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13 Self and Tracer Diffusion Part 3


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Title 13 Self and Tracer Diffusion Part 3
Title of Series Classes in Polymer Dynamics
Part Number 13
Number of Parts 30 (Lecture 2 missing)
Author Phillies, George
License CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
DOI 10.5446/16212
Publisher Phillies, George
Release Date 2012
Language English

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Subject Area Physics
Abstract Lecture 13 - polymer self and tracer diffusion, part 3, the last. George Phillies lectures on polymer dynamics, based on his book "Phenomenology of Polymer Solution dynamics".
classes in polymer dynamic based on
George Phillies book phenomenology of polymer solution dynamics Cambridge University Press 2011 ends today this
lecture is lecture
13 Pall Over self and tracer diffusion good
morning I'm Professor filets and this is 597 B introduction polymer solution dynamic today I am going to finish off the discussion on Paul herself diffusion that brings us approximately to the end of the 1st half of the last time we were discussing tracer diffusion we were discussing what happened if you measured the diffusion coefficient of polymeric throw polymer of a different molecular weight and what was found was that is the probe molecular weight and the matrix molecular weight and were not Tuesday so that the over M 2 and M holds the key borrow less than 2 miles 3 we can save you consistently observed a single behavior namely diffusion coefficient is proportional to use a minor self-esteem the Louvre and the piano on the if you move outside of that range the phenomenology becomes more complicated for example if you look at a probe of faced selectively and we plot the the funeral coefficient versus the molecular weight matrix that figure a 33 what you see is a rollover stretched exponential and that continues until roughly animals over the about 3 and 4 large matrices things from all over that is a very large very large matrices and smaller probes are not being quite the same way that you see when the matrix in the program the same size OK that's what we going to say about South diffusion and tracer diffusion let us advance to an entirely different set of experiments and the inherently different set of experiments burden-sharing and occasionally illustrious group collaborators and what was done was to look at the future polystyrene through polyvinyl Mathilde you once again and call you Oracle for toluene was published in the Federal Government so measurements but they did something different they did the same at Herman's involvement to quality elastic waist gatherings that trusted me and With 1 of the fluorescence technique Our what is the point of doing 2 sets of of amendments will appoint new interim sets of that is to set of measurements measured diffusion on 2 very different distance scales they also each measure my motion on distance scales where she is here clever you can manage to go in and you can manage to vary the distance scale by changing the experimental apparatus as far as they used measurements on distance scales all we wanted to Microsoft might be needed the elastic light-skinned gives measurements on the distance scales of all the maybe 100 million viewers fraction of of light wavelengths you can get down a moderate fraction of white light wavelengths you can get out too much larger distances if you want on the main result Wallace the relaxation rate the relaxation rate which unit should go with the diffusion coefficient Times Square characteristic length met here if you're looking at a relaxation of a co-signer lasers with you looking at a concentration of population were books like "quotation mark co-signed UNIX from light-scattering used terms by scattering for FRS Q was determined by Hun Sen grading but in either case you are looking at diffusion over some range of distances and the major result this is what is expected and that is precisely what is found as as in what he described many of us you have is beautiful graph of GM opposition to square the important thing graft those continue eventually was the appropriate 0 interest said the nice feature of the graph is there have straight line in the sand down near the only was 0 and you can use the range she's a substantial range instead the cell how to I tend to be less presented that over 4 orders of magnitude in square you were seeing a single views process now why interesting Well that's interesting because the polymer molecules is something like 40 to 50 leaders across and therefore you were seeing diffusion not only over distances large compared to the size of the probe but over distances that are moderate Natalie time but moderate compared to the size of the problem and you see the same diffuse process all the way lot now you are getting looking at distances the very small compared to the size of the probe yet nonetheless there are people who proposed I have polymer I have what is sometimes called correlation because my crew was here there is less matrix fall over in the same region of space they do tend to exclude each other a bit and therefore I the diffusion process over short distances inside correlation and large distances outside correlation with might not be the same as well the experiments but not the 1 experiment that has been done sees what diffusion process you all always wish because after all