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30 The Hydrodynamic Scaling Model

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classes in polymer dynamics based
on George Phillies book phenomenology of polymer solution dynamics Cambridge University Press 2011
ends today this lecture E is
lectures 30 the hydrodynamics scaling models this lecture considers the hydrodynamic scaling model which purports to explain the phenomenology we have discussed in earlier lectures in the course we
have now reached the last chapter of book the last chapter will be afterward discusses the theoretical model that actually is at least more or less consistent with all of the logical observations with made that prediction that model used the hydrodynamic scaling down I am happy to read back later lecture and discussed places for further work the model is incomplete might claim is simply the wearer model has been applied In his work OK so was started the starting point for the model this term would the Chrysler of model for will all going Her would rise from most of great deal like the same thing To but it is in fact very different disciplines .period mutually recognized the Kirkwood rice plantations in picture are actually very different inserted the key results what is occurred would rise from all here is the whole of the may think you've fallen as a strand of beads Kirkwood was quite explicit in saying these were monomers of more modern models are little more than guns .period the beads and research frictional forces on the soul the beads are obliged to stay attached to each other like pearls on a necklace and loading model polishing model has basically a bad B bonds between these 1st approximation serve only to achieve the beads attached to each other and now they're going to say we will we have this complicated moving object we do what any sensible theoretical physicist was confronted with this we create an appropriate set of collective warrants and Culpepper who created as long-neglected were at the center of mass associated with there is the center of mass velocity and then press 1st Variable we have some sort of a co-worker yes as the direction vector and the direction of a corresponding direction investors you can imagine the chain gets to rotate around the axis now there is an issue with all sequential rotations not being communities and so you can specify an angular velocity but unless you have a a rigid objects specifying the angle was a little more career however for example specified here is the effective and that is the direction and then you have a rotation right in different directions and so we have horror and fantasy and since Abacha has 2 rotation axis which are already it also has a line heart fluctuate currently doesn't really talk about that because it doesn't come in into small and so we have this we have been the rotation manager and finally we have to have this crisis internal for this simply described fluctuations and heard was that very seasonal fluctuations and says they are a significant 1st approximation so was really coordinates and description of the were marked by how does it work in popular solution how does it do anything and the answer is let us are they the here's bad been and will Bush put it in a influence the 1st statement is wrong timescales scalable so the inertia of of the changes on and therefore we have a 0 forced condition the total force Sondhi particle on Paula changing the 0 now the fluctuate I'm sure times gets this approximation the statement that the direct coefficient of Teesside and moldings and velocity of I minus velocity of fluid twilight tablets is the 4th on the review and up the total Warsaw all these is 0 so houses this work last year as part of the fuel up here is moving this way fluid out here is that way so different parts of the golf ball and chain or being dragged in opposite directions but if you look at the center of the center's simply goes with the flow the last 0 students the sad condition is 0 4 of that is we have this object it's in sheer there's a force here this way of of course that way the shortest perpendicular to the black for the year and angular rotation axis and so the beach here trying to persuade these they're trying that way these days results in the middle are presumptively moving up and down so polymer is doing best yes you see it rotates Of all the oil is rotated and here the fluid is warming faster than these here in the there has to be and that creates a two-hour losing clockwise motion however these these moving down those these removing all there's no vertical flow and all these these are moving faster than the fluid and they created a network pointing in the opposite direction and therefore but the even get your work if horror crossing the I like it the danger posed the question direct all but 1 of the velocity of the flu is not the same here and here and here and we have to take of that that is the fluid velocity has leased the linear gradient share and so there is a 0 4 conditions and from the 0 and 0 to work conditions you can describe what happens always 1 less thing these interactive IV also seemed Tennessee so over the years will relative to be there would be year creates a way that acts on the despair and therefore the fluid velocities inside Hong Kong are not the same as the ball fluid
velocities solution and the client as you can solve this a scattering problem where you start out with the rotating and the rotating a rotating Shane Warne these create wakes that act on the beats those wastes can be pretty scary because now of speed is with respect to all used by industries and the way the Seattle monsters again and so you have a scattering effect and the net result of scaring is the file of the pall over the whole of the of loading the inside this tends to be more similar than you might have thought to the motion of the polymer .period and therefore the drag force the fall oil exerts on fluid and vise versa are reduced because the flow here because of those overseas staring her tends to move with the IOC said tends to doesn't it the net result is that he asked how much dissipation of contributions to the viscosity of disillusionment and get well recruiters press calculations says during our contribution goes down to the 1st off you measure the diffusion coefficient diffusion coefficient with those in the finest loss when you take into account holders the Hall over all of the scattering is to reduce the molecular weight dependency viscosity diffusion fish and so forth all and I have brought us to the end of the current crisis will mark the next step the discussion which moved to 1 final lecture at the final piece of the lecture is what occurred what happens to the Kirkwood rise from model when we look at interacting polymer chains such however were dog and so today at
