22 Viscosity

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22 Viscosity
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30 (Lecture 2 missing)
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Lecture 22 - viscosity. George Phillies lectures on polymer dynamics, based on his book "Phenomenology of Polymer Solution Dynamics"
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classes in polymer dynamic based
on George Phillies book phenomenology of polymer solution dynamics Cambridge University Press 2011 ends today this
lecture E is lecture 22
this Scott City I'm
professor fillies and this is the next lecture our series on phenomenology of polymer they were going to continue with the discussion of this cost viscosity is the resistance of the liquid report the larger viscosity the slower things as the old saying goes as as slow as molasses Janeway I'm going to begin with the general philosophical observation that is we're going to be looking at a very large set of measurements different measurements of viscosity is various polemicist and questions student might reasonably ask is do we really need to look quite although special so there is a fundamental philosophical question here there's no question of approach the starting point is fairly straightforward suppose you have some theoretical model and would like to convince people theoretical model was right well 1 of the several legitimate choices say I have model I will look around for a few experiments from by people waving her book I won't claim that he asserted he experiments to test the model I drop in the future he experiments as the test and I will stop and there is nothing wrong with that or you can say I look at a few samples studies and things work that's good enough now the strong point of that is that saves you enormous amount of work after all phenomenology of polymer solution dynamics of this work was edited down from I handed down from length and there was 220 thousand words he was approaching 300 figures the Collected Papers that I analyzed to do this filthy water off Ireland the other part of the section of papers on a typical topping ranges from something this state to something this state and thoroughly finally got a sample items with much earlier however In there's certain problems with this approach and if your ever tempted to follow it you should realize that some of the problems the 1st difficulty is that if you only show a few experiments anyone who disagrees with you will claim that you were cherry-picking you didn't take your measurements but you selected from the universe of measurements a small amount of measurements that really agreed well with your theory and if you are only allowed to the larger whose collection of papers say 6 instead of 3 it would have become obvious that the 3 measurements you looked at all were not very good and the measurements that were valid were out of a much larger said rather the measurements that are Varela a much larger said the measurements you looked at teeny-tiny suffering 1 of the large set measurements well that's a major problem with looking at only if you take the next issue was always looking at a few papers is that people may without being quite so aggressively critical as saying work on various elections take the position will yes but I know there are a large number of measurements most of which I did not just hear about and if I look at those large number of measurements I know without really looking the model I believe it's really right or left allow all the way to knock people out of that is systematically to reanalyzed everything and leave these people room on the chessboard so to speak in which to claim that all their data is very model was really right just that doesn't happen to agree with few data sets we don't have to look at the the last virtue of looking at all of the measurements is that if you look at all of measurements and do face to the theories in general you end up with a few extra parameters parameters whose of dependence is on molecular weight and other factors you can now study systematically on the virtue doing that is that if you do look at lots of measurements of the research important trends become transparent and you can then advanced to the next step of asking how you understand those prints that as you can use the analysis if you've got enough of it you can do better analysis see what is revealed by all the measurements put together not in individual measurements separately and that you were driven in a direction that helps to take the next era theoretical steps toward the stated so that's what we I did what I did and as you will see the best opposite viscosity measurements and greatness he most of we start off example 12 . 1 Figure 12 . 1 this is work of Jameson and salvaged and they're looking after polystyrene and provided this is as classical polymers system is used in Lowgap then looked at materials ranging in molecular weight from pole was reunited the 720 that ball and Hammond dollars In staff measurements ,comma about forest management to their measurements the measurements will buy back look-alike stretched exponential so you can look at this figure which is worth far more precise than my sketch in this the yesterday
