12 Self and Tracer Diffusion, Part 2

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12 Self and Tracer Diffusion, Part 2
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30 (Lecture 2 missing)
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Lecture 12 - Polymer self and tracer diffusion, part 2. George Phillies lectures on polymer dynamics based on his book "Phenomenology of Polymer Solution Dynamics".
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glasses in polymer dynamic based on
George Phillies book phenomenology of polymer solution dynamics Cambridge University Press 2000 the lab ends
today this lecture E is like
12 more on Paul Mercer cells and tracer diffused
I'm George Phillies and this is lecture 12 of phenomenology of polymer solution dynamic today I'm going to continue my discussion of the experimental studies of polymer self diffusion the basic notion here is we have called the solution and we're somehow able to track the fusion the random walk at the same time Paul Stockholm were of now there are experiments were you actually are attracting 1 single all over it's time more typically you have a dialup solution of label Paul and trapping the dial label Palma's as they moved through the Matrix polymer and unseen polymer which may be done concentrate there are also a few techniques holes field gradient and Amata for example in which you were in fact able to track the displacement of each about Paul with respect to its own location and still the measuring single pro single-molecule self diffusion so let us surrounded discussion from where we left off last time and will begin by looking at Figure Eight as well figure a had 12 shows experimental studies of true shares and collaborators using hot pulsed field gradient and Mark they're looking at Poly High Supreme is also carbon capture now the point of carbon capture chloride is that it's Skinner relative to the Yanomami and therefore you're actually seeing the what they are able to do here used to look at 18 Maryland stock always meaning there is essential for their arms reaching out and her career for year and they look as a
function of plants ,comma concentration for a sea of people about 70 grams per liter they look at stock all owners of molecular weights and you have a lot of weight 340 800 m In the end 16 300 he think said that number killer cauldrons and they do a comparison with a linear which is 300 although perhaps not linear so what do they see when they measure concentrate well 1st the answer on what they see is that as you increase the concentration of the funeral of falls the dependence of the diffusion coefficient
on all concentration is in fact a stretched exponential and concentration they also however managed to find at the center of 3 lines all we can change who's diffusion coefficients low concentration is the same as that hundreds of from the stock value should realize that these are the molecular weights of the complete stars if you have an 800 killed all the material all has 18 terms something out the molecular weight of 1 of those firms is not the goal of all this is more like all old around water 5 of the last syllable however they finally the Prime stock diffusion coefficients at low concentrations about the same as they take off the concentration of the curves track each other with reasonable accuracy why is is this result suggested why should we care so that we can measure a linear chains and the stock chain that start out the same size and that we find this week run up the concentration the diffusion coefficients track and the answer is that it is believed that stock chains and we change diffused through completely different processes 30 no reason to suppose that the person who threatened to clearly always find some linear chain of salt molecular weight which matches the diffusion coefficient matches view of the of the storage but there is no reason for the 2 curves to lie on top of each other if you happen to believe that use completely different views mechanism well rather clearly that's not what we were seeing please see 1 let's jump ahead we just have to figure skating test work me a day after 14 is compost they're actually working pieces ABC D and in addition to the they're being composite pieces ABC-TV I used tricks with displays of 1 x vertical axis relative to the other so that in fact there are more than 4 chemical systems represented there so there's a huge amount of measurement great deal of work by by a bunch of different people all on the same breath and fat in particular you see measurements of polystyrene in parenthetical chloride and benzene see measurements on Polydor I'm apple cider Locke said see measurements on polyethylene oxide and water me and in every case what the hell of it that is concentration on the user again on a broader scale is a long walk along the something that looks like this each of these studies look at all series of concentrations and they look to the series of polymers of different molecular weights now the 1st observation is that if you put on a polymer if you put in and look at what all over 1 mile molecular weight a series of concentrations of measurements on stretch exponential In concentrate you could certainly wish the measurement systems doctors about very low concentrations in all cases had been in and out as far as possible and I found situations but in every case there is a stretched exponential thing however there is something more for a series of these the work was done using policy of