this was not precisely what the experiment was focused on you could always wish to look at a larger set of experiments and see if this result continued the troops however I can tell you what's in the literature about what's not yet in literature right now going to have to work very clever said experiments and very clever said experiments to you and large foreign collaborators and the experiments as described saying the following day we're going to take DNA molecules here's the enabled and we're going to do clever things to them In particular were going to fluorescent fleet had so we could actually see the molecule now is we haven't done anything the molecules of early Compaq all and there's less visible but if you can 1 and you can imagine for example the tale of optical tweezers or any of several other method and drawing the tagged out and you were now going a asked Well what happens if you do this what sort of experiments can you make 1 thing you can do is to stretch the molecule and asked how a relaxed and I think you can do is say there's a molecule here and I've been very Relocation Center an hour and I since I see lots of Will you averaging I can measure the the location of the center was extremely high precision better than the nominal optical resolution microscope OK so what happens if we do that we can exploit means there's a place for the 1st time and we see nice pretty lean years Graf and we can learn inferred from X square with the molecular weight is like what chewing group claimed to do is that they had validated the
reputation and they did this on the basis of 3 observations the 1st observation was that they have stretch out all mental and having stretched it out they released the and they fresh and what they found was that the molecules on a short timescale moved by bullet units and and they propose overseeing motion down polymeric too and therefore they were seeing the presence of the 2 itself red tape they also eventually found that the yesterday for travel to and the minus 2 at proposed to see scale now the very interesting results are however there are certain technical obstacles to the interpretation the 1st obstacle to the interpretation is that intelligence that chain and stretch it a great deal on a short timescale is usually proposed it relaxes by the water called around moves that is the forces that tend to relax the chain .period belonged chain and every point of and because the next worst points along the chain Poland back from the direction of the strength the Forces for Change you do not you want however yet seen the fusion of the center of mass within the 2 that takes a different time scale they can certainly show you stretch change it wants to hold back in again the 2nd proposal was that they found that the Celtic fusion coefficient was inverse square of the molecular weight this was alleged to be a state signature of reputation now it is indubitably true the the revocation model the symbol revocation model does that his prediction unfortunately for the argument there a significant number of models that made the same prediction in particular there Simitis models do schoolwork and collaborators in which you see this particular attendance at the cell fusion coefficient on polymer molecular weight but the Paula's in question are indubitably not correcting for example there's not reacting because 1 of the 2 wins is anchored to plane and the polymers rise above the playing like seaweed above Pond Bottom soldiers resolved the last claim was that's concentrations scaling was seen by there are 2 issues here the 1 that is more a matter of taste but you should the measurements yourself the 1 that is more a matter of taste is the visible evidence for concentration scale and was not very strong you didn't see large numbers of .period users not easy experiments stock for people but the evidence for concentration scale and that the other .period no I have no prior to lectures is that if 1 did find concentrations scaling here there is an important issue namely the result would contradict almost every other measurement of the same quantity and therefore you would have to say all I want all measurements are good but what we're seeing here was some special chemical effect and the specific chemical factors leading to this behavior as opposed to being a generic behavioral the last issue which we will come back to perhaps later on Is that element of the mind to if it's correct leads to significant difficulties with observational results on viscosity which instead of finding an expected him to the minors 3 days of this but being in the minors to enter and plus 3 fine moral life and the plus 3 . 4 patents to some should not however and collaborators did find they don't emphasizes much but it's there in the papers read carefully another very important findings for understanding all them what they did I said to the veteran mean square displays as a function of times I think that it's nice when you heard that going down to Houston he looks like goes straight into Europe and that's very nice that's what you expect of diffuse the however the reputation model says something different reputation model introduces timescale house the but and underfinanced short by comparison with the house the opposite halves of the Apollo change travels by moving back and forth within this initial who so it is doing random walk along a random page and because it is going around and walk along a of had asked where it is fortunately without there not crossover and these models generally do not predict crossovers therefore computers allotted times the change our worst time being described as doing around all from 1 point to the next but because during during times the chain escapes from its finds itself in a new 1 is a Orthodox Random walk and ex-players where proportional to the 1st 1st Hey fertilized accepted should and the issue is the experiment analysts here
