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Choi asses in polymer Dynamics based
on George Phillies book phenomenology of polymer solution dynamics Cambridge University Press 2011 ends today this
lecture E is lecture
27 costs summary I'm
a professor of abilities and this is the next call a series of lectures on the phenomenology of polymer solution dine at all based on my book phenomenology of polymer solution dynamics Cambridge University Press tunes out but today we're going to do is to work through the next to the last chapter in the book the chapter where we go through every hole of the methods we talked about it and say something of a summary of what we learn from each other but the basic issue was going way back to the start of the discussion well how we watch how do we accurately what followed students solution what sort of functional forms to match and I in fact forms 1 was for a transplant operation doesn't care what wants and what they have stretched exponential his concentration dependence and there is dependent on the molecular weight loss matrix there is perhaps we have problem which etc. there is a dependence on election-related probe earlier this object depends on the probe size that's not atypical case and that is stretched exponential the other former we might have to visit the proportional song constant steel minus X reports that scale and not only have stretched exponential formed on off Paul and the question is what fits these forms have 1 very important feature if you take a long long long long to be serviceable or whatever the barrier and you have to stay on what you get out the straight line or if school is the only way to get out the other straight on the other hand is stretched exponential Walker stretched exponential gives use very characteristic feature and the question is is the 2nd derivative loss the loss of the EU Lord I is the 2nd derivative going to be 0 or worse is going to be some long we have several cases in which in the 2nd set of measurements you get both behaviors and therefore there is no reasonable doubt you can actually tell these part because in the case is 1 of the present you can easily see both of them and it is painfully obvious that you're seeing so that was the general began .period on as to what sort of concentration molecular weight and there actually cases where you see lot of working on the book OK so let us reacted to the video which as I speak ,comma flightless because come out and therefore it would have been retained Sunday and we will start off by by discussing set stage there is we take a polymer solution we put it in the ultra centrifuge we spend it up and the former settlements out of solution now there are actually 3 sets of experiments we we can think of here all I of the 1st years 1 species violent solution and unless the analytical applications the analytical application is very old and the this was in fact how people determines the proteins are not Association College the macromolecules well-defined molecular weights 1 can also look at 1 species in a non-violent solution because of task how you have concentrated solution of :colon oils the solution how following settlement had to measurements and then I want to do a system in which the the 2 species of polymers or whatever so there is a polymer that is matrix and there is no problem with this scene that I will not die a little progress system is going to repeat the grade B but in some cases but not others it's critical probe species be done all In which case you are in fact observing single particle of cross-species through the following perhaps not non-life matrix fall although 1 should be careful to realize that the probe may be very similar to the matrix for example we somehow reach him and most of the Matrix followers are invisible and with had 1 major change in the policy background fluorescence dye has on many methods proceedings and we watched a matrix polymer that is identical except for the stages the other choices for example we have are concentrated major exchanges were perhaps not so concentrated and we put froze the species the only part of it could be very different from the matron so there are actually 2 2 sorts of its probes 1 can think of using however in both of these cases 1 arranges things the details of how and technique so you're looking at the motion of single probe articles or dilute programmer of the probe probe actions and that
your looking produce motions through a matrix of some sort so that general is what we do the question is what sort of experimental results and get out said they the 1st answer is but if you start out with polymer and you increase its all the concentration of changes the sedimentation coefficient fall the 2nd 3rd is the larger the caller is the more rapidly it said that is the weight of polymer .period mass urine solution increases linearly and size and all the drag coefficient increases as em to the half some similar section on the net result is larger polymers that look concentration said more slowly than they have been small however if you increase concentration on 1 of several things that from polymers in good solutions good solvents the film curves Esperanza Seeley roll over in Morton last March that's good solvents in greater solvents to see something like this get name leaders rollover there's a large changes all over here the 1st of year across measurements are taken sufficiently high concentrations of quite short on the other hand if you do things in the current system will set the stage for a matrix that what has been done and if you look at the benefits it's fairly clear wears what they actually see is a large concentration of a large part probably chains settlement more slowly than small approaching OK you can also look and compare I think measure as versus the also met viscosity is a function of race and then you can go in and say OK we know what the viscosity is we know what sedimentation coefficient is therefore we can look at prop after which you can demand if you want normalizing the 0 concentration limit values and if you do that you get through couple sort of behavior you get systems in which the ratio stays at least quite close to 1 and that those kinds were released Einstein spoke signing my behavior you also get systems in which the ratio was very definitely not long at large concentration and that's behavior and then invest systems in which there is a deviation oversaw range 1 deviation from the other and