28 Inferences from Phenomenology
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Title 
28 Inferences from Phenomenology

Title of Series  
Part Number 
28

Number of Parts 
30 (Lecture 2 missing)

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CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
DOI  
Publisher 
Phillies, George

Release Date 
2012

Language 
English

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Abstract 
Lecture 28  Inferences from Phenomenology. George Phillies lectures from his text "Phenomenology of Polymer Solution Dynamics".

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lasses in polymer dynamics based
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on George Phillies book phenomenology of polymer solution dynamics Cambridge University Press 2011 ends today this
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lecture E is
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lecture 28 inferences from phenomenology I'm
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professor filets and this is our next lecture on the topic of polymer solution dynamic today with the Ganas discussions Chapter 16 inferences about polymer Dynamics based on the knowledge serve phenomenology we're going to start with the simplest sort of discussion and then will work out to look at things that are a bit more more complicated so the 1st issue is there actually are a very large number of theoretical models out there that make a difference sometimes quite contradictory predictions about how policy solution if I had gone there were suggestions that I should do this a review of theoretical models I would have another book as thick as the 1st With 1 minor differences almost all of those models are certainly at least somewhat more stable great with each other and therefore most of the book would be filled with nonsense this didn't seem like a very useful thing to write I assure you spent 4 years writing about knowledge so however there is a nice feature of most of those models are not going to say absolutely everyone and nice feature of most of them is that most of those models fall into 2 2 general classes and general classes are failing again exponential the usually looking at 1st is well what we may not be able to cram every single 1 of those glasses but we can certainly get most of them those classes and that's good enough for some 1st steps so what we're going to do is to say we have these 2 groups of models that predict either scaling laws were stretched exponential surveillance on the basis of and we ask Can we use the measurements to determine what we're looking at and so the 1st question is can you health so we have a series of men although I'm not saying that current bond with others referring to the question you will linear along a lot of plot or whatever can decide which set of models is consistent with the data or is it that the data are really got to tell difference and the answer is clarified by several sets of measurements what about all already for example we left the direct ability to function outside the storage and lost my online Wychavon functions frequency and both of these cases we
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again using the same set of measurements on the same spot we'd had previously had a stretch exponential region during the stretch at before all and we have our long region which was is pretty clearly power the variations during their school and for the modern life as normal life as we that a region which was quite literally on a lot of people are stretched exponential and a consequent region which was very clearly power loss and this will go over a fairer number of mortgages management so there is no question you really were on lot lot lot looking in a straight line very great experience you can see these in figures such as of 3 4 to Weld was 12 or 13 . 2 you could actually very clearly tell when stretched exponential when their Powell and you have measurements which on a long blocked place these starts very early life was her now in many cases it's a mathematical requirements set statement in their function is derivatives even say there is some regions curve which is these tangential to straight line and so you can say you see scale and also place however model doesn't predict where you see there received moral furthermore no matter what slope you seen out within some fairly wide ranges you predicted you won't find someplace as those of the same tangential scaling law laws would not predict where you should have seen the scale and what there is to say his father's slow use funds for the year were you supposed to see if there were it work as well as well all that's not that's not a scientific theory yet because it's not call in addition you will find people where it will take data and then finish 2 1 of several Powell regimes separated by crossovers you should look carefully and asked how many data points to be covered by some of the how along regimes I found cases where the numbers 2 and 3 and this doesn't really work so having said that we can tell the difference we can do this very clear we then asked Well what do we see and what we see is stretched exponential models to models that predict a lot of plots citizens Peru's part these possibly correct and models that predict scaling behavior that is extended regions in which a lot of variable logs plot straight lines are not consistent with the measures there are however localize exceptions and the vast globalized exceptions we've already used because a localized exceptions particularly from regions of particular types of measurements are we valid claims that we can tell the difference between a stretch stretched exponential Powell how weakened for if we could do that no real point of going 1st not once upon a time there were critiques of the stretched exponential model phrasing of the