29 More Inferences from Phenomenology

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29 More Inferences from Phenomenology
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Lecture 29 - More Inferences from Phenomenology. George Phillies lectures from his text "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 29 more inferences from polymer solution phenomenology I know that this is a short lecture the remainder of the lecture on the hydrodynamic scaling model has been transferred to lecture 30 2 I'm a
professor of these and this is the next lecture on following solution to I was going to do today used to discuss more generalizations and inferences that can be made on the basis of phenomenology we presented most of the earlier part of course all that advanced to treat a theoretical model that perhaps explains how polymer solution works we've reached the point in our discussion of inferences we were going to get discussing hydrodynamic interactions and the wild allegations that dynamic interactions might be straight off the beginning point of this very simple issue we have more than laughter some friction .period it's moving very slowly it sets up a low-wage surrounded solution and the way acts on remote objects and given that we have velocity here induced philosophy here we get ask Televisa related the relationship after all we thought about something that may absent factor on 2 factors is the old intends and all to constants critical this might be a form of the opposing defenses along with the distance From the particle creating the way to the object and which wages acting then there is the test so there is the seemed hands all the notion that you'll sometimes find Texas on all the idea is that if we go from all couple articles of water to a polymer solution with assertions that the intensities screen that is the distance the head goes he miners carefully ,comma over so now screening the phrasing is borrowed from an understanding of electrostatics in ionic solutions that is furious ionic solution we have here positive logical and and surrounding it we've got soldiers dressed in water John Paul line lasers there will be a preference for the negative ions in the solution :colon posted positive on and through the positive ions on the average but not in response to the repelled and if you ask the electrostatic potential around the positive ions looks like well last plot starting at center to the amount of charged encased within endows lost fear so we have charges insiders fear and if it's atypical protein have charges are all of the services so you should also know charging to the surface and until end all all small number of gallons of the surface appearance words charity lies is all surface and that as we make this sphere larger larger well we're encompassing you knows more minor silence positive ions and therefore the total charge inside this is all your fault as the net charge eventually falls and you go out Foreign Office Solutions electoral neutral and no natural now there have been the surrounding David Lyons you just can't belong the shall positive ions service the potential of God has won over or long however because we do have the silence on the surface the All Monica All component is screaming as easily highest capital all park no I send multiple component on the charge distribution may have died all quadruple etc. moments and if you look at the page revived her work but and Scatchard which is about 3 quarters of the old at this point you discover that in general b on elves moment goes as the 2 have talked finds :colon Jolly old Catholic told her ,comma the old 1 item might sensibly asked Congress very interesting for for what is happened and camp but is the dividing line device screening like it's a actually in the 1st place that is the determined by how salt you have the surrounding solution the less salt there is a solution in the long range the interior so there founded by screening workers we can also draw a freshman physics pictures screening in in terms of electrical wires coming out of positive that shirt is the Dow's Lokichar strong freshman mentions but the ideas all marriages positive charge and on and on if there is no other that the role of the ions around the lines and electrical the electrical field lines all come out the positive ions and keep on going and since the service of the spherical shell out here all guest lodges a square on energy she's density of the alliance falls off as well over a square which is what you would expect guests and that's what the rest of the of field lines enhanced forced falls off
however if you have estimated time of year why is it flows out from been positive charge at the center reaches a negative lines and a file and consular staff because swallowed up that's what negative ions to at 6 fields and therefore you started off coming out of of here with a and as you get further and further the number of surviving field lines is smaller because the negative charges counter on the actors said so that is a picture of how electrostatic screening work you will occasionally find people who make the amusing implying that all long-range forces screened and of course that's absurd nonsense because there's this on a long-range forces nature called gravity an acceptance .period a television shows and wife gravity is not straight so you have to long-range forces of nature which you can easily .period at 1 of which is screened 1 of which is not screen all and therefore you were under no particular obligation to lead whether long-range forces should be screened or not while Cameron said that you then asked Well how would screening of hydrodynamics work the drop this type of work so there is a moving object smoothness on the baby it exerts a force on solving because it's moving through direct force that during the