then things go back to the some outside behavior and I described this as you read what really interests is not quite as common as might support now you might worry will show you how to get around associated with a series of their release was reasonable and the answer is the front part of the answer is that if you go back and look to stocks lost after this year's being written or by his staff he solution US Stokes law is continuing calculation and it refers to a particle moving in a straight line at a constant speed well most of these particles are not moving in a straight line and constant speed furthermore we're talking about things that are not in company and sold Tony and solve such as the 1 for which always already is particles not simply moving at a constant speed stock sell-off lofted continued replaced by poses as equations which describe non-standard motion of particle through a intermediate solution a major issue in statistical mechanics at least right branch field 40 years ago was if you thought you you should have spouses nasty equation drag did you get
Stokes Einstein diffusion result which seems to be accurate and the answers the post-industrial those lead to Stokes Einstein's equation however the Boston asking equation include such things as memory function on the behavior of the postmaster equation describes is already only for and petroleum solvents and therefore effectively have be better Stokes law should not really be at all surprised OK "quotation mark we now choking him and we will go to Chapter 3 greed and we look at the other end driven emotion but that that is a lot of work just like to read they're actually for Williams to make a case for dielectric real-estate fight during motion that the sedimentation which is by far told us in terms of polymers electrophoresis started and is at about the same day Of the silliest of folks who developed the centrifuge all of the electrophoresis there are also several that means that many many that it feels popular this week uses the several techniques where you can actually reaching and long-awaited of who forced upon a colloidal program measures motion which is not use driven out of college and I had to put in a case that that were talking about dielectric relaxation mode involves oriented the change hands and that factory a certain sense there's great emotional but you're changing the direction things face you're not causing it to move sideways but also let us consider the electrophoresis and the 1st thing we find general notion that we're talking about the specific source the last this the technique is called capital Arizona left releases the point capillaries zone electrophoresis is that take a very long extremely you've inserted into the plot which had actually flood of material containing probes the polymer solution told territory along with 2 and more detailed than in the rest the the you applying electric field along with of the energy problems and down the details of all of the forces on the growth moving down to were actually extremely complicated began arriving at the time we have to schools you the tends at this point breakpoint closed the at as the object schools and will be different speeds and so they will have you look at the far end you detect the arrival that gives you 1 time and the speed and therefore average drift velocity but the drift velocity at least to the electorate for mobility mu OK having said we're going to be elected for mobility knew what he hears this view of the city 1st if you look at concentrations independence to the approximation you see stretched exponential concentration dependence as the concentration goes up the fallen goes all the home behavior goes the head of the plot against the a long was long Houston with her like this people have measured the so-called overlap concentrating the systems and will serve single-person units there very much the same parameters below sea star and there is no direct evidence in the measurement that you have different physical mechanisms reach already emotional lower and higher concentration now you can find in the literature some very nice well-reasoned papers which prompted the inverse conclusion and the images conclusion is based on the following a lot we have a technique and are in the interaction that we believe would act always there but it is and tangled effects are only effective at secretive and see store In fact there is something entanglement type models sort of playing the Pelosi start concentration that goes 0 we however see that even very low concentrations of all are effective at slowing down our throat part therefore we need because this mechanism stops the stock was up times once we need another mechanism different mechanism that is effective down here that reasoning is based on the assertion that you know what mechanism is up here and you know know what stops at this point however as shows up repeatedly in the literature that that is that he lectures and fantasies will continue with her with no sign of a discontinuity and therefore the inverse argument is a bit more appropriate namely you see 1 per year for offers no evidence that Americans are in fact it was stated to mechanisms solve after explaining why his cross from year to year not only is the sedimentation coefficient South Indian states of reasonable but the slopes the slope continuous says something considerably now there is actually a huge body of electrophoresis literature very little of it has been analyzed from the standpoint of understanding all the solution dynamic historically people did electrophoresis to determine the property of migrating charged species for example the molecular weight I'm offering here the exactly the contrary perspective complementary perspective not contradictory laws namely that we have win church probes and we can use the study of the properties of the Paul sports OK so Celexa concentration dependence we can also look proving that size at the end of the week that for smaller roles we see is French exponential behavior probe size and that there is a quite sharp not necessarily perfectly sharp transition and