made several estimates of what how the ears and the numbers during the reign tall 1 3rd that you should not be concerned that the numbers don't agree sharply this is a somewhat diffuse concept and there is no particular reason to expect that different experimental methods over the same approach will give exactly the same answer nonetheless they give us this nice plot next squared positions thank you going down and will modest numbers that it is certainly true that he found me about how do you sad times in which the polymer chain
is supposed to be signed the 2 and showing this behavior was instead file but is this experimental behave now this is a significant issue with believe in the reputation entanglement to picture it is a complete evaluation it's almost surprising if you believe in the dynamic scaling Mont and at some point and going give an introduction to those models so those are the experiments should and the interpretation that that group for on the work and on the other hand it's possible for another interpretation on the same very interesting measurements OK we're now going to advance to yet another experimental technique it's an experimental technique that was viewed with considerable interest in the seventies it then died out because there were some that basically synthetic chemistry issues it has recently come back the technique was originally called for essence correlations to expect trusted the work at CBS on
because the original measure detection technique was fluorescence there are alternatives affect the original experiments that used what is basically the same method which were gone before World War used all microscope very bright beam of light coming in from the side black background Gold salt particles they're very good at scaring might even if there are only a few minutes meters across and a graduate students are instead of electronic and the time basis was not a digital clock was ticking metronome what is the experiments that can be dealt with these very disparate experiments instruments the answer is we're looking at a small volume of solutions and we count the number of particles within that small volumes we're counting the number of cattle molecules were were talking about fluorescence where longer scattering molecules of talking about bowls soul articles but in any event we count the number of particles that we find in towns and cities the 1st is the and the number fluctuates up and down the larger the number is less dramatic fluctuations appears to be on something like use the same scale and anyway asked How does an 0 standard of do you this correlation from the cat that is you look at the number of particles and an additional time you asked what happens to the number of particles at at a later time and what in essence you measured experimentally is that if there is a fluctuation if the number of particles is unusually large or unusually small the times 0 well you sit around and wait and you peace the number relaxes back to the average on toward the end the relaxation is if you were looking at a co-signer concentration fluctuations the relaxation would be an exponential here you're looking at a particular shape their microscope optical issues and the functional form here may be a bit different nonetheless you can pull out of the functional form workload according to his goal of because of the martyr for the number to relax article here yesterday refused Allah or other particles have defused it and you were looking at fusion over characteristic distance which is on the size of the region you're looking in and now we go back to 1 of my papers in the mid 1970 s and what I said is that if you doing the experiment and we had a small percentage of the particles in the field of view the diffusion coefficient measures self diffusion of and if you had all of particles field of view the diffusion coefficient measuring is the mutual diffusion coefficient the South diffusion coefficient describes the infusion of 1 particle through a uniform back the mutual diffusion coefficient
describes the relaxation of a concentration greater it describes the relationship not only of self-deceiving but also issues that arise because of what Oracle moves the motion of other particles can be correlated with so that is what you theory predicts and the nice experiments the scale of our times collaborators this is actually quite recent now actually sit there and confirm the theoretical model that has been sitting there looking for a test that 30 years is a beautiful confirmation of theory and it makes very clear why you have to translational diffusion coefficients and why they're not equal in non-binding solution Monday that's an interesting experiment undoubtedly got future there will be more interesting experiment but that was the only time be included in my book let us that advance them From Section 8 . 4 interesting other experiments and we advanced to 2nd team .period but the point Section 8 . 