15 Even More Probe Diffusion

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15 Even More Probe Diffusion
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30 (Lecture 2 missing)
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Lecture 15 - more on probe diffusion. Lectures are based on my book "Phenomenology of Polymer Solution Dynamics", Cambridge University Press 2011.
Prozessleittechnik Diffusion Hot working Effects unit Grey Geokorona Day Scouting Measurement Polishing Order and disorder (physics) Ship class Northrop Grumman B-2 Spirit Light Energy level Particle Aerodynamics Ship class Relaxation (physics) Polymerlösung Mail (armour) Fusion power Typesetting Structure factor Viscosity Molekülmasse Sunday Year Diffusion Specific weight Concentrator Aerodynamics Sizing Cartridge (firearms) Matrix (printing) Book design Water vapor Last
Prozessleittechnik Quality (business) Scattering Geokorona Scale (map) Scouting Visible spectrum Relative articulation Multiplizität Light Particle Group delay and phase delay Assembly line Zeiterfassung Bird vocalization Limiter Veränderlicher Stern Color charge Linear motor Structure factor Initiator <Steuerungstechnik> Sensor Viscosity Year Single (music) Quantum fluctuation Perturbation theory Autumn Cartridge (firearms) Stomach Mode of transport Morning Cosmic distance ladder Diffusion Hot working Gravel pit Short circuit Crystal structure Relaxation (physics) Spare part Negation Molding (process) Angeregter Zustand Optics Penumbra: Overture Paper Electronic component Faraday cage r-Prozess White Drehmasse Chemical substance Cogeneration Concentrator Microwave Angle of attack Sizing Laser Wind wave Water vapor Model building
Prozessleittechnik Effects unit Scattering Geokorona Scale (map) Visible spectrum Gyrator Light Particle Kette <Zugmittel> Bird vocalization Roll forming Turning Sunrise Engine displacement Tiefdruckgebiet Year Ground station Single (music) Cocktail party effect Quantum fluctuation Perturbation theory Current density Autumn Cartridge (firearms) Mode of transport Book design Noise figure Funkgerät Cosmic distance ladder Diffusion Hot working Schubvektorsteuerung Short circuit Measurement Crystal structure Northrop Grumman B-2 Spirit Relaxation (physics) Spare part Video Forging Leistungsanpassung Material Typesetting Stoneware Ballpoint pen Wolkengattung Presspassung Concentrator Sizing Water vapor Model building Ground (electricity) Firearm Last
Prozessleittechnik Effects unit Geokorona Scale (map) Scouting Group delay and phase delay Kette <Zugmittel> Assault rifle Bird vocalization Solid Crossover (music) Cardinal direction Veränderlicher Stern Solar energy Atmosphere of Earth Viscosity Year Locher Hydrogen atom Crystallization FACTS (newspaper) Monday Series and parallel circuits Book design Noise figure Hot working Elektrostatische Aufladung Grey Pressure vessel Sunlight Measurement Crystal structure Basis (linear algebra) Ship class Alcohol proof Orbital period Month Ion Mail (armour) Blood vessel Ballpoint pen Concentrator Sizing Matrix (printing) Ford Explorer Theodolite Pager Relative dating Miner Water vapor Model building Stock (firearms) Firearm
Hot working Effects unit Emissionsvermögen Measurement Northrop Grumman B-2 Spirit Spring (season) Kette <Zugmittel> Group delay and phase delay Separation process Color charge Typesetting Reaction (physics) Molekülmasse DVD player Year Single (music) FACTS (newspaper) Monday Sizing Autumn Current density Cartridge (firearms) Contactor Friction Rotation Noise figure Water vapor
Noise reduction Alternator Cosmic distance ladder Effects unit Scale (map) Measurement Northrop Grumman B-2 Spirit Assault rifle Kette <Zugmittel> Bird vocalization Temperaturabhängiger Widerstand Turning Wasserwiderstand Strahldivergenz Orbital period Television set Temperature Atmosphere of Earth Linear motor Telephone Audio frequency Typesetting Cylinder head Tiefdruckgebiet Field strength Viscosity Molekülmasse Carriage Tolerance analysis Year Train Chemical substance OLED Concentrator Topflappen Autumn Series and parallel circuits Schwache Lokalisation Plane (tool) Book design Water vapor Model building Last
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 15 more on probe diffusion I'm professor
fillies and this lecture to if you have a discussion of produce few measures experimental studies of Polish solution Dynamics based on measuring the diffusion of rigid objects small or large through polymer solution In our last lecture we discuss the dynamics of small words programs in which we have something that might be all fraction of an animator of hundreds of nanometers across the diffuses through all over solutions as it diffuses we can measure how rapidly and we can determine how the diffusion rate depends on the concentration of the Matrix polymer former surrounding solution however depends on the molecular weight of the matrix polymer and other features today we're going to push on and consider a few other things 1st thing we're going to discuss with Section 9 4 5 during conference I'm not quite sure where re-entered for instance the discussion you could be described as there is this extra phenomenon see on rare occasions it's not clear why you're seeing it it's not clear what it is but they're not it's been seen enough times that we can groove all the observations to get of the starting point he made his future versus concentration and we're doing this for polystyrene spheres of polyethylene oxide water is a smile or a woman's uterus polyethylene oxide water and similar behavior which is what is usually seen for the future of its users occurred looks like this on a long long plot Texas stretched expansion however and we didn't have actually quite discovered the natural order of things and how we work things out if you take particular size of Sears In particular molecular weights polyethylene oxide and since it's not the small ones for the large ones I think it must be some specific chemical properties particularly