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21 QELSS from non-dilute solutions

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21 QELSS from non-dilute solutions
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30 (Lecture 2 missing)
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Lecture 21 - the polymer slow mode; thermal diffusion and Soret coefficients. George Phillies lectures on polymer dynamics based on his book "Phenomenology of Polymer Solution Dynamics".
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lasses in polymer dynamic based on
George Phillies book phenomenology of polymer solution dynamics Cambridge University Press 2011
ends today this lecture E is lecture 21
Paulie electrolytes small mode furthermore Souray coefficients I'm
Professor fillies and this is continuing a series of lectures on polymer dynamics and my knowledge but today we're going to be continuing and probably concluded our discussions of Chapter 11 on dynamic light scattering and the relaxation of concentration fluctuations polished probably go back 1st to the discussion of the neutral polymer solo that way to bring out a few particular features that we didn't entirely discussed last time the 1st issue is that you look at politicians solution there is for example work of all during he was there a couple of things you can do have 1 thing in common you is to look at the moment 1st cumulative suspected which is a light scattering intensity weighted average and another thing you can do is to do a mode the compensation and what is found we will give is that low concentration there is and it's relaxation rates cannot relaxation increases with increasing concentrations and that at some concentration courtesy of slow on were not on the same scale as all the drawing is began a slope the decreases as you increase of concentration so you have to modes they both show this behavior all of the other important feature of this were saying malls the the car was found to be used where the 10 the significance of the square dependence is that it corresponds to the diffusion then is you have solved that where there is a future currency which is proportional to coefficient concentration gradient and that it will pay out on continuity equation the CGT equals healthy shot dead versions of current and if you take disputing earned here to get the C B he goes as well that the great city of now if you approach this by saying we will put in place spatial Fourier Transform equivalently we will look at the relaxation of the spatial co-signed each of the gray casket replaced fired on you and have been the state proportional to minus the use of the and that as a mark of normal conventional diffusion namely that the molds have him square dependence if you however going to systems that shows full load their variety of ways of breaking the ban on how many votes there at what you're saying there's some question how many parameters you can really out of light scattering spectra and I've presented simulation 11 state reasonable numbers are 0 6 or a 3 20 nonetheless there are alternative approaches for doing this and for example and the work of the plant will cost was looking at last year inspector of the head very wide ranges of Decatur meaning is easier to pull allow out more parameters and who founded the small makes a mixture of Houston where independent models and if you have a 0 Venezuela factory and but how can you get something that's to 0 you're looking at some internal relaxation and the particles do not have to move to change how much like the skin so there's no particle motion involved instead the particles for example change their ability to scatter light from some of them not all specified and they're just sitting there so this seem the same polls gallery pushing the way which the on this which was discussed talk about progress the bankruptcy of cellulose and that is to take expenditure if you don't think that promotes a well-characterized will you try to fit molds to sell all 1 choice is to fit the mold to some of the few cumulative series which as far as I know was perfectly legitimate that's never explored very much all other alternatives it is true that the United and started their here and something of a long day he was minus a data was very slow at the time seemed to be useful this slow printers so form on so you fit to solve stretched exponential sometimes the point of fitting stretched exponential time is that stretched exponential sometimes appear describe all the time dependence ,comma Weld things that really are simple exponential and only use a few parameters however based on the comparison with concentrations stretched exponential where you can pull out a purification based on normalization apartments on there is no reason not to dispose those from 4 so that is the sort of thing you that if you then going on and asked what sort of behavior you have there are a few slightly odd things that you sometimes find off for example there have been found small modes Falwell those his square love what holds over his basically in him so a short distances you're seeing something human independent some sort of structural whatever and at large small few small corresponds to march distances and large distances something but there is also perhaps should know and I go into Nikolai they loaded mold relaxation times they find the slowest and has a relaxation and then let go and look at MIT mechanical relaxations then is you take the liquid you will apply an oscillating sheer and varied frequency and there are internal relaxations that contribute 1 way or another to what you're seeing that those have