the stretched exponential is really describe the measurements accurately through all concentrations not cost perhaps you'd like another set of measurements all I'm not going to do everything here in Texas after all fighting talked about all of them you might be tempted not therefore I thought I had to figure 12 . 3 which and will run with all candidates figure 12 . 3 What we see Garcetti's of signs of violence the outsides of violence have work virtue the biopolymer they're very different from polystyrene were now out water and organic solvent but once again the molecular weight range from studies was 128 "quotation mark what for 3 that's all there is the experimenters had a series of samples each of which separately appeared to be monitored 1st and what they were able to do was for each of the measures discussed city as the concentration was change for skies violence for a given material on the viscosity changed by about 5 workers managers over the observer range concentration the observed ranging from celebrations vary by about a factor of 10 square all you could always wish for measurements to higher viscosity and higher concentrations but you should realize it's very difficult to work with highly concentrated polymers and eventually unless there is a strong reason for doing so will see a few studies is that it becomes harder to justify his pushing on just to save you the nice curve once again is stretched exponential and the concentration dependence of each of the viscosity of each of these molecular weights the same all over lines on a stretched exponential there is a long way and why it is useful to look at a large of different measurements your and the reason is that viscosity unlike a number of other physical parameters of the study does not show a single universal phenomenology is that it shows too different phenomenology is in different sets of materials is not quite clear why it does so by if you only have to look to the few sensitive measurements you might not have realized that there were 2 different phenomenology is out here were different systems and because there are 2 different phenomenology spot there's a physical conclusions be drawn it's very easy to concoct a physical model of the solar cells in which you say here is a simple physical picture of poleward chain it's a snake and bamboo grove it's a bad beads these can escape because the inside a water passing back whatever the is it takes a very simple picture of polymer boil the looks to be the same for all polymers those calculations on and 1 gets predictions which looked to be the same for for all followers well that's fine except if you just don't let you have sort of just predicted that there ought to be a universal behavior of all the viscosity versus polymer concentration and as it turns out there is that 3rd 2 different sets of universal mediator for 2 different sets of system it's not quite clear so far as I know why you get 2 different sets of the all wanted interpretation is home that there is if you think in terms of renormalization groups there are 2 competing fixed points and in some systems 1 fixed point wins at all concentrations and another systems 1 a fixed point wins lower concentrations and the different fixed wins at higher concentrations and that disk that meant a description which unfortunately doesn't carry what further yet but does explain what you actually find nonetheless the important issue is that there are 2 sets of phenomenology from all over viscosity and therefore any physical model has to have some rules someplace to explain why this case OK so let us struggle and was struggling the year 12 . 5 12 . 5 is a merger of 4 different sets of figures on very different materials although we can make several different comments about it all for example in Figure 12 . 5 being the trails the best friends have raised molecular breast waits 330 kilovolt 334 also complained the 16 Villagomez we once again stretched exponential curves
describing the concentration said this time the range of viscosity is covered is quite moderate on some of the the other day that I find it interesting point to be made if you look at those measurements and this is true of each of the other sets measure very clearly point slide his her but I think my understanding where we're planning was discussed now the statement the points while stretched exponential curve doesn't absolutely prove that the stretched exponential is the answer you looked after all could be the case that there is solid functions that used you very nearly the same shapes but has a different mathematical structure all finding such a function would be an interesting extras however Wall data doesn't necessarily prove that a single set functional forms right it does serve this through forms that appeared different shapes her for example something and predicted that long data shows "quotation mark of all of the I'm not sure why anyone would expect is already clearly ruled out by measurements on the same line and model that produces the viscosity those who seek to text these concentrations extend 0 any model that predicts that down the lower concentrations is very clearly ruled out because CDs from loyalists parade year and Terry definitely Americans not only on straight line you may argue what they do on but there's certain things very definitely do not OK
stay with figures of the fight we will very briefly figures 12 . 5 C B and the issuance security of blond locks viscosity Peru's media concentration now the linear plot has did of concentration has the disadvantage that if you cover a very large range concentrations say 10 to the minus 2 of them were 100 grams per liter points down here to get cramps get the advantage of this form is that it's set lot lot what is similar to other parts of the son-in-law of plot state exponentially .period easily in season the 1st power the nature of simple exponential in straight lines the measurements of course not violent straight lines on the spot that's why a lot of things In her and the curvature away from the straight line is the fact but we are looking at a stretched exponential with the agency the case or in terms of law area versus long see something with like this -minus pots it's very tempting to say what we could take a long time we could take a lot of what we can do all sorts of things and you should remember that you started out with measurements there probably accurate to 4 sent 1 % 5 per cent 10 years whatever but if you have measurements that accurate to about the same fractional error