appalled use that of this year and the right size fear is what you see is what you want that there is fusion of the 1st increases with increasing Paul concentration at certain and then goes down again and get back to about expected the to the effect concentration and she knew what is this all that good question you can see the same phenomenon or something somewhat similar there nice work by war on wall and we you want to the whole thing that was a cross-linked polystyrene spirit polyvinyl level the toluene and what they found was something new will the beautiful day of the deference mainly here is the will occur 5 troops if you get most of their measurements to stretched text but in the mail what certainly see Is this region where the diffusion coefficient heads off for whatever reason and then comes back again and we're talking about our polystyrene spheres that are all seemingly reasonable size and concentration was called natural units units where the intrinsic viscosity has dimensions long over concentrations see a itself about 6 and there is this narrow regime where she things don't work the the way you would have expected give them the question is what are you looking at there are other cases that look like in the 1st of these 2 found for Polly electrolytes just shown to examples for a neutral policy questions how are you seeing this word you see on 1 general explanation has to do with the question of what sort of diffusion coefficients are you looking at you were measuring things with Bosnia last light and if you simply have a single set of diffusing species everything is completely uniform your light-scattering instead were dynamic structural factors that falls just reactive worked on Sunday lot he's a nice straight line you can measure measured slope anywhere you get said answer life is very simple and then correspondence as a general statement to Brownian particles in the water some system with no memory and ,comma solutions so life becomes more complicated and if you look at the relaxation spectra get quite scary you can get several relaxation what information was like scary given about the dismal redraw this and now redraw the place the inspectors on a lot what kind of Moses separating 1st relaxation like that that's sort of what they on an exponential looks like a on 1 long long the I think and others exponential were stretched exponential or something and you have different things happening on different time tritium the reasonable presumption of which is there and the way it has been said is that most of these processes are going on at all times and there were few measures the initial slope of the relaxation is the solved the rate determined by by this festival plus the rate determined by this slower and like if you do what we call cumulative analysis that is ask what is this initial slow slope this rural life in doesn't have to be approximated the straight line from
estimated something fancier than straight line what does that initial slope give us will gives us the average of all of the relaxation rates at waited for how much they can go to Beijing on the other hand if you sit around too long if you look out here to measure the relaxation rates you only see the slowest the fastball his relaxed way now it doesn't mean it's certain that if you waited there could come the particles are no longer In the rap about what it means is the particles have moved far enough that the their positions with respect to the rapid and turned on correlated with their initial positions and therefore even older wrapped processes going on the rapid process quits contributing to the relaxation suspect because this is gone 0 in the process relates the particles starting position the uncorrelated with their initial position at it is sometimes said If you see these fast swallowed their people will truly at the time dependence of the diffusion process and say Oh you're seeing kg and the notion indicated which is currently reviewing possibility is that we have a problem particle it is somehow confined into a region of space where it will spread rapidly but I can't get very far and don't want to move a lot since lost for example how would regional areas they have to say it and how the process is slow to now do have aging if European regions of the some sensible potential energy or dynamically restricted freedom within their overtures over short time you'll see motion within cage and a lot of times will see promotion the slower process in which things hop from cage to cage OK now wants the object gets here he still does have fast motion within its UK but these positions and these positions on correlated and therefore this motion has not reviewed the steps having described kg I would like to emphasize that time and attendance gives you absolutely no evidence as to whether the Caijing interpretations correct question would not it's the kind of so I wouldn't be where I think what happens between here and there essential things that this law of both the slower process was doing this is the slow that is there is a part of the position of the object that state is correlated with its initial position as long as the object of his distracting and only when the object is going bonkers hops does the last piece of its initial position get God OK so that is the question of the reason you don't see anything is that light scattering spectroscopy the singles spectra only gives you information about motion on distance scale notes of Foriest scale by linear distance scale so you're looking at the relaxation of a spatial for a component of the concentration that's why c both Belgium like scary that however if you just look at a single here and measure the spectrum as a function of time which would help experiment is usually don't you are not directly generating any evidence of hot hot indeed if you go back a future out few chapters there's this paper by top leaders was Moto collaborators were they at light scattering and sedimentation sedimentation is intrinsically a long-distance process light-scattering waves what light wavelength distance and what the demonstrators the long-distance motions are faster than slow distance which is sort of negative Cajun themselves OK so we have said at short time you were seeing all of the relaxation is put together white skin and a longtime light-scattering spectra only shows you the slowest relaxation you will sometimes encounter a literature and literature at claims that if you look at the light scattering spectrum and short times and measure the initial slope or whatever you were purely in exclusively seeing the fast-growing that's complete nonsense it's simply not true OK so if the several and is better directly that is the answer section 1 . 