25 Viscoelasticity
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Title 
25 Viscoelasticity

Title of Series  
Part Number 
25

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. 
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Phillies, George

Release Date 
2012

Language 
English

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Abstract 
Lecture 25  Viscoelasticity. George Phillies Lectures from his book "Phenomenology of Polymer Solution Dynamics"

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classes in polymer dynamic based
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on George Phillies book phenomenology of polymer solution dynamics Cambridge University Press 2011
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ends today this lecture E is lecture
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25 this go way austere city I'm
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festival and they were going to to continue the discussion almost instantly last December after we stopped taping last time we have a serious question class discussion on how we found "quotation mark managed to find the temporal scaling on sites where models sort of hiding places the control knowledge and still adding some comments on working like what I'm going to do that is to discuss 1st where we are where we are advancing to and what we found so far so what we did was to discuss this elastic properties as actually met and we looked at results of loss modulus was and storage modulus good results on shares in all the experimental outcome is that we have to set all of these measurements and we have a theoretical approach or scaling the reduces all those functions to a small number of parameters not 1 thing you might legitimately ask is well it's very nice to say we have a small number of parameters here but the fear there is still the key question of those parameters say anything sensible or sort of randomly scattered over the entire universe 1 way to answer that question used to take a look at the parameters and asked how the parameters depend on solution properties how they depend on polymer concentration polymer molecular weight and other things would met In doing so they're not the distal elastic measurements will be carry kept in some cases are carried out now are largely reported for fairly concentrated solutions not handing down towards 0 concentration and therefore the measurements we looked at our little limited in some respects in terms of which concentrations they point that some always true and if you look hard some again about fairly low concentration so what we can do is for well analysts call what functions we have been using it the measure and so general form for either of them formalized by frequency decided find with where she called Prime matter that invaded by some of the Shiites here on the dryness major tells and that's all to some frequency native C and that higher frequencies is the bar the the whole matter like this next move there were 2 storage module life and there were a lot of courage as there is a story about unless there is a ball lost money was because they're allowed to monitor there actually sets of these parameters will if we start by looking at he said word the 20 as a function of concentration we see that as a function of concentration is all of the 13 . 3 3 what you see power lobbying the power Powell behavior extends From the if there is not always here and there in the summer systems division trailing off the wall all we should recognize that that's the only those 2 0 0 of the government From overall better that's a viscosity and therefore we are looking at systems that are in the smelled like something that is clearly looking at things with viscosity is gone over from stretched exponential concentration dependence which has always found low concentration 2 Powell comes integration depends which is sometimes not but not always found higher concentration we can also look at although versus concentration and what we see for Alvarez concentration is again Powell linear polymers having the courage and is available on concentrate the stock holders analysts from the dependence of health concentration I finally if we look at the exponents Delta this summer while we can see is that Olivares uniquely stays fairly close to war and the stock Olivares is concentration is increased their falls off we did I could go into considerably more detailed like putting the size of honor time but that's certainly the sort results we're talking about are on the same line we could then ask poultry what happens where it's become offering here is cut off frequency the transitions us from the lowfrequency region Lerach frequency recently and if we apply the cut off frequency versus concentration to me what we see is that as we increase the concentration the cut off frequency falls and fairly consistently these things were fairly close to Powell now in some cases of the safety of these articles power all would you intimately as a wide range of power Lawrence C. and the answer is something sister not seeing a great deal and you might be able to fix something else and in other cases you're fairly clearly covering these range all right it is also the case that you might wish for significantly more points on a single currency are you sure you realize how much work is involved here that is to get to this point you start off by measuring the storage unit lost money last summer frequency you repeat this measurement many many times the whole series of frequencies and now you don't want solutions and then fit the unity in the the Administrator the parameters from this functional form and you now have on each of these grasp on them as a result of many experiments you get 1 parameter pot you notice that there is a lot of work now to some extent you can vote to avoid this by the simple expedient of home automation which is much more practical than it