tallest unusually however West look at something here so here are set of measurements the effect of a stretch that mental In the FAA actually has 3 parameters on the other hand here is fitted with a set of measurements the some really are often firepower but if you will have the power loss has said no major 0 and then how long the world nativeborn In fact Of all that part and made it to the exit there is a great place reduce stock and here is already part is the height of the home functions and only added to the long function may I actually go through at that point it's the extrapolation of want and there is chance to slowly and guess what the 3 parameters also that's a feature of while scaling was only apply in some regions to cut off the twohander parameters and if you said it cut off was someplace else your ominous error she said was down here and if they did this year ,comma Sarah would go through the ceiling having said that you have to say 2 sets of functions each of which are characterized by 3 3 parameters are achieved the functions are not singular for the access values of parameters space and therefore 1 set of functions is exactly as flexible as the other each 3 parameter functions they each cover some limited range of functions space different ranges but the limits must be exactly the same in terms of what measure of function space there problem as a AGF 3 free parameters now you might not have squelchy where the line about unusually flexible and I felt that repeated anecdote period for the anecdote I happen to know with some years ago we had a visitor and the visitor actually talked about something else except she here he I'm not saying all Was it me a research group meeting at the French research group Center in Paris theoretical group at which they were invited to the inhabitants confronts the fact started publishing the stretched exponential papers and the question was what used to be said about finally the strain leader of the group said well what we will say is that the function is unusually flexible and that's why it works and there were a couple of graduate students who said about the feedstock very very good the agreement is excellent and maybe we should take this seriously and all but when you have a research group based on leadership from the top portion the description the Mad Hot eventually we cannot know we're going to say it's very flexible and it's a very clever throwaway line but it's not really very solid scientific presses but now I know where the unusually flexible came from and why airlines started cropping up in so many places in exactly the same time he could manage it's the same idea and the 1015 people think of it once but no that's not quite so that over little scientist cost OK now we have to limitations on this are and what sort of limitations on that started in the fall of my book is about 3 former balance nonetheless if we look at discussions of that there is a fairly good agreement with the viscosity scales fares to power usually set experimentally in 3 . 4 and the self diffusion coefficients scales however usually set to be policy discussed goes public with increasing the goes down
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with increasing that there are several pages which finds something close that and you will see why there is some the issue as to what used to the numbers are better than later the important issue is that if you look at several transport parameters in each of the ones that were traditionally if you look at conserve transport parameters you find Powell error however and solutions to what I'm saying is for example the Eskimos and as the hero each that the Alpha this time because we're going all out molecular weight dependence is is self diffusion about traced only once that's the way it happened don't have pulled this out we then asked she Of these are attached to each other very nicely now what this would mean is here's itself coefficients well here we are in solution and we will typically say diffusion solution might be faster than this function is going to fall only a positive number as an exponential and therefore some molecular weight USA the essence solution if you just extrapolated from him the last year about all that's only reasonable out of it was beautiful reuse of reasonable if you start with the belt and start staking solvent molecules in their systems where you can do this you expect the small molecules of most reasonable solvents to function as plasticisers and soften melt and that anyone was here it was a scene plasticisers in action there's this wonderful stuff called Teflon tape which is a substitute for other ways of attention from plumbing fixtures and cataloged favors this nice flexible soft stopped well short Teflon is not flexible soft its rigid and brittle but you get stuffed with the Teflon tape on she has now softened those all the wonderful things about us so we expect against sold that should not lead to this effect and therefore but if you take polymer solution and we go very very high molecular weight eventually something that has happened and what exactly happens it is not clear however the statement is something does the act since I was a nice conversation and what a wonderful contributions all right and also for this sort of leads to the very highest favored by little measurements that so go out to the melt but also come down to reasonably low concentrations and you can see the whole would OK so that is the army melts trend that is the solution compelled transition you can see cases where there are crossovers that that show what happens here perhaps for example new froze undersized electric current through ability human vaccine cross over from 1 probe size dependence the office that throat size transitions probably not the same as this 1 but the important issues you can get transition OK so there is an issue which is not completely resolved because there aren't enough measurements yet the important issue is that there is not being here there is a solution the here the official somehow have to get from 1 to the other OK so we also said last year year the and Alfonse we find experimentally his or her home and began on which we find for all sorts of different experiments but there's 1 little issue we could do to scam artists corresponding Stasi were gamma as for responding produce fusion gamma as correspondent in self diffusion we can pull out again after each of these and from viscosity Camelot as some of her life twothirds however I'm going no signs of violence in the region noting that it is a really superb said and for those numbers for free peoples 560 cannot be a perfect not British pretty good what shoring up 564 . 