6 and 1926 discusses specter with multiple modes now we will come back to discuss multiple mold Spector again when we discussed for optical problems studies hydroxy broke cellulose however there is so many studies of HPC solutions that they're grouped all in their own all after their own section and get to those sectors and we start out studies by Hong bread a and what was done was to say Well we will take solutions of sodium and it's Polly electrolytes and we will put in probes of the problems that were 48 were all polystyrene latex for hematite particles and look at the and what we found was that there were 2 spectral the 2 spectral modes are were both fairly
close to exponentially to be characterized separately in terms of diffusion of but what was observed under various conditions that you can assemble models life can become much more complicated and you can have loads of relaxation of this and once who's really was that that starts look familiar aggressive polyethylene oxide and most emotionally CDs rose only than my and so you have to walls visible the spectrum and the 2 behavior of the 2 worlds is different in different cases do not having said that there is no possible explanation or partial explanations for some of the polyethylene oxide data namely if you have a suspect system was giving you to spectral modes it is possible that under some conditions 1 Lotus under songs conditions as the other remotest armed with a limited more limited anyhow technology that was available in the early 1980 which is 1 the polyethylene oxide it was on all sometimes you basically see this is the problem of the spectrum and sometimes you see this and if you have examined the same system of modern technology you find the 2 molds were present and monitor the other was more prominent OK it was considered too long in advance to some additional work by gravel and Tom Stone and we're looking at polystyrene sultanate's spheres what is the point of sale polystyrene will notice that I Icesave carboxyl later modified polystyrene here's this modified their modified and in the case in question there is hopeful the the White mentions the modifications like this you have to steer it's made of polystyrene polystyrene is not all water-soluble if it were water soluble you for coffee in the years covered in the morning and the company dissolved and the fall of polystyrene I'm necessarily something you want to drink huge quantities of water source upon and the answer is not to get this stuff and water persuaded state here's what you have to do is to charge up the surface and the charge up the surface is usually done by chemical surface modification so for example have the carboxyl late group it's an organic acid group so fully ionized so based on their stomachs manufacturer and I'm never special charge steers and since the spheres are charged there had been a repel each other they're happy to stay in water is a real solution OK so what Brown danced and it was too low and they see the molds again they said things that look like they say except wealth perhaps it was long before but then let's say something they do 2 things the 1st thing they did was to say ,comma she the diffusion coefficient can be used to calculate Michael discusses aid by world is so signs that way but as seems relevant where variables I measuring particle size diffusion goldfish and quantity I calculated from the KMT and 6 5 the quality I calculated from them is the microbe viscosity the of the viscosity that would explain the diffusion coefficient and was found out for these experiments was that the microwave Stasi this long here is the larger of life the quarterbacks discussing and my strongest varsity with corresponded to the festival was clearly less than the viscosity of the solution that is if you have 2 votes there to diffusion coefficients you can infer from them and because you have to diffusion coefficients that you can infer from army you can calculate and Michael viscosity for each 1 and sits at her for Terrell all you get 2 different behaviors for the Micro viscosity on the next thing that they was just saying well we will look at several scattering and because we're looking at several scattering angles the wave of actor Hugh scattering their durable light scattering experiment change no reason that significant that is the thing that you're measuring wants but structures events on the scarier than what is that what is the dynamic structure factors held well we wait what we wait awhile eventually there is fluctuation in the concentration he co-signed historical fluctuations that has a wave vector cute and the wave vectors to corresponds to the scattering of actors scared like now actually these fluctuations go along all the time they has occur simultaneously always factors not just 1 but if you wait for a moment from scattered light is really bright you can correctly inferred that the fluctuation of the correct scaring investors get laid out of laser beams and to two-year detectors that fluctuation must be fairly large and now waiting may ask what happens at later times and on the average you have to do this many times it's with correlation function that but the the size of the fluctuations on the average relaxes back to 0 it doesn't do all the time relaxing back to 0 or could never get it it fluctuates but on the average of you wait for loans when Suarez the fluctuation relaxes back to 0 and the relaxation is