long last we have reached final lecture course what I am going to do today is to discuss the dynamic scaling a theoretical scheme which is consistent with the phenomenology with struck I'm happy to concede that the phenomenal Optical scaling model is incomplete and sense has not yet been applied all of the questions we would like to quiet and I'll be discussing something with wrong nonetheless within its limitations namely has been applied every year at the hydrodynamic scale model is consistent with the bulk of observations that we have talked about those foreign courts so we start off we go back historically about 1986 1987 and I produced a series of papers the 1st of which was the universal scaling model and the universal scaling model was set to discuss Paul result refused the observation I made was that if you sat down and looked at this in the system that is you actually looked at the experimental measurements that happened on what we found was not concentration dependencies solution properties see scale what after all of the were scaling you would take a lot of lot plot catalog 8 overs what seemed give you these guys visible straight lines well as we have seen measurements government kind in most cases fortunately we did not start with hydroxy probable cellulose viscosity or we might have come completely the wrong conclusion instead we started with Paul self diffusion traces refuse the inspiration for this was actually while I was Michigan we started doing experiments on appropriate use of part-time holding tight in studies on all probes into Polly acrylic acid water work I had a great and have all of I think work all studies on progress usually polyethylene oxide I know I should drop and Robert Winter who was the underground and I actually 1st piece of what counts said that what we found about where we had all of these measurements against what generalization and the generalization was that we b all of these measurements stretched exponential so all the alpha of the stretched exponential appears to be correlated to the size of matrix over that was very different from the period picture which was the polymer solution was Our it functioned as a physical fishermen to resist the passenger probable depending on the regular relative size scroll the whole of last year and this this rare proportionality would be in the hands of the Great Western out all this on its crisis Fox 9 Camelot said the preprint of 1 of his papers on poll results diffusion traces the future I looked at the
1st of all I was driving out from emissions from California to Michigan for my 1st academic position and she alone no that's not right by direct sequence that was all I was driving later when I was sorry wrong sequence all so we look at the lodge papers and we realize she's self diffusion looks a great deal like progress and that was that was 85 86 and sold 86 87 but I did the papers saying that look tall resolved if you stretched exponential parliament and I proposed universal scaling which was a stretch exponentially worse if you believe in scaling was this was a bit annoying because I was saying that only area numbers from your functional forms so this so I came out here for submission to the government the eyes and I've seen the watch and we didn't work control the polymer self diffusion did same 6 out time this was extremely tedious because than what you have to do in period was to take the figures were a few lucky to get data from somewhat below the figures up to seating easily measure offered points you are using any of my promotor caliber to measure the distance horizontally and vertically 1 point in time Our do the conversions to 1st inches into all whatever it was actually going to be that he'll get due to fit on a computer you could do the same if you were and you know it rest multi hundred kilohertz computer it really would get things done all but to work so having done all this "quotation mark we were then somewhat ready to go and I gave this discussion ratio if you look at a few viscosity plots he gave the same results and that was sort of reasonable to expect after all but lot theory and mathematical forms of temple self diffusion of progress you ought to give similar results for each of the parameters so what about 87 and number of people like many where made emphatically point was very nice but what we need to convince people is a theoretical model that explains what's going on well they were right I did need theoretical models but would convince people and maybe not so much nonetheless I had to cook up a theoretical model and I sort of had a general hint of where to go because I started off doing calculations on spheres diffusion coefficients south of Mutual of Sears lower concentration but I was just briefly look at itself you here year did creates some way In the wake passes through pollution fines and others fear this fear translates your rotates but it's in the field with sheer it can simply stretching indefinitely its rigid body after all and now works the head of the way and when the acts that in original
sphere and this gives a series of sensors which can be solved issue and also more recently in ensembles so we're all going to have dynamic tends the IGA which describes the retardation promotion of your officials here do 2nd year of here and that retardation goes as the race serious for the distance between the 2 sides of a foreign power that is during the is returning effect the 2nd sphere falls off very quickly with this and so you have a cluster expansion and you could do with hydrodynamic faster expansion and calculate a thing of the surveillance reports he 0 1 loss carried on after falling prey to do what's that and that was what could do straightforwardly spheres so I already know about it's not what reaction and what right concentrate policy solution was to say OK will simply extend the series calculations until you get on terms and that eventually did their various students but if you look at say we're going to need lots of terms not 2 or 3 that looks a little tedious especially since we're in the days when computer algebra was put it charitably it was possible that it was a bit limited so what I can't stand it is here on the front part of the idea was we have this calculations herself you we have to drag coefficient of polymer .period that some concentration C and this is going to be determined by the Director of the Asian 0 1 plus all the interactions parameter concentrations on chains .period tests and my ideal Walters that suppose we notified concentration the next faces have C minus 0 overseas goes powerful they had where we can make headway in a little more detail about what are my notion was that yes this is essentially the at the scene let's see the portion all of these terms what I said was to use this term telephone and my idea was that thought she wouldn't call going to the of because of how hard it is to the 2nd oil from solution and therefore salvation proportional to the threat coefficient of the 2nd year roughly speaking at a concentration C now that's not what you actually have Europe here is the 2nd parent is 0 Elvis see and what I said is going high concentration this thing manipulates