10 Dielectric relaxation, Part 3

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10 Dielectric relaxation, Part 3
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30 (Lecture 2 missing)
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Lecture 10 - Dielectric relaxation, part 3. George Phillies lectures on polymer dynamics based on his book "Phenomenology of Polymer Solution Dynamics". Mode, systematics.
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classes in polymer dynamic based
on George Phillies book phenomenology of polymer solution dynamics Cambridge University Press 2011
ends today this lecture E is lecture to
dielectric relaxation modes interpretations systematic I'm
Professor Phil is this is the last of the lectures on dielectric relaxation as a method of studying polymer dynamics on next time will be advancing to the next chapter of the book which is Paul resulted future all and that will get us through a single chain motion so where we are we've discussed chains size which protect the measures remained Iceland we've discussed our single relaxation times an hour going to advance to discuss relaxation spectra of the general notion the Cuban manager the 2 quadrants of the dielectric relaxation that is a new phase in our face an almost entirely talk about the dielectric loss as a function of frequency and if you look at spectacle graph-like seven-day level what you see is there is a lot of frequency behavior there is a role or there's something that looks very different things like Powell and then made some interesting behavior at frequency of 1 of you asked Well if you push out the sufficiently high frequency don't you reach something resembling a high frequency limits because the solvent as electron shells stars and the answer is yes it would take this out far enough eventually you see something else to hazards relaxation and she optical frequencies but we do not get out of it but you should however notice I mentioned said the talks like the a towel or a standard comment on fitting things to power loss is that if you're function year range and Europe changes independent functions are not very large almost anything looks like a power over short distances on a long long plot that is a very important basic result namely if you just have small changes in the independent variables and small changes in your dependent variable you can be pretty sure that you could at least draw power or curve that is adequately intention to resemble measurements here however for example in Figure 7 national let you notice the nominal frequency covers 10 hours of management the strength of the dielectric response covers well it's actually really denied orders of magnitude or a visit of data points quite up to the top and the bottom and the net result is you have a very large suites of measurement in which you can very clearly and unambiguously see Powell they're off to the maybe it's only a towel
on the 1 percent level 9 . 1 per cent level those really are power lost what you however there is a curve looks like that's not why I we get this curve the answer is that the pall over and do something that changes style dielectric moment meaning changes the ins and thick and there is a time scale on which the polymer reorient goes whatever else is doing to change the value of the yen is an effect which is what measuring and if we look at the end of an Act high-frequency frequency that acts on time scales short by comparison with the time on which polymer and move the dielectric increment of the polymer tends to fade out that is if you want I'll say I am going to apply unless I'm going from 1 of these guys .period the electric field tests .period in the same way more than loss for the Bibles to get turned around and pointed in the direction if the former died Bolton will significantly
influence the direction of the electric field that allow tries to start moving back the other way nothing much happens and it does not contribute to the dielectric constant material wealth as is loss function that's frequency L you see you run the frequency things now what I actually shows a plot of dielectric function is Absalon novel Oklahoma divided by only if we have information on the dynamic response function and there's just not a lot of it out there you would be looking at Friday from Magna and reasonable in his final Americans where the reason for these choices is that dielectric response frequency dependent response in the phenomenal logical analysis I give them my book is subject to the same issues as mechanical response to Shiraz and therefore by direct analogies functions we will at will guest to on Dynamic Response mechanical response to this but we last visited it's late in the course sort of halfway on this 1 but this was 1 of the issues on I could have dropped Invesco last a city which is a collective property of all the chains in the solution before I did this and that it would be very easy to see why this was correct but that was sort of destroying most of the rest of the set of that book so you have this little thing if you want to understand what's going on have to skip ahead of a number of changes nonetheless we have this function that was proposed by direct analogy with the discussion of this Western response is that this functioning as to to what it has performed deeds in the minors and the momentum of Taliban and it has formed a letter to the minor suspects the new functions these 2 functions are separated by some crossover frequency of legacy so you have 1 behavior at low frequencies and other behavior had high praise for this description is partly incomplete the reason it's incomplete as you have a