9 the problem is the online news about old . 4 energy that is about 5 6 season I'm not saying that it is 5 6 but it's an interesting coincidence and then finally selfdefeating it's somebody close to war the statement that Gamal for self diffusion is something Close to warn she the death of something related here we have the observation for viscosity recalled that the times the intrinsic viscosity is included reducing variable and that is the equivalent to saying that seat signed him to power is what we have from viscosity what the basic underlying variable although we would sometimes find literature statements that sees the 1st is a good reducing variable from viscosity that doesn't appear to be quite true based on our careful numerical analysis parliament there were theoretical reasons for supposedly used reasonable range so that is what we find the exponents of the exponents and there is also does depend on 1 way and because of all the molecular weight slightly different extensively discussing the problem itself Our this last bit already has asia namely their own people a lot of pride in his youth and here's the frozen there is a very large and there are models proposed he is proportional from very large chains and my concentration on the 0 the the reason is the problems almost never close to Shane and it's just closed change middle and therefore can't see how they call molecular weight is and thus must be in the the must independent where will those models of the we rejected by Oxford University Press In the new this allows roughly what we can say about the molecular weight and the next thing I want to talk about that he is disputing over so you and the soft measures self diffusion of weakened measures viscosity we can also do this for probe diffusion of the important issue I want to make in the cases where the experiment has been back is the product Dierdre is not independent of concentrated instead on large concentration the mediators somewhat larger than the 0 . 2 and that is true love for some of the future and also the programs produce and it is rare unmistakably case that what you might well ask why is this
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interest the reason it's interesting is the number of theoretical models follows that we can relate to the future of the nation and the viscosity solution namely the diffusion coefficient is say the tiny wired for the following to distance from certainly we divided by some critical time and this is as a proportionality to make this work out to visit is part of the square the size of the policy change was forced out by concentration and divided by the solution starts that is the proposal is that the an 8 are related as indicate that the point of season it besides mean size of policy change if it's in concentrated solution goes approximately is and to the 1st there is also the behavior polymer chain would have fate salt more good solid state are a huge portion of a media to little intestinal .period state however this is the size of change and it does not care very much what Paul concentration garrison there and therefore indeed a lot of the related indicated their indeed you go in and out of the discussing with model says it is proportional to him the don't the goes against him the minus X Wallstreet 1 and therefore the diffusion coefficient viscosity are proportional to each other Our diffusion coefficient is like this discusses his life and the overpaid ratio determined by a polymer molecular weight and very little else I'd also right is these days that cost more interviews square yes well all that says the product DAT cannot depend very much on the concentration if independently at factories to this former James change sides can't be done concentrated solution all however experiment says something very different from the heart variation here and by several orders men and therefore we can say the model of saying egos of radius where over the last are rejected by experiment and the members of the audience who are not familiar with Polish hearing think idea for Europe and marriage who our baby saying something posted dearly OK there has been a historical puzzle in the melt litter and historical puzzle melt literature is that it was problems the weapons and minus 2 this ghastly the scene experiment will go with him to read like for anyone notice product the ADA if you believe used to work for him to be 1 . 