5 is to take measurements that we discussed 1 says time earlier parts trees bring them all together and see what systematic findings we may I have been given hints as to what the systematic findings were pushed ahead but now that I'm going to say we have all the systematic findings let's assemble them coherently and see what we see OK ,comma along self diffusion over there and we have reason to theoretical models we to theoretical models for how fusion would be patterned on experimental variables the 1st thing we can say is that almost without exception we do not find scaling walls there is almost no experimental evidence all 4 systems in which the concentration the South diffusion coefficient falls off as a power and concentration there are in stark white 0 is variable on the other hand the stretched exponential with if we write this war some of the program makers same molecular weight we have 1 more parameter here well having said we have 1 more parameter life as little easier but this form works very well the the next thing we could do those suppose we actually say you minus self-esteem as for example stretched exponential was stretched exponential recalled what way does Alvin behave in a reasonable man alternatively does just behave in a random manner after all if you just find some empirical fitting function there's no particular reason for your parameters to be related and all closely the properties of the solution on the other hand if the parameters follow fairly tightly the behavior of the solution you might reasonably say that she we have something interesting and the answer on that is found in the 1st few figures of Section 8 and we tried to experiments wants to relate Alfonse the polymer molecular weight and the other is that related health or to the polymer radius of gyration no there is a practical difficulties that involved have different polymers most authors did not measure the radius of polymer directly and the net result is that if you try comparing these 2 you discover that when you translate all molecular weight radius you introduce large amounts of noise and life is not in the interest but in Figure 8 . 34 we have a lot of Alvarez amp he noticed a bunch of different polymers it's fairly noisy but you can draw a line like this you can also reach in and say Gee I'm going to do something a little more I'm going to fuck the very systematic about including very high and low molecular weights and I can do that I'm going to insist that I look at measurements in which if the people plot fever is saying not only do they give me measurements out here at the evening that differences in here so the entire shape of the curve is well for
scaling laws all you need is measurement out here in 70 gunmen solution if you believe in scalable the results and dilute solution are independent of these and there's not much point in measuring and therefore the advantages of sensible experimentalists will get results of here however there were people who were more systematic and they give us nice measurements of Alpha versus and you can find a nice good measurements the insects and once in a day after the 6 the measurements spread out a bit Alpha spreads out a bit low like were weight but converges Towards a straight line at higher molecular weight and fat I give you a straight line and straight line does a nice job of conforming with the other points all the way up OK so we can put a line through .period but I didn't put that 1 to 2 points the alone this is a prediction of a hydrodynamic scale animal the important feature of this prediction is that it has no Brady parameters not at all the closest you get to free parameter is how you relate the molecular weight to the polymer radius but that's a well-understood result furthermore the outline is here it's not here it's not down here where it is strong on the grass and therefore a hydrodynamic scaling model actually predicts health of quantitative better yet we go back this form and we say are interesting physical quantity is the lottery of the self diffusion coefficient performed as a lot of the yes perfectly well what the say there is those areas Alvin C. each the New World minus sign plus a constant In that case was failing exponent and they tell what would we calculated the surveillance to the robots theoretical models which led to calculate scaling exponents there's a big industrial calculated and those calculations are very good if you 100 about the literature that looking for people calculate the scaling prefect years you'll discover there are fewer of them but that's what we have here the calculation of Althaus there's also a lot of and there's another another parameter the other parameter is but the question is how his new movie and on variables as well as stretched exponential form accurate news should be the independent of concentration you just see a value of gives you the shape of the divas C but I'd also met him blind against call molecular weight and I have done for most of the measurements you have graphics text and the question is what you see when you plot Movers is em well what happens is at large molecular weight room was pretty close to and that's true for molecular weights about order a million captain women smaller molecular weight divisions spreads out you and consider actually a lot of measurements of the states With noting that about what the local like you're aware that this is clearly