solid chain it's this big complicated object and it can have several physically entirely different ways of changing which way and vector .period and at each of these will have a dielectric response function that is as you increase the frequency of your reply field eventually each of these processes for moving the ball around can respond fast enough to contribute to the dielectric implement the solution so you will actually have several of these things going on the same time the additively I'll let us look at figures seven-day national level and we will actually see an illustration and so at very low frequency several curves the reason you see several curves is that you were looking at several samples of different molecular weights with increasing molecular weight the loss function becomes larger This is low frequency and that is you increase the frequency get behavior and the 1st thing you get understand this very well off that is and then there is a long period on the graph for what you see is a straight line the straight line you're looking at here is a power loss has slowed long plot a lot more plot you see straight line the problem with this is that if you take almost anything and put on a lot a lot lot not large distance it looks kind of straight and therefore it's very easy to fool yourself into thinking you were seeing a power law behavior when there is no power their here however if few track makes a very tiny and you can barely see the very clearly a huge number of points is a beautiful piece of work by Adachi at all and on very clearly has a this is not point out something that may not be instantly obvious but if you go off to the upper left corner of the grass you see the straight line a straight line and curved lines that are not dawn by points and what what those show it is serious power lobby here and I continue to line up the tourism and year clearly and here's the it's actually often pure exponential behavior the engines the next terms of the week .period so you can actually see the 2 as you head down something interesting happens that Italy is out sufficiently high frequency instead of the highest molecular weight called material the charges value this function it drops off the herbs crossing each other and if you look carefully curves crossed and they have here and what happens a large frequency well let's stay with the highest molecular weight material which is rolled off and it's in a power law and it stays in a power lines down to about 10 to the 6th hurts and then is something that looks like this and it's something that looks like this is 2nd relaxation process that is there is a 2nd 1 airfare quite close to the people who curves and then there is the
2nd power along on the slope the 2nd power along the 1st look quite similar but are not necessarily the same on the other thing you will notice that there is this region where the current time hate politics and if you look just where the we're going over from 1 function the current concave of words like this :colon In other words these processes are edited if I could use some sort of magic and measure them separately the 1st process would be doing this the 2nd process would be doing this except in this narrow region higher frequency process is too weak to be changed person and we were right in here both processes have about the the same intensity and both contributing to the dielectric lost noticeable says you have to be careful and Dewey there is nothing In the measurement that would suggest that this process that goes out high frequencies of non also extended 0 frequency and there's no sensible reason to suppose doesn't but you would have to be a very good experimentalist indeed to convince yourself that's what I was doing so I have not sure you is here is a dielectric response functions are there to to physical processes here and you sort of asked what to physical processes are sensible question well here is a and it hasn't happened investors have followed were looking at this is not the police's polyester 3 guests is composed of long molecular some units which can stifle component along the backbone narrowly got moralists and sales and therefore this space factories space from 1 and to the other is off to "quotation mark bold placard of constant use the dielectric title all of the partners see so how we change this fall the swallows process you can imagine at the site of a man who might be funds of the better the slowest prop obvious process is that you rotate think it's now when I say we rotate I am actually being very imprecise what is being rotated in the direction of this fact and the 2 ways you can imagine rotating factor and the 1st is taken from molecules and the whole molecules those something resembling a rigid body rotation the 2nd wave of demand the perspective rotates is at 1 end this way the other and moved said that way and now all of the factors point in different directions because the 2 ends of more forces said that the 2 ends of everything else is too and maybe changes a lot like this or maybe training is off like that where there is a centerpiece that hasn't moved much in the chains moved along its own like of the people who believe that the only the only issue is the whole chain has rotated and is taking this happens rather slowly and therefore at fairly low frequencies this whole chain rotation process cannot be involved with the dielectric response that actually be applied frequency and the contribution of the dialectic lost his peers then what is the 2nd crossing back that's not the people said and entire amazingly the the 2nd process is sentimental motion but there is a peace which is not necessarily quite