4 and then .period or is not more measurements of perfectly good enough tell the difference it's so the question is what is going on and worked very hard to say even measurements on this issue or that issue or we can do better measurements were you say we need to tweak the theory little bit here and there are the other outcome course so what you're seeing is a basic failure of conceptual model models that leads to this expectation I said 1 of of the by the way view all for for example some probably you hence the 1 way and marginalized measurements a much better nailed down OK there are however several system that is Asians the dueling various static and dynamic parameters and these are the ones that are actually work and what is going and look at dielectric relaxation and dielectric relaxation this wonderful technique that gives us the means clear and and there is this critical time it actually gives us the full spectrum of loans gives you a huge amount of information about neutral always what we sign and this is In 5 of 6 is the characteristic finally made her somehow 0 he should be and then another's stopped and the exponential and there is a constant and there is a seat the 1st and then there is the part where if you prefer over zeros where long distance bacteria long concentration during the power side inside the Union that is the concentration of relaxation time is determined by overall exponential effect and the deviation from exponentially holiday is determined quantitatively 2 good precision by the change infraction we have another 1 of these we don't measure the story modulus will loss modulus or we can look Sheraton in the lower frequency rate behavior is solemn GTI 0 lead to the minus a and felt that if we look at this what we discover years the this constant from the proportional to GI 0 some power In the exact power X the cat is on the ground did she prime Texas about a quarter for detailed time X is about all . 4 I was 5 the approximations and for aid cheers X about she twothirds involved cases we did find 1 cases were resolved .period nice however if you look at the graph for each chemical system the correlation pershare thinning in superb and therefore this object which is basically a dynamic parameter in some sense is being entirely determined by by but some sense our own lowfat the lowfrequency properties Georgia pseudo static property OK and connection so we actually have this OK that's for you can relate dynamic parameters to static parameters and actually see interesting thing we want you to know that you have to use the struggle ahead of them we can and other issues Richard you're going to get our transition to
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power I think transition to provide presentations arises this discussion you have to be a little careful large numbers of people seaward transition and things phase transition phase transitions have feature are shot there is you chug along feeding the proceedings eyes and eating ice and bring it up toward 0 centigrade William K. 0 centigrade you suddenly notice you're putting in more and more if he and temperature does not change at all at least would not within the limits of experimental measurements and then the last of the ice melts and you can start reading it again the specific he is not the same as it was before and phase transition was part of a trend were talking about something that is truly shocked and presented along most reasonable variable Accies portion always do things to confuse the issue when he delivered here transitions they think phase transitions and they must think shot and that is not necessarily what we're talking about here that is there are a number of the cases of theoretical models which say have a dynamic domain the at sign in time domain the get some sort of agreement them and that the founder of the various regional his crossover and cross over into the 2 dynamics successive dynamic effects for Keating and because they are competing we do not see a sharp change from point a to point B I must for example you might say here is a domain here is a domain and in between we have crossed over review in which neither domain model is good enough by itself to apply and don't seem to emerge and therefore there is a region in which you don't see other markets there is very little work done on modeling 1 would expect a wave of these transitions to be the only discussion I have ever seen of this referring to as you make a solution more concentrated so the chain's overlap you get 1 is called entanglement transition is the observation entanglement transition which formed this transient life use percolation transition percolation means you can walk along polymers are jumping from 1 Paul merging the next entanglements and when you have the entanglement transition you could walk across the whole bottle polymer simply skipping from chain chain percolation transitions are you accessories shop sharpness however is not the the desired effect on all of World War II the following discussions because transition to assure that resembles spare and therefore you will see in the literature the assertion of hydrodynamic crossovers brought there is however and there has been a friend from parts of Fallujah absolutely no theoretical basis for this claim if the worst should in theory so much devastation was did we see we could well please do not talk radio about the g of T is the time domain equivalent of the storage modulus from loss market the notion is that we have to parallel plates we displace 1 of them quite quickly relative to to all of the relaxations in the solution there is that restoring force ,comma plates of friction force on lower plate and that place dissipates that forced dissipates in this station was described by the Iran sort of like this except if you go out to the environment is blocked if you start making the former solution concentrated you eventually end up with that closed life I'm not of wanted a relaxation which is extremely longlived and which has a plateau plateau is not really exactly like change very much and then down here at long times correspondent short for you you have what is called terminal and so that it that in the sense transitions start seeing his laptop OK so that we actually see transitions well yes we saw several of them for example for small molecule diffusion of conductivity I was able to point out that if you look at these as a function of viscosity we see something that stands as a reminder to all of this literature all some boundaries off their sea a warranty on