11 Self and Tracer Diffusion, Part 1

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11 Self and Tracer Diffusion, Part 1
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Lecture 11 - self and tracer polymer diffusion. George Phillies lectures on polymer Dynamics, based on his book "Phenomenology of Polymer Solution Dynamics". At about the 20 minute mark, there is indeed a slight gap. I decided there was a better way to present something, and will do so at some point in a retake, something not possible in live lectures.
Prozessleittechnik Diffusion Tracing paper Vermittlungseinrichtung Dielectric Measurement Ship class Relative articulation Dyeing Kette <Zugmittel> Assault rifle Cell (biology) Ship class Cardinal direction Video Engine Polymerlösung Angeregter Zustand Audio frequency Viscosity Molekülmasse Refractive index Year Microscope Diffusion Chemical substance Polymer physics Aerodynamics Gentleman Game Standard cell Matrix (printing) Book design Trade wind
Reference work Prozessleittechnik Hot working Roman calendar Neutron Tiefdruckgebiet Scattering Year Order and disorder (physics) Single (music) Automated teller machine Specific weight Concentrator Roll forming Colorfulness Matrix (printing) Contactor Nuclear magnetic resonance Model building Last Fundamental frequency
Theory of relativity Alternator Cosmic distance ladder Diffusion Hot working Sound Day Scale (map) Force Polishing Kette <Zugmittel> Group delay and phase delay Bird vocalization Potentiometer Roll forming Kometenkern Limiter Spare part Constraint (mathematics) Orbital period Video Material Typesetting Speckle imaging Musical development Tiefdruckgebiet Tool Ballpoint pen Buick Century Hall effect Single (music) Gas Concentrator Finger protocol Quantum fluctuation Sizing Gentleman Series and parallel circuits Remote control Matrix (printing) Narrow gauge railway Theodolite Noise figure Water vapor Model building
Theory of relativity Prozessleittechnik Effects unit Weight Geokorona Magnetic core Scale (map) Optischer Schalter Kette <Zugmittel> Phase (matter) Roll forming Crossover (music) Tiefdruckgebiet Molekülmasse Duty cycle Year Season Power (physics) FACTS (newspaper) Isotope Rolling (metalworking) Series and parallel circuits Current density Cartridge (firearms) Wallet Mint-made errors Noise figure Level staff Diffusion Hot working Bomb Day Short circuit Volvo Group Measurement Summer (George Winston album) Cell (biology) Potentiometer Temperaturabhängiger Widerstand Orbital period Spare part Video Rail transport operations Material Angeregter Zustand Fusion power Paper Kilogram Concentrator Sizing Matrix (printing) Water vapor Model building
Space probe Scattering Electronic component Measurement Amplitude Year Crystal structure Light FACTS (newspaper) Concentrator Quantum fluctuation Separation process Temperaturabhängiger Widerstand Matrix (printing) Relaxation (physics) Spare part Radioactive decay
Ruler Prozessleittechnik Diffusion Day Visible spectrum Measurement Light Kette <Zugmittel> Group delay and phase delay Solid Roll forming Faltenbildung Continuous track Relaxation (physics) Limiter Rail transport operations Fusion power Engine displacement Star Ship breaking Typesetting Stoneware Tiefdruckgebiet Molekülmasse Year Single (music) FACTS (newspaper) Concentrator Quantum fluctuation Direct current Autumn Cartridge (firearms) Hour Remotely operated underwater vehicle Trade wind Synthesizer Stock (firearms) Week Storm Firearm
Cosmic distance ladder Molekülmasse Measurement Year Single (music) Power (physics) Mitsubishi A6M Zero Concentrator Rolling (metalworking) Hour New Year Orbital period Video Remotely operated underwater vehicle Star
Prozessleittechnik Funkgerät Mechanical fan Hot working Diffusion Cosmic distance ladder Scale (map) Starter (engine) Measurement Order and disorder (physics) Kette <Zugmittel> Group delay and phase delay Bird vocalization Sundial Bahnelement Orbital period Television set Video Star Typesetting Paper Videotape Viscosity Molekülmasse Year Single (music) Cocktail party effect Season Power (physics) Drehmasse Concentrator Angle of attack Binary star Sizing Standard cell Cartridge (firearms) Remotely operated underwater vehicle Control panel (engineering) Model building Stock (firearms) Firearm
classes in polymer dynamic based on George
Phillies book phenomenology of polymer solution dynamics Cambridge University Press 2011 ends today this
lecture is lecture
11 Paul Mercer cells and tracer diffusion today we