bounces souls wait all day at the 1st part of the larger the drag coefficient this object is more of balance and therefore I'm willing to put this approximation of the Alpha here so different often Hong on what is this business of approximation calls itself similarities and if you look at this this staff trying to derivatives have over after the health and then advises the derivative over the function is the wall that telephone and the solution is that for see so far so good so I had some of the areas and approach which would lead to exponential the problem is we look at it would only lead to pure exponential and the question was how I got around and so I finally had time I set out for all problem that on day 3 I got this far and I was walking back from the road and it hurt me well outlined his term by this object so helpful goes ahead with the radius of the fall wells were about or out but I suddenly remember back when I was at UCL at with decades earlier I had been thinking how stock with gifts and students as suggested by I joining a seminar group the field Pincus was running long followers they were trying to read all the papers and that's what we did and it occurred to me that this very recollection tolerance trying win the polymer concentration of continuous earlier in the day off the track of what I was interested in and I can go back to the next morning and find parties where proportional seats minus taxes and taxes is about the cost and so this accounts each of the al-Fatah really negative all of them the so this is the same as he can be summed found in the pocket yes there than in the the little 1 minus and X where X varies from 0 4 small changes to order for big chains and that's stretched exponential and now I get purification actually predicted the functional for also if you crank through the final details here and there a little more careful about bitterness discussion at you realize that this piece was supposed to be molecular weight and therefore the front because health of this substance should be proportional roughly half that was approximation and knows future some sort of behavior like that Our identified compared with experiment that is indeed what the fuck that Afghan model was an approximate model like the predicted Greco efficient of you of the fate have used the easier of the 2 finalists held the city this is the state-owned export right to predict how the export dependent on molecular weight the and I would predict how Calvin depended on all molecular weight Alpha is a scale increasing you view this the way it long years in 0 details blindness Elvis seems to inspire more visible that scaling trees factor that I to calculate the molecular weight had called for all should look at this
and it actually agreed with experiment this as we appropriate was appointed to the measurements were a bit noisy until we get the results on Dec story where things became much cleaner are however we actually predict how healthful and who should quantitative on municipal polls on those calculates scaling 3 factors but there was no place of K well also announced the results were people who were impressed arrested were people were interested and then I decided that we started off looking around a bit and asking what you can do things better and there were several different things you can do to do things better but 1 thing you can do I think there's a asked if there was another way to replace self-similarity and turned out after a I happened to read the paper and Jake and his right hand Oldenburg who said you could get out of his renormalization group method exponentially more power warts and all this year's talking now about the Altenburg positive function renormalization although it is important to the emphasized the positive function renormalization group began emerging from he is not similar to a number of other renormalization methods in that it does not say we're going to collect things on a larger and larger scale and by doing so we ended up with arms smoothing out the local features does not resemble for example the old-style blocked renormalization let me give a fraction of how it works supposedly 1 the right pressure in the 2nd quarter of this year well we have Katie concentration lost some of the concentrations player also other constant concentrate in you most said 5 days in the snow well there a variable expansion and if you want to go to higher concentrations high enough evidence to change and there you know find well-defined approach and you have the issue that the more firms after peace the term during the actually get interesting all although if you go out to about 12 hours so it is quite clear that some place around 12 to the variable patients change signs for example all are however and said he had this expansion on the way go take the pressure a higher concentrations of natural ways to change the number of choice and the choices that I will reach here and I will be scaled directions In a fiery scale the injury actually make it longer that's the same as saying We're a box of some size and I'm changing units shrimp box and therefore we got a higher order higher concentrations by changing the interaction parameters so the interest in this method is that it actually gave exponential and also may actually gave scaling lost power was retrospective my obligation desirable so we have this feature and we could then use the renormalization group to crank through the same calculations and get the same result :colon namely that of gotta stretch that the other thing you could do those say Well how strong interactions between Paul what the answer was alive that give region introduced Kirkwood would rise from model to calculate the interaction between all 4 days here is :colon oil there is following .period and we can write position the years the work we will write the location of polymer as the position of the the center of mass plus vector from all the senators may have to be on way to the interest and what we would say is is the approximate the motion of all positions all its people also states were little or than the this is part of policy on high and we can say there you are the it's going to be a center of mass velocity plot the measure Oregon by rotation velocity yes I think it's a rigid approximation is a rigid body we know it's not rigid body in Kirkwood is quite precise on this but the fluctuations but it still we can still introduced these coordinates and then introduced to the physical conditions physical and on the total cost of all the oil which solved drag coefficient is all over we all velocity of -minus but also to be some people told me and told me toward the parliament the director of the for a while crossing the like the students 12 have been using crops because worst thermal equilibrium now here not 0 at every instance because will insist they asked the jury has ownership however at low frequencies all of the inertial terms of stamped out and the Torah average working average forced 0 overall brand purposes and once I say I can trade that is the series polymer and sets of and I can calculate the way over here and for example whole intensive so this that's not the way to reduce I was thinking except I will expand the on cancer in terms of this displacement this displacement and that displacements and I can do power series expansion in the little Aras an average over I can't get any interaction tension between 2 all courts oddly unsurprisingly the dimensions of the tendency of the tennis on almost the size of the following reports introduces me the fall of the dollar part of ,comma surprisingly on the on the patterns of the tenses on those distances is exactly the same as it was year because that's basically a on dimensional analysis when looking gradients for press however there is also a numerical constant front and we were able to calculate at least