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was 20 years 4 years ago the Korean people will go back 20 years on this for 30 years who were experimenting on automation of lot of organic synthesis of but the net result of all this is the way like more whites and there is a huge amount of work to get to where see no less the the kind of frequencies does in the fall with increasing concentrations although it falls more slowly with linear polymers falls more rapidly .period recalled OK so let us perhaps chug ahead of it and let us ask what happens higher frequencies that flowed freely but a lotta frequencies we have power lobbied here and the 2 sorts of things we could plot and we have a lot of people are against that is what this unless on that's not exactly a physical known is the value the the models has formalized by frequency would have any unit frequency if you had power loss behavior in frequency cost you don't have power behavior in the frequency and therefore this particular number :colon is perhaps not quite like what you could imagine it's not what I have to go for flight instead the following only because the transition minus taxes and then all over all comments the demise of the call this size of he felt from the old bark and therefore we will actually give the value of the models and the frequency at which there is a kind of transition that would be perfectly legal to do it will be a little harder it would be a little less strict here if it is you probably have a great deal of about the new squares that you will probably find the fitting process was a little of more insisted that give the sincerity of parameters and get off lightly variance OK so what do you find this thing .period yesterday increases with increasing concentrations and actually go back back to to the original the original data and holding the many variants of loss of like this 1st the prosecution the also stretched exponential cards the extrapolated to do so was happening is we're moving all we are moving the rollover of the lowfrequency lower frequencies but we're not doing it so fast that these curves in penetrate and what is that what is the slope of the widest slow here was slow there is doubt about some negative at minus now now so we can ask for lack of so what is felt a little like the the country's concentration and the answer is the Delta politicians start of lower concentration tends to absent and for own no don't corresponding to to the storage modulus again about 1 . roughly half for the corresponding the loss modulus you go something like 1 . 2 5 now those slopes for cheap vinyl over America's where prime over all that if you were actually looking at the 2 curves the actual chief primary GW prime she eagled prime self all of what you are saying is that this is not all automated minus 1 . 9 it's amended something very close to 0 but slightly negative and this would be a lot may not the 1 . 2 5 this would be only to be of old . 2 5 and it would be very slightly climbing will come back pretty pictures of the dead OK so that's the concentration we can also talk about the molecular weight dependents and molecular weight attendants of forward ,comma figures people directly or by on the molecular weight the tenants results are a little constrained in that there's not quite as much information as you would like there's very nice information 600 worries about various leader I told him that he would 6 and there's nice information love going down a bit odd followed a linear polymer but there's not quite as many results this week .period everywhere there was room were a lot of different molecular weights and fixed rates nonetheless what do we see well I 0 it's going into be the final with increasing molecular weight we are going to be about like regime where you see towel or behavior and we saw that the concentration and here we also see it war molecular weight the problems like this from the start all over the slope is relatively speaking for the linear polymer slowly with less pronounced the presence and we can also look at Al purges famine and again we see something close to power behaviors are the best I safer Delta is that there are lots of values of Delta used to modernize their still samples there a bunch of life and we can look at Brazil's molecular weight and there are a lot of values of Delta but I didn't see any easy generalization OK what else do we see
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itself which will bring you yes there is the power I respect at the and if we look at people eyes from molecular weight he and its all that's certain welldefined if we look achieve our eyes and molecular weight depends well you see a results the best thing said end 1 Estates power lobby here is that it's a rare week power walk because of variations she arrived and user range it's not hearing lot and therefore yearon year if you wanna say its power lawyers evidence isn't as strong as you might want to forget you see something slightly I'm peculiar and it's a little more time emphasize this is a linear scale and the accidental scale you can but what's going on and there are nice lines on the plot and therefore we can say that access to version laws of the molecular weight the slope is very we it's not flat and that leads us to recalling Pennsylvania miners next year we have something that is a matter of minus concert posters additive constant all when you have something of that slightly unusual structure you can rearrange and you can arrange say that it is and this was already the fastest parliament but I'm not sure what if anything that tells you it's a rearranged nonetheless you look I actually gullible the figures were you see is we can extract parameters out the parameters we extract out artistically fairly well behaved in the sense that they show smooth independence is on the solution properties in the pot in Germany and therefore in some sense you're going quantitative description that having centers quantitative description west OK quantitative description what good is a qualitative description and the 3 sorts of good the 1st is that if you actually have qualitative description you can say how the fitting parameters depend on concentration of molecular weight you now can use the fitting parameter behavior and measurements of some number of points and you can use that as Interpol you