characteristic time and if you marinated characteristic chemicals and polymer it corresponds exactly were approximately to the slowest time you see in the optical Spec however there is a complication the complication is that all if you do this and I think all when take the temperature if you take out the temperature the optical disappears mechanical motors still there so apparently mechanical almost was couples to something scattered light and whatever coupling was either cut coupling may not have disappeared the light scattering however the slow loan is still there no 1 thing like was after all have fastball which gets faster and faster as the increase of concentration you have small which to years slows down as you were forming almost constant reading polymer concentration and you recently asked about how is this to be a territory where we see I have an indication of this is done by crossing over and looking Polly electrolytes it is not for around a long time the Polly electrolytes show as usual with Polly electrolyte along with asking what it was or was not some of the same the dates that also took place with neutral always loom over President and the issue is that if you go back to 0 1980 digital correlated technology was really at or beyond the edge of what it could handle although I do recall when that we were working in Michigan with Polly acrylic acid and prohibitions polychrome gas at all you hit a point at which there was a viscosity transitional sought to discuss it on the diffusion coefficient of probes the public more and more from the viscosity of the solution and there were issues with the scattering spectra of problems and that's what we had at times a fairly limited 128 channels linear correlated you really appeared as tho you were getting additional small loans we we it wouldn't get with technology of the time so we sort of cut off where we were going about the time the slow OK so that most of this text does not treat all electrolytes which are very complicated across the reason we are discussing Polly electrolytes here is that we have a specific set of experiments satellite would clarify what the Polly electrolytes is and do so in a way which makes it reasonably clear that similar sorts of things are reasonably interpreted this happening for a neutral response a satellite network with the and 700 and killed all of them on sodium Poly Styrene solvency of polystyrene sultanate is a polystyrene that it's been chemically modified and out of the edge the area In late group that can be neutralized them at this point polystyrene sultanate is Polly electrolyte water soluble and so what set elected was to work with the East and the 1st thing he did was will dissolve the suspect all power from typically comes out and we will look at the Spectrum ancestor some question of whether we're equilibrium or not we will simply keep looking the same spectrum and he did this out from a 1 year scale which required patience and what he was bit after you which is the light scattering intensity peruses angle which gives you the distribution of sizes of whatever their solution was proportional to tie into to 0 I and therefore the distribution of clusters sizes was not change however is that the scattering intensity fell that was the the rates now that's a little peculiar and the question is how can the diffusion coefficient the increasing and the intensity fall and if you are on the size distribution is a change of the following picture it appears which is consistent with everything else you're going here appears to explain this we started out there some of the variance Foster but as varied as clusters of occasionally at a single policy states and this is not yet an equilibrium arranged over a year what happens here he's very exposed chains if you're not very well attached to whatever it is fall off a number of changes in Foster decreases change is get out of Boston and not get into not because the Costa has Marion scares last because clusters more porous because you've parts out it has a higher diffusion coefficients and this picture From the initial cost finally monster explains all of the experiments measure that doesn't prove its right and 1 of the questions you ask is well is it possible you just looking at the fact you didn't really does all things completely and if you had waited to win 10 year or a century of scale is it possible move from the data and indeed there ,comma glass problems there several Dutch troops set samples we need to do long timescales on working time scale of the experiment will not be done by the current people completely is out of the century the report did not agree with that so can ask Is this equilibrium follow said from Price and others that spare style of the back office staff and a straw poll of the Polly electrolytes slow probably should the early studies should all be credited to making sure very recently hired a quarter there is going to have to use in the feature that is observed is that if you have a poly electrolyte title there is no alone but if you take the Polish electrolyte that low-salt period will dissolve salt you see the fall and then there is
the fact that this is set on salt sensitive also shows that it's appalling electrolyte in some sense of the fact that you see artifacts from Polly electrolytes in solution in the absence of background ions on this is a general issue and low ionic strength only electrolytes her even more complicated problems it nonetheless what about 7 last year which was in line with this was to set we make sodium polystyrene In my "quotation mark passes through the whole point of my life from although 0 . 0 5 micron is about the finest filtering confined commercially filter water soluble whatever getting anything through it but it is the feast of great patients but didn't and haven't done all this if I Saltarelli welfare Wisconsin it goes on not essential access those lowered his experiments did 1 thing under a lot of others not as is there are a lot of experiments that with effectively ratio densities of what's that elected was to use unlike scaring standards to calibrate and he was therefore able to measure the absolute intensity fast among its own Sabra and so you can actually say how much faster than the the reason this is of interest is revealed by what happens when you take the Samples and dialog lies to remove salt or equivalently just make samples of different salt concentration namely you do dialysis strength sold from solutions and after you've done this following his loan move no question is why are you seeing slo-mo