on lines Britain's so we now see experiments that on validate the computer simulation 2 what else can we do well I'm saying that deserves single foreign and so here it is From radius of the here is dangerous particle radius on him are added to the larger them or western part of the and you can measure the South confusion over the role a huge change concentration of parole and you can't do this for the tracer particles that are small and large relative to the matrix article there's told brochures it's all relevant ministries and political science and hear more about groans and slowly particles and you can actually do these experiments In the measure how the probe diffusion coefficient depends on the relative size probe particles make there are almost always firmly in the hands of time this party year and is forwards fears the staff Polish concentration as a fairly consistent on experimental form that everyone In the year to date with hypothesized the points on his lower concentrations in of lead the health of trying to include shows along with get this summer please and it's only going the power of the you're trying do you can interested continues method that birth stretched exponential David In at least a few experiments people got Terry posted here and it does not appear that there's any crossover regime in most systems all we talked about a similar behavior from Paul solution viscosity before polymer solution viscosity after crossover the slope of the power lines and sold as fresh exponential 1 said for her exteriors crossovers violating the Powerwall I'm just takes off there have been a substantial amount of work to study this or that study viscosity of words fears most people did so well in viscosity goes all always goes up very quickly and they didn't have a functional form description that would tell you sharply What you receive you can measure approximately where this year's and his crossover person volume fraction of the way for the whole place for life it's a little harder hard to make more exactly the they and slightly different different systems and in her as a "quotation mark crossover voters in Wisconsin it has been over the euro is euros sold viscosity all 5 feet also slightly different points of view now most of the studies were interested in something completely different mainly of continued with her at all and all for the line for Target there is a viscosity .period that thermodynamic phase transitions sets and that was the last of the news about it this is also line it's a little hard to be more precise because this is an extremely steep curves a smaller and determining the size and concentration is leads to a significant difference in viscosity the form .period irony is that this cross over to them here what happens the phase transition year and very varied certainly stress-test the power walk position is not clear to us that the same location as is the thermodynamic faced friends we are out of
time pretty close that's it for this election


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