approximately miracle comes from nap that when we wrote I'll see you there which comes out of the virus positive and normalization threat coefficient of drag coefficient of 0 and 1 lost helped see maybe I should also help and you have to be careful because this little careful running this year the interaction strength depends on radius of gyration radius of gyration his concentration that you can be a little weight with To that end but where as from I calculate America now there was a number which was the size of the polymer radius of gyration and there was a numerical constant given decided dynamic which we can calculate exactly as the calculations had been gone from spheres will not exactly exactly series you go off hydrodynamic boundary surfaces calculation there if a calculated quantitatively what was on the calculated health over his In Europe eventually and here is the theoretical curves and when I gave an invited talk at the news was more things 80 s meeting in 1987 I was able to to say I have dollar calculations there is the calculation and here's the theoretical curves and there are no free parameters and that we get the Curtis line might be right about moments here it's not years it's not year so we could actually calculated Alpha quantitatively I did notice and there were some work I did with underground mining Paul colors and what we said is well all this was the OSI calculations but you prove that you can also do calculations on change but the change in the spirit small sphere will be this it now the interest in the spirit of the calculation was that there were 2 things you calculate what was the effect of polymer boiled on a nearby sphere is probably few who talked about earlier reports the other thing that you can say is we calculated the effect of the .period on mobility of the single B all of the home check that is you have pro-life was inland from where Paul Boyle looks like and we can calculate how the high value interactions in perfected probability the effect of the logo the reason this is interesting is that there are people who take the position that well the motion of the individual segments 3 charter and you can determine their by measuring the the future of the small pool room Paul Merson and what we were going to be precise size said and what we were able to demonstrate is that the effect of polymer while on the mobility of own sectors and if the effective called on the mobility of something small that the outside people are not the same and then pranksters can I have through detailed calculations what but they're not quite equal to each other and therefore saying take out the policy will be be mobility His measurement of solvents also is it's an approximation of its theoretically not for there is 1 other thing we could do with the same calculation we calculate the interaction between sphere the all course now I'm doing that and I had slightly skipped over this there was 1 the question the calculation there is there is a distance of closest approach means year and the call and all the distance is determined by a sort of a radius of the austere here and the cross-section of polymer oil that's how close to things can get that's also true if you have a lot of the interaction between alters the distance of closest approach is determined by the cross-section of the 2 checks for the 1st time we did this calculation just putting we know what the molecular shape is this fall will put in the actual lowered and perhaps we were lucky but that turned out work quite well this side however we had a very radius is polystyrene sphere of this radius quite well we have a little radius and if you do the calculations you discover that if this leak probe is much larger than the thickness of the the thickness of the coil approximately drops out of the calculation the simplest written with distance of causes approach oversimplified is the sum of the 2 radius is in process national bring a and guess what day is much less than so far is approximately right now and therefore the cross sectional radius monomer the monomer dreadful vanishes when I gave a talk on this lot of Gordon conferences and in several of the French critics saying Well yes the theory requires you have the deed of greater efficiency is an unknown parameters that something saying that you're theory requires my theory has risen to a higher plane of getting that so we do the calculations and then that he would tried and Jesse Helms about 100 Greatest Kid experiments in the polystyrene latex polymer because we get very electoral weight during the period when the rate was almost Poly Styrene soulfully which is polystyrene which has been chemically substitutes so its charge and putting in a reasonable amount of salt litany Polly electrolyte effects course that sort of equal saying passes this charge and mass charge this is the likelihood of coming into contact is expressed in this number is no longer quite what it was before but it's still small also still doesn't matter so we were very little we can do better and they're a factor the leading concentration too many have come to light out here very small polystyrene sultanate's and the very small ones on the approximation this is a random Correa told probably just work here and I 20th hearing 1st they have the hydrodynamic series gave the right results for any really did all that sort of not surprising because the theory works perfectly well for birds years and therefore all to work here if you do calculation right not all last week at the calculation and at work on another thing that came out about the same time as I have to run in the faces of wonderful things dielectric relaxation from which many positive things cannot