In theory advanced 2 sorts of explanations 1 of which is ruled out by myself Alexis Ferris all 1 Ocean relies on the statement I have cholera solution Polly electoral I'd pull was sold out unleaded intensities scattering the intensity of the festival In the case of sold out and what I find is that have always sold out the intensity quality the particles repel each other it's much harder for them former concentration fluctuations and so the Foch concentration fluctuations are small and therefore the amount of light scaring small now 1 thing that could happen if on the other side is the home intensity fast-flowing is falling rapidly is there actually was we're all walking however at high salt salt was so weak that it could not be seen on scary by fast as you pull the salt out of the tent tent city stronghold perhaps in the end of race some of data and therefore slower rises up out of the deeds like a rock left behind on the beaches tighter receipt well that's very clever however you can't rule that out if you do absolutely intensity because if you tell the absolutely and the here you can work out how and to tell also intense the slo-mo would've been here no problem that is fast food is here and you can simply ask if there were actually this looks slow President wouldn't been didn't know the answer no not the way and so a satellite that showed by measuring scattering intensity is that home quite clearly the slow-moving actually does appear when you people sold now the other thing that satellite was to sit there and on lotus staring from soloist final and what we found is that as the guarantor of the it is you get some distribution of objects and solutions that were contributing to the small and there were marching off to be comparable in size with a light wavelength entered and the size distribution did not change you let the samples for very long on the other hand let things said the intensity of the long long roles as this year's as the fusion of fat
and if you look at the intensity of the viruses How did you start with less sulfates and pure water and the intensity almost fell as time went on Ed you start known clusters wants solve things in here a lot on poles sold out and intensity change the and 2 attempted to converge there is a reasonable interpretation of this observation which is you were looking at equilibrium clusters if you have all the the the the interinstitutional concentrated the Internet's empty out if you have 1 of the entrances to dive moved in Poland were changed and they tend toward an equilibrium sites and therefore the reasonable interpretation is that you looking at equilibrium domains in solution and you can approach the domains are either from our side where you have initially to concentrated or signs were there initially to die lewdly they converge the same point then we can also go to other sets of experiments once that is Parliament and all this is result of room In Louisiana and what they did was to say Well maybe these let us look at this accusation the domains urban problems with this all out Will synthesizer holdovers from scratch and we will never take them out of solution they were made in solution they have always been in the solution there is no dissolution step in their history causing difficult 2nd experiment I didn't used to to Manitoba and they did not have in essence optical microscopes and they looked at systems among other things systems that show Goldman well if you look at the system's showed domains microscopically and they can't actually visualize things that are about the right side they're not very distinct is after all these years solutions structures they are solid bodies and solution structures whatever they are are about I said there were about half a mile from the lessons the soda quite large the much larger than an individual and can actually see the maybe you can't see them very well that you can actually see last experiment said said when I started out again and this century out of polystyrene soulfully that was not neutralized it so that will manage realizes not precisely correct that if you have any gasses group water organic gasses whatever it ionizes to ionizes to some extent so it has some charges but mostly structure and what he added was to say we will not air sodium hydroxide and will neutralize the polymer meaning we will pull off the protons from the acidic groups and the Apollo will now become extremely have the church and what was found was as the at an annual wage the intensity of the fast-flowing drops dramatically and the intensity of the slowed you sit around and the intensity was followed by then is you can approach this and all on 1 more access where the solvent basically doesn't change the polymer is dissolved in solutions and all you're doing is changing the charge of tolerable and you see the same behavior his way OK so we have seen all of these alternatives question will be here with you in this yes the experiments all conversion to agree that you were looking at equilibrium structural solutions a structure that is considerably larger than a single ball add the various properties some of which I skipped over this picture agree completely with the home a small world seems neutral polymers mainly for neutral polymers the on both modes to where have and the fast followed which corresponds to a nearby to James interacting with each other single James D. increases as you increase the concentration of this change would tell each other the slowdown the vitrified region whatever it is it acts like of diffusing larger objects and that behaves he were doing probe the future and therefore