several different molecular weights and each Holloman like the raising of always stretched exponential but in fact for all those different molecular weights there is only 1 stretched exponential stretched exponential is even worse than the minus health some althought concentration of power polymer molecular weight and so to describe the measurements that 3 The whatever molecular weights you have become a standard of proof after concentrations the next on the whole life to await scaling next that you have a very small number of parameters used to reduce a lot of different measurements furthermore this form as seen from the 1st is successful at simultaneously reducing both the concentration and the molecular weight dependents to what is in fact 1 single curve let's take curve things like a bunch of her well the year is really function of various concentration molecular weight and therefore could imagine doing some three-dimensional graphs or at some science fiction future in 15 years can be some blackboard display concentration molecular weight another 2 perpendicular Accies seen perspective the diffusion coefficient display 3rd axis seen in perspective you notice these are permanently all
perpendicular to each other prospective Vermont and as the years that followed concentration of molecular weight DNA you're going to cut the concentration annexes molecular weight axes fusion that way this function gives me a smooth surface when we do measurements for a sad face polymer molecular weights and a whole lot of concentrations rabbits much easier to do do measurements in a series of concentrations than a series of molecular weights that's just the way chemistry works out what we do know this fall leader who is taking looking at this small service and taking cuts and faced constant constant molecular weight each time it's been a long time which is the shape of the service and that value of Council from molecular weight excesses this way I have a copy of this service here I have a copy of the surface here I have a copy of the service here that's 3 lines and I was the 1 some of the great but in fact I am doing something much more complicated than just saying I can represent concentration dependence as curve or I can represent the all molecular weight dependence her wizened fan being honest to say I don't represent simultaneously concentration of molecular weight as a smooth sheet and this function does OK let us push at head and we will now push ahead we will reach 8 quite section 8 . 3 people will phenomenology of policy solution that can discusses tracer diffusion the tracer diffusion measurements are substantially the same in somber suspects as the former self diffusion measurements but its core respect their varied get what is the center of the same respect is that we are measuring displaced workers asked where displacement the 1st time or we are measuring CTI view that's scaring investors twice area not displacement in time and we are doing this for 1 share in time so we may actually do an average by looking at a bunch chains simultaneously but the physical parameter describes only how a single chain moves gives you no information on how 1 share of its relative to to its neighbors it just tells you a lot and that the sense which traces is the same itself is the also however and asked I was registered in south of the province and the aspect arises from question and tracer diffusion is how you get some book on trying to answer the question the question is this if we look at some confusion as a function of concentration and molecular weight diffusing species as we increase the polymer molecular weight the solutions become more and more effective at slowing down the particle trying well that's very interesting why does the solution become more effective at slowing down the hall it's trying to and 1 could imagine the answer is I'm the defusing polymer I'm getting bigger and bigger and bigger and therefore in some sense I get attached to warrant more things and the resistance increases because of falling object is getting data that's incidentally beyond the statement the fusion cooperation and concentrated solution is to follow the pattern is proportional to the diffusion coefficient in the tie-dyed Lucia if you look over the 0 performed just talked about -minus held to you and there are there's electoral weight that of how effective solution is on a fractional bases of slowing down in the future so what possible explanations for this survey is that arises because the diffusing object is getting bigger however it could also be the case that the core issue is not the using it object is getting bigger than this year's and last year is trying to move and used around the chains that are longer and longer and longer to change this year because the water are more effective in slowing down the same moving objects are a little let's be reasonable about this suggests that you shouldn't be surprised if both of these effects are acting at the same time materialized so we have 2 different effects acting at the same time they both contribute to the molecular weight in the hands of the self diffusion coefficient how can we sort them out the engine