course of sold in this direction so what happens is bombing momentum into the soul and the viscosity of the fluid and assures that the momentum is Trans World away from moving object fact moves out in all directions that would be overseen by a series of describing the transport of momentum which is factor this way but is being transported sideways so the moving object creates a wait out here prompts momentum and fluid out here so let silence about notion is this if there is another article in the spirit of this article Of all the more influence and counters this turtle and points force take the on the particle and since there is no worse than the government particle the usual the Aloha says there must be a forest miners have been on the soul and therefore because the solvent is put into force on particles out here there's a backwards and forwards the other way and momentum is sort out of the flu this is a remarkably perceptive and totally wrong Oregon the reason is totally wrong is that we're talking about a solution these particles are a free-floating and because their free-flowing over any significant part period of time the motion is completely beyond the fact that have ownership is basically irrelevant except on very shortest time scale and therefore almost all timescales the particle minus the solvent is the 0 therefore the particle bobs along with the flu and exhaustion Warsaw From what these particles out here or a thermal equilibrium and because their thermal equilibrium we know that the square outside the hold the square outside Europe some of the waste that sometimes accelerating particles bayern by it must be the case with the particle woman was assaulted friction and was sold out again and when it slows down the momentum that has gone into this particle has not been destroyed momentum is concerned that's the opposite of this situation where Potters Field line flows into the negative charge yes and comes to a stop will given amusing electric stare Paris Is this shoreline is swallowed up and destroy the momentum that went into this particle on it has some bad moments storage mechanism Bayern biographer and set scale has to come out again and there were moment comes out again and he made the standard there is a movement that has swallowed up here may have out different directions but it's scary but it is not absorbed let me give the correct elected think this will just now correct electrostatic analogy it will put around here he said Mattel's OK and a piece of metal as acting on a positive feel like and what happens with his physics to also compile updated charges on his side but because you pile up negative charges on this said instructions had come from someplace there are enthusiastic about working inside the level courses given that there are managed by positive charges out here and therefore the feline comes to hear and it comes to stop when it reaches the level but metals do not screen except in their own interior instead of positive view life years out here goes on its way as any company freshman similarly the momentum is absorbed here briefly but it also has all that needs to be amusing question why would anyone think that there could be and the answer is there's a related but different problems in which there is great and the related problems is the standard that I have this big their crockery finely crushed rock Beach sale and exert force is on the fluid in the same water air and ask what happens if the answer is this is not a free particles of sand To say that the fluid comes along and users words on the sand grains and the sand grains Shania it's all up against its neighbors so momentum delves into the and now woman's transfers through sand grains at the speed of sound and disappears and is not clear if back into the let's put at a later date but I wasn't doing reasonably expect hydrodynamics screening standards but if you understand the loss of mechanics is perfectly clear but at low frequencies you cannot have a high about screening hydrodynamic on when emphasized I said low frequencies and very high frequencies where you have to worry about the originally the solving the inertial mass of particle life could become more complicated OK so that is a picture of hydrodynamics creating 180 should expect that unless the whole of experiments on recently there was a in the year friends except politics were always your friends because you didn't make them up OK so let us consider experiments that adorn the speech the hydrodynamics screening OK so what experiments can we do all of the 1 we have 4 spheres and ball boils itself diffusion coefficient a 1st cumulative
always inspector a rotating a rotational diffusion coefficient and these although was the 0 value times 1 lost some constant times the concentration of power plus acknowledges stuff well if you believe that you have something to shake and you know the dynamic interactions or you can calculate savings calculated separately for each of the Sullivan also used the probe the future of this approach fear going through all the and you do all these calculations and data the feudalistic carefully discovery that yes there is 1 over are part of the part but there are a whole series 1st were 1st developed by huge and then by the market storm and in addition to the 1 of our challenges and on over due to come the along work for her etc. etc. etc. these objects on the different parts of the full hydrodynamic interaction cancer of which seemed cancer is very important for the lowest order about of you these moments quantities and give their case because not all the tenses in in different ways and therefore when you look at different these your looking at different parts of the hydrodynamic interaction that's a decent wages and you can calculate all of these spheres for a probe going through Paul recoils or if