advanced to a lecture on polymer self diffusion this is actually the 1st of about 3 lectures on the topic we're going to begin with some general phenomenology and get in more detail self-defeating that is to attend a vote student told single called share is the 1st of the Orthodox traditional topics polymer dynamics that we're going to reach if you look at standard first-rate reviews for example reviews by law or by the jury both he and his defenses in chemical visits were a very nice review by the man to growl and they asked a robbery technology Warren the classical book by gracefully problems little forget but this discussion of all the diagonal concepts classical very much really worth reading or if you look at the new well 2003 installed very nice but on polymer physics Tripoli's central offices you'll see a certain was half the topics we treated so far in the course mostly you're not discussed what you do see discussed is discussion of some units coefficient piece of ass discussions Paul viscosity discussions of Paul this city which is to say the viscosity becomes a function of frequency that it's not quite as simple as saying it's a function of frequency she very different people ,comma list of topics and there's a wonderfully written reviews that are definitely worth reading OK so where are we would itself in any of the general notion is that we have a policy which do we really talk about all of state although there is a feeling of that is this whole about turning into a simple liquid or out of a complex little anyhow but there is a polymer went with them yourself well able to reach in and buy something like 1 change so we can see the emotions of the wild even the other chains are also they're not there several very different physical ways to do this 1 approach is to say we have college and we're actually going to label at some for example we take some quantity of polymer chains and we attached to them of fluorescent dye and we can if they're big enough you can actually visualize the chains under the microscope what we talked about DNA electrophoresis there were beautiful examples of people who actually manage to visualize polymer chains the NHL games and see how they moved in polymer solution under the influence of what was supposed to be we feel here there's no external field were just looking at the future some 1 thing we can do is to say we will again there is a polymer chain and we can't measure it motions as time goes on we can do this by labeling the chain that's fluorescence recovery after the allegiance at that it works we can also use fluorescence correlation spectroscopy off the related technique in which we so in my 1st start with you feel that a very small ones we have former McShane and we cannot determine how fast the change will begin to work out solutions you can also see the changes you can do encourage cultural and you can actually measure the big enough for bright enough and how position versus time and do statistical analysis of the motion entirely alternative approach this cos that static lines gathering is say we will look at the system and thorough systems have for all problems molecular weight he and of dangerous Paul Merck's molecular weight down slight up some authors reversed the 2 unions he the mean the molecular weight matrix and engine mean molecular weight pro for what I'm sure were obvious reasons there are normal last week at and we can then arrange the tertiary system as we discussed in our dielectric relaxation chapters of OGE here's assault here is the latest Colorado you can't see the matrix polymer can you you can see it because it's index matched to solve however we know have the traditional the traces of not index matched the the solvent and all it stands out you can see it you can use a posse of plastic light scattering the other techniques to measure the diffusion coefficient and as long as you were careful tracer chains are guys who you well technically light-scattering measures of mutual diffusion of In the the the species you're watching our guys you're really watching the South diffusion coefficient process advance notice of technical complications with saying makes to followers of solvent the 2 homers have to be compatible with each of the 2 followers both have to be compatible with the salt if they're not our year trace overlooks at this hostile environment for by nature's followers and tends to fold up and change its confirmation as you change the confirmation of matrix trades
alternatively you can say well we will have a polymer chains and someone say this is just a hypothetical example BCH too and some of them mercy the 2 and so we have the Polly hydrogenated the Perdue rated formerly called purity form and you can then use either neutron scattering or you can use and are and you can tell he's DG's were finally got even is the manager of a single single-chamber diffusion coefficients using nuclear magnetic resonance on the specific nuclear magnetic resonance technique is called holds radiant work she and family it's a very clever technique on will get some references of honor I cannot pretend to be in America but in essence that lets you measure yourself if you OK so we can measure the self diffusion coefficient we can measure how how 1 moves through a polymeric matrix what area but no 1 wants to do that cost some confusion color vision also tells you however low concentrations species moves through a high concentration matrix and those of you with some interest in biology they realize that here there is and the inside the unique that is the same very cleverly designed the insiders say is filled with all sorts of stuff and if you look for single species most of them are not concentrated but somehow they managed to get around inside the meeting at a cost some systems their opponents and some systems there is no future there is a biology process there's another single change from years of last year to all the pieces that we brought in contact with each other happened only some of them sold right here if you there warrant off