problems were about this traces views the course recognition kind traces his which is an instrument we have seen before when we talked about dielectric relaxation we have seen before we talked about some of the few occasions we've seen before we talked about the lack of reason is that you have a problem .period have lawmakers and if you did so way identifying your broker articles and seeing them and making matrix holdovers invisible you can saturate out the intended use of the on the left in the wake of front and at the hands of the on the molecular weight matrix and you can study separately or you can study these intended there are hundreds of other things you could also start to study the quality of the program matrix you could study the solvent quality the corporation would trace diffusion is we can sort out the problem and matrix Paul molecular weight effects yeah word of warning to repeat what I said last time but there are a number of offers to buy and sale molecular weight probe and the Stanford molecular weight of matrix also all I can say is there are reasons why life notation ran over Iran's Tony notation for derivatives and the reason is the lightest thought about his notation so to make useful and Newman was so bright that he didn't have to think about it license was there with smart man who spent so there is the the calculus issue and there is notation you and here is the experiment and the question is will that's very nice so how are we actually going to do this well the main answer is you have to make the Lakers visible but 1 choice is to use pollen light scattering spectroscopy which gives us the ability to diffusion of and we use the train that Italy had a polymer for example and will start off with the unique in this thing and we have a caller falling levels of Bakelite and we are an assault on the side of fence in pretty nasty things were really great if you're looking and that it should appeal away May and benzene are relatively close to being ISO refractive and therefore if you'd like staring from utility vary but you get to this polystyrene which is also soluble and that the new canal to watch the diffusion of very dialup polystyrene matrix should be Polisario probe always through MMA matrix all this works fine except for 1 minor technical details and a lot of minor technical details is least of all are incompatible with each other that is if you intend to make stuff there's unfavorable From dynamic interaction and the net result is that there is if you go in and near polystyrene chain anywhere in the world later the solution you expect of polystyrene chain will tend to get smaller and smaller because it will evolve electorates failed me being held by the May and therefore you have probed particle that is doing something inconvenient daily its strength if you actually look at the measurements of this case the plot the subterfuge involved of polystyrene species in the against the concentration of matrix fall over the counter columns concentrations varying because the probe polymers always left what we discover is there's a drop off in the the problem solver .period about 25 syllables but without help from up to kill all of which is a very low molecular weight were down at a very low molecular weight all what happens is that if you can efficient just sits there the all polystyrene chain-store don't shrink up on themselves because very short chain and also they apparently had returned very effectively in the motions by the presence of major on as a practical matter there are a fairly limited number of sets of measurements were people have studied the motion of a fairly low molecular weight polymeric pro you can find studies it was nearly a chapter on solving diffusion war small-molecule probe scene for example or any of a variety of guys but if you look for the behavior of small probes small polymers you don't find it quite as much information as you do on larger ball just the way "quotation mark we out charges and advanced to figure a day at 16 the 16 is a series of papers associated the names the here are intervening and the graph is noteworthy in particular but this is more or less 1 of the 1st systematic studies all myself to you and the author also did traces and what observers don't hard breath it yesterday to increase concentration of all the Celtics fusion of slows down as you increase the concentration of the matrix of although the diffusion coefficient of the probe slows down on you will also notice a slight anomaly if you look pardon the South diffusion measurements on you may have actually looks like that that is there is this :colon which is all planning to my 25 per cent 3 described as the largest information "quotation mark where the diffusion coefficient of the probe 1st increases with increasing matrix concentration and then falls again on this is going the itself the Treasury measurements of now you could say
this is an example of 3 and 3 10 times as long as we will be hunkering once and again as we go through the course and in this case where executives and so on go low concentrations of Paul I however each could also be noted that the Serie a whole series of people who studied at least was the same chemical systems and know what all the facts are the answer magic phrase did specifically ,comma the fact point of specific and believe is that you're actually dealing with the product of a complicated synthetic process that you know you have been very careful and don't all sorts of good things every so often something odd happens with a particular sample of material and as for you may not even realize it's happening and it may not be worth chasing down exactly what can however be it out .period of specific chemical effect is that you were seeing something that is not a generic behavior all resistance and therefore you have to sort out