for moderate growth sizes we see a unique power loss dependence on probes are based on the scale of the figure is very clearly a straight line must occur if it's well power walk and there is a sure is will here and there for a case where we have stretched exponential behavior and yeah power behavior through most of the sector but might reasonably ask what this transition is that is not really been worked out I don't want to answer however it appears to be suggested by the fact that the location of this transition depends on polymer concentration depends on hold molecular weight and at least loosely speaking appears to the region in which removed from the transport coefficients that's now and the wide field with transport coefficient that the hands on the applied field there's clearly went from a linear response regime to a non-linear responses there is 1 more more thing you can do with the letter read the video measurements and if you do the video maintenance on Argentinian and the final margin DNA spate of configurations like W. B you can actually see the chain's spread out as they move if you do the experiment with stockholders you see something that I'm not throwing currently accurately looks sort of like this we have the arms spread out in front of my fingers and squeaked moves along like this it's just a little light lapse the cost cleaning up from the June weights I if you actually do this and asked what happens with the stockholder hits the shelves this Crossland fears across here the youngsters historical "quotation mark sleep through it's the and crashes to stop on the services can penetrate because the holes are To the motion well if you think you were in the linear response Regine than the fluctuation dissipation pheromone linear response theory says this is also the irradiation except not so exaggerated that the polymer uses defuse this configuration of the future whereby the influence of major changes are being driven off from world is not the same as the arrangements supposed to solve all our solution dynamics of Oh yes task of the Boston material clever fellow who did a bunch of theoretical calculations on how objects would move through cross-link mechanically crosslinking mobile jets and what he predicted as applied to elect Greece's music music on the Net :colon minus and that his theory predicts the powers it predates concentration 1st power part of the 2nd power the molecular weight 0 about you will find in the electorate for literature's reference to Muriel receiving me and that refers to the observation that they're seeing each other minus concentration versus the other dependents is being more well you can measure the other depends so you have to view this is an interesting topic and if you do that you discover that our square is way off the actual hours was born and end 0 is extremely wrong the powers considerably greater than 0 there is a molecular weight hands and therefore concentration dependence is what is being said to be 1 more than last anyhow also the predictions for the radius and a major molecular weight attendances are not consistent with experiment so it doesn't appear as if you don't really get boxes he said we have reached Jeff chapter for talks about quality life led activities that process which I spent 4 years doing research on Bosnia labor closed for years was the elastic light scattering spectroscopy also is a standard scattering technique the main issue in the chapter it's not a full explanation of the method in villages are only methods chapter was to discuss a few issues which are sometimes represented incorrectly literary all along bonds is that you will find people said the case factory corresponds to Article followed him to the minors use where he was gathering back ex-players means where vertical displacement that equation is fine if you were looking at model dispersed particles not interacting In a simple Italian food it's already brought pro particles his 1st Palestinian of spectrum is right In this form is right in his plan the relaxation expect from his monolog exponential decay if the spectrum is not even a minus constant the that this form wrong that's actually a very important issue so on if the Chapter 5 of the actually reach measurements on how things move from solution and so we're going to look 1st small the movie that we didn't have start here and look to the word of a lot of review articles .period called herself diffusion the whole chain I decided to do things in order of increasing the size of their is no completely satisfactory arrangement and I have decided what 1st let's look at how small particles move through woods the biscuits because all the sugar solutions the something similar and this goes back to to the results of the example he green 100 years ago and if we plot different people of measured diffusion television or conduct kitty that's electrophoresis experiment summer by versus viscosity of lake would you find and he is the 1st region which stands out something 574 I want to emphasize there's nothing magic about 5 cents for reports
however this ghastly afraid to go with its my soul is about 1 percentage wise and someplace of here is 3 and a half 5 where someplace where there is actually a fairly sharp transitions and involves the concept that viscosity we I guess it should be able minus-1 you go fish we have areas minus 2 thirds that is the dependence of the diffusion coefficient connectivity on viscosity only shows no signs of being here all too .period question history and 1 of the 2 of wanted correctable 20 9 Klosterman the outcome what a lot of money but found that it's a lot of room temperature between the EU it's just melted ice and it's about while there's something like a factor of 5 changes viscosity that's a big change in Stasi but if you ask yourself if you ever noticed that boiling water sloshes a bit more on ice water if you look for it you can actually see it moving ever noticed that just the arteries discussed bodies replace this with all these kinds of small molecules that can replace this with polystyrene latex spheres and the diameter of like the hold commanders and things were bigger what you find is that he is proportional to overseer of the solution to it and that is quite accurate overall 3 orders of magnitude changing discussed then is is a small few probably fair me so stop behavior is very different there is a lot of literature of people duplicating this experiment are in part because someone that once got a different result I can point out Hello now we come polymers after all if you want to make a a liquid this is 1 of the good news is are something like that all the work the other choices I used to get hollow and if you measure the diffusion coefficient of almost as a function of polymer concentration when you have a limited eventually get off melt everything stops but before that you have this somewhat interesting effect namely layout and he was like in a fight to the 1st U.S. purists all and above .period you have stretched exponential there is a smooth transition between them are there is a zone in which both curves described the measurements to within limits the accuracy of the experiment because of tension and close to the tension to perjury close together are you can sort of a asked a sensible question why is this and in fact I don't much the book and developed that since there is reasonable explanation for this transition which occurs the volume fractions something around the world .period Water World . 