what happens is polishing and each side tends to propagate in to the other side and the 2 polymers tends to stick to each other and if you were trying to cement always together you get this to work on the process is not very fast and if you're not however is not very strong but they can be made to work in it's interesting example :colon herself future there also fundamental physics reasons for being interested in in the southern in order to explain what the fundamental physics reasons are what I have to do is is to reach in and to discuss for once the major models they're wondering out there as to what helps ,comma dynamics works solution now there is I've mentioned it once already I mentioned high at all another context and it's worth looking at but we're going to look at this very basic issue with the 2 sorts of questions I didn't want to question is I we modeled what polymers is being fixed and None released most of them was being
fixed costs are a whole lot and fairly clear performance came to live with her mobile and fixed models you don't have think about as much you fixed in distinct status it maybe you're looking at things that will fast and the other objects that quite slowly and
approximating the moving objects is not material is not such a bad idea the other questions boils down to what could be sent to the water the forces and what they tell us about Paul promotion the 2 sorts of forces there were all emotion and want a hydrodynamic forces and the other orally the old Fred Davis ,comma logical we also say change crossing constraints but what do we mean by that you see the hydrodynamic forces in action if you put a school in a large pot and Polish polls voted through the Lakewood and notices things remote from the school but dragged along by the eddies the water that's a figure dynamic injury there are also thanks to the fluctuation dissipation of the hydrodynamic forces that they act between diffusing objects they're not as enormously strong because the objects are moving as fast but they have the same range the same attendances on distance and relative position those a hydrodynamic forces the other forces you have a topological arise because the Americans call him names they you go through each other they're not ghosts no change crossing is not everything but it is a large piece of it corresponding to these 2 forces there are collections of physical models that have been used to attempt to describe what's going on and all I think you will cost of those I'm not going to use that I'm going to point out major models will correspond to the results correspondent topological and Shane crossing constraints the 2 groups of models their eradication and scaling models in which we will have named Edwards and the voice and then there are also a set of of models in their homes by the name of the 1st author of the papers obstinate and these are models in which most chains move very slowly in the corresponding hydrodynamic models will heighten the models and traced back to the greatest statistical recognition of the United States and the 1st day of 1st century with more and better prices .period who was a student now this is a single chain model other extensions to the young college and then there is a systematic development the hydrodynamic scale model on which in large part my work you see I have done something useful OK so we have these various models on the original injured interest itself diffusion goes back a very long time you suppose I have always solutions diatribes story of how makes however a lot of terrorists experiment with I and say are happy to say they were inspired by direct scale so let us look very briefly in the revocation scaling the picture and how it works and 1 man says about why self diffusion is interest From this Parliament that associated this is now the reputation scaling picture at low concentrations of polymer or well apart from each other and you don't nothing much happens however if you increase the calls concentration through sound critical concentration the polymer chains injured had each other oversold the Paula change that form of learning how to handle that it is important to emphasize that in this model there is no specific description of what it kind of looks like In some sense you could say it's in the infield model the some of the old and pangolins those chains wrapped around each other 1 way or the other there is complicated .period entanglement but the model doesn't rely on any detailed description of how the entanglements work what it does say however is less consider another Hall of Shame Europe :colon we started increasing concentrations and as we crossed this concentration theory is a theory doesn't savants and narrow transition worldwide 1 really doesn't but somehow we get from here to here and each other ,comma change has all along its length a series of entanglement .period and in some way the number of affected over the exodus of entanglement gas around to any and now ,comma solution is said to be entangled now what and me for Colorado or what is claimed to mean much to test 1 change during the talk about some of the changes tries to move sideways can move sideways through some modest distance but after its moved sideways when modest distance it finds other polymer