not true in every system and then a crossover function like that from move warned moon half but if you look are you realize there are a lot of measurements that do not fall this curve and sorting out why has not yet you also known as to what the points out here with greater water that is the cases where stretched exponential has been stretched in the opposite direction it's really been compressed and so if you may have the careers water and plot lot of these see well if you had a simple exponential we all want to see a straight line with no greater than 1 using no greater than what has been with this sort of starting from very early times it's a fairly clearly seen so there is the case versus following molecular weight my OK but Sanford said Why isn't new not 1 as we will eventually see new was not 1 because chains expanded In the cases where we can measure chain expansion and contraction directly to the best start with dielectric relaxation it's in earlier chapters that we've already discussed what was found was the the extent of chain contractions as measured by the change in the length of the end-to-end factors you change concentration the contraction of the chain with increasing concentration as measured directly this affair towns quantitatively for deviation the usually coefficient from a simple come on exponentially concentrations of quantitative explanation it's not proxy OK that's new and invented anything else Oh yes when we're talking about Trager diffusion well for the Treasury the problem with molecular and the problem may decide to stay ahead in independent molecular weights and these 2 molecular weights are not too different saved both of these numbers are lesson about 3 you have a fairly consistent behavior you have stretched exponential you have something for the 0 troubled mind is made by the way that the title phone book is people this is the 2nd draft manuscript that shows up as an enemy and don't have exponential speedily blind as they see the new fans and then you encounter a little closer and the little pummel you encounter is that in the cases where these qualities of the manager is a about powerful way to 5 . 2 and 3 please the Delta Delta is about 12 . 3 and therefore you you know how close the valve that is about all going 6 for the last always hearing nice except if you look in the systems where you were looking at South diffusion you found 9 0 . 6 per larger number close to what that is not quite clear at least I didn't find way to analyze data and explain why it is that if you're looking at traces future you get a weaker dependence on molecular weights than you do if you look at South diffuse all I suspect it's 1 of these you were looking at certain ranges of molecular weights you're looking at this you're looking back and the 2 numbers are perfectly consistent don't referred quite the same thing but I didn't solve the problem book 1 of the more powerful ways to study an unknown all right I have used to bring to bear on the same system simultaneously several different experimental techniques we saw that effectively with dielectric relaxation because dielectric relaxation and measure at the same time in the same experiment the media means square and and vector of the chain these it's the right all of the characters characteristic relaxation time he had more sophisticated than a characteristic relaxation time is full relaxation function including secondary relaxations encountered by frequent you knew all of this at once although those of us who are less fortunate have several different types of experiments people have done In particular our worst margin 2 to 10 worst do follow and what both of these experimental studies there was to pleasure and more or less 1 school bus polymer self usually hold and the home viscosity the solution viscosity so they measure 2 rather different things about the same system for Martin this system was yes the usual polystyrene and polyvinyl method either but the important issue was that the matrix was
about 100 thousand the probe molecular weights that 50 people with all the lives of hundreds and there was work planning and at the top and there was a 900 and some put in some very different size probes into the same matrix and asked what this eh Ontario probably compared the in area you could put them on the same grade you have to use different units you wouldn't want to apply the which decreases With all dolled up recent major concentration and hot air versus the fluidity of the solution to the views of the ability which also falls as you make make more concentrated that would be a very legitimate way to go what was instead equally legitimate was to say OK I don't have the measurements I will plot the product of years age well-defined product you multiply the diffusion coefficients pro 5 viscosity of the solution which is basically viscosity matrix and we do this as a function of major concentrate do is a function of matrix concentration was fine is it for a very large the U.S. Ada is very large polymer probe BSA is approximately constant but as you will get smaller and smaller and smaller programs and Remember the Titans laser the probe of the the work and 900 syllables and metal makers molecular weight slightly larger comments 100 head well if you look at that what you find is that the SAT increases with increasing matrix concentration and it continues to do so until the probe is much larger than the major the problem is much larger than the matrix he much greater than ever you find that the area is approximately Const now there's another experiment you can do with the same kind which I