scariest thing good if you change the scattering them you're changing the distance scale over which you watching emotions now since you're looking at a concentration fluctuations that looks like this oracle emotions over distances there significantly less they are this way .period contribute to relaxing the fluctuations of the particles and various different distances but if they start a maximum head off toward the end of their reduced the size of the fluctuation so you're not looking at exactly the motions on a single distance but here there's a distance scale so what happens what happened me in this spirit of nerds who follows the fastball and and what they found was a diffusion coefficient swallowed is independent scattering and that is the proper behavior you get if you have a process that is truly diffuse a single diffusion process will give you will realize that you go through the use of minus the diffusion coefficient used squared the that's single exponential relaxation the relaxation radios used square but he only use clear out test was diffusion coefficient the diffusion coefficient is the same on all distance scale and so what they said is that the swallowed process goes to 0 and then implies the slow process in effect diffuse the fastest followed process however was quite different you know that measures the current diffusion coefficient a different scattering vectors largest gathering that enlarges scattering vector corresponds to a small typical displacement large Hughes shorter distances and what they found was that as they made the case to stay on shorter and shorter particle motion was faster and faster the important issue is that since the saying and shorter distances the particles move more reacted with we're not discussing it diffuses on process here were discussing something really different on the other issue is going back to the slow process is Hugh independence and so she that actually speaks to cater models the reason it speaks to Cajun models it is have the article said doesn't ground in motion by Ferdinand at the age of 2 others part of the FAA hot into another case in his brand of pop pop pop random walk into the slogan if you look at variance shorter distances something should happen to that slow process because short distances the slow process of hot cloud start becoming visibly distressed well that's not what you see what they see as the slow process whatever it is all of this independent room today was charged that's prevalent dumps Dunston and will look at another set of experiments and the experiments don't think of all the notion in excess of experiments is we will look at whole the polymer that will get the 1st foxy then will travel to and material they looked at was fairly high molecular weight and as a result the radius of gyration of all happened to be house of the Indian the question is evidence that those used in the of arms you might say I honestly don't know the shortest form institutional distilled water soluble so it's not just in all believe that a lot of you should remember this analysis all our always the others of water water-soluble but then do crosslinking instead of having a linear chains form blob that is being big big and it ceases to be
soluble in a practical way and now you have a call but this is not cross-linked and what they did was to take also fears of 3 sizes 17 47 they hand what happened there and guess what they have years and years of considerably smaller than the and then on the other hand fears the security of our view well by history they have fears the FAO said it also she's already have 3 sizes of spheres and a comparison diffusion of the 3 sizes of sphere In the same system and you are now comparing the diffusion of objects that are smaller than the polymer molecules are the same size as well margin now that's a perfectly reasonable comparison viewed abstractions Maine you should however noticed the theoretical models saying if you have a polymer solution and it's fairly concentrated you have Long American tangled and once they entangled models as well as a matter of how long they are because the ends don't do very much except for repair work and the interesting distance scale the follows this distance scale CSI and CSI is sort of a sizable hold the ball match and if you say that's true that the interesting comparisons decide between objects of different sizes and the size of the whole of the was much smaller Benedict College and the sort of a little lighter no-balls Marshall Hall of Fame was supposedly have a dilute solution is just off the edge of the Great Neck Face the distance between 10 points can be much larger than a polymer chains because there was this enormous change would only be entangled at 1 point there would be a mesh with Soviet entanglement notion is the lowest concentration which you possibly have and is approximately with radius of change is the same as the distance between the 2 points and also higher concentrations becomes smaller and smaller radius of gyration shrinks much less and that the on interesting land scale and solutions of smaller well having said that they did the experiment and the reason the experiments Peronist chapters spectrum they found were buying mode there's spectra were adequately fed by SSA single exponential work to exponential that is each mode was close to being a pure exponential that said that each mode separately but perhaps being viewed as a use of process on the whole there must be some kind of applications we're not quite seeing not unless they do seem to float now the reason have to worry about saying it's an pure exponential rise and fall of follows 17 logged lost here is the dynamic structure after years of trying this is what I suppose the actual spectral light that home several meaning the relaxation is not pure exponential occurs