chains and it comes to us stop the alternative courses finds the polymer chains and now they all move forward is about the same speed follow the model actually does not explain why the changes are supposed to stop grim everything moving but the assumption along with that comes stocked with stop OK so we have this very long chain and Arab distances between the entitlement .period did or perhaps some people different terms symbols and then there are as old as the chained him sideways the least you can move sideways very far relative to its great line instead chorus of accreditation pictures the only thing the polymer oil Can you it were Paula chain can do is move backwards and forwards parallel who 1 he want an image of this OK I will give you an image while the polymer chain is a very large bowl constrictor the ball or constricted is in a grove of sugar cane but it's not strong enough to crush the sugarcane plan it must slither forwards accepts moral Beau Bridges backwards just as well it can only slid backwards and forwards the continent sideways however can sideways what it can do is rocked back and forth and there is an interesting feature but what we want is backwards distance here there was 1 it tries had forward it doesn't remember we haven't found any intention him now we have as a technical name surrounding this policy change our limits on its sideways motion and the limits on the size of a motion to have obtained there is to it the poll is confined to 1 2 but it
has a way to escape neighborly went backs however the 2 it's not like a piece of plastic trained by the 2 vanishes and 1 Apollo moves ahead again it loses tool with the other an efficient way long enough polymer rocks back and forth and he eventually it is completely escaped from its tool and I was always somehow he didn't get over here by moving sideways he got over here by going backwards and forwards like trying to back column of the driveway it's full of the stuff you can do it with education so that was the humiliation of the own reputation now I went there the polymer matrix invisible and we're just going to look at 1 polymer chain and invited them to I'm
greatly oversimplified the purposes of discussion the core issue is the if you study self-defeating she's that's a work prediction of the reputation models OK so we're actually going to talk about self diffusion there's a reputation predictions but he has cautioned that have joined too on the other hand we could also talked about the hydrodynamic scale and models and predicts based on renormalization group analysis with the Astros errors some each of the mind of a political right this see Elvis seated to farming could write this would be a answers on pro make select or take year minus season with you and with the animal dealt a stretch checks for them and so we have some rather different predictions here on few very clever you go ahead and have also putting predictions from the concentration the hands of the self diffusion of vision and predicted a scaling walls there is however 1 of the differences between these 2 things this issue only works if all changed party and we should write this has the grace to listen this model works for all concentrations subject happy at that if you push Paula concentration of there's no sold left for a little solvent left and the interactions between 2 neighboring chains 100 interactions are no longer passed by solvent that passed by a fluent composed of oxygen and so the model recognizes is something that's going to happen out there and concentrate on OK so I have given this discussion and I married you wouldn't that next time however the core issue is we have this very interesting parameter which has been studied experimentally if we push on the floor of the place to look is undoubtedly although Figure Eight day Ashmont which shows a series of measurements of polymer self diffusion all very good measurements but in each case you might say concentration diffusion coefficient range were a bit limited nonetheless you can see In general a lot of these fellas current rolling over in a few very hard data on the chance that will notice there's something like that what is happening here this there is written all over it and there's a phase effect and so you're seeing something where g the Polish change their relative positions in a systematic way let us instead however pushing ahead Figure 8 .period and there is going to co-host polystyrene must might Seiji polystyrene is important Industrial why should you study it but there is not much more fundamental reason why you find lots and lots of experimental studies of polystyrene solutions and the reason why find lots and lots of these forms studies is that their arguments as to what the effect of molecular weight distribution of Paul on the Net properties to measure what do I mean by that effect of the former molecular weight is to be the short answer is the government's theoretical calculations and say there is some the and on the molecular weight matrix what's find involve your homers are exactly the same in the molecular weight after small molecules that natural presumption of you have water it's H too low molecular weight except for isotope whose 18 for polymers accepted by all through the much more precise and sentences for some normal polymers you make think pot and you get some chains of lines and some chains of another line and you have a major holders of different lengths for polystyrene specifically we can go in and we can make polymers will not be enough over the years and we can make polymers that are very similar in length and therefore effects that arise because some changes short and some chains along can be suppressed so that's why you see polystyrene while Figure 8 . 