on a lot of the hours because are going to be about the same size everywhere along her that is if the error is a percentage of the value when you take the wall the lot of the errors of linear model the values and the error bars of the same size that's what the human eye expects to be able to handle looks graphic asks users are amendments on the graph consistent with what the human intuition sort of expects all the data points to the same roughly similar only equally accurate and have error where is about the same size if you keep manipulating measurements say supposedly plotted as he considers the laws of the loss of a new good there and if you blow up vertical scale not very quite impressively however if you do that you should realize that when you take the the 2nd logarithm you distort the size of the era of relative to this end in terms of the display of whites on the Brady some sense of measurements are much more accurate than others in terms of how the era of hours here the alternative way of handling this is to nonlinear least squares weighted linear least squares where you can put in direct weighting coefficients so different measurements are accurate to different degrees you can account for the and asking what sort of her efforts and there are at the end of the year well what that the year 12 . 7 are results of such all you looking at all 60 to 34 300 still it all and the Polly healthful level styrene the he should furious wide range of molecular weight and get a lot lot of plot viscosity concentration and once again this season tops that is once again stretched exponential form counts for the behavior of the men so all what does this tell us tells us all since the other directions all we can advance from America to call what's next year 12 . 8 . 8 but we have polystyrene the character the horrors nature of a fluorinated by feels it's safe and effective ,comma solvent the advantages and disadvantages that can be quite biscuits and this allows you to move phenomenon into timescale that your instruments can handle it's also will interested in its own right "quotation mark the measurements well you're looking at 10 were changing the viscosity and the changing needs of that is previous curvature you're seeing the figures are it's a bit limited however you very clearly are seeing terms can you on not seeing straight lines To say that flights "quotation mark let us advance on and we will advance on that said remember viscosity shows to different phenomenology warranted to different phenomenology discussed the water of the wood a single stretched several stressed that there is some assistance from the years you have an issue that has stretched exponential behavior works fine except in very low concentrations there will be fewer points red insisting that lie below the stretched exponential growth however let us push ahead and let us look at the other phenomenal many other phenomenology this the solution lies we don't want to hear about it I should 1st dropping viscosity this will be a long stalemate concentrate and we have fresh testimony the here and then some concentration there is a cross over so down here we have in the office and end up here we have a straight line ran earlier due the power of the case here's anywhere he able to describe through the use of 2 functions this with great precision on the 1st experiments to recognize that there is a solution might not like transition of adult life title people want it graduates knowledge and my universe national chains while universities American measurements that's what it looks like the what happens if you're taking up the new round of concentration somebody and that stretched exponential hiring now there's always the question is do you about using 2 different functions is this real or is this some sort of an artifact
also his incentives crossed over here is the crossover really fair or is a crossover someplace else and your choice of concentrations generates various other the answer of question Where's crossover and how accurately can you measure it is readily settle by choosing a variety of different points of crossover feeding time the material at lower concentrations stretched exponential and demands of higher concentrations of power now what's going to happen if we do that well suppose I made my move part or all this the same argument applies the address so I cut off down the stretch as financial management continues to feel quite accurately because after all the data that is stretched exponential however you know trying to fit on these straight points something .period which is a straight line part of which is moved away from the straight and as you move the cut off away from the right location wrong location all the RMS error in this thing blows up it blows up because you're trying to force measurements don't look like your function to agree with your function on you go in the other direction and have the same problem namely the stuff here does the power will also be the powerful words that has stretched exponential rapidly diverges from the powerful and so on and on after all year the in this region it's not going to be good distorts stretched exponential get the best agreement on and once again the RMS error in the 5th goes up quite dramatically but Carol Quinlan I continued this analysis Carol women's data on these data were quite emphatic there is correct place for the figure for the transition and if you put it someplace else you're obviously doing something OK so that is the notion that's why I think there is a transition we discussed a great deal of work on article produced fusion among scaring from hydroxy probable cellulose that's in the chapter on on appropriate use and these roles studies done by last year and by studying how probes going through all the solutions and by studying light scared by the polymer itself we found a large number of optical