ran more rapidly fast times and on the 7th floor of lot less rapidly longtime suppose you had a spectrum like that suppose you charging not paying much attention to detail this this was similar to that of the well you could say it's an approximation but there's a problem with the approximation if I just 15 measurements of here and I want vote if I was the commitment the stone you know I don't quite different slow and the pure exponential fit on last year's careful and I'm not saying that they were talking about was not fault showing where there's answer here the hazard is that if you feel on different time scales you get different slopes for the exponential and that's because the exponential somewhat cooperative you could always prostrate line through a set of points it be foolish so straight line his points don't resemble a straight line always brought a straight line and you will get a result and so what happens when they do this will 1st of all what they found was that there were 2 modes and for the small spheres the fastball was dominant for the slow spheres I didn't say their life stories at low concentrations they found the festival was at high concentrations the slows down and so far we've only talked about the intermediate size fears I said that there is no need to upgrade your the other thing I found out it was found the small spheres and and world both slow down you increases the political affairs on all this and the 1st thing I find is that for the small spheres the slowdown over the observed rate of concentration is also a factor of 3 years 6 by being proxy for worst fears figures in the book and you can look at this and for a lot of years the slowdown maybe affair and for the
it's sort of like 300 to 400 per cent more than words hand and so what you're saying is for this songs for small spheres the 2 owns a affected only modestly will actually expected 3 . 6 I'll buy the for the large fears the effect of polymer is vastly more dramatic and there is a crossover regional lenders fears are about the same size as Paul and it really does appear at costs that we have 3 spheres sizes it does appear there is a transition between this sphere of what smaller than the people they have this fear is much larger than the now if you really wanna say that statement saying transition you would really want more than 3 skiers sizes all for the simple reason that you as well is the continuous rollovers the real change from the major classes behavior when asked if he does the rollover actually occur when horrors equaled RG words it's all lies to 1 side or another and if you want some that question would have to use 5 here sizes and that if you're walking like a transparent bullets Carol Stuart skated my PhD students for his doctoral thesis he did this HPC not her boxing methyl cellulose but he the whole once-obscure sizes and he in fact find out exactly what is being acquired by very nice firms Delfino namely there is a behavioral tests through the years small Virginia there is a difference behavioral by astrospheres the other several ways characterizing the size of a polymer molecules so alone you that song spots a severe imprecise as to exactly what called the size of the transition but advanced transition is fairly large encouraged approximately the size of the Paul oil and therefore the solution in my opinion on surprisingly has a long list characteristic blend which is the size of Paul check list finalist who believe models because entanglement models stated the characteristic Wallace landscape was this much shorter length scale side the added that's our problem through OK With me now advance to section 9 points said and I'm going set loss about rooms in solid electrolyte solutions about problems involved Polly electrolyte solutions are something that is not covered very heavily by my book and some minor decided I have to stop someplace or the book will get bigger and bigger publisher only gave me 500 pages and the time required to complete instead of being a fixed date within my lifetime will be divergent and all their finished the book so I had to to stop at some point and I remind think is the son of Oregon the answers folly electrolytes to tolerate the crystal ball there's a lot of all a mail "quotation mark threatened like myself there's small molecules that they form dynamic structures in solution there along and threat life ,comma chains accepted not covalently cross-linked and they can go straight through each other well having sent that through much things we had not cover not last nite briefly mention some of the results that do exist on Polly electrolytes salute systems and I bring out some of the Polly electrolyte results so you know they're there so what do we say about Holly electoral "quotation mark Will the 1st issue is the selected variables of Polly electoral and is as Polly Alaska 1st period we worked on Polly acrylic acid could you call intellectually was working with the indictments relies securities the results of Indonesia the carboxyl acid groups and the mostly not neutralized will on from spontaneously ionized but what you could do was on the basis of the systems and now you have time on their arms on changes have sodium ion solely by Russell and guess what amount neutralized Polly electoral well much space deal with there is presented neutralization determines what fraction of those groups church also you salt concentrations to by its Ionic Strength eyes which for monovalent ions is simply warily solution we can go on more complications the Polish electrolytes and the extra variables and Hammond said the extra variables are all sorts of experiments you name OK for example and we will take and we conceded Monday that I think we can manage to diffusion coefficients were looking at polystyrene spheres in a partly