be set this this and the issue dielectric relaxation is the measures have been square and in the distance Britain's concentration In is you run out of concentration camps that's where the linear rewards scales the chain's trend you people also manages relaxation time which is a rotation time on the rotation time was lost along Phelps's concentration well the growing numbers might look like an exponential but the data that involved a lot from the curvature however is concentrated his statement there's curvature is wants me to do is explained by the contract by the home changing the size of the change correct however that is this going to the on each of the relaxation time those results a concentration are as clear as the 1st year heroes tower they have to rethink their monopoly and while we were able to do show quantitatively former on particular material with the deviation single exponential behavior is indubitably quantitatively matched by the degree of change and this is a really good quantitative next week well we calculated the gas the series we calculated the monomer we have calculated the probe that resulted in arrest of qualitatively at low concentrations all we have solved were putting in entire workers are hired dynamic interaction constants in his life and talk about closing answered a call for birds but that's only the beginning series a over art and there are available higher-order terms the next 1 is a over on you and if you would say I do the calculations higher order in a world where are you get slightly different on so we have what else do the calculation of alliances is viscosity eta now there is a history here the history is precluded crisis published the calculation of the on leading terror effect of polymers ,comma viscosity and leading German effectively Pollaro discusses these comparisons place on his way the other the way we pulled 1 oil in here and we can then do the same calculation to weights we can calculate on how this fall sheer field can comply with this years old and worst of all ,comma all and we can calculate how scary field create cited by British forces on 2 plates or we can say already walls velocity and therefore there is anticipation that we calculate and want all world by itself is enough to do this then is Lederman concentration and viscosity is there is a polymer oil presence is not your interactions with however she wrote about 150 early fifties there were a number of people end who tried to look at the interaction between Paris Paul and they set calculation they turn chronic Over a reasonable and they got divergent intervals and the issue was achieved wiring getting divergent here but it was realized the simple calculation would obviously do gave you divergent and because it gave you a divergent you couldn't calculate what the next summer and you can do something about the divergent staff hydrodynamic diverges in general will arise in the aftermath of the government boundaries out here boundaries are doing the approach I did was to say we will apply ocelot Tory Shearer field admittedly this would be a little more can we will apply an ocelot Tory share field and therefore the total force we are putting on the fluid is 0 because we're pushing it 1 way or the other and then did something so very demanding computer algebra fortunately mathematically came along because some of the intervening steps whole thousands of terms do calculation looking at something with thousands of terms and and will not here to do this by hand on notwithstanding the famous 19th century example the French astronomer who did the orbit calculations by there we have a team of 4 graduate students who each this is heresy landed on moon cannot compare results and in the end he had this huge hole formulas and when this was tested with computer algebra they found 2 terms at the very end of 1 unimportant series The Tudors did not go anywhere in further and 1 of them had overstated both groups said they not fall and although there it's correct it's beautiful child care of human artwork work I however page here but I was pushing the limits of what the value is much better now instead of having a computer gave a few hundred megahertz I get computer that genes the castle Warren get a computer that can execute this 1 Aeroflot and the cost of housing blocks specialized accelerated so you can actually do this much less painfully clear with them but nonetheless we got at work I calculated the viscosity behavior and got home after the disaster and a nice feature is the term for the viscosity is that of course it depended on the cooperation that is the and our original calculations suggest that began to change and they can approach the latest touch each other in the electoral conventions because we heard freshman chemistry that I used to eat fresh chemistry all so we can do that however may be the proxies and the complications however whatever this distance of closest approach is it's probably the same as the closest approach to get all herself and therefore we were able to sit down and say Well we have done the viscosity measurements yes and we have adorned altar viscosity calculation the comparing viscosity measurements with viscosity calculation that on with this closest approach Out of discussing now we can
march the viscosity data over the cell fusion these 2 sets of and certainly had that remind you of something call England polymer cell fusion they have viscosity solution over low concentration values using also Bose-Einstein in diffusion the diffusion rates do not match the shit out of viscosity Paula's itself diffuse much faster than you would expect from the viscosity of the solution reality there's nice favored by the the the terms from justice they have a slightly different interpretations but it's still wonderful all patents said this the 2 distances of closest approach are the time so therefore I should calculate with absolutely no doubt about how the self diffusion coefficient of like right there is a lot of little complications might worry about which is how accurately do me no chain expansion area so the chain expansion is something we can pull out of self diffusion measurements or whatever not less if you would figure skater there things 36 here is health lovers and can there is a this and 1st and there is a line that is also the sole people out of work all what it's all about employment .period and something else to the 2 lines they're slightly different slowly but there is a heightened has no free parameters and the lights go right through the measure so we could actually eliminate question about 3 parameters don't OK so that's about as far as we got hold 836 Galvez and no free parameters on having said this was 1 last thing we didn't even get quite as far In the last piece was to say we have this in and the image is a renormalization and then introduce them what's going and the temple will stay on the analysis says that if you were looking a lot of dissipated properties in plot at those frequencies the law of the sea and divide out the very all pointless frequency dependence so that at low frequencies this material properties frequency independent would expect which people are probably be interesting parameters says the force is proportional to the acceleration not to displaced you get something that is stretched exponential these power walking and eventually discovered pottery high-frequency kind like sold in there and maybe there is a high frequency range of polymer has