3 5 0 0 5 someplace there is no polymers solution the cross-section Paul Kane and someone typical all the all the all cross-section may be narrowing cross-section along this would result in molecule small enough that you can't treats called solving the space between polymer chains continue their work is solvent molecules used to be and that's roughly where crossover although the last thing you can do which has a strong interest is to say well we can go in and measure the viscosity of the Lakewood with possible Tory sheer and we can try to get off to infinite frequency well you can't really get off to infinity we don't have to get this far any the idea of getting up there in the streets of the city and the frequency of those very much therefore adjusted she'd see the solvent Wisconsin that doesn't quite hold up as well as you might expect instead Ada mangoes affinity those of the finest songs concentrated comes polymer concentration and some constant therefore a high-frequency viscosity does not behave like the way he thought might in a small group of his followers small motions all or dropped item striving you at hall things slow down there are a few systems they're very nice experiments in an hour and lodging a string of other names which showed a few systems in which you get hold and when you get hold over the poll plasticisers the very viscous sold the solvent molecules move faster and since you can have some polymers slow things down and others heated up using create Oliver's their mixtures of 2 types of backbone and if you were clever and how you do this very clever as it ,comma law they eventually work out looking at how far the sold moves with the range of the effect of Paul Molitor warm solvent it's only a couple of solvent time it's a somewhat it's a very clever but somewhat indirect experiment shows that yes the polymer does change the solvent properties and were very high concentrations were less all of polymer most of its properties change mustn't OK having said that if you really want to it we talked about said that all along In the and we also talked followed gesture about dielectric relaxation to sentimental discussions the varieties of ways of measuring how rapidly is said to haunt the hall and statement with he and the rigid PCs optically active dipole the major excelled on the Internet on asked how rapidly the wreck several peace for your you can do the same experiment without chemical manipulation using animal and what you find it's polymers all large the orientation times you see from almost relaxation goes down to to the 0 if you make the call a small enough this is no longer true any sort of there for here's a chain and it's fleet of flop around and there were things along here find it easier to
reorient something in the middle of the range of its effect in terms of how how far it can tell you hear something like 5 or killed all chain and if your further in the land can tell chain is infinitely long for the most part so there are a range of locomotion dielectric relaxation there's only 1 we can arrange things with organic chemistry so the Paul recoiled incorporates the fixed died over there is something dipole created by chemical bombs and the dialog hold has the component lies parallels the polymer chain if you add all these factors off and the whole chain is involved in those valuable to solve all these cycles is evacuated points from 1 end of the change to the other and the change follows and in fact you can now With the staff and solutions you can measure the dielectric you can measure the dielectric responses of function of frequency and you can pull out a whole bunch of 1 you can pull out of the mean square and then you didn't pull out a characteristic relaxation time half that is sort of a single Garrett about exactly a single characteristic time and you can determine what you can also look at dielectric loss as a function of frequency the curve that has several modes to sort out and I knew some clever organic chemistry you and say I will reach in and his piece of the changes is biologically active and this season the change is somewhat different organic chemical that has dipole moment and now I use dielectric relaxation to look at the motion of part of the change relative to to the rest of the chain so dielectric relaxation is a marvelously effective and what we demonstrated important result this is the relaxation time house there's a form in the package has a stretched exponential concentration dependence will there will be towel increases as we increase all concentration and the tendency is to see that 1st forests where 2 powerful side and so it's about 3 that is the concentration dependence is the concentration find solution all of poetry out the agreement is extremely good out the high concentration of the deviation of concentration dependence power from a single exponential is described in greater accuracy by concentration dependence of the square radius that actually works quite accurate I OK we have not talked about 1st in the area of about 1st chains we're not talking about a whole chain motions and particularly to start talking about the s south toward Fraser funeral diesel gas has been very extensively measured experimentally it has been very extensively measured experimentally because it is a core quantity and several theories Paul the plot the so this is a lot more plot against the logarithm concentrate fully fairly uniformly fine is once again in a stretched exponential and the form the stretched exponential years exponential mind is a concentration of power molecular weight matrix saw how Milan were made of probable source of power and found out here all 0 this it's probable presumably those minus a berth on we see that and there is very clearly in uniformly stretched exponential