spectroscopic features all of which means but there is a cross and all of which agreed crossover is about the same place OK let us 14 had 1st and look London was that In towel at all and how will it all measured ,comma viscosity over what was in fact a full range of concentrations only applies to the following spring ball and then went out to volume fraction of what that is they work actually looking at them now at the other end they got to at least on way to and what they said was ah measurements agree well with Powell of or if you start out at the mill and worked out and see how it was an eye and fair balance I have been a little more conservative than I in extracting and saying how far down the clean power loss forms saying if you want to argue they go for "quotation mark however I took my staff were it was very clear in the figure and all over the region that examines they found that viscosity goes parents were addresses about 3 Best Classical reputation value for the predicted concentration so that is developed very close to the mound and these concentrations certainly did so you can find concentration skills I should note that most of the experiments that I discussed were referenced in the earlier part of this book are confined to regions down here and there not great on the of measurements taken at only about 4 . 4 volume fraction of about 400 350 grams all so Talal explored this area out here which has been very little study may actually very clearly do find concentrations now let us push ahead another set of measures to get out there and also 1 of the solutions an relatives of holding it all the measurements Colby at all all seen in Figure 12 was 1 yeah and the lower concentrations they see a stretched exponential and at higher concentrations you carry this out the issue Powell however they did something that many people did not used to salt and 1 of the solvents was insolvent and 1 of the solvents was Faisal someone's always based on this the other solvent the viscosity was higher fares that cross over there you have to end up here because this is a tough sell volume fractions want no polymer notes polar solvent at all just follow low-salt and there were no matter which sold you were using when you get a clear same on and I saw 2nd first-rate power Walter I on here there's crossover someplace so they say actually saw this behavior where are these crossover roughly well this system crossovers are about 5 people who agree that rocks that is you've got a lot concentration range reduces the power law and much less receives stretch text all right another set of measurements natural wonders I found myself what found favor with the paper is by a Soviet World itself former Soviet Union told Times by the name and what always able to do was to collect from the Russian literature and the Russian conference literature a very large number of sets of measurements of Paul viscosity are at different concentrations most of which is not available in the western English language English of alphabet the literature and what he was able to do was to call said then we did these very through measurements now ferocity measurements were throwing in several respects for starters the measurements used a range of different instruments so they cover about 4 or 5 orders of magnitude that were covered in a lot of the other things we've talked about the viscosity about discussed how overnight health orders of magnitude that is the author's started out with dialup solution and they pushed very close to the melt in the and therefore the number of the figures from the area was concentrated the arrange the staff for a while there is a very large change in the the viscosity of the other
thing that was done was to do it's been done pleasantly in some other papers certainly not here was to say we're going to vary the sheer raised by a great deal because we very share rate by a great deal we can ask Well is it possible for looking at a system that is they shared thinning Austria thickening and therefore the fact that we're seeing her particular results but arising because as we change concentration and other things the amount of of sheer thinning sea change so they were able to change a lot the on applied stress by wanna have worries of meant to and they found that the measure viscosity didn't shake and because the measured viscosity did not change they conclude their deal in the low-frequency low shear region where there seeing linear discovered last year the other thing they did was to look at their measurements and asked what the he variables off and what they found was the key variable the intrinsic precocity the area no data is the linear leading slope and the viscosity it's a dilute solution properties however Ada also characterizes roughly how large the intact polymer chain and what they demonstrate as they take their measurements for example Figure 12 well .period 12 . 12 on results in the mountains however traders and the A-12 went well she if you look at notice we're looking at college dining with his theory that almost not started In Hand said in looking polling you dying were sold in the home the plot discussing the issues concentration Stasi Law and affordable housing areas due to Nigeria's management which has a lot and then only date is a looked at all Polly buiding means having a wider range of different molecular weights now just plot discussing various concentration you would expect the same law molecular weight material has Stasi really means a lot of great priests and as we increase following electoral away from an increase in the fall of molecular weight and viscosity increases more and more rapidly with increasing concentrate however at what they did was to be part of the stars of constant but as a function of C data were aided in Syosset suddenly all of these measures which cover lots of ranged from a low of viscosity lots of range