diffusion coefficient of blindness to and that transition was clearly going to depend on what the solvent but advice and assisting with systems that we looked at was someplace near 5 cent points and in fact that's meant to be a somewhat imprecise state but you can also look more teams 1 times the polymers and there is that we don't go into any detail the lecture there something interesting here about to stand OK on the other hand if you will polystyrene spheres after hundreds of ancient crossed in water glycerol the polystyrene latex spheres those in the a solution over at least 3 orders of magnitude you take that out of pure glycerol or nearly pure glycerin you can go over a wide range of temperatures this what you see eventually few super glycerol something else here's another transition we saw we are looking at the South diffusion coefficient as a function of polymer concentration and what we find is an exponential out someplace near here and then beyond year a stretched exponential to behaviors are very clear and very different at the cross over the 2 versions tangent to each other and there is nothing but there really is a crossover something like 350 years 500 grams per liter all I have proposed I don't put into what we do and had thought of the time I proposed an explanation which is roughly in here the polymer oils got fairly concentrated and roughly in here we have solved most the gaps between the polymer Boylston to start approaching the size of a polymer afraid of solvent molecules and statements the solvent is continuing really stopped working now not how exactly small GSA after the relative to the size of the solvent are next quite imprecise should be doing more more accurate on geometric calculation is pointless because there's this constant go Oh yes so there's real transition and if we look at 0 share viscosity low share this Stasi we found that some systems but not all of them do their transition is there's something English the Johnson's Justice fresh exponential concentration on the way up and the other systems would get stretched exponential .period and then we have something that is very clearly power what this is the solution lies you know like transition is quite sharp now I have said she varies theoretical models and say you get scaling here we see scaling and Wisconsin however you should realize it's always the viscosity insolvencies
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furthermore there is a transition concentration which is during the transition concentration in natural units in province of as a function of the intrinsic Red seating and the use of this war maybe 35 artifical but maybe as largest therefore transition of transition occurs then nothing like the on concentration which the chain's start over land lease not this way however there is also a transition viscosity and if we look at it firefighters told us that we discovered his rare consistently 1 of the 3 question the 2 of you the next items that yourself supposedly worked during the New year the worst thing you the experience In school somebody has new order different dates look in that situation USA the theory what will these statistics and you will have the following list In the claim that it the the history of the plot against if you want to know what you're going to do the right thing and for this sort of answer is no .period and fortunately is quite easy to tell the difference stretched exponential power and what you good go in and generate you want part of the measurements and it will be painfully visible whether as far out as long as often stretched exponential behavior whether this colossal power and once you don't know whether they you were doing industrialized stuff you want to use a single stretched exponential where you need to functions
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and unspecified crossover this crossover by way to his staff is shocked and so the answer is there is a sharp concentration is typical in the case we looked it's always found at about the same relative viscosity that wasn't about not and therefore you know roughly where look whether something interesting is going to happen Of course this issue they actually have a system that have a lot of data points to make it less happy with this statement you did do need some decent number of measurements to see something OK so there's an actual crossover In the viscosity we also talk however let us stop for a 2nd brought up on some of the future the Salahudin coefficient is just stretched exponential To wideranging goal of all items that won't do this you increase the followed concentration DES falls it's stretch explained and therefore I think that that model think the test on the square "quotation mark data consumer approximation well that doesn't work at all as the concentration offensive viscosity and concentration dependence of the self diffusion don't use the same function in
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all cases so we can all that again I don't know what else can we say about transitions like mentioned several times for the electric frantic mobility is a function probe size and I sort of made guests of what might be looking at what is looking at a leading irritant nonlinear dynamics transition and the linear nonlinear he's shown because the mobility depends on the last flight fuel to power 1 last transition the last transition has been seen at several points it has not been seen very clearly because there's not a lot of measurements would appear to see if it is to work late sister project and in the transition area at about 800 branches and that is very approximate because the measurements that the data cases that I've seen ,comma spaced 100 grams per liter part and it's not clear that it's shop or anything else and Corey issue is that if you look at lightscattering has also experimented with both the BHP at