is to increase the polymer concentration the probes of that Will so you might reasonably ask Our how does this compare with what we know about last things where you might see this and there is an interesting analogy which I will personally professionally as the analogy His will kill last month but in the end and publicly that he was 1 of my post doctoral supervisors seasons past n the issue this fall suppose told officers temperature we look at the behavior of political liquid versus temperature and we look at the viscosity and if we look at the viscosity versus temperature is the school's something off the simple behavior is to pull it off you pull it off you get to the melting point the I think like you from solid principal and she there's no more viscosity it's thing just sits there that's simple freeze however many substances if you take the moon pool you cross the melting point and you just keep on going and the viscosity goes off about now there's some substances in which you cool and cool and you eventually get a lower limit below which you cannot have a on liquid and the like the lower limit what happens here is on your form you stop the likelihood of forming crystallites in solution goes all very fast with decreasing temperatures and material turns into the crystal salt but there are language were used to cool things off all the involvement of all things off and in the anti-Vietnam War was on the intelligence to be solid left the question of the nature of the glass transition is very controversial and very complicated and it's mostly beyond what we're going to talk about there are however a few other peculiar features of the glass transition 1 of which is used political office you know what you're up against duties up to Algiers on Mondays and you see excess light scattering relative the amount of light scaring you expect solution and the exit access light-scattering stays around for a very long time it wasn't he originally wanted to run away with down and back up again and get this access light skin and the question is how are we to interpret all of these different phenomena what Kittelson proposed laws you call the off and some temperature it starts me postures he talks about his collaborators talk about Foster's there I cost legal things and the clusters are Thurman dynamically stable however clusters cannot lead to crystallization why not because I costs the drop art space if you get 20 cited Dyson tried hacking them together you can pack Humvees and make the ice crystals you cannot persuade I prosecuted repair because the it's not a space-filling geometry in three-dimensional space and as a result the IPO last year principles objects role but as they grow old because it's not space-filling may have distorted and they the strain energy coming in and some of that some size you have a frustration landed at the 1st Foster's not get bigger that's the front now the fact you made more and more of these clusters down here sort of explains why the viscosity goes up the viscosity is going off for the same reason the viscosity of ice slush is higher than the viscosity of liquid water nearly varies little unbending things in solution and they get in each other's way now he told the create truly brilliantly creative contributions and creatively brilliant contributions the statement these structures are not space-filling making in crystal but the film dynamically stable that is the clusters have been melting temperature and the melting temperature of clusters is higher than the melting temperature of as a result there is still stable and liquid put out here once you make you
heat up the on the melting temperature and the clusters stay around to some significantly higher than and they then contribute the Stasi increase they then increase that and the large increase in the extra light scattering they explain why you form a glass and there's 1 other thing suppose you make these and would like to crystallize To my rear as a principal in order to get from here to here you have to break up this structure and form the preferred structure well the potential energy all free energies area is clean "quotation mark so even tho this is the preferred structure the stable structure local content and low temperature In order to get from here to here you need to supply the very large number of miles of thermal energy transition state and guess what that thermal energy is not available and therefore even though at low temperatures the frustrated Crystal less stable real principle was to make them you can't make them go away easily not just not just by sitting waiting so that the procure Kittelson last month I have done molecular diet with Paul Whitford all molecular dynamics simulations which appear to show revealed the presence of cables and postures that have exactly the property's here also strive to including a few that I have gone into the only difference between clusters we found once he described is the crust Foster's referred to a found shows that funeral sevenfold were not bypassing the dropped 20 fold over the past Saturday he drawled ordering is extremely unusual in nature and if you didn't think there was a reason to look for it might not thought so but that is what we felt something weapons what users have to do with the song the answer is we have a tolerable rules and they form these objects which is Polly electrolytes have higher density and the surrounding solutions and in neutral polymers apparently do not NBC objects are frustration limited growth limited meaning they can grow more than they do clusters are they form a higher concentration and contribute to the viscosity the posturing and so these are the last the objects of the last model except we have a working expect experiment case where they actually exist it will take and we are now approximately with the army discussion of this fall and the question is where we push on to the next and 1 investors realize Brill once but I only talked these about really this is in some sense the guarantee interests press by "quotation mark Alicia daylight but many of them are the answer is that we have set this thing up we have a link with the scary light from and the like to some extent changes frequency when scares me to do this with a simple liquid that does not contain defusing all of the scaring a lot of changes in frequency in the areas of fighting for her life and the life of birds meeting on you don't use a digital correlated to study the every parole from were 1 of several relatives and what we "quotation mark after that laser light years frequencies I'm phone in the laser