should simply pointed out of which is to say I have a problem might have solved diffusion coefficient of frozen and I will plot diffusion coefficient of prose versus the probe concentration why would you do that program caring about programs and where in general the diffusion coefficient of the probe could be held on how much progress and therefore if you want say wanting a true self diffusion what you want to do is to extrapolate here from the probe concentration you're using the 0 growth 1st some experimental methods and probes this is somewhat pointless because you're already at such extreme pro-gun control the diffusion coefficient approach doesn't care with the pro concentration it's at least understand however you can do this experiment and if you do the experiment what you find this Net a series of slopes that is the diffusion coefficient of the probe is sensitive probe concentration at the slow curious initially weakly positive but as drop in choosing is the increased the matrix concentrations and increase dangerous concentration the attendance of the Piquionne of probe on prone concentration becomes more and more negative so at 1st it was buried under matrix led 4 will always be the diffusion coefficient increases as you increase the matrix concentration of elevated merits concentration as you increase the concentration of the probe the diffusion coefficient promo falls yeah but those are resolved of the Martin now advances in various ingenious and ingenious experiments of solid collaborators what they did I was look history Ternary system and they have a series of and they have a series of major polymers and they can combine them and then we will have a product the product of the diffusion coefficient probe the radius of broke there's a lot of probes diffuse more slowly this product might be independent from concentration and Mississippi the solution there was an and you look at this as very the majors concentration in the majors .period away it's a well-defined set of experiments there's some very nice chemistry getting all the work that someone has to make almost always where after all and what was done was to propose that you would like to see 2 sorts of if you had a small matrix and a large froze the proposal was the Stokes Feinstein's mediation here at all and if you see some of the time inside the major this quality would be fairly constant because stocks I signed
him in diffusion coefficients goes inversely is discussed however as you head this way as you get to looking at Marja prose mediators said marjoram matrices and still lot of approach if she makes the matrix ,comma larger order make the concentration larger what is going to happen well if you believe in the rare occasion modeled as you increase concentration and March majors polymers the Matrix Chambers can and entangle and once they have entangled the expectation is that stocks Einstein behavior goes ,comma over ratification of the here if this product yes Our Ada over its value when you got get to tangled talk here is quality some of light wall and down near the reputation expectation is that the S R it can become March because the polymer is more effective in increasing the viscosity of the solution the matrix increases the viscosity of the solution but the probes are able to thread their way through the Matrix and are not slowed down the slot so this product becomes more experimentally that's what find find Regina where the US is about constant and when moved to large matrices and elevated concentrations when you increase the concentration of the Matrix Fulmer and the concentration of the matrix color you discovered this product increases Mark market well that's very good the question now is is this proof reputation among and the answer is that it is not it is considered result is consistent with reputation ideas but it does not prove why not the understand why not we would have to invest in chapter we have not yet reached namely the chapter on probe diffusion and probity please look at
March there's always small-scale refusing fuel pollinators this we change the concentration and the universe In probe diffusion measurements
diffusion coefficient of the fears probes and Walter several things you can plot 1 of them is indubitably Diego now enlarged sphere is very different from Paul oil in 1 sense if she believes in reputation and the probe is reasonably large larger than the holes between the think is drawn here being probed Maryland there you can't predict sphere Iraq takes it can fit can't move like that instead of this year has moved through solution which of which it is exposed to a fair amount in that case the prediction on expectations and up from 1 thousand patients was that data Wendy about constant there is large spheres which shows folks I 2 behavior well at low matrix concentrations and with small letters always that's not a bad prediction of have the biggest fear and very low constitute a lower-level away all of you see behavior like this however is increase the concentration of matrix and you make matrix chains quite large so they are towards being entangled Dierdre experimentally with probate was this but actually that's sort of what the solace work probes that were smaller nature's always small all use there was strokes unsigned behavior that is you made matrix followers large matrix concentration heights of up like that what