UC OK so long law and the solemn slows down to increase followed however there is also other feature which is the slow loan depends on scaring investors squared it depends on scaring investors where you are at smaller concentrations were larger characters the statement that you accused where independence of relaxation means the relaxation of the Houston Dallas and his thinking the combined effects war and continuity equation where scholars cosigned concentration relaxed be relaxed as it is decaying exponentially time he's the mind as he is aware of the disease you from fixed along but when you get a relaxation of those Escude square however if you take this you go to larger concentrations were holding the relaxation goes this Houston is 0 there is a CIA relaxation but if you study the relaxation on different distance scales nothing interesting changes the relaxation rate does not change and that is characteristic of relaxation from which were structural on I should emphasize that what I say structural and as the name attached to it have tried to be picky and asked What do you mean structure while you're seeing something that is related stuff moving over a distance there could be confusion but something is happening inside like happening changes or something and there were something from which lost a lot of money and the net result this you see change human the 0 behavior and this her someplace near here and is more prominent in Boulder sister and if I appear to not be very precise as to what is going on that's because there's a limited number of measurements at the scene and that that's about I can say 2 you know you know you know that you can do to OK so let us push on and now we come to the transition will dancing supposedly looking at more unless all parameters we talked about as a function of concentration and what we see are smooth curves my hair loss University agreed that they were that we see movers and smooth curves have faced constant parameters and selfsustaining parameters were here here and here and there is single of that describes the whole range of concentrations well In particular the solution struggle again and some ladies here called concentrations and 1 of the 2 years since the start of the overlap on the right and the overlap concentration some small interKorean might want war divided by the intrinsic Stasi this is the concentration on changing and solutions Arizona shouldertoshoulder and if you put all came in casting through the others because there no place else for while there is an overlap concentration and there's an entanglement concentration is almost all and there are models that predict dynamics changes dramatically as you cross these transitions in may not change instantaneously sharply but you get different dynamics at higher concentrations of lower ones and therefore things should happen as well pointing at very large numbers of measurements using very different physical parameters we can say quite definitively except maybe for the solution lies not like discussing but these expectations are correct it is not true that you have 1 set of dynamics dilute solution and a different set of dynamics and send the entangled solutions the experiment is our fairly thorough in rejecting that's the only way you can avoid this is to say will the dynamics a completely different modes of quota completely different but everything is sunset of conspire with a smooth curve with constant parameters and parameters to calculate up here using 1 set of dynamics and the same parameters must come out of the other set of dynamics that their others could happen but I don't think the spot money is betting on an hour the only exception to this is the solution like smelled like transition but there we have caught the issues you might say the solution lies about like transition is an example cross over here except of course that is only seen some not universal viscosity is not universal function of the golf ball in concentration there that isn't very good for some of these models leader are however the important issue is that if you look at most sets measurements like self diffusion and look someplace near the overlap socalled entanglement concentrations but nothing on what happens here and there's not really a crossover anything like that but I inserted into the discussion of college and returned to the college dynamic told is college ball and get to the similarities and 1 beverage a lot of similarities the forces between the parties said the other similarity is dynamic equations meaning all of Mori's sponsors were wary offered way are the same thing is looking at most heavily of motions of many interacting out the difference between politics and polymers Is there is a policy that is it could call a satirical collards cannot tie each other in knots polymers can certainly do so whether this is dynamically important is a separate question but certainly the twopart to apologies are the same policies can Jr that is if you have of something that's like 60 per cent by volume spheres doesn't follow very smoothly all but of chains presumably crosssection also In fact that might be the 800 grams per liter transition however that result is if we compare to Manager of polyester polymer chains we can sort out which features of the system are due to quality and which are not and so for example we will discuss it versus fear of all involved fraction or reverse of polymer concentration and call a stretched exponential comes off and then there is a complete shock cross over into various the all of this is solution lies melt like behavior it seemed spheres so it has nothing it is not a lot to do with topology with 1 minor exception From polymers occurred just keeps on going the years there's a shot of orange term he should realize that concentration viscosity exceeds the very different system if however you look at many arms stores the armed