neutralized Polly acrylic acid on this 1 happens to be 60 per cent was not a nice round number is a virus called correctly 600 or slightly more all the time and we measure the diffusion coefficient of skiers as the at Salt the saloon and so we start the Delaware assault vessel that may say Gee that's symbolism no it's actually quite has the reasons quite have Water ionizes a bit and so you really can never get lessons in water about 10 minus 7 Moeller ions because the water furthermore water absorbs carbon dioxide from the year unless you really rigorous about dealing with the issues and therefore the people of pH water if you actually look at these conditions is more like 5 meaning you have something like 10 to the minus 5 solar hydrogen ions and other groups of people and since our last year extremely careful in your work I think it's very hard to avoid introducing at least traces of small and therefore if you want to know what's going on the experimental processes to be shortened these tiny amounts of salt sodium fluoride as you or I would ever get the minus-3 more attendance miners formula and then work probably closer to know what's going on in solution not assets I will 0 Weeden anything and as we increase the amount sold well it is 0 hole concentration is of polymer concentration changing the salt concentration because holds nothing but it hires out salt concentrations with increasing ionic strength was 1st flattened out and applies to you increase the US salt concentration the polymer is less and less able to recharge the motion spheres why West you can come up with all sorts of explanations are she added salt polymer is less rigid you added salt to the electrostatic interactions between the followers of the sphere of weekend you can come up with all sorts of explorations notice started to get very complicated you can also look at Stoke science I'm being here England there are other diffusion coefficient of as many as fast as you can so you do what you have and what if the stock's Einstein equation work this number would stay long as you run out of concentrations will increase the salt concentration that's not what I In fact what happens is you have a lot of stuff outside society in behavior and the viscosity goes on the diffusion coefficient goes down but the matrix Paula is more effective than in recent viscosity than it is to charged you and this number is larger than other systems works less than what the statement it's larger than what has the attractive features we cannot claim holds just the Spears a irrigating the stuff sticking the spheres that given effective alongside not so as we proceed we see nonstop signing behavior and we well the ways to make the the monster of Stiliyan behaviors are less and the answer is that there is no longer attends Torres wanted doesn't get there is to make the spheres larger if you make the Ionic Strength Florida or for that matter if you weaken the Volley electrolyte effect by all retailers in the procession neutralization if you do any of these things for all of the degree of nonstop outside signing behavior goes back there is not a theoretical he said and the theoretical pieces the people will climb up the play in the final literature itself but to you get nonstop sun sign and date your problem size is less than a month less than all of the characteristic Langston solution however if the problems are they the claim is that you want to get those signing and behavior well that's very nice but if you believe that I achieved you sees fears and those traveling nonstop signed signing behavior the spheres must be smaller scale how they were in serious really name experiment there were a series of size the years from 2001 until you 655 down the years have diameter and based on measurements since we he announced outside signing and behavior except perhaps for the largest in the longest wide-scale the solution must be greater than on the air 300 managers certainly there must be greater 50 in an area the grave 384 let's very long length scale that's not what you would necessarily have expected but that's in fact what's there today In that figure I the fear is again working for myself and its work
with the crying out for on this figure if I recall tonight there is a lot the area the versus seeking but if you look at the figures yes it's a son-in-law it's a linear is a lot lot will get you realize the doesn't change very much to have a lot points and pointed to concentrated on finding what is very clearly the initial assault and in some cases a simple expert at Salomon plot a simple exponential slope is inadequate in some cases a linear slowed fate was inadequate and we worked very hard we use fears size said there is a war and finally called correctly 95 million years the measurements you see hard for to home sizes of polystyrene sold today we had a fair amount of salt and included several molecular weights of polystyrene solvent the question is why did we worked so hard the initial slope which is what we did we determined the leading Lemierre affected areas polymer and how it slows down all approach you the reason we did this isn't there was a theoretical model type off too To based on current Reisman picture sustainable change and what it says is there is no clear we are invited into solution 1 final leading slowly is Diallo's was so here is a polymer chain this year moves and as the spirit moves collagen guest response but somewhat constrained you can move could translate so it has some translations Bigelow Rosen decided the chain is closer to the near this is so we can rotate it has some rotation that will let go through with perpendicular lack and we can describe chain Wallace approximation as a sort of a bailout frictional beads that translates rodents but we cannot calculate the behind his idea in reaction back and forth between this year and and we can therefore calculate quantitatively how effective this chain is slowing down the and the kind of this was to see what can we do the calculation of this calculation work and calculate the direct calculation and up with a single free parameter there's way of dealing with the government didn't release but the point is