concentration wider range of molecular weights all of these measurements collapsed onto a single over there is Ada is of good graces the missing variable the of the behavior of polymer how fast users even in things very close to the belt is determined by the size of the entire column checked and if we use the data is reducing collapsed everything on this the sitting over to stretched exponential to concentrate and beyond the stretched exponential growth Howell now as I said there are a lot numbers of different measurements to collects and there I will drop in the peace which is you don't actually see all measurements you see and some others have simply noted as you approach the there is crossed over to another increased which is a little harder to make out the terms sale 4 the Balkan daily life it's not here there is very clear that this is the next year but all of the viscosity of all of the different polymer molecular weights line on a single were used the intrinsic viscosity as reducing very polyester where is this crossover over the occurrences about me all data has another feature I said that it is approximately the size of beauty part of polymer chain of aid ahead of U.S. all volumes the word it while see as GM all you see a different asked how concentrated on these chains as well as on any of the others the chains are put in the care of the rest of the year shoulder-to-shoulder courses statistical reacted not their bodies in the capital on this the data is some who might also want to work for so these crossover personal changes are already considerably with those results of Multan on the other people for example the results of loss these measurements are on Polly time fueling her again called on the same insolvent this kind of and once again she uses spectacular In terms of the range of viscosity discovered at the values of a variety of instruments there's probably waters of Maryland who viscosity represent and we see it stretched expert at the National Institutes French text and then there is Nice power cross over power law and very high concentrations of melamine being approach there is further increases of something else is happened although the cross over here and see data is for something around there a crossover is so some concentration much larger CAD war on useful .period it's implicit in this fight isn't spelled out because of the way things to write these amendments that many the variety of different molecular weights the use of the intrinsic viscosity has taking measurements on the series of different molecular weight all measurements the overlap in concentration .period considerably and is compressed all the measurements of the stuff that the single work off however if it is able to compress everything to a single curve but lost the case that there is a natural viscosity of which this transition occurs as well as a natural concentration and that's brought out by other sets of measurements will also get to bed is a model for
this compression were all we have to have crossed over from stretched exponential Powell behavior BAT currently at about the same value data and all of these different molecular weight and that is exactly what it was for all can we do this again well I could take note of the the results of data failure at all represented to us by the fall look at once polymer which is a 220 kilovolt poland's polystyrene and 220 kilovolt polystyrene also is studying a whole lot different solvents if you try to use the data to be heard he discovered were sold well using different versions of the crossovers are however on the CAD reduction clearly does not work as well for accounting for changes in solvents strength as it does in accounting for changes in the fall of molecular weight OK the results collected by the the poll also shows that if you look at the problems of the case of a case of age is effective making certain further reductions in the measurement and generalizations described it was but I let you speak for itself he has a lot of lessons that will get
him at the end results due to "quotation mark so this is not the result of currently figures 12 . 2 they studied a very wide range of molecular weights when he tried to deliver also held 3 thousand people then start II my following a different color they looked at Pollyanna Hextall by society and haven't done that haven't looked this polymer range of different molecular weights they also use solvents used toluene and they use them for the day of a very solid quality and haven't done all this what whether the plot shows is viscosity lose concentration and there's a stretched exponential revealed and there is cut off at about the same viscosity and all the systems and above the cut off the Powell was seen the next the value of X the greatest variations on the 24 . 9 9 at 1 end and as we increase the molecular weight asked decreases of 4 . 9 3 4 so there are power was out here there slopes of power Wallace and explanations and the explanations themselves dependent on polymer molecular weight when the crossover the crossovers are located in Tainan over 8 0 reduced this gossiping about 100 exactly 100 will not necessarily exactly pretty close if you ask for the crossovers are located in terms of what the on discussing the terms of the concentration the concentration changes a great deal of molecular weight see it's something in the range told war however Washington shows very clearly and spectacularly the 2nd phenomenology the transition from a simple stretched exponential power walking the export of the power will be depends on Paul molecular weight saying the expo Copeland of other things consists of and now