light was frequently hero and I will ask what frequencies of light or scared out the answer is the spectrum shortage horrible like this and there is a sense of it and there are 2 shift and he swung shifted often frequency 1 shift doubt in frequency all and how we interpret this all this he is the you fluctuations in the local energy density and salute the energy fluctuations creating mass density fluctuations so they scatter light the army when fluctuations go away is they the energy diffuses out of them which is you and so the this fear is determined by the diffusion coefficient for this two-sided around frequencies sees announced the lights and the frequency sees the local speed of sound waves and the solution wire sound waves solution the firmly excited just the way the use of smoke site and the sound waves he also heavily weighted and the wave is determined by discipline patient kills off sound so you have 3 three-piece there and 1 of the things you could imagine doing all of this and that's what happens and the church answer is Paul molecules her ovaries long scale this material is gigahertz range in very short timescale and therefore although the 2 coupled with each other a lot however should go through from low polymer concentration out to the melt all what we find is that the frequency shift here changes with polymer concentration the weird strange and therefore there is solid source we sensitivity of the really prolong spectrum to the fact that your change replacing the Solver Paul that shouldn't be in very surprising after all there's no reason for farmers have the same formal diffusion coefficient the speed of sound solvent and as you move from pure solvent
through ball something about him Dutch another thing you can study is the call for a vote the notion that story coefficient deal by the experiment citing the use of laser interferometry to creating interference grading solution that it sending 2 beams of light saying source so the coherence they common 2 different angles and may interfere and because they interfere they appear produces brightness rating well if you do this with a high power sources you don't just have brightness rating you have locally heated material and now has several things that half all the 1st thing that happens to produce a fluctuation the local energy density and that if he loses out to thermal diffusion the 2nd thing going on is we have also raided fusion and the notion here is that you have a matter current which is proportional to the story of and the temperature greater as he created temperature gradient solution were the guests objects to defuse parallel to the temperature great all the couple of minor cuts complications here 1st of all these factors also known in gasses and the mechanism and gasses would appear to be quite different from that 2nd unlike some other diffusion coefficients Souray diffusion coefficient can have design that is if I produce temperature gradient like this the temperature gradient will just drive the motion of macromolecules but may drive a long way in order to drive home the other way in each In this open allowed out all that's Saray diffusion coefficient people they actually observed that polymer solutions and you can actually see things investors Cerrato I was describing so we have an energy among lapses we have concentration which relaxes with the diffusion coefficient concentrate Mascalzone race and that in some systems also will include the we is perhaps sometimes described as the health of and sometimes described as structural mode however the evidence that if you ask you What is the structure that is doing its structure rating there's no real answer just described as structural is a reasonable interpretation by comparison with this bill we bless this city but if you I ask you What is the structure of world that's moving toward yeah but OK another set of experiments and different said said experiments or appearances current all members hearing tall and we take the initiative in the politics of solvent and say that the mixture that is the Paul merger such that both Paul merger concentrate now he previously talked about cases in which there is a matrix ,comma was allowed to be concentrated art and a tracer polymer which was always dining rooms and we looked at the single particle that future of the tracer followers matrix of here matrix and tracer on post potentially concentrate there an extensive series of experiments on experiments to test the revived and will not the agreement is reasonable there are a number of tricks you can In this is the 1st of all if I clever I can arrange things to do in their expansion the fighting next match perhaps I can only see 1 of the bowlers and not the other 2nd I can arrange things was called 0 the average from process so that is all I increased the concentration of and I increase concentration of me but I think the radio constant that is by having concentration fluctuations that moves more mixture into the solution that's a fluctuation I can arrange the fault the southern there there is no change in the index of refraction and therefore fluctuations in the total concentration polymer assuming its uniform policy compensations to not scared like under this condition what scares like his something that changes the concentration of any relative concentrates the so you was very from this and get our institutional wants the correlation was as follows there's a diffusion of automotive and he is driven by concentration gradient and that causes the concentration of a change also there is diffusion coefficient but got concentration gradient and that causes the concentration of change I'm actually on the insistence on the right he 1st of all these concentrated time us however check-writing non-violent solutions to prosper there is a belief in which the defendant the driven by the concentration there is