can use them to calculate the storage and lost model and polymer concentrations of molecular weights that are not the same as the concentrations of molecular weights they you actually studied experimentally hotbeds of election is potentially quite useful emphasizes a lot of work required in these measurements and if you have a good instead of interpolating functions you can significantly reduce how many experiments you need to perform together measurements to what the 2nd point is that if you discover you know how the serious parameters depend on concentration molecular weights solved all the way those includes those are clues as to how you take the theory and pushing ahead to the next step they don't tell you what the theory is that their hints from Mother Nature's way to what you want to be doing finally if you do manage to cook up a model that added a detailed calculations that actually explains what finding may have some point if you were able to do this you have a result namely you could take the experiments and actually used to test your model and see if it works not so and so the phenomenal logical approach I've outlined here actually has 3 sorts of users at the OK Our going change topic entire we're going to talk about chronic From chronic problems relations are a statement about the relationship between time response and lost finalists and storage modulus various certain sets of mathematical relationship that must hold because the system has many so let us consider what we I mean by that and we start with Sheehy of no which is the sheer stressed relaxation function and with the shares stress relaxation of God said the following is access and we cannot hide your test with the plates and displays place some abound very very fast and once we've done that we ask what forces on the other flight and what we find is that forces 0 until we displays the place and then there is fight that has some sort of a relaxation details I'm not
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giving there is a relaxation and if you look very hard at 2 or more will play also asked about managed to get out of here not that statement is since the veneer and therefore we are making the motion of the plates we can do the composed all his into a large number of steps and each step separately creates the time this happens it's all change the shear stress OK To system so going and we the man making a 2nd step Thursday or you could make a whole series of steps to the form "quotation mark when you were signed so we're saying we have a linear system and therefore it must be the case that the response of the alarm system to scientists or oscillations and to a linear oscillation stepped on motion must be calculable from each of the last these causality where is she is supposed to be 0 if you were at times less than 0 because you should not have a response force before you let's if you do you can use this construct and use that time machine a device that lets you communicate backwards in time now I will make the point that results from chronic problems to separate offers 2 separate states that press statement lessons calculate need I knew from the time of the that where or when the gold price in the home there are a lot of different ways of writing policy inaugural 0 2 in Venice the Omega is the function of and then you have already signed for the seat the or we can do is integral in the field and the key from all over America and
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there is a "quotation mark already the already these frequency time transforms the and for a ball and so if you guys tell you what he is 2 years I have told you what the prime don't from both are correspondingly if we look at the time and she's got prime they're not in the independent that is if I start with what I knew of calculated achieved the and then from GE
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injured around calculate the other and if you want you can eliminate the middleman recalculate 1 from the other end of the year OK so we can do this calculation and chronic Acromas relations herself consistency there is however a constraint on the chronic problems relating to you actually want users like this then we need to have lost the storage finalists or loss modulus of infinite frequency because the upper bounds on instruments roles are insanity what you're actually doing physical measurements to cover for orders of magnitude frequency issue due time temperature superior position you can do several orders of magnitude frequency but 1 that was full there is a reasonable estimate is what the whole function life Maryland initial stretched exponential rate Powell already and some place out here were looking at the loss modulus there should be a rollover because in the end the solvent as a viscosity and that viscosity does not frequencies waiting out there and in between there may be let's see we saw several deviations from the civil power and power walk there may be some structure well as only measure up here you can't see the structure which is issue but if you measure far enough that the functional face in essence have another use namely the functional forms were quite well and therefore you can use the functional forms as extrapolations cover into regions to the Nazis also if the functional forms a reasonable latest private measurements accurately and there's always an individual measurements used smooth out when you use a good fitting function to the moon is based on the that's quite correct the EU can now have something that extrapolations who the input into the crime problem urgently well that's actually it is Figure 13 . 30 but but