obvious and you think about it here is a there is the intent and actors which sentimental motions help well you could have a purely internal world and purely internal modem for example takes this and turns it into the base that is part of the inside of the polymer his move but if you look at this purely internal all you realize that 1 drew does not rule the end and vector and therefore does not contribute to dialect relaxation How segmental lotion the contributing to dielectric relaxation answer is used to change at some distance over which the fault model sort of lined up resistance by the end of the shame and there is an internal the changes the chain ends the it's a local loads of whole change rotation but looking to move this to ends around you change the direction of the in an effective and therefore the 2 ends of the pollen like my 2 hands can wiggle and those wiggles contribute not very strongly to the dielectric relaxation is not very strong because it's only a small part of the polymer making the contribution also if you believe that argument you would also tends to ss this a feature going to point this out both did I but I would point out that here is very long on the motion of a party near end can contribute to the dielectric relaxation however if the amount of chain whose motion and in his contributed with is correlated with the location of the endpoint there is some
distance in here or there more bombers here and has come along with the end of that distances 10 20 and monomers this behavior doesn't care how long haul his re-election of high-frequency relaxation that is due to I love loads is wilting and data of the 2 ends of the chain well guess what if you're only looking at something fixed molecular weight no matter what the molecular weight of the whole chain is this behavior should be independent polymer molecular weight approximately speaking about the very careful with arguments like this and not taken to completely seriously and I would say that if you look at but we all over again power loss dropped fast relaxation it should occur it's sort of the the same point at all polymer molecular weights of polymer as opposed to the chain rotation which occurs very differently depending on the molecular weights and that's exactly what see and that tends to explain why at very high frequency these curves all come together I think we not come together perfectly exactly but they tend to come together yes the cost of the increase in the bidding interested in better shape I'm you were applied in the field you were not applying feels that strong enough for example stretched pulled out and therefore the 1st approximation of the confirmation of polymer the shape it's the the shapes and Dobson's solution as opposed to the directions are not greatly perturbed by the electric field they are perturbed somewhat as you rotating using these local sentiments from today but the configure the following the shape is not greatly distorted from equilibrium Our In particular got a high frequency the effect of the electric field as you can actually see that curve dropping it drops a great deal on if you were looking for facts sort of like that my proposed if she were very low frequencies and apply a sufficiently large electric field trip practical experimentally you might create addition orienting things you might discover that you were getting local field gradients that tends to stretch polymer however I wouldn't count on there being easy to measure OK that's let us push that had the seven-day and 14 and 7 day at 14 these 2 figures the figure refers to all having a single molecular weight of being so we had fallen it has a single molecular weight but we change the concentration and as we changed we ask what happens to the polymer behavior as we change the concentration and the thing that happens bulletins things that have and 1 is elected 3 lost function increases you notice this is not normalized by polymer concentration but the 2nd thing that happens is that if you will please the American for a long long frequency behavior and there is a region which is used to minus terror Omega to some power which is actually posted 1 of its executive on and then higher ,comma frequencies the curves almost but not quite blend with each other and they almost but not quite all relax its power was about the the same now Virtual what we're seeing here is that when I say there's power law I am not saying of we have a big sheet of graph paper and I can draw a line through points I am saying we have an area that identified as showing power won't behavior and I will do nonlinear least squares I will do computer that extracts of accurate parameter and the virtual computer faces you get numerical results that are much more precise than might have gotten out of graphical analysis measurements have quite good enough to to support this fall and you can actually do it what else you know is there since that way interest concentration and larger and larger concentrations the frequency at which you start to see the rollover gets smaller and smaller small frequency corresponds to a large that is what you're saying is that increased concentration the time required for art that is needed for tolerated to reorient gets longer and longer and so on you were actually in the concentration dependence Of this phenomenon seeing something about molecular dynamics not necessarily something very surprising namely that if urine concentrated solution of Paula has much more difficulty reorientation show that is 7 14 another figure that shows the same sort of behavior is Saturday at 12 of you go back a few pages and in 7 and a half 12 you can see 2 very clear