a DEA agent the which is constant which is the defendant the case driven by concentrating on the To the prosecution go further their reference frame the basic issue with reference frame effects by saying ,comma the ayes particles moving vanish are sensible ways to measure current and was to look at the motion of a relative to the salt and the other is to to say we are in close container "quotation mark if there is any particle moving that way it must be because it's supposed to in must be this ladies and solve solvents that way added it just displaces everything and preferential and therefore the the particles pushed the other direction because a is displacing this is the reference frame affair reference the group can you get what then and the reference emotions are independent of the prostituting coefficients says 2 effects an independent the consequences of the reference frame effects is that if I write the diffusion equation In a reference frames fixed on scattering celebrated the soul these various of these get mixed up in different ways to some extent so the FAA concentration gradient a private emotions and will also directly to the reference frames contribute to the promotion of the and vise versa and so there's some interactions the probable losers sold followers by bending moment there in a series of experiments test his theoretical models on the models Wells worked pretty well generally there somewhat coarse grains models the description of the colorist is on last year looking at single all the changes ,comma 199 it's the Reisman sense is a very coarse grain description of what's going on but at that level it works quite well I should very briefly 2 alternative lifestyle from here but the student-run scattering is in particular you didn't ask me to come here we send the neutrons 100 there scattered by the sample was the first one or approximations they come out themselves direction and they come up with some changes in energy the change in energy is equivalent to a change of frequency for visible light and corresponds to the fact the scaring off something that is moving system no the 1 difficulty is that in order to use this to study said diffusion the energy changes are extremely small and therefore you have to do something very clever in order to measure them is resolved and decide if there a new problem Apple and on an experiment which is very clever is the daughter of a small number of laboratories and in fact gives you the energy shifts to very high precision OK so scatter from neutrons it's like scattering from life there's 1 minor differences might have stalled the president said polyethylene might be reviewed at regular there also replaced protons will use arms and now we have heard Buturo ethylene in which all of hydrogen is the place to be and we can also do this so the different amounts of each the scattering properties were neutral of hydrogen and hydrogen water and deuterium are radically different and as a result by changing the isotopic substitution in what is otherwise exactly the same system you can see some fairly interesting results all at the gruff particularly those with just the to radio just right you have saved Paul it's randomly substitute ancient the if you get the ratio just right Paul becomes very hard to see with neutron scattering and you can focus your attention on other things and this allows you to do what is in essence tracer diffusion itself diffusion that the following but what has been done all is also experiments on dialup chains value chains have been studied and the featuring is this because there was like correlate fairly specific predictions namely there is a mold that is diffusers there is a 2nd alone includes you and also a relaxation of the relaxation of plot you on the issue there is you can actually see the tumult also opened on before you light-skinned however with the trounced area a representative where my might working a job so where you're looking at motion on much shorter distance scale with neutrons with visible light 2 that brings us to the of this why scattered 9 waiting put a break in the table at this point and greetings to the
2nd part of today's lecture renowned going to advance from a discussion of what elastic light-scattering neutron scattering such a lot to this stuff and viscosity call of the physical location of viscosity is represented by a single Saskatchewan have been extremely large flat plates 1 of the places stationary 1 of the places moving with some speed yet the 2 flights are separated by some distance and all in the direction and there were quite a lot of the subtext the station the traditional assumption was the is station is being here in the state and therefore PDF the we call it the Euronext the actual losses Over he's a velocity gradient velocity that way gradients that
way all the assertion that the velocity gradients the same everywhere across all has recently been shown writing some severe problems he was shot on the system the worst there's obvious alternatives so if I take 2 parts and moved on to if I have a solid block and I started with a solid block topped with respect to the bottom I get crazy insurance claims and the things centers well Palmer a somewhat in between simple liquids which this and solids which break a few twists the murder of all come back to that later cost Hammond said In order to the upper plate movements have declined to you the area and the forestry unit area is determined by by the velocity gradient assumed the same everywhere across and constant data is Greek letter and stands for viscosity is resistance now that is this was told she here and and this year's starts the 2 other viscosity is the rise of what what is it that had little volume of material here viscosity policy and the compressing or decompressing the flew for example at some frequencies and changing its volume and this is what is called a halt to the us of followers solutions we're talking about are mostly dissolved in substantially in compressible solvents and therefore you can do this a great deal there is however a 3rd viscosity which is extremely important in polymer engineering the 3rd discussing Iraq take the long piece of Paul over there is usually done with and granted to with that pulled in opposite directions and as you stretch there's a resistance pressure the resistance