we could actually calculate the slopes and we get the right answer the fact that you have favorite the theoretical model that this spring will important theoretical model test because the test at the hydrodynamic interaction theory and it works Monday you would find sometimes it's a story the late OK let's step ahead again and the steps that India has to say there is something called sold players walked quietly other players sold all along supposedly all we have stakes of the system in which his company ,comma was going to default injuries drawing in here comes another piece in the 2 more in the last direct contact yes and you might ask does this fall will 1st have another piece of Paula Correia was neighbor where is reserved preferred this is always apart from each other and against solvent molecules strangers it is an absolutely must have 1 of the other is a thermodynamic preferences ,comma Act and the net result is if the following changed preferred to be next to each other the polymer oil stays fairly Compaq if Parliament prefers to be on in solvent will you have different pieces of polymer this you have to push apart from each other so they don't fall into each other's much and suddenly the Home oil gets larger and if we have a solid we choose our solvent we can hang out with called good solvent emissions ,comma refers to see neighboring molecules the soul we can ask what is called a fatal also in which there is sort of indifference and we can also have a poor result an extreme example of former solvent behavior approaching molecules protein molecules to and neatly folded and have particular groups on the outside and our lumps because proteins view water is a very poor soul and so there .period tightly and they fold up tightly so that all the aliphatic groups hydrocarbons tried to hide on the inside of the apology sticking out all demands and the group some of Poland's the carboxyl gasses groups the amid Ameen groups that charged sit on the outside of the charge and so polymer charges on the outside with tries to tend to use a little more like oil on the inside and understand at all and this is what I call molecules a stable because water is a very were sold out the GAO Pop proteins soluble in water yet there's still some because they this but it's still causal effect OK so we
asked what happens if we measured diffusion coefficient because of the concentration and we don't use take sentiment Paula and we put it into 2 different salts well the gazetted 2 sets of experiments both the book and what what approach is to change the chemical identity of the soul and if we do that we see that made us all behavior we see good sold behavior and the diffusion coefficient in the face solvent just falls next stretch as a pure exponential the finest health was seen as something close to 1 and the solvent you the latest helpless you Yanji at high concentrations throughout Europe and concentration with various solvents slows down and told them to effectively political assault both rare called on later sold slows things down more often now there's another way you can change sold conditions without having to change the solvable the alternative ways to do things that instead of changing the soul of this change the temperature because there are systems that approach being good solvents at 1 temperature but if you change the temperature you approaches data .period and the faded temperature there's different behavior and those for experiments were done by Delphine formerly and once again In the various systems you see here something it's sort of like a straight line as integrated systems using something this sort of like this and all want what's occurring over the answer is you have different good faded and for all of this period we were the 1st appeared enthusiastic Cheney we found the solution we found a prediction actually made by my model of polymer dynamics and you see exactly what you expect to see and I realized but if you look at the alternative models all models we found actually show the same predictions on this very pretty experiment doesn't really tell you anything except that usually in some sense models agree with the last thing on this stuff the 2 carriages to there was a period in the fall Lake Haiti's early nineties grand go around giving speeches on probe future and what you saw what appeared to imply about Paula dynamics and so I will go here there's someplace else I give my remarks and someone would stand up and complained that I had not reduced by measurements of relative to to the glass temperature out now hiding behind this not all innocent question is a very complicated pieces spirit theoretical issues with a piece of the all of tourism policy of tolerance would and I represent and always looking like for all that the rate at which the all movie is determined by direct coefficient With the resistance to motion of the individual would be that's the same as the stock-swap radical vision but it refers not to the whole chain but to build peace now if you work in polymer melts the issue is that she as you change the temperature I what were there during coefficient of the individual polymer beads slows down or increases the direct television goes down at all and as you change the temperature therefore hold dynamics of the system changes on scale not because something particularly is happening to the whole training most of the drag coefficient of the individual pieces change their careers on hold experimental protocols signed temperature it would reduction the notion I'm temperature the reduction is that you can change the time scale on which things are happening by changing the temperature and therefore you can do what appears to be a measurement of over a very wide range of frequencies response frequencies by doing the measurement over a much narrower range and doing it over a series of temperatures and at each temperature on the same behavior occurs at different frequencies and therefore by changing the frequency the temperature you can compress all of these behaviors that you actually look at the experimentally on relatively narrow frequency all this time temperatures that not housed time temperature dependence "quotation mark were probably future the answer is that on the strength of the nation and said that it was a very vague question was detailed analysis exponentially on the concentration and therefore I changed the concentration was changing the drag coefficient aware what this here I want to tell you you think so the properties the head of how easily beats and there was this the resistance to foreign and local offices of function of temperature and if I thought this is a function of temperature what handled that the off the viscosity increases that