which measurements you look get the of them and which measurements you decide something exotic happened which is not fault of the experimenters work I should be noted however that 1 of the consequences of this decision will affect the issue here is the scale of the behavior and uses moralists the only measurements and there are quite measurements but they're pretty close in which you actually can lay down ruler on waterlogged plots a look clearer scale and what behavior not stretched exponential and all now we advanced to will launch a series of experiments and launched a series of experiments are to spend lots and wonderful and reaches who the other names on these pages and Wheeler part of this process and not after getting lost but noted authors and what they did is to find a system treasury system with the following properties property you have a polymer policy finally metal that even with the salaries of its decision to reduce the ending and goes into all were lowered world toluene there always important feature of the the media Is there quite thoroughly irrational practice not long after the ISO refractive but there is an approach to bend shoe he looked at mixed solvents that is you have to small-molecule solvents instead of 1 you just the composition ratio and then to the temperature because the index of refraction changes with temperature and you can get
really incredibly good matches positive working people while I was lucky enough to find the whole Western and where he had a useful Kroll the yes polystyrene polystyrene is probable for this system has to enormous advantage the 1st advantage is that even make polystyrene synthetically they're very pure the molecular weight distribution so you know exactly what the molecular weight Paul the 2nd statement about policy sirens and me is that the compatible so that all where he is usable solvent with both of these materials and materials the polymers makes together rather than having some very negative from a dynamic interaction which causes them to fold up and that's very useful because it means you know the pro behaviors reasonably well OK start having said that what did he do well for the pedia me there were 3 major exporters 100 warning 630 and get over 13 thousand people was the magic number I'll ask if I recall correctly there you the old so you have a fairly low molecular weight ,comma immediate molecular weight all quite respectably large molecular weight and since these are readily soluble in the view of the it was possible the experiment sure to take the concentrations of these farmers have sold large In particular if you go through the fall series of papers you find that they took the concentrate on how to 300 grand all they also did viscosity measurements will talk about viscosity morally later in the course of the war in history was the intrinsic viscosity or rather its universe was for these 3 materials always let states were the 3 branches of of the year a France's is in use program wars and these are only concentrations the stock you can have different numbers of hearing others and therefore they estimated entanglement concentrations the concentration is with all the changes intertwined with each other so you have worked with the general would call a assembly died polymer solution they estimated C and 50 were small 11 billion kroner with the ball and about 6 March meaning it may got off to see overseas he promoted artists all all to something around the mouth the transitions we're talking about here are not Thurman dynamic phase transition it's not that you shot up to some concentration you hit the solubility limit and now you have a solid phase period right at there .period instead you have changed their intertwined with each other and at some point in terms of this vision the intertwines the Cumbria logically affected and they become real logically effective over a range which most versions of the theory cannot calculate and starts becoming effective you run up the concentration so imprecise amount and now it's really effective but they got up quite high concentration Oh I should thoughts I'm aware of what model analysis which he does predict the sharpness of this transition the prediction is based in essence on his assertion this entanglement transition chains all getting entangled with each other is a percolation transition as you move from chains the on attached to chains that have entanglements so you can walk along the chain hop entanglement walk along the chain of resist percolation transitions are extremely sharp and you are however the people don't agree that's how you analyze it I just bring it up but there is this range of opinions on whether transition should look like and at least some of them say shop and some say otherwise doesn't matter here we clearly got way out of the transition OK so that was what was done and then lot I worry about problems this after all is all that information on the nature however there are Croats what Washington was realized with a new synthetic chemistry and we make terrible there is a 3 Armstrong and we can also be made etc. athlete his fellow on stars and cost him linear all of the fueling of all as being warm start and the linear polymers and were made each of these were made with molecular weights William always molecular weights from 6 to 5 10 15 killed all meaning was small white Moors the 3 armed stars were the same the 12 hour stories that from 55 to 69 for a total of all things you should realize 614 kilovolt spread over 12 firms