you go back to the chapter on dynamic positive lasting light scattering 4 although portals using you encounter label of these and you always get a reasonable answers for came down reasonable means all a minus the wall on concentrations in volume fraction units in some cases the agreement is considerably better than they are you should realize these things if you mostly sensitive to short-range interactions you really have to know accurately with the injury potential is now how often the particles were closed down and therefore those calculations intrinsically you're going to be heard and well offered dimensions experiment wildly and also work OK so what else can you do well there are a series of experiments USA Crocker and I actually get a list of other authors of the book various theories of the government to do 2 .period hydrodynamics and they ask where are we going to do with their converting we couldn't see both of them there is refusing and we can calculate measure displacement part what the displacement of particles filmed that on the average of these 2 trains are correlated there is a cross diffusion investors which tells you that the motion of particles on the motion of particles to or not the and that you were brought up on logic value equation maybe you didn't realize there's a lot of honors quarterly bottom water approximation extremely does bird on its 1st spotted by the there is a correlation is measurable there was someone look for a century ago but didn't quite know know what calculates only to find that apparently was very firm was at all so there is a correlation and the 1 to is found the proportion the sensor is it's all seen Tenzer also to actually worn over the uniform I lost part our I'm still about answer on included forever this strategy for the solution of prosecutors and however if you're doing that you're also saying the army I dynamic into reactions fall off as 1 of the park well the experiments that this form does seem to work know the people who did the experiments were looking for a guy asking if 1 over ah was correct at least they don't mention this paper they made known as usual so obvious there's say and what they find the bodies of water over or independence even for Paris probes in concentrated always so that people looked directly for hydrodynamic screening and it is not the case we now home to the experiment that tests 4 hydrodynamics and this is an experiment to mark this is not a model of the model equations and Delaware was now Los Alamos and what we have is a 48 medical Paul and there's water the tiny number of them and it's bad formed by 110 kilovolt folders on other species at at a concentration of 40 per cent and we have chosen the solvent so index managers citing all so we know it's there you can see it and we can look at this is a huge all over you doing light scattering we can look at the internal loads this is something we talked about that about Jack AT and what we find is that for a reasonably large human you can see the motion 1 part of the polymer with respect to the next and the relaxation rate you that is the on Marjah Q is smaller in scale and distances if you hadn't diffuses process he wants the rigid object will see where carriers hue hue and there's corrected theoretical calculations here in the calculations that a rousing small trees beads on chain and the beast no hydrodynamic interaction position model treats speeds on the same chains actually exactly the the same thing except revoke the interior by the intense the round finds in the form of a position finds you will be here you see here and therefore for this object in a solution where 100 dynamic interactions ought to be screened as a matrix is very concentrated very substantially high angle on you believed in screening said you should see non-interactive B the In fact here human behavior and therefore is Martin says the interaction to dynamic interaction between the seats must be full of off long overall on-screen behavior last week ,comma that all of these results are in literature some of them have been around for a long time however but what I just showed you putting them all in the same place and saying we have all these tests the existence of the alleged hydrodynamic screening phenomenally well no 1 has ever done that at least you and me and therefore at the peak of people who believe in hydrodynamics training even think the experimental tests that show up site Our cable us that trouble ahead and asked for water about theories with theory of water the actual details theories as opposed to him tree and the
several important theories free as long as the default of brother and all the murder look both at low frequency and also at higher frequencies and where all the workers said Well here's a moving object creating away and this thing is fixed easily the child tribute straining this is .period seasonal office-and beds it's a 19th century calculation on the other hand the same time entirely mobile there is no screaming at all the harmonica didn't calculus about food .period being after being a really clever calculation what he said is welterweight title dynamics works as we have moving particle you creates a play cats out here the electrostatic analogy of screening is the way is standard of will talk more about why the scattering them either later this lecture on the next and some the scare off his solid particles and other particles and eventually the text here or eventually he gets there well let us suppose we take these no courses what's scary patterns some of which like they complicated but let us take water called the regime diagrams I know what this is the least of the long-estranged I agree the diagrams if you do the electrostatic calculations on the diagrams that call screening in the water strange part well he does the rates of Greece almost the