services start out on here as you increase the number of arms to get all the way up here it is you as you look at things that look less and less like spheres achieving lesser less like a single round of oil and more and more like skiers like 200 rounds storage referring instead of as you go from here to there I'll let you find he is a transition from all of the data was terrible behavior and therefore this piece would be decided policy however this and the fair use your power loss is clearly not an apology because you see above all spheres all OK what else do you see along you could look storage wireless work lost finalists as a function as functions of frequency we could certainly do they are and what we observed for college is exactly the same as the behavior we saw From following oil's the general form of the dynamic models get the dynamic finalized both of have the same standards on frequency forced fears for random boils and therefore we can say to you :colon I'm putting a question mark on this if you do this :colon warrants and go far enough in frequency you see over for use in Boston to various things that's not seen her parents fears however if you look at the barracks all homeowners have been carried out much higher frequencies using time temperatures and it might be the case in talks fears parts and you know studies over a much wider range of frequencies you would start to see exactly the same effect you see the ball well there is this fear measurements were not carried out his foreign frequency and therefore you don't wanna say his quality difference here because it's not clear if actually looked at OK what else can you do well you look at the dynamic structure there here this is the last thing the inspector cost which has relaxation and if you got lot to elevated concentrations for sphere is always a certain sense all sphere systems are saying they have no real ability to be different from each other and for many policies you seem to what you see his fastball a relaxation that is fast is the relaxation year's concentration and they get faster is increase concentration and an elevated concentrations you see is slow slowed the guests lowered to increase the concentration and both of these except that distinguishes chest Pontiac and of our voters to square the difficult issues of and so we see this scene both for spheres and from all boils so that there cannot be a topological effect here OK there are significant studies that have been done using video might cross could be the video might crossed the aisle less is actually deserve more motions of objects and solution now you have to work hard and you may have to add a small number of them so you can watch the small number with background but you can do this and if you video light prosecutors years confined to the wall the move slowly and find that there are what I would describe it as reductions were particles fairly rapidly it could this be a microscopic artifacts will also do computer simulations on for example supercooled on jobless fluids and are very very nice sets of experiments for example Michigan rooms there show read clearly U.S. studies stationary most rapidly moving ribbons and therefore what is seen in my crossed the agrees with computer simulation and this become so you don't see this as high temperature but at low temperatures mean spheres I concentration you do see this dynamic effects all side we have heard spheres the attention of the Boltzmann instead after the minus daily you is either 1 or 0 because of potential energy is either 0 or infinity therefore miners stating you used temperature in the hand and while in are jobless fluid you can see things that happens you hear people at 1st series here who Windows nothing is in a thermal systems and their you can only change things by changing concentration the last visualization spheres but in fact there have been experiments on polymers which of my breasts and literature and you looking at and there were systems which show solo in which he is of experiments of upset Alexei the is walks the equilibrium objects and you can actually see the irregularities were the naked eye for at least 4 months so you can actually see the slowmoving vitrified reading and therefore the video appears to show both for skiers and performance of the vitrified classified read the nature of the identification is on you know you can you know 1 gets vitrified regions what else can we do experimentally Wells college campus self diffusion coefficient they have a mutual diffusion of the rotation of and these things they have low concentration of the year so we we spotted the versus concentration we get word on new worries self diffusion coefficient again downhill slope and for mutual diffusion coefficient calculations I've gone traveling downhill slope do the calculation for rotation other rotational diffusion coefficient is 1 that is most sensitive to OMB shortrange forces sphere service because the engine behind a dynamic interaction falls off very sharply like 1 6 distance so the odds the hardest capital but we can write for example the U.S. and the 0 long lost son constant pain water volume fractions and the calculated came along and we calculate came on the assumption parts fears we have imposing interior hydrodynamic interaction it's extensions which historically you're actually can't we have words fears BOC in China's dynamic reactions leading calculated came along and it's at least approximately acted within plus or minus 1 work better I should point out from mutual diffusion all I can say the cost initial slow has the contribution from direct interactions has contributions provided dynamic interaction the additives other each cell number around said 8 and the addition happens to give us a number close to 0 but terms set quite large and therefore were actually doing measurements and calculations these the accurate and we