do you find you find for change the product idea increases quite markedly but that's exactly what different spheres that is the only observation that the Dierdre increases from large brokers and large concentrated on molecular weight matrices is consistent with the reputation picture but it does not in any sense proved the reputation picture it does not prove the reputation picture because you see exactly the same phenomenology from prose that cannot possibly be wrapped but that actually brings us approximately speaking to the end of the 1st half of this course In the 1st half of the course we discuss things that correlate with driven motion of polymers and we have discussed motion of small molecules sections of polymer and single polymer chains and the rest of the costly a requirement to eventually talk about probe diffusion Richard objects moving from polymer solutions we're going to to talk about collective behaviors mutual diffusion coefficient the viscosity and disco elasticized I'm also going to drop into their 1 completely non-conventional topic namely we're going to talk about college dining and 1 about college while colliding particles or spheres they don't have all the infrastructure motion that polymer oils to however the interactions with other spheres are hydrodynamic and excluded volume the forces can call a systems are exactly the same as the forces you would encounter in polymer oil says the 1 difference is this fear is indubitably cannot rapped a state can be formed to get through small holes in the solutions they just sit there and therefore anything that is common to see dynamics and coil dynamics can be attributed to the ability of the coils to change shape we'll see what those common features ,comma when we get that check let us however spend a few minutes recalling what we've done so far we began with Chapter to chatted to talks about sedimentation that is we take a centrifuge we sped up we borrow polymer solution the centrifuge before we turn it on and what we observed is that the polymer settlements all over relative to the soul of a down depending on its density larger smaller sold we can also take a polymer solution the centrifuge and they had to probe particles call always other Paula chains and we can look at the Turner a mixture and asked how a April component is moving with respect to the polymeric matrix we don't want to buy but we can talk about this discussing said 1st time and what was observed was that the the ability of Paul matrix increase the viscosity of the solution was significantly larger than the ability of the same makers to recharge the sedimentation of the pro-American OK we get sedimentation and then advanced and we talked about she electrophoresis we take charge Provence we apply electrical field and we measure the diffusion of the probes actually the migration of the probes as well mostly migration there is confusion going on through the Matrix usually of Paul and what we found was also seems that have made the plot sedimentation the plot Frederick mobility versus concentration of matrix and there is a prominent reduction in the sedimentation rate on the mobility as you increase the concentration of all that's what you do find experiments there were several models presented for how these qualities my on matrix concentration matrix like but what is often the 1st part was a stretched exponential concentration From the patterns of mobility upon approval molecular weight was a more complicated the case here namely that a stretched exponential in pro molecular weights until we get crossover and the crossover above crossover which this system pretty shocked there is a decrease of very weak decrease of mobility was increasing probes size the decreased turns out to be sufficiently we that it's at least tricky use the attendance of mobility on probe size separations and there is solid evidence inside as well sorted out was 1 might wish that this change is actually a lineage transport change namely the dynamics change if the force of the program may follow matrix margin I'm not sure I view this as we did in information to the source light scattering spectroscopy and its ability to make mutual useful so we talked about causing elastic light-scattering which is sensitive to fluctuations in a single a spatial for a component of the polymer concentration for call always it's possible to calculate how the diffusion coefficient depends on the size of the the
protocol this defusing spheres and the concentration and concentration calculation in that style .period let's light scattering spectroscopy I did at the end for once tossed in a few comments on experimental constraints the comments on experimental constraints work will be very nice to take our light-scattering spectrum fitted to a huge number of exponential is full of diffusion coefficients separately of everything present you can't do do that you can pull out of modest number of parameters from a light scattering spectrum and when I say modest number I mean 6 to 8 not the mobility of 2 thousand species just doesn't work that way OK that checked for at the end of the push ahead and what did we push ahead to do 1st we discussed small-molecule along and we began with ions and similar such things doing either diffusion or electrical mobility through biscuits and nonbusiness solvents and for not very viscous solvents and found the diffusion coefficient Milan and electrical mobility disclose their very long