we reached the ears of life the measurements were governed by whether to retire early on to what measurements harvest custody versus concentrated we're looking at a couple of molecular weights St. Paul and if you look you very clearly see stretched exponential behavior and the behavior although the law of box in the instead chose using narrow regions fresh exponential and and narrowing transition to the straight-line Powell what is unusual about measurements is that there are 2 dozen . 2 dozen points out that those were the only like 70 points or more the viscosity measurements were done using overloaded can fenced-in sculptors Our here will there is a lot of command virtually available started we find as a result out here float times were on the order of 4 or 6 hours searching in morning very carefully set everything up and make sure that everything was going get the experiments going for the next day and then I have not great deal students don't have nice lunch while waiting for the offload over the flow occurred all over a very long time to be sold to got to the scholars can give fairly high shear rates because the times were extremely long the sheer rates were that I will also she repeated the experiments with 2 Golota's giving 3 times the float the other which means there's really long experiments here and the float times were exactly proportional in a proper way as as you change the flow of time by a factor of 3 you change share rate by a factor 3 and the tell which set points which I right so we're we're very clearly in the low charade although at least 1 senior editor of 1 of return only his name out of way to Paris commented beautiful probably the best set almost Vural and set of measurements viscosity is called and they very clearly shows stretched exponential very good greatness and the power loss what can you say this is phenomenology that is not the same all OK and so for hydroxy probable cellulose has extensively studied there is a solution like well like transition it appears to be a very sharp transition year appears to be an analytic transition in the sense that a lot of these long enough went see his peculiar choice was made so that if you had a power law and just get constant out if you look at the logarithm derivative of the water and function of the function concentration something looks more like that the Wiggles up here all their larger than the current noise and we weren't quite sure whether they were real or whether this was an artifact of how we were having to extract this area that father is buried in there and important lesson it's very easy if you have Cecil measurements to injured roles of the data and get area under her curve if you try taking derivative of real data like becomes much more difficult years Europe .period and if you look at a narrow range of measurements the signal-to-noise data is such the vertical variation the data the stated is is only moderately less the verification measures the fact that the function self-restraint and if you intend to think this to extract the slow you run into difficulty derivative becomes waste are solution was this sigh they all rely packets by 5 7 points we will face this 5 per cent points here and what works by the water at a news agency 0 Plus Long plus a ceiling where concern always parameterize say what brand and the slowdown in this and absorbs a fair amount of Norway's we use 5 to 7 points with view average over what points you get more accurate results however refused 5 7 points she encourages caused problems so we say encourages on inscribed by what best-selling pulled our slow about and what we were able to show was that this system not all systems but this system of the slope actually makes a smooth transition to function McCain now the other people we could talk about N and not very bright light financial certainly acknowledge that and rumors and rumors flew to stop all and reversal polymers with lots of stock of arms like 32 or 64 or 128 were to impose itself on a few of those measurements you say this is stretched exponential there does appear to be crossed over Powell the crossover herders it goes something like old . 5 5 then is the crossover workers in different systems at different concentrations the crossover occurs at a very high volume fraction and the crossover SUV increased the number of Lawrence tends to look like these share crossover in the sense that the slope of the strip Powell or increases and for the largest arms stars really doesn't appear as tho the measurements of the viscosity on the power of power or the life of all the use of application would have stretched exponential that's exactly the phenomenology fears and with the movers measurement shows there appears to be a way to show continuous transition from linear changed over the years by looking at many spots of day we will now advance figures 23 but and Israeli necessary Monrovia all measurements on the animal here also book by the way Edwards would have mostly about on all over however they drop in this 1 set of measurements and discussed what it means in terms of the theory but if you compare my measurements the original paper of no the and with what you discover the few data points that do not appear to be in the original fears that clearly albeit also