reading diagrams for equal work and what we find is that the ROC intensities really normalized that is the strength of the hydrodynamic interaction is changed by all of the area effects however range remains as long over OK then so we're undergoing an extreme income from the just appear by magic and the answer is no there is a paper by early seventies paper and he says the range of hydrodynamic interaction those of our work side by side is bringing and how is it calculated as willing does calculated at all in fact what he does site is faced 5 free time and words and he has taken by freezing or reporters to derive hydrodynamics while having said reports derived hydrodynamic screening auditions constant literature is that it is very hard calculation method lot approximation at a later date free Carrico that calculations and then as the normal process of doing various things better and better if you're lucky you eventually get closer and closer to the right answer and a free pair of calculation shows now there is no screening of so this paper on being yeah that paper and newspaper sons of paper that well has been improved upon and the improvements says there is no spring however lots of people reference this source without bothering to trace back literature and see what's going on that's what want yes there is this that is there is only 1 division the central park it was the intent day so much for the death of hydrodynamics scream and now we push ahead to when scales when I 1st wife presence of length scales is theoretically sensitive there actually there is a core issue which is a lot of these calculations failing are the scaling arguments saying that we ratio of say a particle radius 2 To solve 1 solution that ratio was of course to mention was its length over wine and we can then do but very flattered radical argument to say this is going to be raised to somehow rebelled and if I am very smart indeed I can actually derived values delved former melts for diffusion there is actually a rational purification of a scale In solutions scaling and least of all the papers I found his I'm sure of has been assumed as the core issue is derived Delta and there's some nice favorites for example by Shaver who shows how get out of this very nice stealthily critical to the statement that I can use scaling lost drive on Delta is there is 1 of the dominant length and whatever the dominant lately is I know what it is the reason you need 1 way as if they were too long there were 2 of these things like so I there tested mentioned was testimony was and now you don't know what power scientists the calculation is you have to well-known exponents and basically when plays so she want this to work you really want 1 scale that has to be done if you have several like scales simple scaling arguments cannot be made to work not because of you there might be a scaling but you have to be more clever arrive OK and said that we don't sensibly asked OK so there has to be a scale What is the latest and taste standard answer is we have a transient on the transient life as long your on almost every so often the polymer oils moved close to each other and for what called and hanging .period downward talking about covalently cross-linked gels that is the real truth is chemical jets these would not be entangled with points they would be covalent bonds linking the large changed the covalent bonds are permanent home Varadi Oliver a dynamic basis will also provide house and therefore you say there is a real physical gel here what do Johnson said is you get these temporary and final points of their transient lettuce and there are timescales on which the jury at the polymer solution looks like a cross-linked jet all he is the original development of this he was quite clear on this is that this is a guest and we explore the consequences of the guests and if I want you to guess worsen if it doesn't were no worse off than we were before now there is 1
of question 1 critical issue you want be careful of is very easy to draw up plans and .period there isn't any there is absolutely nothing in theory the describes the physical nature of entanglement .period In fact falters as a point they replied that they actually see it infinitely good vision on you can also say this is some sort of me field approximation and there are really brilliant handling points all stressed mean field description the city the reason transient lattices of is that if I have the hallmark oil coming through here like this and tries to move sideways the claim of the division model is changing sideways until encounters neighbor and it is that obliged to stop now troops shall we sort of know that's true because if you watch I call very-long-chain Paul doing electrophoresis through of true gel like the huge DNA you can actually watch the DNA movable there's an interesting complications of how DNA is 3 jails in fact they do have been sort of a snake-like motion that happened this way because won't have that over long distances a lot of time may be related polymer emotion called River patience from record territory so that is the picture that associated with this is the meaning of the whole which is claimed to be about the same as the distance between men and women .period if you think about I waved my hand very fair and this is called side so the reputation picture says the Shell looks like efficient and it has also saw his side I thought we can actually see the shelf the frenzy of life as a hangover .period Beckham would necessarily we were looking at 10 points we were looking at it because we don't know what they look like so the question is how do you find how big science and the following although I believe I should press their offer this you can't talk the notion is invisible fish it cannot see the holes that cannot seem to match how wide intervals