waiting time for people to work inversely interested viscosity but there was crossover and a viscosity of said boys not sending every system and above their interviewed coefficient and the conduct unity when it came to minus all In theories of cells and that Back to results of Hebrew bringing more than a century ago and more recent measurements sets on the other hand if thought polystyrene latex spheres of state planning man years in radius and and big objects and you will in small of later you find diffusion coefficient of these probes those temperature over solvent viscosity and does that even if the solvent viscosity is also a thousand or a few thousand times discuss water so large probes and small probes not in the same way well what happens if you raise the viscosity not by using a viscous small small-molecule sold but by having a whole if you can call her and measure how rapidly the the solvent moved to the state you seoul loses concentration of follow you discover that measurements Kendall look about the same there is a lower concentration in the region which is more or less exponential and polymer concentrated 10 someplace near told 350 500 grams of India's told there is a crossover and there is a stretched exponential concentrated so the diffusion coefficient is falling increasingly concentrated you cross through something and that the ability of the small molecules to move falls off much more rapidly as you run up from all concentration I interpretation of this fact clearly not true but it seems reasonable is that if you have some characteristic distance side between neighboring all over the it's not the same chain not nearby on this thing and you have a solvent molecules which has some characteristics size roughly speaking with are becomes larger than the size of the solvent can consistently find interest which passed but becomes larger than size captains about this concentration doesn't change concentration sizes on what you cross over the mobility of the solvent changes because it had problems finding this finally local measurements of solve mobility insolvent ability to rotate and what is demonstrated experiments Laura what whatever other people the yet ,comma oil here and it has vagrants solvent molecules we actually fairly tight and roughly speaking was discovered is the polar bears a dramatic effect on the ability of the solvent molecules move out to something like who sold Diamond there is an imprecise number but it's song number like that on the effect of Paul by the way doesn't have to be the interfere With the ability to solve more because if you put the right polymer very flexible fall into an error or solvent Erika is a chlorinated biphenyls it's extremely viscous what you discover is that the polymer acts as a plasticizer Nugent and B Our solvent molecules are able to move which rotate more and more rapidly to they that's at work the chapter on small we then Bush and what they're about to sentimental load the had a series of different experiments that measure motion of segments motion of single reorientation of single bonds and we could do these we change the matrix concentration area we also putting probes the tell us the alignment of backbone and if this was done by attaching the program on what was demonstrated at least for the fall over in question here is to promote his polymer and behavioral the program changes to make all over a longer and longer and that effect resistance to the next something like 20 foreign monitors once you have more than about 20 foreign monomers once you have long called for a change making the change longer and longer has very little effect on the mobility of the change hands that sort of makes sense what it says is there is a distance over which all or chain orientation motion along the chain and different pieces there's is a distance over which the different pieces talk to each other but if you have 2 pieces that are very far apart along the chain they're really not aware of what each other's game we finally pushed ahead and we talked about dielectric relaxation strategies such the leader and this quite a dielectric relaxation is wonderful because it is those means to and distance it gives us a characteristic times house it gives us a relaxation function which is something that is more people relaxations we get all of these very different experimental numbers out of 1 system I was able to demonstrate how how forest where quality mainly help we need to be on a concentrated version of forest where are you going have Our where changes with changing concentration and
that drives the concentration dependence away from the single exponential however deviation depends on change radius this is actually quantitative results the concentration the hands of where explains quantitatively White House is not a single simple exponential involves we're also looking able to look at relaxation functions and how the parameters of for the final details that discussion today we discussed all itself the future which I summarized that and follow self diffusion we find how the self diffusion depends on the concentration of polymer the size of the Matrix polymer and separately size from Paul so out on the full set of discussions of moralist single all single molecule results and the rest of the cost we will push ahead and we will discuss collective effects and other related .period however Friday today that's it
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