Powell or regions of 1 function is not being replaced by another 2 functions or edited and you can actually see very cleanly not how good or not good I it's called fairly good the functions I'm describing hours giving fixed the date and the answer is if you look at those you see you get lines lines go straight through measures points and it is fairly clear if you compare those that the functional description I am proposing is quite accurate on the other piece of saying it's quite accurate most current there's a low frequency these days he was the exponential there is a high frequency behavior with power loss and if you look very hard at the intersection you can't see some region in here where things don't work quite work right instead you see you have lot behavior you have the other behavior and you have a very sharp transition from 1 to the other are there is no reason why the transition should be shocked and furious
fairly clearly see units this you expands the figures there remains obvious the sharp currency OK what else can you do with respect for the something else career with the Nunavut said his column policy and so far we have been talking entirely about Paul molecules composed entirely of monomers having tied a diet holds there's a dipole some points along their however if you were clever synthetic chemists were worried about up there and say I won't get hired ,comma is this long but it will be a block copolymers that is there will be a piece of 1 species he's 2nd species and a piece of well could be varied speech and in particular I will choose things for example only this section the polymer has Taipei titles and the rest is not and now I'm looking not for how the whole chain rooms I'm actually looking in an emotional this small said an hour if you can actually make this experiment work you can also and that is what you see in Figure 7 6 this is a dialog opponents there is the division .period the 2 chains are of the same line there she we both along together said and so we have at half and that white land and that have affected your life there and the relaxation includes a term that tells us the correlation between this direction and that direction and how they they liked In my correctly assumed that this is basically a polymer half as long as the fold all over he relaxes work quickly and alignment of these 2 vectors relaxes more quickly however the relaxation function if you look at 7 16 the relaxation function is stretched exponential frequency short times a power law have more times and this is a fairly large figures so if you look near all along tend to pretend for hello herds but there is a point in the middle where both curves are very close to the measurements see were both perjury post measurements and the 2 Koreas attention to each other 1 encourages switches over to the the other in a fairly sharp man now he would ask his crossover really shocked will always have following problem here's the 2nd over fantasies the period data points which their however the experimentalists is on a certain amount of waste and not quite as much as I'm wrong and there is a region in here in which the accuracy of the measurement does not really let you distinguish between the 2 curves and while I saying crosses over the intersection if you wanted to say something else happened and the correct function itself in line this is then hopped over I can't prove it's not true you can't see any hop over and they just see a small pair of functions that are 10 however experimentally statements there is nothing else there is always subject to the fact the year experiment has a certain limit now there is more complicated this in the public paper on this along try to win it's very hard some them the point of view here as of Paul we will take 2 identifiable said and we will generate long rifles pointing that way 2 1 of them fled 3 the other 1 fled the scene as well as our record as both of them fled and Ireland manager for dielectric response function that is I produced for polymers and was the type of a guy also pointed this way and the 2nd I've lived this piece around so the Taipei is going the other way and there is a 3rd World status living this long life that 1 and there is foreign which I flipped both of OK I now have 4 different compounds each of whom has a dielectric response that I can in principle measure with sufficient and I didn't say this wasn't easy experiment you know with digital electronics high accuracy measurements the here and now I and subtract the dielectric response functions in the correct had sold the paper responded give results In a conventional experiment with just 1 a dial your measuring the direction of factor too long time the direction of the factory the other times that the solitary average behavior Soviet and love times like this and later timeline like back they dipole eventually forgets which way it is pointing relative to which way .period regionally and that is what leads to the dialect response if you just measured these 2 this 1 found your dielectric response is a combination of that and long is each time has which way it is .period relative to itself and there's another part of calls to pieces a B b the orientation of 1 piece of the following over time euro and the orientation of the others piece of work under the yeah good well this is what is called cross-correlation there's were asking how is the orientation of this piece of change at 1 time related to the orientation of this piece of shit and all the time and that tells you a great deal about the dynamic behavior it's probably tells you more to pieces a right next to each other than with the way off in the distance of the 2 pieces are way off in the distance relative to each other you may discover there's nothing very interesting happen other than theirs all 3 rotational