3 but is a specific example of this sphere at 23 is a lot more of what so we have be here concentration and the various measurements have been fixed for To stretched exponential zinc concentration but if you look at these measurements carefully the best of the easiest the square .period procurement told polystyrene if you look at these points yes out years stretched exponential managers but then the various series of places around here and it comes back again and then appointed state of relations told the point sizes you will forget about it .period the Mafia and if you drop a ruler or let you get and that reliance on the use of the asked for additional to see minus etching of wall what straight lines were on power there you actually see an experimental measurement that shows scaling behavior that
is a very early paper it got unexpected results it was widely hailed not reasonably as being approved of the replication scaling model namely model predicted concentration dependence of the self diffusion goldfish now there's only 1 problem with that namely the other people who have measured Culver self diffusion federal lots of them were measured Palma's self diffusion and not all of them get the same result In fact that was unique let us look at some of the other things and knew more of these in future is the 1st of all if you advance to figure it out for a period of the summer and I stress time Volvo legislators and we see here amid the self you for what they did is the measurements for a series of different all over molecular weights now they say Jeter quite many points the are remember each of the points you see is different Paul molecular weight you're required of whole synthetic process to make the polymer to determine its molecular weight to see that it was a good material those points are much more work and what their motives data show it Is there is a region where there is a smooth curve going about with his duty in the minus some constant and will power and then beyond that there is a straight line molecular weight of the college will power bomb you could always wish for more points but in these measurements there is no sign that anything other than a shot crossover from 1 of the areas the of there are actually 2 per members responding to different forms operations and they both look the same as you have 1 behavior often with certain molecular weight and another behavior beyond OK yeah G this is reasonable is normal and why don't we skip ahead promptly from this figure which is here for the year staff said which is the paper how at all while and what they did was signed Paul that they can effectively over a wide range of molecular concentration as far as I volume fraction part of the volume of the solutions of Homer the mother and points are in fact we felt that the lake tolerate this is as far as you can go in concentrations there is nothing that they're Paul and what they show the following lines Hey years out here the diffusion of relations scale goes concentration with power and they did this for a series of different polymers different molecular weights now why is this interest as long as 1 say what you will their new article I recommend he pointed out there are very large numbers measurements on polymer solution guidance but most of them go all out about 40 per cent by weight 400 grams per liter or something like that and there is a paucity of Michigan's between here come so what he did and his students did very hard work very well alone was the only measurements Israel there was a specific rationale for this but the specific rationale Is that I done a fair amount of discussion the chief if you look at these right last concentrated solutions you stretched exponential behavior however off here at the mouth of the was rather good agreement that the case fusion coefficient those of approximately in the hands of mind to on the making of that is that of babies and minus 2 . 3 but there is good agreement that there is power no new stretched exponential In between mother nature use these continuously connected so someplace between here and here something has to give and what the answer is that if you come down this way you're going see the diffusion coefficient behavior of and 1st U.S. solvents and the melt becomes less viscous that's not what's plotted here the diffusion in the mouth becomes faster but the system still about some sense just very pretty said expense I will not step back and figure it will not and the year he was 5 2 shows us 1st time 1 of these currently resistance territorial yesterday looking at Poly ethylene oxide but and you're looking at diffusion of polyethylene oxide and it's in the cell substitute home of polysaccharides and what is not for a fixed solution is to report on the future of the polyethylene oxide as a function of the kind of guy I have radius of the isolated polyethylene oxide chains and furthermore what has been involved in this dispute involving over diffusion coefficient in pure soul there is if you looked at all of the on systems there that wealthier purists all the hassle over the around his wallet and now here are some it's some elevated concentrations and we asked with a BS in Brazil's foreign looks like it was like this there is we are looking at a polymer solution were looking in