apply to their clear collaborators and so violated his promise is actually based on the figures would at work having said that what is going in these 2 figures whose class scoffed for his molecular weight and the same data points viscosity versus concentration that is the original authors looked at a given system they look a whole bunch of different concentrations for each molecular weight of all that look a whole lot molecular weight polymers and so what they really began as a three-dimensional object concentrations molecular weight and viscosity and vertical direction what I presented figures 23 . 4 slices of the three-dimensional objects and if you look at the slices you see there are bunches of stretched exponential and molecular weight and concentrate the measurements wanted as long as discussed in the office the measurements clients perhaps all of this figure is in a certain sense triumph of doing things like computer namely in order to generate 2 figures all that was needed to do was to rearrange spreadsheet in telegraphing program where to to look and again and only 1 of obtains results book now why are these homes results of particular interest the original reasons they're more interesting there's no scientific namely the silver medalist the Hawaii Edwards site has proven viscosity is proportional to the molecular weight some power and they pointed the figure they say Here's here results confirm that you see scary what's now if you actually look at the original figures you realize that a lot lot lot measurements lie on smooth curves smooth curves as a function of polymer molecular weight smooth curves as a function of polymer concentration and therefore not only the measurements may prove that there are power loss scalable behaviors the measurements the air here's straight lines Americans reject the claim that there is scaling of the however here is 1 the set of measurements in several respects Stanley lots of concentrations lots of molecular weights the wonderful measure no-fault medical school and it was a sensible choice to take up the issue is that by selecting a single set of data rather than looking at the those data those other data quality was possible apparently impossible look very well in other words a modest deviations but they're just modest deviations we don't have to worry about please that's what appears to be heard because the Office of the Polish and indicated they were seeing scaling walls behavior when the results don't seem to as viewed with a more skeptical eye in the house don't seem to sustain that line OK the last thing we and for all that is discussed what happened when their leader and stop and we will be looking for the moment at figure of 12 . 1 5 12 . 25 shows as a function of concentration and molecular weight on the on the viscosity of Polly Supremes hits mostly intact for decades mostly renewals gracefully all polystyrene after that the several of words the other 1st noteworthy feature is that the molecular weight is high enough in the concentration studies cemented and the concentrations cover a range of people 20 the several hundred years and when 1 is talking about molecular weights the molecular weights are hundreds of killer dolphins were higher than the concentration use 330 grams per liter so the 2 sets of parents years along with a given column molecular weight which was about what Meggett although looking at on concentration dependence and then there was a measurement at fixed concentration using a series molecular weights and in both cases in this system the viscosity of linear material won't let us go the what therefore if you been looking for a key experiment that clearly demonstrated good layout great experiment was on lots of measurements all the things you might want human looking for a key experiment you could widen this 1 said yes here is a system that does show scale and In terms of architecture where there is a lower concentration solution like routine and copper concentration of power will melt like regime are this is a system that shows the solution lies not like transition from the do and this is a solution in which we are in the middle like he however was comparison name the comparison was made with foreign 6 stars show that the number of firms and it's 6 AM what 1 guest as a function of concentration is heard and what is immediately visible is that .period Homer you're not seeing scaling behavior you were seeing stretched exponential the viscosity of historical always starts out being significantly less than the viscosity of the linear polymer and increased concentration or even increase :colon life way persevered costs if you look at the figures mask other person peered across where there are a lot of measurements of the above the cross answer is not the only very few points set that is very very give thoroughly and agreed to stop all workers are more viscous and linear all so you look the changing shape and eventually found an interesting feature namely there is a solution might not like transition for many of these linear changed as the measurements role not likely but for the star polymers released over the range that was examined there is no cure corresponding change from solution like the melt like you always see stretched exponential concentration molecular weight and all of the other figures for example 12 . 26 in our show exactly the same thing namely from branched polymers you there is no known system in which you see strength stretched exponential power walk across you only see stretch the all qualification the number of studies of solutions of stock polymers which is much smaller than the number of studies of solution many of their a lot of systems in which the transition does not occur for many years all and therefore it is possible that if you look
at different stockholders you would by and by fine groups of polymers that do show the transition however you don't see the transition systems that have been stalled for a more you don't see the system In a system for which the linear trend homers does show the transition so if you say it's a chemical effects that you see in some linear chains but not others it's more complicated than simple chemistry because she has stopped all others never showed In any event I have run us out of time I have discussed how viscosity depends on a variety of variables I still have some measurements left to discuss and will discuss the remaining measurements will discuss in the next lecture Systematics how all of these fitting parameters I've described interact with each other then we may be able to push along we're approaching where we're going to discuss this week last December ,comma however we're out of time so players


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