chief financial officer well in principle you can do this many questions that took in them of watching the community or on the street image and not just in 1 the show that's correct this function for this 1 we start like this and we understand that you could have done this rather than it does both of them is a three-dimensional behavior however it's kind of hard to draw some black were so perfectly correct the relaxation occurrences does not occur in plain words in three-dimensional space and so one-sided that I missed the time died holds this way at some later time like this 1 the biggest this yes and therefore you have to take a bath remembered as a 3 the problem on this is all the EU there are mathematical descriptions of this call spherical harmonics like treat this the fact that this is three-dimensional and view few remember when we were discussing fluorescence relaxation I said there were some complications in mail this is the same complication arises because the system is three-dimensional images have live with the two-dimensional we will you can study into the system but that's not what we're talking about OK what else can you do what would you like to say I have called and I am going to decompose the motion of the polymer into some sort of normal warrants for example I will say here's in an effect here is another word it's the difference between the tractor from the middle long on the vector from dealing the other those 2 pieces those 2 factors are perpendicular this 1 tells you about the largest-scale motions Paul this 1 tells you about somewhat finer scale all now there are 2 general Sorenstam approaches to how you handle this would go back the theory that if the London Times would it have Chrysler now the Sturm und Montes they calculated Barnes who wanted to highlight her response however back doesn't care about them and what Kerkorian Reisman said is hearing polymer chains and it has a center and rotates annually on also changes internal shape fluctuations but everything with any interest for for example viscosity or an emotion is hidden in the translation and the overall rotation that's right there is another description from Bruce and there is 2nd favorite by examining the case the Rous model does something with which it gets called grouses Sam because about half of what is really browsers and burden both nice models and they decompose the polymer into a set of displacements each perpendicular to 1 exit and I'm not going to get from here however you get out of this theory you say we have a shape of the polymer on the polymer issued to store tends to relax back to equilibrium configurations and the relaxation of these a song of the year well if you have something that relaxes the exponential time what is it's relaxation would like if you have to risk and frequency domain and the answer is that if you have the right to remind him of the and the frequency the behavior His veterans here there is some constant decided by In essence Omega square policy some of the worst in the the universe where I'm skipping the Back details as to Tyson such not the not so called because the important word here Is a long time the high-frequency excuse with which those already in mind as to the well if you look at the high-frequency behavior and by the way if you had a bunch of things that are decaying is eliminated the minus 2 and you catalog they still the case four-legged minus 2 so we follow the same format minus 2 and 5 3 in the OTC however if she look the slopes by actually can't look at them you have to do numerical thing and would have Europe a copy of my book from labels the threat idea of military or is the supplements to the Cambridge in his book I published giving all of the numerical fitting parameters for all of these Kurds I'm showing that for example in 7 -dash 16 there is a towel on the something close to an exponential and each of those has fitting parameters their numbers well I tabulated all the numbers and I have published them so if you're curious what the numbers are you can move up the important issue is that if you look at the slopes of the power loss you see something that is life already minus the there are 123 somebody like that you don't see the correct slope and that tends to say these the symbol rouses entitled models are perhaps not quite doing what you want that I have we have to be very careful on that it's a very simple often if you take a simple model and tweak it very gently so it's really the same model except to fix some minor details it now works perfectly so the fact you don't quite get it right prediction doesn't mean the ball is totally hopeless it means there's an opportunity for theoretical work here but there is there's slightest discrepancy the aware OK this will decompose now