is something like the 1 of the forms is something like 113 Philip Dalton's ran very rare moment of my aunt and therefore if you look from here crosses there is nowhere near as big as a 640 people when you change so here is this beautiful experimental system and the beautiful experimental system we have a bunch of different molecular weight problems we have 3 different molecular weight matrix Palma's all we have 3 promote policies there are a lot of different kinds of combinations and what watched it was to realize we should systematically studied composition and see what we find OK and we started 8 at 17 and through the inmate after those little change and we continue through the other figures we find we are storage and mindful our stories and therefore we have a range of different polymers with different set numbers of arms and we comply the yes versus concentration and we can do this for a series of different from fourth-quarter pro use more slowly than we get measure also the integral probable versus concentration the major for work give sizes of let's hurry up and if you look at the grassroots he's nice lines really do a fine job of going through the data points they really do within a couple of exceptions I will get to and what are Erdos line those lines are stretched Western infidels in mind so you matrix molecular weight to power the pro-life people away from our as you work through there is a 3 redesignated followers there 4 different from polymers yes and is concentrated there are 12 lines generated the greatest show you
although 1 set of matrices and time for a series of different probes however the 3 grafs along figure corresponds all 3 matrices and also concentrations that were used in all of the problems of and then there'll lines from those Greg we showed in some faces 2 sets of lines the 1st hour of a single stretched exponential effects once stretched exponential curve pro majors from combination and then we do the hard things namely we say we will take all the measurements at the same time and we will fit all the measurements the same time was stretched exponential and if we fit all the measurements of stressed at the same time it was stretched exponential we get a family of 12 girls the all defined by saying I want to read parameters and encouraged to a very nice job of representing all of the measurements simultaneously there is 1 point if you will ,comma were clearly things aren't nearly as good neighborly if you look at the smallest molecular weight problems the measurements this b the current knows that there is quite physical discrepancies in mind as to what's going on well what is going on if you compare with the single fist is the concentration next fall at the canons of molecular weight of the probe and the matrix and some companies and the concentration as former starts very near water for smallholders and hands down words about half from article this is the reason for is 1 proposes is that small are not do not change the radius of gyration very much as you increase the concentration of the matrix of large polymers contracted and we saw that dot dielectric relaxation were small smallholders by direct measurement did not contract this year in matrix concentration a large followers very definitely did those smaller radius and we can actually described it on faith that is an earlier but well the form that was used just to be constant and saying was a constant threat isn't so well-defined functions of probe size part is not quite good enough approximation for a very small role if you wanted to go to the next step would have put the new itself functions of all yeah I got spot on the stage Delta and the Tamil tea and tell them they had all been in draft being treated as a constant wealth approximation OK let's arenas for linear revolvers however there were also 3 around stop over the world norms .period problems and lodged in bottom is very wonderful group did not only the linear chains the three-hour stars and 12 stars and giving us 3 families of graphs 1 the linear chains 1 of the 3 armed chains and 1 for the all 12 armchair 3 families of grass for each family is greater this expression was applied to the number of sets of measurements you would be on 6 separate would be looking at the moment it's not the same number of sets of measurements because there were a certain number of linear chains and a certain number of 3 on chains a certain number 12 on things but for each set of change its height change three-year 12 we do the same thing in process and we see alliance which describe overrated nicely not only the molecular weight depends on the matrix of the molecular weight depends on parole and a reasonable but not perfect job for reasons I explained with a concentration so that's very nice music absolutely beautiful measurements were taken to matrix concentrations way above the entanglement concentrated and there is 1 market feature these arrests and Martin feature look at 1 of those that Americans is the study has reduced concentration you see moved on a lot of people you see movie curve of constantly increasing salt we started out like closed flat we roll over and go down the aisle there is absolutely no indication that measurements of a well-defined regions in which you see in transition scaling being and is involved in a lot of time and asked Where is the scale and it's quite clear there is something is no regional regional warlords "quotation mark restricted free on instead the the cost reasons for and that smokers