several things going on on that functional form readily be tested against experiment and we go back to the chapter on last city we have passed over personal terms while sailing on the sorts is on socks it's not a full derivation and say This is how you do it produced exactly the observer for all Georgia do that the we have also stepped down and say Well you call a symbolic chains have the same forces between them except apology and therefore we could do with serious analysis of spheres and all of the properties we did this particular viscosity of birds for years and very rapidly reserve area visible offers years have a solution might not like friends so blocking a see a solution while reading there is then an orderly sharp transition work with me on the shower In these once said that humans because data .period which appears to have managed to be taken right the transition and it is right at the intersection of lines and in a statement yesterday Stasi increases very rapidly at high concentrations yes this is how a lot this is stretched exponential This is an interest section and this encouraged concentration of 5 powerful . 4 1 given carried a relative viscosity of 15 and some places all here is the place where the Kurds fears you supposed to have some sort of phase transitions and his occurs at called going for an allies in concentration and the relative viscosity that's part viscosity firefighters Solomon discusses about the thing this transition that will lead the different and the soul of the sufficiently well separated the they're very definitely not think OK good all what else can we do well there were were questions about so if you on and foreigners the assertion is that if you appear to strains of the same total like way stop all over smaller therefore its radius is less therefore it's Alpha's less and that's approximately correct you really need more stock measurements more and more different forms sizes for about an hour and so Leonids stars explained all there is a competing question which is what occurred in the calculation of all the interchange fees to warm socks supposed to compare the year chain with 3 years of war or whatever the stars and Tomlinson Is that calculation is much more difficult to do well that been on the seems to view I think it's something OK Paul the renormalization group calculations also tends to
explain why the sum of all systems the here and others received the only the rising stretched exponential namely the transition is fixed .period transition between a fixed point 0 concentrations and the renormalization fixed-point someplace out here if you movie out here a bit we arbitrarily in concentrations can only get off to mail and if the face .period doesn't take over until some hypothetical numerical reaching beyond melt you'll never see it so calculi the renormalization group calculations explains why it is not universal phone I shall however itself but if you read the book I do ,comma viscosity has these 2 properties I don't actually played out by the way this means that it is not universal concentration function concentration and therefore models and say it is a universal function of concentration like scaling Our fundamentally incorrect I don't say that those that I have the facts of right and wrong all right what else can we say that experimentally is confirmed well there are a whole bunch of experiments using problems that we look for the longest length scale from non-bank followers and what we demonstrated his longest landscape with dynamically affected is the size of way and that sort of physically demented aware how much should concentrate things the Paula the beads on a single chain will always stay attached to each other and therefore over distances like this all the motions must be correlated if they were not correlated the polymer the shredder biologists will remind us that if you were trying to isolate all DNA and you are not careful you will Shearer and you will get a little fragments that are much shorter than the original well you can she recalled were talking about Europe slamming their work also in addition to all we can compare marvelous period less than a year viscosity of the year chains the Stasi read and if I have a rainfall over the linear polymer the radius of gyration of bringing with him after all before grew up part on the reading is smaller than the linear shapes and therefore should be less effective in increasing viscosity of solution precisely as In contrast past reputation by models say rare thing this contract interesting there because of presence all hot and therefore readers should be more effective in increasing viscosity linear chains and that prediction is rejected by experiment we also demonstrate that the government our concentration that is being carried well the calculation just shows that he indicated is not constant and models that say it is From state OK so that takes us to about distance the hydrodynamics scaling mountains and take it makes considerable number of predictions some white quantitative and those predictions have always been confirmed there are however recent papers along for example there is a recent paper by high at Al freeing revocation treating produce unit from reputation .period view it makes a large number of predictions and these predictions do not appear to correlate very well experiment all right I haven't said much about their blood but you can read the paper for yourself and ask yourself this is true we them a lot OK at the back of the book I several limitations paid our home fearing what is the issue of the souls of the interesting features refusal to solve fusion of about 100 grams 3 regional that's not there might be a reason to unified but at someplace near here transition in concentrations the and at times I wrote a book I couldn't explain that I can now do so the explanation is His following oil's here something right here with the following and and about the concentration of which the issues with solving the granular array and continuous you see this moved so having said this water some directions for future work well we want picture relates to things that I said in the book are missing treatments of interminable treatments of the case were looking at trades future and the molecular weight of matrix along way the other thing is that right now it's very different from the molecular weight problem and you can sort of see what would happen only if you had a small role as a very large matrix somewhere in probe will invest very different effects on on different parts of the matrix polymer and the rotating added beats picture of matrix polymer is inadequate and you would like to treat internal loads well that's not as simple as it sounds I'll let us consider what internal loads of the models of all over the you and I'm going to draw comparisons the 1st comparisons between the turtle Reisman and browsed the standard models Fernwood Reisman is model I thought about 400 scaling and here is the home of 1 of it has a location if we put it in Deerfield it has ascertain your velocity Omega