mesh size of the visible the answer is I don't know where and I buying bonds the issue "quotation mark different sizes and I confirm the all of match and the small fish you slip through the environment officials debating not that they can get through the match yes I would note can actually get size exclusion in real Crossley gels it works very well that's the basis of 40 year-old chromatography met size excluding the small objects get into the gel and therefore don't move as fast columns big jets well happened said all people have sort of experiment but you can do the experiment also do not with optical problems like I the impression you would get from this picture pipeline diffusion coefficient British far there is some size over some radio after all this is a random unless the large particles are blocked and cannot advance on very slowly and the small ones can swim right through well danced with this model predicts and it's really not true yes jet of polymer solutions to a certain amount of seeding and therefore In some systems small particles faster some systems particles in move faster small is what is usually the case however you certainly do not find a blockage from particles books on sites and therefore this picture is simply not sustained by studies of the diffusion of broke through followers the experiment been done well you can however later all solution In looking the light scattering spectrum for a whole lot of different sizes problems and that was done by Carol Lasky and my laboratory and something like 10 different characters in different sites from which quite small quite large it's also been done by Paul Russo smaller approach than we and what Carroll suffered is that if you look at the problems like scary inspector buying more work that means motion on some fixed distance scale as you looking at a single hue hue period fixed distance scale there are just some always motion which allows some of the particles quickly and others to move almost and you can now since you have these 2 relaxations they each have a relaxation rate and look at the behavior of the relaxation rate as a function of probes sites and for example fine all of which were increasing and if you apply the relaxation rate verses from the size you discover for example 1 of the relaxation rates the on diffusion rate does not depend very much on polymer concentration of little bit until you get off to a critical size and all of that size there's much more dramatic if dependence of diffusion rate rather than "quotation mark relaxation rate on particle size of dispatcher you find ourselves of stretched exponential so there 4 or 5 counting the amplitude ratio parameters you can look at and what you discover is there isn't their characteristics of small probe behaviors their characteristics said March probe behaviors you can get into a discussion of all as you move from here to here as to which mode you were supposed to associate with which you have to molds relaxation rates that are incredibly far apart so that's sort of the sort obvious and so there is a critical length scale in solution that you can actually see the progress using them alongside question and this is critical ,comma there it's not even that of all this is a critical problem aside so that the yes no yes and you see the problem size and the concentration dependence of the soul of the spectral parameters which are different for small more probe In the critical to size is approximately 180 twice RG radius of all that is the visible typical length scale is something like that the size of the entire polishing that's very different than having a scale that a small part the size so there is a visible light scale
but it's not ones that are being predicted by the small there are a number of other experiments you couldn't say the same and we say the things speak to the same question let us consider a set of experiments let us look at the future of a and we can also be used in the experiment in scattering respect trust me and once the IRA inspect prosecutors sensitive to solve distance work on Basilan approximation depends on scattering anymore but this is distances Apollo all for example 520 you can get smaller than their words somewhat by changing its together you can also studied the same experiment forced release him the idea enforced Rayleigh scattering the several other methods such as fluorescence recovery after follow bleaching route he said said you sending a laser beam that is being displayed and is being brought in to animals this is equivalent to walking to slip interference and if you look at the little there are regions that right the reason is that are and there is here space and held its 1st title might mind and this angle itself becomes an undergraduate physics calculations but you can create a great thing to be on solution at the next step is to create a rating for example photo bleached particles some distance or you have created his own server lower or higher concentrations with some separation you've done something and you can then observed the relaxation of the grading as for example articles were written here refused Philip again this I'm leaving out a great deal of the detail of the experiment except for which is that you were observing all vertical motion over much longer length scale and there are several people who have done this in the several people on the sort of thing at all that is what Yamaha relaxation breakthroughs is where you get out this nice straight line which covers orders of magnitude article this and therefore diffusion over small distances fairly small distances and diffusion of very large distances proceeds about the same rate not in particular channels veterans here gets sufficiently short scales so they're looking at the motion of this article over distances but a small part of whole article