matrix and the Matrix polymer is more effective than the current large probes that it is returning small worlds well even decide free shelter this reasonable or a typical but OK let's show him and we're going to advance to figure 8 . 8 these current life the rationale for the experiment we won't get to in part for a number of chapters the rationale for the experiment isn't on the basic issues during an experiment if you study the same system with several different methods you may learn things that 1 single method would never have told you the other method these methods were measurements were gone and unwarranted himself the the other amendments were gone light-scattering this fact the next year when Houston was dynamic structures there OK why are we interested this system and light skin what is the dynamic like the dynamic structure fat be well it says will look into the system and we will see if the concentration fluctuations if there are no concentration fluctuations the system would be totally transparent it's not it's opalescent because the fluctuations mean that the system scatters light and that's what we're looking at is a single spatial 48 home where there had concentration we look for 4 other components which looks like co-signed by now the amplitude of that component is very small and we have a very sensitive technique so we can actually for optical reasons longer 1 component and haven't looked at the the 1 component at time what we discover is that if we have concentration fluctuations and we ask relaxes this will be a lot more this axis is on the main the amplitude of the fluctuations this is long time what we find in a simple solutions that just get an exponential decay is however is a lot lot plots of the exponential prostrate however and ,comma solution you often find With increasing and that he will for the survival of the concentration fluctuations in hasn't piece of resistance and resist laid out here this is what is called a slow that might reasonably ask How do you envision slower lowers its said for 1 thing you can say this year's policy solutions and instead
of being uniform it produces operations they're quite concentrated this is blotted sticks together like a bit of flower when you're trying to get on with the salt flour to make a Polisario it doesn't break out instantaneously and therefore have these objects that lasts a long time well this particular picture has some serious experimental problems but what I can say is here's a homeless solution is concentrated and now these regions which are vitrified turned into stone and the changes inside for whatever reason would condone actually explained stay in the same relative positions relative to each other for a long time the vitrified regions of the start direct experimental measurement of this in at least 1 case can be shown not to be regions of unusually high or low concentration so that vitrified sit there and last a long time and therefore we looked at the solution using light scattering their apparently regions where we concentration fluctuations momentarily human chains chains quite quickly and we have other regions where there is a concentration of fluctuation briefly
the chains only about very fast OK so why should I was saying I don't measure the relaxation of the concentration of doing all fusion of a single Paula shame well all measured a single chain diffusion coefficient and lets you do that on lots of chains of what and where you find is terrorism fusion coefficient does depend on concentration does followed stretched exponential and concentration but there's something out there if you look at the end of our spectrum including measures the displacement of change versus time and what you find is the individual chains are all moving rapidly there is no sign of a group of change their track in vitrified region and just sit there not moving for moving very slowly and so question is how do you explain this discrepancy all 1 thing you can say is that in fact there are not very many vitrified regions but there somehow very efficient garish light so you see lots of low-intensity but if you actually have chains in here there are many of them most of the moving chains are in the low concentration regions of or not or at least the last start slightly less concentrated regions moved faster than that the other explanation is yes the vitrified regions but the vitrified regions are like salt along with their stable but their membership list is not stable so polishing the region is stable ,comma changed pop into and out of vitrified regions quite quickly well I'm not almost as far as we can go on will go a little further in Chapter 12 were about limit of modern research arms from OK what else can you do well I I think that left for his here there is a