have constantly increasing slowly is the extremely uniform behavior and for Paul herself here well we can push ahead and we can also look at the their findings of the figure in question shows us comparison of linear start James B. is the for small change linear for a change if you get to match have about the same concentration dependencies and for the larger chains were early on big change there's some different stars of linear chains are being affected in quite the same way you you look OK let us pushing at the next figure this study Martin and Martin also lost polystyrene TN Media these with the actually will 1st this is a lot early work on this article he covers his measurements ,comma arrange about him too so you can go vision that is the diffusion coefficients starts out a lot of value and it falls to about 1 per cent of its value at the lower end of her several different Poly Vinyl methyl ethers and a joint fail reflecting the various sizes of gives us the courage to see which worked reasonably well however Martin did something else in addition endangering the yes he also measured a viscosity of the solution the issue was solution viscosity is that you have a solvent and you start storing tolerance in almost all cases as you get older the solution becomes more and more investors and say that there is some therefore salt approximate resistance flow and their approximate resistance long should protest respond to a change in the diffusion coefficient if you have measles kopecks fears say 29 and new spheres diffusing through a small molecule which would then quite uniformly fight Diaz proportional to Haiti all ceasefire the Torah where the salt is now under assault viscosity that's only have positive sphere radius kiss is known as the Einstein's equation start signed standing equation derived by Einstein a century ago corresponds to an estimate of what the diffusion coefficient this year should be in a simple way it works all right for me says Scott experience as we noted in Hugoton ions for small molecules and run out the viscosity involved in voiced stops on-site doesn't work right because the
diffusion coefficient is not proportional to 1 over data however if you believe you're looking the system in which the stop sign inside waiting right or approximately right here protocol and really fears you would say it would expect the U.S. aid to be about the same as the value of the product your soul that is as you have holders the system the viscosity goes up the South diffusion coefficient comes about and therefore you might expect some of the people that the product ought to be fairly all independent farmer matrix concentration well it really is and have not allowed those times starting in the year in almost all cases the months-old science society and behavior is that as you increase the concentration of the system the product of the data also increase that is the matrix Fulmer is more effective sometimes orders of magnitude more effective in increasing the viscosity of the solution than any reader and the diffusion of polymer work hard sphere next nonstop outside signing in diffusion but it's fairly unambiguously observed by Martin for polymer poets all unfortunately there is not nearly as much data as 1 would like where people compare Shane diffusion and viscosity so I can't go into a great deal of discussion of this because the measurements are quite there for probably diffusion matters quite different for studies probe diffusion spheres refusing you always lose their lots of measurements of viscosity and probe size probe diffusion all on the same system and much more extensive comparisons are possible let us struggle To the experimental study data what data stars is something slightly different it's only 1 system the fumes measured 2 ways of measuring on the plastic waste scary spectroscopy and its then using false field gradient and the virtue of this measurement isn't 2 techniques are sensitive to hold motion on very different distance scale have correspondingly there watching motion on very different timescales because it wanted to travel further takes a long what was the elastic light scattering is followed sensitive emotions over some reasonable fraction of a light waves like all polls field gradient and Morris sensitive demotions over considerably longer distances and what Davis demonstrates the will of the to distance scales and the diffusion coefficient looks about the same where she might as well how could it not be said I will give an example it's a very standard example you should realize that doesn't mean the example does not have to be right but it is 1 way to get this result supposedly has a system in you this boxes inside the potential energy of the diffusing particles fairly flat and then or potential energy barriers but the particles get climb if you want a single particle of random walk inside the box but only rarely will find enough kinetic energy to get over the potential energy for getting the nest box into which it is soundtrack if you look on short distance scales like this you mostly only see per year in back where the box that you can do quite rapidly you've however you use of their union diffusion Castelan isn't a terrible get you here test falls field gradient and mark the apparel have that have repeatedly from the blasts box a slow process and in this