size meaning that there looking at here is horrible and fall well within sight of what is known as a correlation Hall on various other chains and less likely to be found here the small print said this change here and the motion of part of polymer inside correlation all the over fairly large distances are not looking at only short distances the motion over fare over moderate distances is the same as the long-range distance there are theoretical explanations for these finals back from the same period of Oracle it's since some sort of all the solution of old created by an article you and therefore part of rapidly over the workers said following what more slowly over long distances and thus to see fast modems sold well if you wanted standard light scattering spectroscopy and realize that I just refuted 2 completely different nations and the 2 measures on flights are well known along fast slow motion that's timescale and number 2 short and long-range motion that's the issue that you would see by looking at a series of different values human on an experiment started a single scaring all along the vertical motions over a fixed distance well it's suspension for using components relaxing so fixed distances the difference what you see on our but of the core issue is you're looking at a fixed distance and therefore the slow and fast loans both correspond particles will save you a far not forget means small distances Borges OK and what this experiment says he is that all we don't seem to see small and large distances effects OK more experiments done by strong Leske of hydroxy probable cellulose came to the conclusion that at higher concentrations used 3rd very slow and very slow corresponds to the motion of objects that are quite large however we now corresponds to the motion of objects quite well we took the same policy needed to be put in that spheres of different sizes and we look for when we discover how fast this year each different different-sized diffuse and therefore we can infer what size polystyrene sphere would give us a relaxation rate about as fast as the relaxation rate we see is the slow each single and that corresponds to object which is 0 half of the year cross is much bigger than a single Paul McShane which is only almost half half of my from across the after the this is about told flight time news and the single polymer chains of long life of coal-fired you what this is not a bad years and therefore moving victory objects are much larger than a single ball court and make described these pictures I read what is the nature of the victory violators will hear them 1 thing we can say is that they're not local regions of high and low concentration wife because drought can't make his defense that he taught at his intensity you concentrated versus concentration if you simply have objects that did him in fair and think the intensity would be constantly if the objects repel each other which is typically the case seeking
through each of our estimation more concentrated against verdict former concentration was good and we are in the hands of therefore falls here's a concentration which start seeing the swallowed and there is no hallmark of concentration as you cross that line that is the vitrified regions or regions that are dynamically paralyzed but they are dynamically paralyzed because the settlement centers all over there by polity we mean the connectivity of fall merchandise and so we have been here chains we have bring polymers we can stop all members of the ring start we can make that life president called from Paris vaguely resembles an object used by cheerleaders football games well once upon a time you can also make something like this age you can also make something that looks like this and be astonished to learn this whole home although the allotment information on there's a considerable amount of information on stock there is solid information on bringing all now the early studies of rings have problems but synthesizing bringing home the same ring polystyrene is actually traded start star about living in all linear polymer flooding back prelude to and persuade the analyst with attached to each other not only change in Washington this in such a way it the accident form from the happening that is rain is our guest brings they're not actually can be bothered by pain and when people did measurements on rings in like the expected result there was a lot of controversy as to what was seen under modern conditions it's there a much better solutions you take any of a number of viral DNA so their viral DNA the rings and they're clean remains an issue put them down electron microscope there's no sign that they are not at all what we stand on the normally appear to be on top and therefore there are also size to the brain and the government was restriction enzyme Yukon things once you get a lineage that is exactly the same size with an apartment tenants the 6 as the original rate of so you can actually started college that said and son of the growth the past the last bits and pieces here and there on 1 1 effect or another effects and here's what happens when we change college I could arrange this for had a chapter effective topology like I had a chance to run colleagues and all dynamic studies in college I could have had a chapter on stopovers and all of the dynamics stuff involving stock all of us that I wouldn't have had all stop always readily available to to be compared with linear Baldridge for each so let us consider a few bits and for example we have left Friday the and if he comes the appropriate chapter you will find this nice picture of frantic mobility which is all probes that allow compliance has applied based here except Solomon linear and some of them are extremely synthetic stars you cannot have Stora of DNA with the normal synthetic process cells but you can