DNA but what was done through a very clever synthesis was replaced linear polymer with historical the stock although he has at different firms unless a G 2 years following that has not stopped you say I want to point this is now and that he wants to 2 arms stop all over it's the same thing as many of all and we can now do measurements of self diffusion of Stockholm owners and that is we are continuing in the text and we can do measurements of the form .period fall what sort of behavior that would be fine well we have homer this entire process means we get some of the center and weakened attaching more and more firms to and that that the data the test trade will have in the world so we can get up to 18 hours start all over and those measurements and what we find is that is the increasing number of our and if the molecular weight of each arm stays flat so we're just putting in more forms of the same way the diffusion coefficient folds but we can also instead of doing there you can take solace Stockholm and we can make the arms lower and week you have slapped palms longer and making arms longer be self-defeating coefficient of the storm falls now this is not an isolated stock we're looking at stars in a concentrated solution where they must move through were around each other there is a nice set of plots of diffusion coefficient his concentration and if you look at those you will notice she curves have so far ,comma downwards solid economy of words we hear the U.S. report of the as health was the rule however you can be either greater than or less than 1 that is we have diffusion coefficients and yes it's a stretched exponential behavior but there is a useful life .period on phrase stretch namely I knew it was less than 1 the exponential stretched out it new was greater than what the exponential curves downwards and it's been stretched in words but they're still stretched exponential communique now what a struggle it and and was struggling at the start of the war the we are going to look at the a day after less an a bachelor shows us 3 or
stars and very nice measurements there are lots of measurements and there are plenty of points here 1st pre-hearing flat the points down considerable distance this away and that means you can see the current rolling over these riparian good measure was if you're trying to extract stretched exponential what has been done if you will pardon the graph each said .period affairs from lines through a solid line which is need the minus out of the 0 there is stretched text and animals evolved from and for each of the sample studied the 3 hours stories and studied by From there at all you see this movie 1st however we also did something else the only thing I didn't say Well therefore molecular weights here and we all think this all of these 2 In the 0 and then we needed molecular weight of the changes some power because she of different different-sized change their different zeros and there isn't need the minus a the new In the Tamil and so we think that all of these measurements 2 a single functions and there's every New year deal with this intersect and then there are the ones who 3 received parameters to describe the concentration dependence of all the samples were different molecular weight over a wide range of concentration and if you look at those what you do is you see the national I'm
certainly not as good as the solid warnings but instead Beyond that these era each of the solid wants him to parameters so far this year these heroes the 0 concentration in the numeric 8 parameters describing the shape of the curve now he pushed we have reduced the parameters to To the parameters and it still works were nicely announced Friday described both concentration and the molecular weight OK so the original and insecurity .period 11 often however makes further important
further .period in his original paper soldiers quotations in the eye talents in the text and what he says is that we look at the actual measurements we seem to be in DNC concentration in pendants lies on a smooth curve and artists along B version was long seen her the diffusion coefficients lie on small birds of progressively increasing slowly on the particular there's no sign of a straight line agreed a season minus taxes scaling wall region no matter where you look of particular search was of course was for the theoretical predictions sees them I just want to point out too far now if you have a smooth curve and it starts with the local considerably less than minus 1 . 