stretching is known as the expansion will varsity it would be a the point on extensional viscosity others resistance stretching well this is how you make all a lot of polymer threads in some part you push the pall over through holes and then if you want to really find thread you may for example stretching from here will stretching is not quite trivial matters indicated how not OK so there several different viscosity that you can mention measuring and what its founders of the viscosity of policy solution depends on concentration and so it can't fall over the viscosity of the changes if there is no longer the only areas 0 and viscosity sold and then have something that 1 who lost a I the he was going to see where was thought up .period I came along has then a lot which is usually used In that embraces the intrinsic this doesn't use a lot of concentration leading the years of guests local concentration leading the years-long all we during write this he played traditional really right 1 it was the only thing that was really the data where that's all anyone is greater In this form -dash acted a human who he had CEO squared OK agency respondents thought the company coefficient is the lowest concentration terms that reflects the interest of Paul oils with each other Lydia here appears simply because there are polymer oils and you can calculate at some level of precision by calculating how a single polymer chains moves and then saying well there are a lot of them so there's lots that however confidence coefficient describes the interaction with all chain the last phase of age OK so having served as the basis of age we have no intrinsic viscosity although what do we do next well 1 thing we could do is to ask what happens is higher in concentrate and classical dances that Martin with Martin presented a they were 3 my footnotes accused the papers title thanks to work very hard work in library I have not found another source supplies the title of the original conference were and what Martin said the problem was taken to the it's each to the constant times concentration and he had data that supported this it a nice approximate formula and that is the Martinique wage now 1 can do better than that of white phosphorus and point out some of the the intrinsic Scott all of this information there a sense that mentioned was therefore this must have been mentioned 1 and units the intrinsic viscosity in units must be 1 of the concentration so clearly the president mentioned once the Ada work being described as the natural units for discussed concentration units for discussing viscosity are how they wear is seeing what well for a largish industrial type called meeting molecular weights on about you something in their CAD is some our aid Ada is 1 when the concentration of all wanted 10 grams per liter or something like that it's a fairly low concentration is not like volume fraction were 5 1 is unattainable as you can get better .period set to see
if you can get up to be approaching melt
100 republic now the 2 other sets of predictions of this Garciaparra concentration and wall there's some nice things which failed Schaefer this and the prediction is discussed at elevated concentrations of sea the X and line X and Y power this is a reputation scaling South of now I have decided to polymer melts the theory derives not only I but also the fact that Powell it is for a mouse model actually predicts a functional form for solutions that's not the case for solutions you can create the best and what all can we put in some numbers here should begin to get more Paul Newman actually matters discussed in the fall of the collective way plate is not quite as easy as it sounds and have a serious engine that if you have a polymer how do you determine exactly when its molecular weight it's and the answer is there a bunch of methods that give you information but there several 10 per cent methods not . 0 1 per cent please In the reputation predictions looking at the next it applies some number of traditional numbers 3 experimentally while it is about 3 . 2 4 in the middle of and there is there are some theoretical treatments that can never resolve the differences for solutions you can also ax and exercise longer in the running of 3 . 7 5 5 depending on solving predictions that's predicted and so you can actually predict some exports the alternative to this it is stated abortion is they also seemed where Calvert is for working an I had lesser stretched exponential form from viscosity based on current prices moved higher dynamic and based also on all positive function renormalization group you can actually predict this form if new inventory numerical values with no previous history and the agreement is well the coppers half-empty here have faults actually pretty full stop those are prediction let me just started on measurements since we're almost out of time and we will start with figure 12 . 1 while was shows measurement of Chambers and Alford measurements ,comma onto a set point in the polystyrene in I appalled directly affect theory about 7 . 8 magnitude Dalton is an extremely large they will only discuss the release of latest other things during the book however if you look at viscosity this is lost on museum was stretched exponential form the stretched exponential form works well at all concentrations you can also look for example Figure 12 . 3 I 12 . 3 shows measurements and Volvo In these the skies of violence In again if his former is custody his concentration the guise Kurdish lines released decently close to following you look very carefully at the highest molecular weight Hall guidance the measurements actually show called a viscosity which is a bit lower than you'd expect from the curve which describes everything else quite well but if you look at those positions knows viscosity of here are extremely large indeed were looking increases in the viscosity of multiple orders management although in some cases of 5 and stretched exponential describes nicely over the the full range of concentrations of the viscosity I see however we're out of time and therefore we will continue this