make this is a synthetic chemicals it's truly clever thing to do and then we have a matrix fall over prior the 15 to 20 times what was going to establish a telephone call various concentrations so you and then look at the mobility of linear chains mobility of as a function of concentration and let discovered this 2 lines is pretty much of a problem that is if you look at a lecture for probability linear chains and stars the same quite large size moving at the same speed pretty much also all the self diffusion where PCB concentration camps some of the whole thing is characterized by by parameters Alpha new AU can compare Altha and new for many years chains and stop all minors an especially if you say you comparisons were to keep the size of the probes constant program you use linear chains stars you find on treaty the department stores that Alva Moore were certainly not very different from you can and it's a lot different golf but not enormously different its stock checks always get different methods propagating and linear chains yeah these actually use that all the South diffusion studies are almost all synthetic polymers South diffusion concentrated solution would face the issue DNA is charged and you're now looking at charge concentrated Polly electrolytes that is 1 of the topics I did not consider OK so what else can you do do the same experiments well 1 of the things you can do is to look Wisconsin around this was actually 20 years ago and he was compared to range linear chains and found to be discussed the rain was considerate was less than viscosity and check although and since this was the opposite of what the reputation model predicted there were lots of Let's attack the experiments discussion attempting to explain how this troops in terms of trace amounts of linear changed because of the effect of this discussion because how recently however did
the experiment using DNA is removed he and a copy of because of the manner of synthesis of reality and there is no possibility of cabinet there are good reasons to suppose that the ratings are not routinely tied in knots the remaining and linearity and are really really the same size and Goodman found the viscosity of revolvers news the factory three-year firefighter less than the viscosity of media always different parts of each so there apology the I'm dropping of theoretical and sooner or later that so why can't we pull out of the area well there is a computer simulation was told me says there call to all the came as the Holman chain of font will serve as a warning that bonding more because of the way the computer model works allows following news of death about 1 water so bond so bobs up and down a bit but it stays basically service what is going they will turn to the fusion of the the 2 chains and the feuding politicians have developed and to now will find people who might be warranted and is to use the signature prove you have reputation and this simulation conclusively disproved claims for the excellent reasons these changes cannot possibly directed his attached to at 1 and they can only move sideways anomalous you see this they all 1 may propose what reputation is saying is that you actually have also some general features of constrained motion there is what appears to be a significant calculator has applied for a friend and grossly this is actually the by law which is excellent commentary on the traditional-style beautifully Ferraro covers melts covers mostly adults limited solution and dropped and there's this interesting page and what they do is fluctuations anticipation that he would not say more responsive calculation upon how changed and what they said was furious polishing is subject to random forces the same way that they also Brownian particle is but there are a whole lot of random forces scattered along the way and what they say it is therefore ran forces are highly correlated states and they opposed the home 2 the space the movement polymer occupies the transient let all to model is an example of this they're able to stress that however the conditions required to get scaling laws are actually considerably more relaxed the assertion that you have this transient lattice and was already going back and forth along its length to but the the issue with the stress tests is if we want to talk about this we Leicester city we asked the question How does 1 part of the fluid put forces on a different parts and the general has refused earlier @at like this is the particles tractor repel each other and the intermolecular forces that act to create this part the fluid pushing and pulling on their part discusses works and what the revocation tight models said is that working polymer the yield on the issue in this year's polymer stretched across the you can the easily change here there's a lot of stuff on the other side and therefore intramolecular forces are dominant in creating stress test here intermolecular forces broke through anything only in like 1 after however there have been a number of calculations on yes I decided to walk any conclusion is the net contribution to this he said the interactions stress test was small and it is really all the intermolecular polymer forces there creating stressed that best director calculator finally returning to something that is very early on in this summary was preparing for viscosity is not reversed it's not a universal of concentration and that's very important because any model that says Well we have the general considerations about Paul McShane's can represent all strings and the general considerations were equally for everything and they lead to a particularly predictions like scaling laws those models have a problem the aid of if you plot universe is seen not have universal functions concentration and that is yet for this part of the lecture so we should stop horrible