and also has fluctuations were we skip over and therefore recalling that rotate all 3 of these media 3 translational modes 3 rotational loads and if there are any of these we have 3 and minus 6 modes that our internal and internal long Islamic changes the relative position in the now skip over to browser Zimmerman says here's a pall of exactly what the representatives feared being there by spring of this spring was only told distance from the thing along those access control rotational angles and if we set off worst constant matrix we just say have a and be so we have 3 and coordinates and we can set up 3 and differential equations motion this looks like a bunch of cults friends on the way the analysis is to say well we set assault and the X or Y and see parts of the problem or separable basis and therefore we can break 3 and buy and matrices as opposed to 1 of the 3 by 3 and therefore we have 3 translational had created by history loans which are part of that history and minus 3 modes in which the distance between the beach is changed by motion and you set it up and a looks perfectly reasonable doubt problem between this if you compare her license and arouses idea there are 3 and minus 3 in the world what arouses impasses Warner 3 and minus 6 shoes walked but you have to be be a little careful here there is a difference between normal and collect 10 basis vectors of collective awareness of orthogonal is quite visibly through the rouses in coordinates for a set of orthogonal coordinates in which you can do when expansion Dario Perkins Reisman is sort of all but difference Asia relies she arouses in gets a different account of the internal coordinates her breasts that'll kill there is an interesting analogy you know because there is another problem that mathematically looks just like this 1 accepted system as well as the 2 different the 1st differences system is under the Saturday is the bond angles in various ways ,comma region welcome to said browsers Ian Reisman but there is another problem and the other problem is called from the average were you for address that crossed the Turkey elastic neutron scattering in all 3 of these techniques have set up properly are sensitive to to molecular vibrations molecules and crystals and if I have any molecule in the crystal beading has 3 translation problems if it's in crystal the next 3 modes are migration if it's in solution where I don't experiments on the molds our rotation and 3 M minus 6 mos in which would shorten and there's a nice set of views of calculating the Olsen and what Wilson said confirmed Friday and we can demonstrate how we can write and rewrite the system Hambletonian in terms of 3 and minus 6 internal waters in which we have correctly factored out 3 translational the 3 rotation books Our question was why would you want fair after about 3 translation of 3 brokerage book because if you are in a solution or to the expect crossed the around on V-6 models have high frequencies the 0 and decided we would like to allow both frequencies of these loans you have difficulty of the Matrix you're looking out to do this and because the matrix a singular usual item value I function approach does not work guests however Wilson was a very smart guy and he actually did this instead said something 3 and minus mode so if you can look carefully arouses in the contains no rotational someplace buried in the browsers coordinates 1st 3 whole-body rotations which whichever frequencies 0 and therefore everything after that must be slightly suspect on the treaty unloaded relaxation times they get are also little Julia unit relaxation rates go up very rapidly as you make them more the because was going higher and higher frequency frequencies go up very fast in contrast these frequencies stayed fairly look at the low and intermediate frequencies of hydrocarbon these frequencies don't change very quickly at all 2 and therefore making latest safely locked himself in in his successors have started work with rise and you have to advance to in orthogonal coordinates there are consistent with the translation rotation In doing this you have 1 problem that Wilson titles in DEC is crossed paper coordinates assuming that the atomic distances Her face iterative with that's fine the Anglesea fixed and therefore the relative displacement of large parts of molecule relative to each other don't changes follows were less effect assumes this displacement of the Arabs with respect to the equilibrium ,comma positions or small blessed totally reasonable for organic molecules and Christian it's totally reasonable for small organic molecules in the soul it's totally on the use of color and therefore the
idea is right but the method method is going to help you the last major place to work advance because if you could do that major advanced you can handle all of the fluctuation issues the curtain rises now I come to another will get his 1st prize model makes assertion that a certain sense of propriety all sort of resemble the statement that so cited signs workers the statement is began sheer field with security the the law and the state in the year's something that is free to rotate and his rotation annual Israel's annual rotation rate have not to my over to because well I guess it should be rooting for the way because it tries to move with the oil and that creates force and there's a recurrent costs because these pieces are moving up and down with respect to the solvent and ask where you get 0 tour is when the rotation rate is scam gone to now we step ahead we look a calculation fears of bestowing last lowered and capitalization inspectors suspect that 1 of the things that I apologize dance In the last year and what is shown in essence is the isolated is constant and calculate what time is it disco elastic fluid as we increase security just Christopher politicking fears of a repeat the assault against the use of finite element calculation falls off that is the spirit moves less and less rapidly in the viscoelastic fluid relative to In a normal that that has to do with that presumably has implications for hydrodynamic coupling that have not been worked out I'm not more problems than were making run out of problems on the same line of the 1st issue is but the viscosity and it seems that if you calculate the viscosity terms you should be able to calculate the points that is that we center going to the renormalization group approach pushing out high concentrations however in order to do this we need to to find a fixed points along 1 of them was clearly at 0 however the solution might not like transitions implies some plays out here concentration areas fixed points and if you do the calculation it should become visible but the fixed points moved around a bit changed pre-empt all properties and therefore sometimes they're close 0 transition and sometimes they would only drive the transition of human physically impossible count concentrations well a little piece of this start