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the but if you look at 13 .period 39 there are measurements all of the the Prime she double prime and they have been used to compute she's tea and this is all done for 1 ball over a series of concentration book The Seeker ruled over and there's another line which is key the calculated other storage modulus liberals over I accepted very near to 2 wins this works just fine it's quite active right close to the 2 lemons things start to get lazy and the if you you look at times with the you start of the issues the times which you start to see issues corresponds to the upper and lower frequencies at which she at home and was matter that is the extrapolate does a nice job of smoothing the ends curves out for you but you really didn't better Out of very high frequencies at least that those results therefore when you get into the region region measurements and frequency space of time domain numbers get a little more noise could Monday that a chronic problem relations I'll let me say about 1st of all there is a physical results so you should certainly be convinced that the original measurements is found in the original papers if you actually look that storage and lost models the original numbers must obey the chronic problem actually there's no absolutely no when we went to hear what we did was to say we will take the the thinning function and we will use the fitting functions as parameters her to calculate analytically achieve the most calculations were done and when you do those calculations you get the curve seemed to fade if chronic Ramos relations have not been satisfied the effort to purge were not right on top of each other there would be a very strong message that something was wrong with your fits and furthermore it was something the level of the Seifert described measurement breeze in the original data did should have done this so far as we know and therefore when you have the the FIS which seem to me that if given courage right through the data by emphasizing on at all it should work and if did something to me really well it would Monday now we come to the next section and the next section of the rule of law what is called the "quotation mark finding friends but the I virus for engines is the notion that I have a material object Ray of light through I consented through linearly polarized light saber at EU borders on the ball if the sample is by referring to the few crystals thereby refrain in high school all virus stringent those index of refraction is not the the same for wildlife polarization the at all that His phenomenal growth lower ancient Norse navigators they had devised some stones looked stunned through it in a completely I don't think you could tell when someone's and the reason you can tell where lot where someone was was the of the light is scattered through the clouds even if you can't see the song picks up polarization this way scattering worse and experimentally someone out both tried this you can actually estimated some with some reasonable procedure because you can't tell where the polarization waiting somewhat I'm not going where he with met except in the far north where magnetic compasses and not very useful that the respected feel somewhat on any of theirs by refreshments down less than is is that you have a system and where you do something similar to it and you line up polymer chains now with what exactly where a lot of waste to to the experiment and the net general notion is for example you apply apostle Tory sheer and get transient alignment molecules once you have persuaded molecules line not only don't stay lined up they try to relax to random directions but once you've done some sort of arrangement of molecules you now have a system that is optically active in ways you buy refrains we don't need stress the idea here which is that you can describe this will line the molecules we see relaxing and so we are applying a variety technically on wars and driving after the disposal melody and response they added you face component would you sounds just like storage models and our faces component which sounds very much like what wanted was a these who should be the same these 2 should be the same as the corresponding objects they find him dynamic share now that says something about the system are namely it says that what we were seeing not optically only corresponds to what is causing the fall of discovery last year they can speak on all variables may have to be in the same period and on what is traditionally the world literature music 1 of that were they face the because you get poland's phased out of phase that's the same as 1 component amazing the the state right
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complex numbers and on to face that's the next stage and therefore these 2 ought to be related to the fact that the example were right to data on I was told by region's measurements remodeling this some of the bonds Indians many the lot frequencies something during 19 has however that this section of the whole world was extremely disappointed all the primary issue since the research about writing here and writing every became so was that I was really not successfully able to find an entry point literature revealed solution that there is a very considerable clout of melts data on all models followed by referring to the Group of Stamford Conn please NOTE mind you there's some very good people who work on it all however although it was seemed all stuff I have not since I decided not to cover bills there wasn't much to talk about I have the distinct suspicion the sooner or later someone is going to send a lighting up here is where you should look here is obvious said search warrants used to have signed me would have found a more objective or results it was almost as frustrating as hell holes field gradient and Nevada where all the principal is on march studies not only that translational diffusion but also outside motions and induced by the discussion late afternoon hold about after 6 were with their argument that more studies sentimental moments but I have the distinct impression that once again there was something I did tell us that there is such a technique section of the country he said what is that general results 12 1st I'm going to talk about picture the point of the start by talking about the stress relaxation on so we do something to the system and we look at the response and we ask what the response shows us and what we find that is Is there is what we told blasted region and that there is a transition and then there is what is called a play about and he eventually