what would happen if you go into concentrated solution these indictments of different models what happens in on the islands in the chain for its shares may be an injury or 2 of which will be that's absolutely correct and so the question is OK entangled What is this going to do to and we can give a general answer as to how systems that show mode behavior 1 the reactor start patrolling and the general statement is you may still have normal mode he called Waterloo the normal loads in the linear combinations of all loans right after the break 2nd the new loads are linear combinations of the old models but at least at 1st the old are pretty close to correct for a more you can always since HMOs are also we just went sideways different frequencies are thoughts you can always decompose the description of the molecular position and these models In well concentration as time goes on view excited only 1 mode is state is the only people that is excited things became just as if you take any stringed instrument and plucked spring you get motives cited the string oscillates and as time goes on you mostly see just the same oscillations sitting there the same frequency however if you have something that is done Palma's entangled the modes yet interact with each other and if you excited long-haul initially you will decay and other modes as time goes on the free the relaxation rates all it changed the relaxation rates typically a change before the mold description starts to get more interest we're not going to go with I point out that you can do this thing and the results OK so let us struggle on Sunday at 17 comes back to 1 the theory that the but following is a trialogue called and the central piece has a dielectric response and to answer dielectric Leonore Arafat is so far as the measurement of Cerveza invisible and we're just looking at the motion the central piece and if you look at the motion of the central piece you see relaxation will use the nominal was flying in the face 7 days after Quality dialect is lost through free from the museum piece like this and then you see another piece in getting on with a long high frequencies and the question is how you interpret this and the answer is I'm not giving my interpretation of the authors say the same faces a Adachi it all again yeah at high frequencies the change in the reordering the rearrange itself announced several these changes is ended and record because the changes preachings changing its shape and so there was a central piece the things were and and vector moves a bit because the changes changing shape and sentimental however this piece is attached to to the WHO ends and the only way you can completely yet this around with high probability Is the whole chain has turned around that how a turn-around will hurt wheels or it could following until the 1st ends here the army melodies you're pointing the way and the and that was all year has now moved down here I'm not telling you how it manages to rotate more flipped hands and as dollars and you can imagine very different physical emotions that gives saying that result and when this is when we go on from here to here with a gun and rotation disciple Fulton Allem pointing in any direction and therefore labeled centerpiece shows something about the senator relaxes and it shows something about whole chain of lakes it data 7 and now we're going to advance pushing on to old eventually we get to the final discussion of what is happening in the system OK and I guess the 1st issue is that would be a sort some arising will stand with what we think will 1st of all we can measure the meetings where and when and why mean square and and life is not the most commonly used characterization of the size of Paul most people will cost about parts of the radius of gyration which is quite yet which is physically in a different number however is what the origin tells you during the fall of oil here is the center of mass here is a vector passed out from the center of mass to monomer and if you average all of these gasses the use of means where everyone will get parties so it gives you a sort of mean square radius the mean square radius and ending and vector was different however is fairly clear of polymer spends a lot of these will grow if the polymer contracts both of these will shrink the both characterizations the size almost there just not the same what we find fedoras Britain polymer concentration is that it's flat for small change in platinum status doldrums but it was solvency change trains will increase the concentration there are people who proposed fraction is a power loss at higher concentrations and 0 at low concentrations the 0 at low concentrations part is not seen to be well-founded and something that says forests where is proportional Midas some constant concentration power that is stretched exponential again that seems to be a reasonable picture of what's happened OK the next changed sides compared to other methods of that during change size and this chapter puts all of them in 1 place you know some of them use very different methods neutrons the might scare OK you can also say there is a characteristic relaxation time for the dielectric relaxation in terms of our proposal like this characteristic relaxation time something like home is the University of the frequency it's not simply 1 of over better there's a frequency range in which things roll over and the inverse effect frequencies time and this is theirs characteristic time and I am not putting in Constance and we can ask what happens to the characteristic line as we increase ,comma concentrating on the job In particular he he goes up there has there's some confidence today there is because it's sort of periods and and then there is the forest where the retail the radius is shrinking as we increase following of so low concentrations is fairly close to the exponential restraint .period but at higher concentrations this longer radius gets smaller and smaller and began to roll over relative concentration and if you put in standard policy static measurement finding that of the mean square size at the end of the year in this case you describe extremely accurately with discriminatory .period "quotation mark what else can you do well if you will find let's see for a few years 0 7 . 