concentration you can also write this is finest golfers who were at DEC parents got married health so you can actually see this form and quite clearly there is stretched exponential all of there are almost no systems banking 1 founded in which you see of power along major actually extends over this there there is 1 well-known early measurements which reduces troubled Powell behavior however if you will to the measurements they also the University of Asian increases with increasing matrix concentration before it goes down again and since the number of points involved and this is quite small my inclination
is to say the experimenters who after all with the world of cats somewhat bad with instrumental noise I don't see any sign they did the experiment wrong it's just that no other for experimental on the same over in the same solvent shows the same behavior Bloomberg well hands said that water constants we look at the Council on Health disproportionate power in the power of someplace in the range of 1 and that has been on the 6 at home got serious about problems all overweight 5 of 7 you can also measured gamma delta separately and there's a bit of an issue here because the animal and when added together should that would affect the and was dealt the whole way through 5 all .period the biggest explaining the complete molecular weight that now these experiments were done on different systems you're measuring the export of an export which is not the
world's most accurate measurements and are therefore it's not quite clear there is a and the enormous challenge here you should be aware of been the discrepancy you can also ask the behavior of new ways if you know what you were this fall molecular weight Austin Ventures do you have any yes and each call molecular weight for a lot of concentrations and if you wanna see will be held in the hands of all molecular weight you must repeat this for bunch polymers of different sizes work and what you find he is that a small molecular weight you somewhat scary someplace in the range downwards and then you get a fall of about 250 new someplace close to and I and the Indians and that is what you actually find experiment no there are 2 specific experiments which should not shown this and and reference both of which are both very nice experiments and they were 1 of them talks about experimental data they have here in concentration and the other this similar point was the In the 1st set of experiments talk about the 2 towels that help hello and all talk about with logical who look the polymer final the weight and they took the ball out to mound and measured the self diffusion coefficient always have that and then I tried come downwards from forwards the solution but they didn't come later McCain down volume fractions of a point to so high and what they very clearly found was we Washington too only volume fractions from either side of the recall 1 . 8 molecular weight to minus 2 thousand 2 . 4 2 good approximations that is they actually found top clear Powell behaviors and the systems which are taken out to the mound itself much higher concentrations than the other stuff I was talking about you very very losing Powell there is also an experimental model of unfortunately is the face of integration of what we're doing and what is found as a function of molecular weight the has stretched exponential I knew that I had quite a shock crossover that was clearly a power machine and it is generally should you 1st of all you really do see Powell crossover 2nd very clearly see both of them said the same set of measurements and says you can see both the same set of measurements there's no doubt the filling crap process that gets us to this point can actually see power loss when you press but there is always something you and that the problem the literature on the appropriate use of Mormon we're talking about something that is not the the same as self-interested view mirror talking about experiments in which we have called for a solution and inserted colloidal probe and we can measure the translation or in some cases the rotation of the probe and the question is what we observed experimentally and the answer is probably using prolific growth follows a stretched exponential the minus Elvis concentration In cases in which you have done measurements on a substantial number of different polymers molecular weights sent them a source said you can actually talk about how the health of the Fed's on em or how to and his followers like me and when find is that this is measurements on prose those on the old place more cases books on newsroom falls with increasing all the molecular weight now Merrimack before tracer diffusion coefficients I've South diffusion coefficients I said new plateaued wouldn't not all . 5 in probe data there is a lot
of probated that doesn't quite get that far however there probably diffusion all the other thing you can do which is how turnover people actually got interested in you can measure the diffusion coefficient you can measure the low share of viscosity is a function of concentration and you can report this is just wrong perhaps normalized or you can report uses computers turn higher than in the previous role or and say I know how the probe is I think capitalism might up stocks and this is been around for a very long time 1st experiments with Turner and how Brady and if you do those experiments are what you find is the prohibition of overfishing even for a very large growth is very definitely not covered by the solution discuss on this ratio easily can be increased by 3 orders of magnitude go March solution viscosity of finds that big problems we have to see the viscosity of the solutions are simply express there have also been experiments .period In which in addition to looking at problems in the jails yes now frozen shelled and you started serving cross-license you can take problem-solver and converted to program just and if you do there what you find is that probe diffusion jails is totally different from produce fusion solution In solutions to their problems an Easter week size that is the ability of policy solutions slowdown probe depends on how the program is so that the reviews thereof the depends on probe size but it's not a very strong because its independence you can see its independence of the electrophoresis community uses sort always out to the start of the on the other hand cross-linked jails are straight size filled there is a larger size involved wage pro particles presumably