if you go out to sufficiently high frequencies there's a terminal region as the terminal region is the response going down the point where you look as a function of frequency and basically what you see he is the sole let's turn this around and let us put this rate was building in and I will show you plot is is traditionally gone replied that he cried when he dealt pride itself and not normalized free you never take off and then take office was called for in the and if you applied in the frequency domain but wasn't quite as called for in and the answer is that it kind of made its terminal in frequency domain will yield high frequencies corresponding sure short his longtime correspond to low frequency and then there is a rollover and we get plenty of we get out of here .period after the transition and then where and if you prefer referring their to previous lecture I do want to figure out where I take the on and I replied everything in this 1 and I showed the lowfrequency spread and to the source someplace and here is on the scene and the Honourable matrices Powell already plus catastrophic high frequencies used the matches measurements .period and currently uses a small number of parameters whose behaviors so this is less a transition player of terminology did not describes nicely to the next 1 make is but if you start off with the solution and gullible polymer make concentration and molecular weight a lot higher than this fact gets longer and longer there is you have a final relaxation alighted on the side of the wall if you plot linear it's much less impressive because you cannot both see the final details of a short time and see what the happening at 1 time and therefore what happens you increase the molecular weight on the travel time moves out as they consider as a powerful molecular weight and that is a general behavior of the system the banks of their are time and frequency domain pictures it's the same picture in a sort of cemetery and in addition although there is traditional places in the case but they don't want don't what do we find experimental well in the 1st place we could say about experimental work that way they included the .period Donald results from the 1st point I would make is the kind of moral scale and when you worked extremely well if you go back to the early figures in the chapter there
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are plots of the storage and lost on analysts which cover a considerable number of powers and frequency and which show considerable decay over the number of powers and all that you have in mind once the right through .period it's not there isn't line in the sand .period say has smooth very gentle curve and we tried to figure out what to do it's the lines go through .period scale it works very well furthermore it was the prediction here is the behavior of low frequencies here is a crossover that higher frequencies in stretched exponential curve and things like this Powell offered for things like this and that the transition the transition is very clearly moved ahead and there is no ball and it can only get is the 1st derivative twice the only thing was that we cross over from 1 other so there is there is there are very few cases in which this year will there the power of all the time data and the question is why do you see gap what answers will only need to improve the model in some cases slightly and inserted British function is very small .period and the other answer is if you have something that is doing something that large frequencies and as a result the curve is not quite as simple as you thought was followed when get the here there will be a very small deviations for example there is extra activity in the data that this place is that are all fine and how the I'm not going to make any explanation as to which it is trying to rationalize away pesetas at large frequency we do see something not regional phenomenon and 1 choices with Cordova who added a constant source of corresponds to to the top another possibility is please see however analysts added that each of those Powell was discovered over a decent number of workers managers are so it's fairly clear they really are powerless in this region region right crossover really is well described him soon to power losses again and finally in some systems we see what appears to be an additive exponential bald as if something was happening all the occasion an extra relaxation of the higher frequencies over there isn't a lot of traffic of continuation down here said exactly what happens a lot really large frequency we see on exiting the additive access to a relapse I can tell you whether relaxes and increase the power or comes back to the original power walk her all measurements just quite after all if you didn't know they were and what would you do that it's very hard work OK so that's the frequencies there are a series of fitting parameters he he pledged Council for each story lost 1 was filled out 1 of the alleged 1 each and then there there's our Europe and acts so there 6 parameters well maybe we should have won bronze were 5 parameters was said each for the storage and lost model the cutoff frequency is not exactly union and around the reason has not exactly been and grammar is that if I tell you what the history of art and I felt slowly here yes and I tell you that when we cross over from 1 to the other part the slow and the home altitude can be consistent that constrains what some of these parameters are so there really are quite that many free parameters but I'm sure all of them because it's not quite clear which should be viewed as the independent free parameters and which are a sort of along for the ride all the behavior of these parameters of solution properties is leasing power loss and there were powerless in the face of excellence the power the government there and forget all we don't always see power laws excesses straight lines with gentle slope plot against wall all so there is a behavior which is at least consists OK Is this good or bad well I'm going to fight 2 quotations from the book OK and so we have "quotation mark this is not going back quarter of