was done by the our calculation Susan area and I we calculated change change change change change hydrodynamic interaction cancer which corresponds to the 4th quarter it change change of Shane hydrodynamic interaction and this gives us a more extended series for we didn't expect the herself to you so you could carry out calculation of higher and other modern conditions I suspect computer algebra like this fact and hopefully you go up higher concentrations get clear higher-order terms you get a clearer understanding of what's going on also the addition going out this way you can use the representation of all chains in addition to looking at the translation and active Rio translation rotation presumably you're also will think that this sort of thing all oil and if you get a nice internal low representation the helm higher order internal modes would presumably at 1st simpler ones and that means more complicated ones would start contributing a way to America the hospital and the obstacle is a I don't currently know-how and tackle this problem I thought of several things that do not work on the issue was his fault all the hydrodynamic scaling model calculations we don't all the calculations not counting the time scaling on results which is not a real calculation way the other one's odds on resorts or Flossie stance that is what we said we have changed here it moves and rotates and induces the motion rotation of change here and when we do an ensemble average we entered the average over all possible locations said 2nd Shane relative to the 1st however were saying that the fact this translation has been going on for a while is only interesting in the sense that the forces that this change creates back on this 1 is determined by the current velocity this change and the fact that this change might have been different philosophies and different times well inertial effects down and the presumably not relevant to the issue would and therefore there is no frequency because all the calculation is effectively for everything seen 1 instant in time and in different elements of the ensemble there different vertical positions but the fact that particles move with respect to each other does not contributed OK well I suppose you want terms for example to stress relaxation from the says displays this later stepped to the other place there is now force 2 because we've misplaced 1 played with respect to the other and of iPod he is the 1st of the really blocking stretches out welfare of very dilute solutions to some relaxation which takes a little while costs just sold a little while almost no time at all however the band called the slowdown and eventually get this features a series of reading told by act of In the long run and the plateau region isn't actually you don't expect to be flat this sort of a single exponential but if I a single exponential and the relaxation times out here in the early pieces the exponential very nearly flat on 1 side what and then there is region fall roof the terminal region has some characteristics time power which is terminal relaxation time and the terminal relaxation time gets very long forward all the analysis there is no concentration and was about to break but it may also at the terminal relaxation time traditionally is the oldest and about 3 . 4 the power it grows very quickly with increasing polymer molecular weight well in order to calculate this demonstrates again the behavior you need way on Friday In the calculate the time dependence of the forces that were part we have at this for this particular stage is a completely different calculations from those that have done and done so far and there is some question as to whether or how to make this work and the answer is I have not actually made it work so far so the answer is I can tell you but that is certainly a direction for future research all right and so that's certainly a major challenge finding which is not yet been carried out but if you approach the field from the standpoint of polymer fiscally last December that is if you start out looking at all of you dynamic quantities you started out doing reality you would say this is the most conspicuous feature of polymer dynamics and therefore this is where you ought to start looking trying to explain what is going on and if you start there you cannot easily get behind a dynamic scaling model because most of the phenomena we have talked about it a few others would try to bring up was born the 2 normal stressed differences with Europe .period we're hearing about all of the books along things we have calculated all these years prior the AFC how does this work all you start here you will not come near dynamic scaling policy static calculations because you're looking 1st and definition although nonetheless I have now describe the phenomenology polymer solution dynamics I don't think I have missed any major experimental techniques there were some topics we didn't talk about what they might not offer the natural world the learned about belts please not talk about we talked very little about Polly electrolyte we did not talk about many viscoelastic effects tighter the classical nonlinear effects of normal stressed differences were more modern ones like Shearier alike all along didn't talk much about home will mostly because many of them Our Home Holly electrolytes loves the interest on the loan deal with all other neutral almost over course they and think although however we did introduce a wide variety of experimental said he did this week did introduce a wide variety of techniques many of which are sort of Standard Life said that volatile South future creation Paul Lo sheer it's possible this coalesced the addition also talked about such things the people sometimes can forget sedimentation all of the costs we introduce sole motive we talked about the huge probe diffusion literature now we had some totally new thing we added electrophoresis which clearly gives driven probe motion justice said his nation does in fact you use electrophoresis where unions probe sedimentation has never been noticed we talked about Holloway's and at the end that said this week drew some inferences namely some models don't work or some and finally I talked about the dynamic scaling walls and the research on model certainly incomplete at this stage 2 Adams said that the courses to completion tablets or
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Metadaten

Formale Metadaten

Titel 30 The Hydrodynamic Scaling Model
Serientitel Classes in Polymer Dynamics
Teil 30
Anzahl der Teile 30 (Lecture 2 missing)
Autor Phillies, George
Lizenz CC-Namensnennung 3.0 Unported:
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DOI 10.5446/16230
Herausgeber Phillies, George
Erscheinungsjahr 2012
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Physik
Abstract Lecture 30 and last - The Hydrodynamic Scaling Model. George Phillies lectures from his text "Phenomenology of Polymer Solution Dynamics".

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