trapped in jails in only 2 back-and-forth with in small cages just can't and therefore followers solutions are very much not like jails all on time scales in which Carl whose parents fall distance through OK that's probably of lighter aside there are actually 2 probes diffusion there is a problem diffusion literature that's been around since 17 were 76 in which 1 technique is often called optical program using your interest in the diffusion coefficient with no pretense that you're getting information out on the viscosity said there is a separate checks the same physical methods called Micro reality in which various claims are made but you can use the probe to determine the local viscosity all those claims do not appear in my personal opinion to be well-supported in some cases they're supported by experiments with the analysis is clearly fundamentally wrong on some cases there's a comparison may be with the macroscopic viscosity and their differences of factors of 2 were 3 inches brushed off well None so signed behavior can be a factor of 10 years but I'm more typical Nova is 2 or 3 and therefore the Einstein signing and behavior but the probe diffusion literature has been studying for 30 years is being treated as moralists negligible by the so-called Michael reality communities on now you might want to know why isn't this contradiction resolved in literature and the answer is solved by citation analysis then as you can find to literature's which are not completely contemporaneous and the more recent mostly Michael reality literature proceeds of the optical probe diffusion literature is not there all agree that "quotation mark but well having said that we agreed to push ahead to another chapter the test chapter we're going to discuss his collar if you go way back to the introduction I have listed a whole series of different very good review articles on Paul dynamics review articles written prior to mine and you will find they center on measurements of Loescher viscosity measurements of self diffusion perhaps
measurements of disco with Leicester City I could go on for a bit but you may get a general idea and Herring said there all of these matters that all our day discussed sort of stopped there you don't see sedimentation or electrophoresis dielectric relaxation offers you may see sentimental motions discussed and now we come to a topic that's completely not there at all college dining Limewood Color Dynamics the interesting interested in in a discussion of polymer overnight after all here is called for political analysts it's a original it has no internal motions why are we interested in his behavior the answer is but the forces from college and solution and the forces between Homer Wells with 1 exception said there is media hydrodynamic reactions which arise because the that's all properties we also have excluded volume interactions lining their literal sense Paul call a or call chains and not simply moved through each other now as I did not say what happens when they tried because they're too obvious answers and 1 answer is 1 moves after the other is brought to stop because the other is like any other industries 1 warms up to 1 and concert those are both answers all the number of more theoretical models that are based on making the assumption 1 of the however there is 1 fundamental difference you can say to college aims entitlement not and as long as they are tied in knots and build on 10 will mark which may take a while the polymer quarrels at constraint together it skiers can get in each other's way is a phenomenon Xiamen's which occurs in various guises I however it cannot hide his fears and knots around each of the region around objects like Mark .period marvels cannot may not and therefore the 2 systems In their policies and because they differ in their topology she furious soaring out what hydrodynamics excluded volume grew from what apology because this is a very natural tho some people wonder if there is 1 other there is vulnerable it has characteristically which can be drawn on the way however ,comma called "quotation mark comes up to to it because ,comma is basically empty spaces with little mixed the distant minimal distances to Paula Sanchez chain centers can get from each other is very small relative to the rates 1st is the distance of minimum approach is the distance of minimal approach I say this fear and this chain are about the same size these 2 spheres can never get close but these 2 chains get very close together in the fundamental differences and college dynamics gives us the more direct access to looking at topological effects so what make all the measures that have been callers behavior and while we find if you look at those is she on many of the behaviors of college of polymers are very similar in particular the far higher himself fusion cultivation of mutual use of there you go against concentration you find apparently initial slopes they are the leading national although you can calculate the spheres the calculations were now calculations somewhat sensors in the form of hydrodynamic the reaction short distance which calculate and therefore the potential energy short distance which is hard to control so these are actually difficult experiments to do extremely high precision but particularly for the South diffusion coefficient you can actually do the calculation that very good agreement between experiment theory and therefore will only say the interactions between Spears a hydrodynamic converts fear not only is this obvious by inspection but the theory makes a series of predictions for the concentration of the self diffusion coefficient mutual diffusion coefficient all of the breakouts rotational diffusion coefficient of scientists and then measure how fast to reorient instantly and you can actually measure these variables there are some differences between spheres and Paul Paul Boyle although 1 of them is the final thought viscosity was concentrated the staff these fears comes up and it's consistently easiest solution might not like however and polymers the transition is simply analytic and the 2 Koreas stretched exponential Powell said slovenly the interest that this year's there is a transition and it does not appear that the 1st derivatives continuous something turns off and about particular concentration this you can also look at the dynamic taught law at the time of the novel Spears systems and you can look at these viruses frequency of course as we point out products