case the diffusion found on long distance scales is slower than the diffusion found on Ferguson's Irish you really read papers of motor were precisely the opposite circumstances is found on long-distance diffusion seems fair students slowed although I don't have a pretty picture shows you how to get this result not unless the core issue is Davis did measurements on several different distance scales and he found the same results we not struggle Our you know Brown readers is a magnet Bolton all following her and up to 1 . 4 4 3 three-decade-old gold all former so program makers followers be very large and once again those columns only the matrix molecular weight was very often matrix dependence is captured by joint stretched exponential the last shot dead and gone we have to all look at 3 combinations of matrices polymer probe over the 3 combinations of labeled by the life of the all and accommodations happens to be in 33 the agency based in during the 40 there was only 1 9 20 thousand foreign inmates goes the wrong the fire was 1 of the 1st answer on why they're inviting you actually have to purchase were synthesized Paul Our synthesis is sure purchasing you're limited in what you buy and you find farmers particularly molecular weights and take as much advantage and you can of what will I do want to be the 2nd point is that these combinations actually do had feared that a problem with molecular with animators selected away for about here and here we have a probable like to way much larger for much more than the majors like that is we are looking at 3 cases in which either the probe matrix are about the same or pro animators are very different from each other there are models that predict that see on behavior from the Bali them and very different behaviors here and we're very different well maybe you do get this behavior the different not and and we'll get to that bit more and more of the important issue here is there were 3 terrorists were on the streets of nature materials and the precursor accurately described as the concentration and there is a piece to me Delta and and the camaraderie the matrix molecular weight also now you can say only 3 pro-life await end there are only 3 Grove major foundations the fact that that you have be probe made 3 combinations 2 parameters makes life easier for you or less partly true however although there is no particular guarantee this sort of program molecular and major selection were waiting light workable nonetheless it starts today yeah but the when advanced to very nicely here which in practice part of the plan the on Holly properly I felt we also have measurements on and on she other polymers and what is interesting about this figure well the 1st set of measurements this 33 kilovolt rolled in a theory killed all matrix except the mixture theory to go along with the long syllable .period this is what is called was in a land where you do that several molecular weights of this case a given Vollmer you've makes them in combination that virtual bland yes the molecular weights of various but the 2 chains you can at least say so you have long chains and should change and there is essentially nothing would persuade the matrix homered should not be soluble in what is the proper solvent which is more of itself except pieces and therefore you do not running whose solubility limit the way you do with some homeowners instead the
combination is soluble in all proportions and now you dropped probe ditto the other groups that humans have committed 25 kilovolt 12 you have matrix followers which dramatic molecular weights 93 250 and something really large 20 thousand killed all is when they called home and Veteran diffusion of trolls through the Matrix however because sold simply below like weight version of the the same fall over In new measurements of the various concentration on some scale and actually was not taken measures have not been to start out with dialup matrix almost no later it's all just from UBS program U.S. majors following you end up out here and eventually there's nothing but matrix polymer notes sold people expert about this we do not talk about Nelson this cost something where you have to stop writing someplace where go along for him and start almost go on forever but not quite things were abruptly stopped these what we got some on however quite is we had stretched exponential concentration because b it starts here that ends up there air and absolutely nothing happens all the way out to the highest concentration as you can imagine even with extremely large ball so you have a fitting function description phenomena logical description which actually at least in this case works over a very wide range of concentrations yeah "quotation mark during balance Gus when are the other experiments we can do well we might want to get enthusiastic saying we will try a much wider range of probation will on on matrix molecular weights and if the German figures in a lot of diffusion coefficient we are in this case going plot diffusion coefficient bruises from life way and we came out in figure showing South diffusion meaning program matrix are the same molecular weight and we have another curve which is very very nearly the same we have a he have her and he had case where the probable is much smaller than the matrix about the same time will be a year and finally the isolated .period shelters set up our laws which corresponds to the probe was larger matrix as you realize this is the only certain over .period you can feel and certain extent now we end up finally firing all correctly investing in the on and what was done here is to say what the authors did was to measure the diffusion coefficient and menu the diffusion of efficient control measures like weight ratio ratios pull . 