19 is nice but did find 7 . but Cameroon needed were going to do with the composition of the data combined warm data into a simpler and simpler forms the front-end honesty is we thought out all told you form I showed in many deal with proper plot Absalon novel primary long on primary and you get something that is coming back and varied in here this a characteristic time talent and how is the inverse of the frequency so we've taken this curve lots and lots of points and we boiled down to 1 relaxation time now that's actually an oversimplification because current is more complicated than that but a characteristic time for many purposes that's quite useful and now we go in and we thought 1st concentration and those are the courage to see in the 7th after 19 what you see is that they're going sometimes he increased with increasing polymer concentration you looking at a lot lot plot I'm lot a lot of plot there aren't really any straight lines sterilized qualified and if you start with 2 points were from 83 points you giving get lots of straight lines but that Saurav misses the point the it's not quite what it but if you just look at the entirety of the data what you see is how there was no reason be some constancy that is the relaxation time increases roughly exponentially with concentration of games of 1st of all I would like to see him in the beginning of what will get to that said so what is happening is you have these relaxation time versus frequency very huge number of measurements of the dielectric response you collapse that occurred to a single mathematical point here which is its characteristic you would keep measuring these personal hold large concentrations getting the it's all very hard work very well but NEC How the relaxation time changes as you change the solution in which you were measuring there and now give to figures Saturday at 20 the president said here Saturday at 9 15 there were 4 of these curves he she has is exponential with salt exponential constant and saddened -dash 20 I'd take the next step pipeline gamble the increase in his courage verses down the molecular weight Apollo and 7 Danish 20 is again a lot a lot of plot not a lot of points less you started here with the humongous numbers dielectric response points in collapsed and far fewer points 1 per sample the collapse of the owner 1 of the sample to 1 purple Paul molecular weight and you're down and out of 4 . 2 5 draft and straight line which camera is proportional and can be and I actually given over over for the fired calls all the or 6 however a reasonable person would say call ahead after you're probably not measuring it more accurately that if you look at points are perfectly on 1 and then you might suppose that if there were more points only 4 points less I might not be in power on all that's a reasonable approximation within the limits of the available measurements and we can finally say talent is proportional to the aid times concentration and is the whole song constant and that is the exponential was the exponential depend on yes this is a less demanding and we have something of the former constantly molecular weight long have concentrations of 1st editions of the event is aimed at the mistake getting stabbed face with myself other characteristics I would retired told the called the elsewhere increases exponentially more concentrated and there is the molecular weight attendance this is actually a tank so that's sort of what we find and you notice we take we've shown phenomenal logically only that we can take a very large number of measurements and we can reduce them to very few points and finally we can reduce them it was single function and the single function tells us how relaxation time is determined by the fall of molecular weight concentration given the small number of points there you really wouldn't want to bet the saxophone and perfect on the next following this excellent on CDC 1st this being a simple exponential increase actually appears fairly accurate OK figure 7 . 21 which is the last thing you share it what about let's step back and assess curves earlier chapter the frequency dependence the dielectric loss from I said there was an early and he's like this will talk about the other was Powell maybe there was some kind of things down here this is all magnitude mindless acts "quotation mark arena at you can find out how big tax is vital in figures 7 . 1 2 1 4 I'm fond acts 1st said a substantial number of different polymers of polymers that are smaller or larger than each other all and there's a bunch of different combinations of polymer insolvent there but if you look at a single set of points of single style will discover their much the fairly smoothly behaved but if you look at all the points at the same time difference in different systems give you different values of exhibition but if I pop back acts for this concentration what I find is a serious things will play like that and they start out by all 1 . 