a century all fairy discussing the only dependence on concentration molecular weight it is evident that concentration reduction scheme for transitions described involved specimens review or was referenced check the introduction cannot be applied in the plateaus of and indeed that no simple method for combining data different concentrations and exists the shapes of the fiscally lasted function change significantly with Di Lucia well as I've just shown you while there are changes in shape it is possible to describe the concentration of my weight the attendance was fitting parameters and therefore it is indeed possible to you know I didn't give shape now combined what Ferry Road in a slightly different meaning carrier was thinking in terms of reduction plots that is to change the scale of the frequency with the concentration that function or you change the vertical scale with the concentration and function and the courage just lying on top of each other that actually works reasonably well from discussing as a function of molecular weight will vary the same reduction approach does not work here we show something better than the reduction approach was to end the game there is fire referring in another poll here all the income
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from the point of view and on the other "quotation mark which is true Gerson preview goes in essence that if you don't you think this is obscure what's going on the security has now been lifted we can now show you want at least in descriptive sense what is happening OK there is 1 difference between what has been done here and what has been done and all the parts the book that I really want him in earlier parts of the world we were talking about for example the self diffusion coefficient of viscosity we took standard disco elastic standards transport parameters as actually found whether we took the transport parameters that are actually in literature and we didn't analysis in terms of universal scaling here we said we're going to replace the standard literature functions with to move functions he got primary is where he's from all of his other primal and we are going to analyze body new forms in terms of what we know now costs what is it exactly that she will be prime over as a 0 the sources and were interested in viscosity you think that we would like viscosity and primal already be consistent with being analyzed crime over there and once you've done that it's also sensible analyzed appeared to achieve price requirements the real motivation using the needs of society additional motivation is slightly different namely we have something plot against Oman the reasonable expectation that transport parameters that is dependent on frequency is that the intrinsic transport parameter and very low frequencies shows posse static all just as you can do electrostatics you don't have to to worry about radiation variables electromagnetic free well in order for that to be true the soldiers who headed 0 frequency ought to be 0 and these functions have their property the traditional she tried to dollar prime GW prime functions both go to 0 1 0 3 Monday so what else can we say well we can say 1 last thing and interesting horribly and the correlation between the Taliban and she the corresponding to unite Europe and what we find we go again Is that health those during his telephone 1 problem Martin was the other goes is that the 0 11 mindless somehow at the correlation is somewhat less impressive for we storage and lost models that turns out to be for now the year then however for he the about words virtually doubled from feudal X about roughly that's actually a very important correlation the reason for the correlation is GTI 0 which is 0 Shearer viscosity is simply a concentration is number determined by concentration molecular weight and in a certain sense this 0 Shearer viscosity would talk about euro all doesn't depend on Friday and friends this is some parameters that gives us the lead frequency dependence and therefore to was also being determined by Paul concentration molecular weight and the lot therefore the
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lowfrequency behavior is seemingly being determined by Bossi static property not entirely because the results of the parameters of Delta close to 1 please more people nonetheless there is this very clear correlation between the 0 frequency level which is sort of obstinacy and he frequency dependence parade that's about as far as now you could repeat guests but we can help them the here the cheer fittingly measurements show the same general properties that the this unless other is to elastic properties to that I talked about Cox versatile and Cox murders rule tells us that creator of travel crayons and area of Omega and you don't crumble member of Roman should be be the same or very close and therefore the parameters and for the easily get interesting thing here and we are to Figure 13 . 4 1 2 In Figure 13 . 42 all with his 0 and there is a very nice straight lines .period right on the lines :colon the limitation of course is that Jeter's material dependent part which is different materials in meeting and we find that is proportional to aid 0 and therefore we can write of capital on business this year then this is 0 exponential some constantly reviewed periodically but it's the same at all concentrations in light a status is 0 2 and a half they there you have the export of gas flows on so we actually have a formal offer for the shares being entirely in terms of 0 should Wisconsin that ought to be a theoretical look but I don't really can't really tell you what is now there is another clue on that figure of its most visible on how top long his service local notice that some of his service as a whole but in some of circles and this is explained all of the lead on the search open filled circles correspond to linear polymers historical always as she there while 1st from start and the current for many years and stopped all members of b they rely on the same line that is replaced linear polymer with the start and so far as sheer thinning is concerned nothing happened and you have a set of points ,comma stars as points of polymers and there is only 1 liners so the policy doesn't do anything the best thing of course if you use only helpful me siren so it was last seen discussion all sheer thinning and his very Hillier correlation which once again must sort of be any hint of to do calculation of only you I have about 15 minutes so what I am going to he is a few our on reading in the next chapter in the Alps discussed this we got the