7 5 innings close 0 and ends up with a very steep slope someplace in the middle there's going to be quite aware this curve is television's power law and so there presumably some group set of points rather short Reeves a look scaling however we there progressively increasing slowly you better predicted a number here over a wide range and unless you can tell me it's supposed to be here 2 years seeing it as opposed to hear that you were supposed to to see it better unless you can predict the concentration range numerically were his 1st of scaling theory is not falsified falsifiable yes that's the philosophy of science idea namely that if you have a theory there has to be some way to prove rock and the issue with saying I can draw attention to this curve is that no matter what exponent predicted here don't matter what slope you predicted for her you deserve so unless you can tell me I'm supposed to see this slow here as opposed to I'm supposed to see the here right down on this very clear that this standard does not all support the theory of visitors from the scale and model as well the scaling model has a loophole the failing long it's not really a whole new fundamentally very sensible restrictions is as follows terrorism polymer chains entangled destroyed symbolically the United and the chains are very long so long the shares the considerable number of and having what happened as I reduce the concentration of the solution what happened as I stir more and more soul well what happens as I and warned sold their last unless chains and this distance increases what's that distance while the National Guard Shane coming through here and the change process and can move sideways ,comma than any of those distances this distance is sort thought the size of the so if you and moved following on the radius of the 2 life of the 2 but the radius of the 2 think that is a big sausage casing were looking from the side gets bigger and bigger however as the dial solution further and further we eventually running problems family chains and earn points with entangled but these chains have a lot difficulties the molecular weight is not real name worse by the heart and soul changed not stretch far enough to get from 1 .period work would have been investing 1 . 2 the next as a result we increased the size of haulage To the extent that we increase the dialog Lucian of all we have to walk tall 1 the Polish concentration goes down the and the entanglement points moved further and further apart and suddenly we crossed the concentrations C stock over song fan whose position is not really a specified period we moved from an that solution two-way value solution but there are some further complications over here I say tangled died and I'm going to skip over those for the moment all we can say panel we also say sentiment I mean those are not precisely the same thing all you could have a very long for a solution very short polymers and that 1 angle for a long time but the solution is still not losing sense there a lot I can go into more detail on that so with respect to the measurements on 3 stars but failed to show concentrations scaling future always claim claims that the reason you do not see concentrations scaling is the stars simply are not large enough Ian molecular weight the other thing climb completely there cannot be any response that is 1 point about both of these is that many versions of the model if you have to start all over again the school difficulties it actually cannot directly we cannot move along its own way it is and the reason it cannot walk on its own line of this diffuse the amendment would mean a lot misdirection there's this arm sticking out here and the arm standing out here guest In order for this change what have you used to be tracked the Armenian soldiers either trailing all advancing on guests and probably rather messy and therefore he will propose perfectly legitimately that the reason you're not seeing all reputation you're looking at a system where you're not supposed to and the reason you're not seeing scaling is well reputation arguments leading scaling laws perhaps the starters after all the red tape prediction the scale the dynamics have been very different according to reputation model and the dynamics have to been very different than can very well be saying that home you're disappointed the theory work because of most were from the several escapes by again To as to why you might not see scaling and 1 of them was elements to small and I explained my fault ,comma molecular weight means you wouldn't expect to see reputations scale and the other answer Is this a good play looking at that area of the stars in addition to moving in a different way do not walk away from the dynamics are described by scaling although the explanation OK what we have done today is to open up a discussion of how polymers move in solution and we have looked at single-chamber motion the reasons single-chamber motions are important yes but there are theoretical models that are very sensitive to the single-chamber motions for predicting all sorts of other dynamic properties particularly all of the reputation tight models are insistent that you calculate all sorts of other things like the viscosity it could hurt me you calculate all sorts of other things such as the viscosity by reaching in and doing a measurement of single chain diffusion and from there all sorts of other results fall no the outcome so far as the reputation model does make predictions for viscosity and self diffusion we've looked at some self diffusion measurements and we in particular looked at 1 case in which the authors emphatically believe they have found concentrations scale we also look at some other measurements were the outcome could be different in the next few lectures will continue looking at more systems continuing to measure sell people measure the self diffusion coefficient in binary internal systems and we shall see what we can see that's it for today dismissed


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