get the right answer this statement on that we home we are seeing able to calculate the slope reasonably accurately says the creation of the of the case don't understand the there has been a very long time there said her rise from all over people say we will treat the hydrodynamics with the unseen cancer we will treat volume exclusion by saying these things operates fears are however the question is is this writer we completely off the track is wrong a time scale and the answer based on these calculations it appears we're very much on the right track will be OK so that is what we can say about college although 1 last year on the call overextended concentration during the diffusion television follows stretched exponential that's also true the ball is now the numerical coefficients may be different after all there is some difference in is but the functional form is there and therefore we can say at this stage we fresh handful because not all of you correctly concludes insightful kept saying not apology not apology not quality there is not a role model room left for places in which these things are different in shape and therefore the behavior is qualitatively different their quantitative effects but the fault possibility of qualitative differences between college dynamics and chain dynamic are substantially suppressed not completely for example home series have this phase transition started volume fraction half going up on a ranch home . 5 8 and then following fractional . 7 7 to slightly less than threequarters by volume the closepacked you can't get any more ponderous will form melt in which more or less full states still might fall and that actually is a geometric pattern getting let's go back to to the video we will look at electrophoresis here are very nice experiments on synthetic DNA starters why he signed but if you have to start all over on the list headed that way stop all moved by stretching its arms out and the body stands behind pointed this out for a year this category and his chief said it's been like the change like this we appear to be a lot of the old regime that is if you going lower and lower electric fields things move more and more slowly the extension becomes less and less but we seem to be in field or if we are in a big way below field and there's a very good being here because there's plenty of room for going to very low fields and trees onstage but if you were in the low field reaching the fluctuation dissipation apparently near response theory says that this class of motion is how stop always diffuse through all solution and I should stress that solutions not if you a start through solution and here is the crosslinked shelter when it start comes onto the gel can penetrate just out of service well if that's correct and stop always diffused through solution fired to the the parents the bodies during the fight on the other there trained by Hall Fame the other and trained coils then it must be the case that's all you must be the case the along change is being dragged a lot Lopez says a great deal about helpful the solution because it speaks to a very fundamental moral issues and I'm going to stop here and I'm going to point out the fundamental moral question here is a hallmark was changed and here comes another 1 In diffusing and at some point it's something that tried to draw the overlap so you can see which changes in front of me energy at this point the 2 chambers are like this the changes like this not the question is what happens next is this change prior to their In 1 answer is if I won the 1st time that the 2 chains we have the moving chain with traveling along and it reaches the chain was sitting there and the 2 chains that and come to a stop because what change keeps the other from moving to the excluded volume the other which is the interaction seems a rugby scrum on American football games Is this China's is moving and encounters this check the 2nd change and they get dragged along and there was a 2nd changes direction along by the 1st now forced to chase after the same size probably will so there will be some compromise what would they do no they're very close they will have this very much the same brand of samples worst loss go the assertion that both chains when they collide is the fundamental basis of 2 Of all the 2 tools reputation the assertion that they dragged along is the fundamental basis most of the high dynamic this experiment is a critical test for determining which model is correct because if I only saw recalled here I am I stock although I am headed this way through concentrated solution if I encounter another pall over here when I have is effusively retract my mommy and stick out on the far side and now I've freedom this disarm and I can move ahead again until I arm covers something that I have to be tracked my to disentangle it and after I trapped by our rights and stick it out again the site of the obstacles you noticed you try walking this way through source set of obstacles this is a very clumsy way and that would be great slow down behind the dynamic models say I stop all over by moving this way if I get near another polymer chains here I am as privileged as is as to whether I'm we are also subject to somewhat similar external ground forces as random a spatially correlated BOC and therefore we will continue to move and I will not have to hold my arms in order to and there is a critical experiments to test these models and rejects the notion that pallbearers functions to that is the critical experiment if we are in a lot of the old regime of statement which cannot serve I started bit late so I will not last for up to the In the last somewhat short knowing what the shortcut because it's actually a long time that is the end of today's lecture next time I will finish off the current Chapter 16 inferences that can be made from observations on polymer dynamics until then class over