increases very rapidly in the eventually I get something called last time picture I just promise for Apollo will and notion is that is how all he approaches his temperature he she will last temperature viscosity sort of diverges now it doesn't really refers to the viscosity it has worked the times the viscosity chaos when himself to melt it for it's all it's practically but not quite solid that's the question if you look at large numbers of behaviors in the AD variable team minus the the distance from the glass and if you want to compare how different polymeric melts for behaving the sensible comparison is not compared to the same temperature but at the same temperature distance away from the glass Tennessee now also being and you think maybe what normalized like this because the systems that have very low glass temperatures and systems that are very kind Alaska but that is the last temperature right yeah the notion of home care From ,comma solutions is that we look at 1 D which is sort of like viscosity and we look there is constant polymer concentration was over these to invest according to the nearest phone call asking themselves said that is eventually things don't move or something else and therefore I ought to reduce relative to this the so far only when 1 this fair and what we say is well only reduced relative to last the answer is we don't want to the a series of 10 at a series of temperatures and the reason we will do this in a series of temperatures fall this picture here actually leads to something called for all the way along the way and says that these should go ahead as long as these 0 and then there's a temperature teaches basic diffusion coefficients scale and that there is an easier minus some constant the constant Over here minus the you know is the same has the features we probably lost sight of the scientist costs not meaningful because it sign but the issue is this attempt to bring the blast that this factor becomes extremely large and there were all the minus sign here and therefore this summer because large and therefore the temperature goes to 0 as you approach the question well if I'm doing this and polymer solutions the plane is that each concentration because the cheese a function pot holders as I changed the the policy concentration and changing the glass temperature and therefore instead of quoting everything at the same temperature I should follow all of my measurements of saying the minus G OK so someplace I should establish the chief these solutions and if I "quotation mark measurements end if I called measurements at different concentrations I should also be at the same time the comparing measurements at different temperatures rather than at the same temperature which is what I do other analysts equation has features the prediction as how the should be handled temperature doesn't there is however no prediction how the should depend on parents namely seizure if we compare the With the over a lot of solid we should get a straight line yes it occasionally In the 1st half of the American Indian a series of beverages and effectiveness this you discover that teaching is extremely low light minus 100 centigrade that's not physical temperature cost water freezes however we felt that attempting this a series of different polymer concentrations you asked how does the current TGV whether you believe this makes any sense about depending on temperature and the answer is that he is independent polymer concentrate and therefore believe that you were supposed to reduce relative to the well we did the experiment many answers he she is the same at all concentrations contrary to what was being said and therefore the reduction relative to each he wouldn't do well the 2nd that is well within the borders of TO it is so yes an apology the Israeli air and sea over a but the it this is made up of the solution working the solvent doesn't really matter which considers director In addition of curvature of the year well candidature slightly larger than scary .period so you could say there is little curvature which by the way is independent of molecular weight and the best we can say is very quite good approximation all the just scales of temperature over solutions linearly and there's no sign of any deviation from linearity all maybe there's a slight cited sort of 1 or 2 per cent effect your measurements are accurate to update their long traders soaring quite you were leaving the heard our data claimed that you're seeing a deviation from what stokes Einstein tell you expect from the temperature dependence so that statutory however we were challenged to reduction relative to blast temperature and what we show was at the relevant question nature of these experimental measurements is independent from Paul concentration and since its independence from polymer concentration the reduction relatives of glass character doesn't do well and we can also say are was the dependence on solving viscosity with temperature dependence and the answer is the is linear and TO AID solvent and therefore any hydrodynamic picture in patients as the sole viscosity controls that it works just fine so that's it for temperature we analogy in today's lecture


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