1:03:42
remark on the next chapters the next chapters so the engine where the ball was going and the engine where the ball was going was not only year this going elastic property so far we've talked about linear Visco elastic properties where if you combine a series of displacements they and linearly and therefore what you see is fairly transparent and you see things which made frequency sharing on the next stop going to take up were loosely described as model year properties and he's actually fall into 2 sets all the 1st arises because the pressure of liquid pressure has actually displays tensile properties and therefore a alcoholrelated would be cheered the pressure this way the pressure this way and the pressure that way or not necessarily the same you actually have pressured answer not symbol the new pressure and there are a whole series of slightly odd phenomenon here that it appears that are in some sense seemed to be related to this piece issue there are about secondly they said what I describe as modern art we here at all phenomenon will actually sexual shows some of these and these are things such as large ocelot touring where we have to place instead of doing this they're doing that we all share fluid and stop and we lookin and ask what happens when we see a phenomenon known as sheer banding in which all of their displacements in fluid but they're not uniform across the height of we also do some experiments and there's amusing background story here get to where you for example applied shear 0 4 while apply a 2nd sharing the same amount or opposite direction and asked how the system response and you look for deviations which for a linear mediator deviations are quite substantial we could also drop in turns out to be a nonlinear issue on discussions of what is called extensional discuss OK so I'm going in the right now have some modest number of minutes to explain how I got off on the front end of the year is that waterfront sponsorship from a lot of it from him was that I had for a very long time been interested diffusion of college theoretical problem and the traditional core question is how does have the diffusion coefficients the self diffusion coefficient the mutual diffusion of began on concentration if you go away Back in time for 40 years you can find people believe light scattering spectroscopy measures the self diffusion coefficient Amien square emotional part as well that's entirely wrong and 1 of the key results of my doctoral thesis was to make emphatically clear the diffusion coefficients depend on concentration lightscattering theory experimenters homeowners and furthermore light scattering spectroscopy ,comma ambiguously measures fusion so there is not a question of how you calculate the the mutual diffusion coefficient from another properties of the liquid that was something that I worked on for several decades increasing refinement and improvement in the calculations on some of the details of that confined my other books all elementary lectures and statistical mechanics is the last chance are however that the arduous you needed a fairly solid background in hydrodynamic interactions transport systems about 100 dynamics have also been introduced polymer experience and the introduction of Paul and there is due to be good Rice from ball to the dynamics of a single ball and chain that is at the polymer chain and the notion of the polymer chain if we have a
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change in his case of the rooms he creates a hydrodynamic weight on the parts of change and that modify some the change in the last hurdle Reisman model all 1 want natural thing to do at the time was to take her rise Vermont and extended to treat interacting Paul Watson finds that people did all unfortunately a major part of the the emphasis very reasonable part of the trial calculation of the viscosity is a function of concentration by treating interactions between pairs of Paul what's if you tried to do this what you run into a few were not careful is the longrange nature of the hydrodynamic interaction causes the animals to rationally said to be divergent and therefore the theory seemed to hit a dead end that was in the early 50 s and the personally OK in any event coming back we were comes to I bossy elastic scary they are all very early on about 1980 we started to probe year the original idea was that we can measure the deal probes we can compare with the viscosity of simple liquids and we can look and see if there's anything interest I did I was doing this in terms of cold water water glycerol temperature dependence and before we got very far into this all once a graduate student who doing research rotation came by and spoke to various professors spoke that might hurt the wouldn't think final longtime afterward it was Allison White who suggested alignment Yulia polymers variant of particular policy suggested would not have done well with the particular polystyrene secure probes we had this was the wrong charge but that's easily fixed in final hauliers she readily told me we you can easily find Polly electrolyte farmers higher charges and fined neutral waters all fall and Soledad measurements from the field and after peace became the probe diffusion follows a universal scaling form please provide this case seems to me this is the program you can also compare the diffusion of probes small and large viscosity quickly and what is found here is that the all viscosity of the Lakewood does not determine the probe diffusion coefficient even for forward from that is if you look at it the the data over the serial concentration values shows up the protesters accused faster than you would expect from the