4 and 1st perhaps they increase there too 125 notices a lot spread that measurement and they then head down again and by the time were about to about size concentrations were available for himself for the whole Europe backed down from the wall to wall .period so access concentration dependence and if I give a series of these curves for different values of Conservation Alliance out here ,comma quite parallel to those taxes weekly dependent upon concentration that naturally brings us to the end of the destruction of the chapter of dielectric relaxation this is the real problem so we have discussed dielectric relaxation I have also now given all of you here next homework assignment which you should try to read carefully it's basically another literature search and I've tried to be a bit more precise on what you're supposed to do although I imagine we will discuss it all it's not due for quite some time but we will discuss it next Wednesday you should try to make some progress by the way she wasn't wearing only talk about next chapter 8 and what is the title of Chapter 8 South to future What is the experimental "quotation mark have halted the use of coal haulage so grossly have some clever technical means of reaching in and taking 1 of Polish aims and painting a bright green In suppose we have more powerful than is actually physically possible microscope we can watch how how this polymer moves as time goes on and for starters here is the home of oil and it has a location and if we waiting while still in Brownian motion diffusion at their sermons velocity of particles of systems and just as you get diffusion of sales of food fuel and air solar fire spray perfume in the front of the after a while you would also but that's actually a bit of cheap diffusion is very slow the turbulence please convection of era of the rooms what means the molecules around Wednesday there is no direction here diffusion it's very slow but if you wait awhile Hall of Shame moves and I'm looking forward isolated shame In dilute solutions well if you repeat the experiment lots of times sometimes holds a large distances sometimes a lot but if you repeat the experiment lots of times you can savor displays along 1 of the coordinators taxis the mean squares placed increases linearly in time you can also say the probability of getting some displacement tells text the is proportional to the meeting the finest Texas clear they think about draft comes and the decided to move forward restaurant constantly but the important issue is that the probability of seeing the displacement of exorcism calcium and the width of the Garcia increases linearly in part at large times this summer is very big and there were over he only less than 0 dealt access to the area short time these small this function falls off rapidly and there were short times the scales are not quite correct the important issue is the policy object and have it's always more likely not to move more farmers who many large additions the normalization on these 2 curves is saying this is charming probabilities all this place has to be 1 has end up someplace but the tallest for if you watch football moves supposed-however you go into a non-violent solution of the things that have grown more correct non-violent solution more complicated nonetheless it moves the spoke generally of actually used by about here is a appalled and if you wait a while they actually moved the issue is also users posted the initial time polymers will react around each other like pair of earthworms if you wait a while the 2 polymers moved there in different places in this I'm not going to say is the entanglements that looked like this but the topological interlacing looks like that after a while they go away because the chains away from each other I'm not saying whether those that significant enough just saying they and their theoretical models in which going from here to here is physically extremely and so it's interesting to ask how fast Paula Shane diffuses instructor straight straight-line motion do random walk how healthiest Random Walk imagine John Heard on the Street Solomons as strong as as possible and still able to walk he puts his feet up and asked for a 1st step gratuities and had the same direction but after a while yes that is a drunkards what steps the distance of the status or fixed there's no uniform pacing but somehow he gets away from the Borodin's up someplace else same so where's diffusion the question is how measure OK how we measure for 1 thing we can imagine doing said we will take all the chains then we would have done with a fluorescent material obtained now it will certainly have to laser beams at slightly different angles and we will get an interference pattern the results of 2 laser beams crossing at slightly different angles and all the places that are bright and places delivered the news a really bright terror of laser beams and 1 for defenseless fluorescent molecules really bright area if guests Friday and is no longer fluorescence and so I had destroyed Tanzania's role of and not status of those for now sample again for residences and I measure where there is fluorescence interior is I discovered a short time but fluorescence intensity versus positions but looks like this the actual experimental method for doing this is a little more clever than walking into microscope I am missing experiment details the advice space retired Paul Russo were terrible he uses this technique of the name of the that last summer however what happens this time goes on all the fluorescent lighting molecules here at the ground during in here and because of Brownian motion molecules move back and forth not all of the likelihood that the a polymer molecules here this way almost all of whom there are in the other direction are exactly equal but there are lots of fluorescent molecules here very few left here this week bleach and therefore there all this there is a lot of fluorescent molecules in that direction In this he's as time goes on the concentration gradient the concentration profile the fluorescent molecules decays and eventually the you think well that is actually a measurement of Paul ourselves to use the technique I just described his call for essence relaxations in October but only I worked for it up to you and France gives you the self diffusion of the abundance other techniques which I will get to the next time they give you the same measurement but this class is at an end but


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