from there's the same information as to the source saying we can look at both of them tells you things but doesn't necessarily tell me quite as much as you thought and what you see is a member of the stretched exponential change in frequency and power frequency and it looks very much like Call Report except there's no possibility at all for the fears tiny John Harkes I using extreme form of this there is an experiment in which you may pay heavily across the way cross-linking anyhow Paul and spirit but if you a series of don't stick to each other very firmly and you can make a leap without you even knowing quite large I need to look at the dynamic model reduced frequency and the spheres looked exactly like so-called entangled in an all points that call actually talk about Bosnia last light scattering spectroscopy bond with centrally concentrated opponents of I say potentially concentrated because most experimented the Grand Met look at the concentrated regime also covered the by the less concentrated down low very low concentration reading this story after all was much less work this part of the few sets of data that fail to do so and the 1st thing you can do that is to say that these gatherings factor will be -minus songs began but sometimes also reduce capital made tea that notation is not the same as the standard Model rotation looking back in years and we can ask Omega the 1st human depends on the concentration of all and how it depends on the scanner there are a variety of theoretical models that do this at various levels of approximation starting with work force and if you put all of these together you the fairly low concentrations potentially large even large Hugh regime is fairly well understood based on a purely hydrodynamic calculation even then however push ahead and you can say all suppose we look at single chains in a matrix background and we look at very large steel and while there are we will all the and its smaller unions was wearing and Marjorie you put in what should be be a very concentrated more on the way said matrix always concentrated Lucy out here you humiliation was so clear behavior the alternative is endeavoring browse year and browse the to the difference between his roused speaking here is that in the same model you have hydrodynamic interaction interactions with all and in the Rous model there are no hydrodynamic interactions since early very clever approximation well you seizing behavior you see hydrodynamic interaction with fury behind dynamic interactions with parts of varied work for him to call hold all boils unit intended matrix and therefore you not appear to have ordered the so-called hydrodynamics screening phenomenon by direct style OK that's part parts b called Civil War so I will block long pass through the steepest scarier spectrum starting time domain radio frequency domain you can do things do more convenient the kind of thing you see in the exponential moralists and then means some systems vary with is set some 3rd this shape 1 of the next very along with the question is what is the very model of this was an extremely controversial topic the 1st recent controversial is that all systems do not show In some cases what appears to be the same color samples from the same supplier in the same organic solvents which you hope has been adequately purified in both cases there will people won't have season and 1 those and it is not at all clear in some cases by different people do not get the same result we can say it's not due to DOS because someone find systems that show its systems that don't and they're using the same experimental protocol we can say it's not wholly dispersed city because someone lined up if all watch polymers with different degrees of molecular weight distributions and show that some systems Monroe's 1st systems show and some systems Holly disperse systems don't initially makes the model dispersed systems they continue to show it and this goes on there a certain extent was never completely satisfactory however beautiful series of experiments and the center-left ontology electrolytes but cures to show what the costs will it's at least shown something that has properties was sold what appears to be consistent when all of those properties is supposed to take a system that shows the and passes through the were swallowed stairs and now and then rules out any interpretation is this being an extra hydrodynamic among of life are rarely brought along a spectrum of because you can't filter out the really spectrum solvent prolonged spectrums of those in USA for a while because they I was something lacked demonstrated while a series of experiments I've discussed or is it more fairly looking at an equilibrium structure and even promptly equilibrium structure either from too much of it or none of it and if you wait long enough years we wanted to years any structure comes to about the same amount in solution and who seem to be looking at different from region regions within which all slowly in the interpretation of advanced for this is that we were looking at him long life there is you were looking at regions in which the change in the density of change does not have to be different react I might have actually did experiment you go through from low concentration of Oslo high concentrations for almost 2 years and the intensity of the normalized by concentration does not change when the solos appears that's not forming aggregates your former regions within which chains and not OK that's the way it's good to inspect Ross we now know that this is not the the discovery last visit 1st viscosity and we do measurement of where is concentration and what we discovered this was about to make a point that is not in the book is the result is there and I point out the phenomenal but I do not tested capstone named what we see phenomenal logically in some cases going now is that some systems it has stretched exponential dependence on all concentrate other systems we see versus French exponential and power loss and then we see a solution might not like transition also systems states and I go through a large chunk of literature and see some of the some of the now if you ask Where is the solution might not like transition the characteristic features guest to where it 1st appears to be the best expressed in this viscosity oversold viscosity is always on call old times and where 102 103 you can also ask loyalty is the transition over a characteristic concentration concentration hundreds