faster than ever as a practical matter is serious or if you found the pros diffuse more slowly you would think well Weld stating the probes and its increasing the size the Paula's causing the probes to stick to each other and were looking at the future increasingly larger aggregates but all of those effects would cause diffusion of the insolvency the other direction fortunately nature was not arranged like this and it was clear we were seeing something physical read some poems .period part at some point in here all about 85 on Camelot said Prince 1 of his studies on Paul herself you and I looked to data and it was immediately evident Devers C was again stretched exponential N and while it took me a while to get around to the idea after peace was able to sit down and analyze divas a scene for a substantial number of different Paul on this got this got considerably easier this was after I got here only the eye you have microcomputers were available at midnight computer resources UPS feeding programs that help you do all of this all and therefore you combine all of these things and by combining all of these things but it was apparent that the phone
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herself diffusion coefficient followed stretched exponential viscosity and furthermore if you look the viscosity you also have also lost stretched exponential behavior now we had actually seen final Lin might want Michigan grad student had actually seen this the solution like like transition we noted all it happens and the concentration dependence goes from stretched exponential power law and that is roughly the point where the probe diffusion spectrum becomes probably by Mobil which was outside dynamic range for correlated with 64 channels linear correlated we get our dynamic range so I put all that aside because we didn't get the instrument and to a certain extent I never completely got back to it but it was clear there was a regime at least 4 people Polly acrylic acid if you went to large molecular weight and to higher concentrations something complicated but in any event at about 87 I published the heart universal scaling waving paper which attracted some and since there was a very controversial I made a point of viscosity in particular and also for probe fusion days more viscosity of going through the literature result after results showed that the plot a lot of on the the price which I draw a line through and a nice smooth curve did not have a straight regional power along the 1 power with its it would eventually be discovered polychrome onto the rocks on top of cellulose but there was a system that showed a straight line region all we got age PC for a considerably different regions reason namely you change the temperature you can change the sole quality from good faith and so the original interest are interest was reasonable wanted the good and the fate of polymer transition and that straightforward so Ben we're Syracuse privately admit that if there is an equation there ought to be a derivation for what we that I sort of had him somewhere to to go and I found the derivation and was selfsustaining similarity that is the health of the CDC's proportional constant finds of showing that came from and then health becomes a constant flow proportional following size and power but only gave the exponential pure exponential however that while I was ucla's about 78 I had sat through a series of seminars with Phil thinkers was studying polymers and who was working through the details made following various ports in and humans and my postoperative fights all beautifully did I have not been involved in it on what I the factory's United holed up and finally remembered was that it was known that you don't fall over and changed its concentration is on track not lecturing contracting and you end up doing this in beginning last fall and didn't do was small and if you put this in the year you've got stretched exponential behavior of products respectively if you are on the increase concentration of ,comma against it doesn't get a lot smaller but it gets a little smaller but so it put this together all that would make it 1 of the things we used to analyze and was sort of the front led to this book all sorts of things that were halted transport properties :colon and announced in all the other thing I did I read happened to run into a paper by hand holds where he discusses Paul positive function renormalization and the appointment drew my attention was the depending on where the fixedpoint will as you can get either stretched exponential were Powell my interest was very strictly at that point stretched exponential and therefore above 98 I didn't derivation the renormalization group derivation that leads to the stretched exponential using the 1st few terms of the hydrodynamic performance imports and how that actually leads to the renormalization group derivation of concentration wants spot 0 I was sort of aware of Visco elastic properties and if there was solid .period rented really recall the details I try reducing these and I found the temporal scaling analysis and eventually those bit later I found the rationale of leads to heart really isn't on sorts they do not have the I happen to be fortunate that I was doing this and doing calculations for example viscosity concentration I had come in from the behind hydrodynamic sites to call its that's why we have apology after I have had some exposure to biology with out someone after ragged parents get off the court and conference calls I happened to run into paper by Robert Baer prompt box that's in electrophoresis chapters where they referenced 1 of mine suddenly realized he is another way to do it during motions before the major driven motion studies I knew about were the ultra centrifuge studies which are now a halfcentury Arts on any of the things sort of came together because I I happened to be in the right place at the right time and was able to bring things get all we're out of time but I give a little bit of historical events In our next discussion we would be next week we will take up not only you this goal elastic property yeah that is today but it