1 5 Reading work and maybe it's too and we played better yes various combinations program they might wait as a function of concentration and because of the way things are arranged into the on the other Lucia energy data and there are still wines and they also said we will look at various problems look at the and its various pros the politics of major select weight and there are a lot of froze at all not at the matrices you see another series family of Wall which most of what we go through all the measurements the trade agreement of these curves with the measurements is not nearly as good as the agreement these however what you see in the 2 figures parts a b foreign wants surface you work you see it curves but he acres are independent from other instead of having been involved in the U.S. is the zeroing in on a little out there that is changed probe size 0 change even prior the government and again in tell to generate a family of hers using single values down the so they're actually only 4 parameters policies there'll be and all the curves are a separate slices through the multidimensional she described by this fall the concentration slices were extremely well the molecular weight slices do not work as well 1 function and a very small number of parameters describes an extremely wide range of Kroll and matrix molecular weights of I can't tell you I function works quite well after the final point I would call your attention to but if I recall correctly the next best thing which I recall correctly and important feature is here is that we were looking at the of guest of polymers but they're really small owners they're not Maggard altogether or hundreds of gullible and in this case what 1 finds is that the use of these 0 the probe molecular weight minus a fair primary listing friends on 1 of the 2 and we get a a C is the is the 1st tower and some of our so we have dependence on probe molecular weight we have dependence on concentration and you can judge for yourself the agreement of the it's data not that there is however 1 on a little bit you very well molecular weight problems will evolve and 1 expects were very small problems program is more or less independent concentration if you think back to the chapter on dielectric relaxation May I that the concentration dependence the redundancy part radius over a radius of Europe concentration you and the deviation from the simple exponential wasn't entirely covered by contraction changes to our and what we have from dielectric relaxation this unity between Shane size contraction stretched exponential rather than simple explanation from the case here we have changed the the radius is independent of concentration and therefore there should be all the concentration and there is isn't exactly what divides the concentration dependence as you see the oral pure exponential concentration and because they're pure exponential and concentration minus 1st best-of coherent description of what's going on and it's coherent in terms of the stretched exponential reality arising from a change in trend all right whatever I've done today what I have done today is to go over a large number of measurements holders of diffuse there are a a wide variety of variables can be varied through studying molecular weight concentration we didn't have much to say about solving quality you can arrange things so that probe following matrix homered different tracer diffusion and in that case the pro and matrix behaviors can be sorted out separate their experimental studies the lodge on the effect of Froehlich topology many years 3 Armstrong 12 hour start we explored there is some limited measurements were people measured the viscosity as well as the diffusion coefficients and there we saw clear evidence were not Stokes I'm signing in future we also look cases where the March variations of pro-war matrix of both molecular weights and we asked him how do things behave and throughout it also would not apply all cases we found that right stretched exponential he minus a secret new moreover allegedly some matrix will like way some these 0 Cassidy said we probe this functional form describes all resolved you there is almost never any evidence for scaling behavior in which the South diffusion coefficient goes on for example the proportional emphasis on power by trying to minors .period 3 seasons on our backs wouldn't stop and on the England behaviors and not always what's really work if you have got a theory and critics scaling laws and actually predict scale monster theories In good correspondence results if you want a theory that treats all herself diffusion it should give stretched exponential is not our laws the areas but we're going to continue with this theme in future lectures we have 1 more lecture on Paul result future and that 1 lecture will be used to unify the very different results we here after all began there results Gamma Delta Nu and if you're doing something sensible you hope to find these coefficients have some reasonable behavior on the other properties of the solution off for example might pose a constant reminder of the delta have well-being Arabs numbers that are about the same in different systems assuming you're looking at some generic property ran some property which is the outcome of least said Prop you been pushing and that's what we're going to analyze but that is it for now


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