of stocks concentration overseas stock and here is not you can find transitions foreseeing a long war the 3rd and 5 work 80 hour in so-called natural concentration units transition birds all over the place however in terms of relative viscosity is involved in this stuff relative to fall transition occurs in about the same .period now .period administered level the fact that you have the means to curves says that the viscosity is not described by Universal I want to universal concentration In any theoretical models says versus concentration where you may have to put concentration and natural movements rather than grams per liter any period says viscosity thus satisfying universal for this because viscosity doesn't do think that actually a major result officers current standard theories that may the final viscosity as a universal functional dependence on radiation mainly out of here the result this scale all well you can find systems where it was scaling law but the others were isn't and therefore play starts using universal functions concentration is state home I said stretched exponential mind Al Pacino Alfred portion called the election a strong power around new Indiana shows it starts off somewhere near 1 with a lot of the and so here 1 half of last year behind awaits experts that finally we almost got tighter and tighter the mystery of this column last week the you go back a quarter of a century and ask What is the concentration dependence discussed below last parameters will 1st of all they have lots of measurements because it was something could measure a long time and 2nd they had claims that measurements as functions of concentration as functions ,comma molecular weight and what they said was what the reviews will say is that the behavior of Invesco viscoelastic functions as you've done to the molten salt is mysterious you can't create what were called superposition plots because the shapes of the functions change as you go as redundant persists and what I did was to introduce the temporal scaling up sides which predicts a frequency dependence worst case was words look at what the ones but once predicted frequency and the frequency dependence is actually fun and if we look at the time ,comma that up with the goal of crime and all that are work we look at discussing the here than in a function here what we find is that lower frequencies the jury the well 1st of all if you want to do this to have a normal life that not work on the way to the region normalise these is if you're looking at material parameter you expect the low-frequency parameters become frequencies the candid and these things in goes Omega square omitted the 1st low-frequency so we divide out this subject that is clearly not part of material Brown based on me being here and we find a low-frequency accident that stretched we find a transition stretched exponential power and very large frequencies well you expect to see the soul of the Stasi and some people get down there and in some systems used in additive solo which may be another's stretched exponential Powell for amazing thing just that's all when you see this complicated shapes which we can fit with extremely high precision and I emphasize you go over many orders parents on us and we go over even more hours there frequency in the trees with and when you do that the model predicts these forms with extreme precision as far as I felt within precision measurements over the full range freely and that is the temporal scaling down we can also show that if you describe these curves wholesaler of thoughts and of chronic promises relations which he reasonably was the true from the original data while a few is not original data but within informs you get a good agreement with chronic problems relations OK so we sort of pushing ahead and we look at this that was the last the stretched exponential goes the eyes hear all the time helpful they get some power and if we compare Althoff also wants shares that if we all compare also leveled off we say saved features and those minus it's 0 B minus yeah well so the cost of fuel all we discovered is that health was worsening and she the year about power to to vary the precision he hears that the relationship is extremely and and therefore this parameter out here which he described as frequency dependence is being determined by low-frequency transport parameters which in turn has been concentration dependence on OK but now we get to discovery last my comment on this story Leicester City is faster wants another wonderful reprints and consists of a whole lot of experimental measurements and Analyses 1 of which points out that Shearier something I discussed last time actually appears to be a matter stable outcome not stabilize How we know this well suppose we take the the same polymer solution and we check turned up to Solheim sharing we can imagine doing this by turning on the sheer rotating column of flight and then leave it staying high shear continuously or we can imagine ramping up of very directly from lotion yes we are not same .period well if you do this sharp ramp up and sit there you see share if you knew slow ramp-up you do not see share all this result was probably in few of his earlier preprints which were released from my discussion too late for my discussion book and simply going saying there for major aspects of this topic are still on active subject to research things have not settled down and therefore I'm not going summarize them because I don't yet know what the summary is we are out of time that's the end of today's lecture the next couple of lectures will bring us to conclusions to be drawn from all of these measurements have some already in a theoretical model that actually explains the system as opposed to theoretical models which only explain hypothetical phenomenology not seen in nature and with that we're not
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Metadaten

Formale Metadaten

Titel 27 Summary of the Literature
Serientitel Classes in Polymer Dynamics
Teil 27
Anzahl der Teile 30 (Lecture 2 missing)
Autor Phillies, George
Lizenz CC-Namensnennung 3.0 Unported:
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DOI 10.5446/16227
Herausgeber Phillies, George
Erscheinungsjahr 2012
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Physik
Abstract Lecture 27 - Course Summary. George Phillies lectures from his text "Phenomenology of Polymer Solution Dynamics".

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