17 More Probe Diffusion

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17 More Probe Diffusion
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Lecture 17 - probe diffusion, part the last. George Phillies lectures from his book "Phenomenology of Polymer Solution Dynamics".
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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 17
final discussion of probe diffusion good
morning that will be your last lecture on probed few were going to consider refused particular special cases and sorts of experiments but also problems these of articles moving through ball solutions that will see what information we get out of the match will also stare at least a short length a summary of sorts of experiments that we have looked at and what we get out of so the 1st thing we're going to consider its rotational view that no policy we put into a even as the pro-business sphere we can arrange it in areas to be lowered some sense To take the answer awkward what light impinges on the sphere scattered light is the whole world the intensity of the polarized light because on scattering angle and the orientation of solemn firm orientation of the Serie a with respect to the incident light at the end of the line hiding in between there a
description of the state if the CIA rotates the intensity of the polarized light changes and therefore if we have polarized light polarized light out and monitor the intensity intensity correlation function of the scattered like we can actually measure rotational diffusion in times of war nominally spherical particles in a polymer solution this is being done by several work offers topped the title of the year for example countering who look at spheres formatted also examined by an intermediate school lunch different experiments the much different experiments is useful because you have a system you look at a series of different parameters and by comparing the behavior of the parameters you get out considerably more information than you would out of the sand for parameters being measured for differences what was filed looking at the experiment and what being various concentration of Apollo during the concentration of polymer what was found was the appropriate thing to do television and rotational diffusion coefficient fall but not very much following folderol of booking figure was the it's heaven asked what also alleges that the sedimentation coefficient which was affected considerably more dramatically the probe rotational diffusion coefficients and also allegedly was the viscosity by blocking the inverse of the viscosity fluidity
on the fluidity was part of the solution was much more effective all although there were any of the halt end broke transport of what we can infer from this 1st of all you're seeing here is very transparently milestones Einstein in motion that is the viscosity of the solution macroscopic viscosity is not Germany transport furthermore the sedimentation measurement is what can be called Micro reality measurement that is you have an object you were applying the true external forces to the object you're watching the objects fall through solutions and the apparent viscosity that you can infer from the sedimentation coefficient is not the same as the man who
stopped Wisconsin full by direct mail US similar measurements have been done by any number of other people for for example we have figure on but the race this year .period 9 . 8 billion which looks at Accra Wednesday at virus of virtual tobacco mosaic virus the across the it's a very uniform brought all the tears the molecules are the same size the disadvantage of the team of 2 years and the ability of the biological problems is the charge you have to worry little bit about electrostatic interactions between the probe and environment while you can always have everything on nonetheless what was done was measure all the Oregon and once again on the appropriate while the art of Frazier always found With stretched exponential concentration he essence quality and defuse the on interaction between the always in the probe giving us the decay of the decrease of rotational diffusion coefficient ,comma concentration Fritz I an interesting variation on this attacks together with looked on quality Basil will have assets of formal examination of the rock like all words like he and the other background material however in this case performance fears so you're looking at a broad diffusing through all of us spherical particles that's very clever additional experiment will come back to Spears diffusing 1 we get along to look at all she college fentanyl chapter on college and we're coming to light so what sort of other experiments can we do an extremely important holds Saturn experiment because it is provided by Hurricane Fran I voted to merge reference is that instead of looking at life inspect trusted which measures the relaxation of the spatial for a component of fluctuating components in the concentration on looking at fluorescence relaxation at will after photo bleaching or some similar manner methods which gives you a diffusion amendment but only over fairly long distances will actually look at the particles through a microscope will use modern video technology to measure position versus time of article and we can actually get detailed it's a detailed statistical distribution of vertical position as a series times and therefore we can get details test displacement vectors for power lines our closest TV and from the particle tracking but what we can do is to actually talk about somewhat detail how how particles solution now the limitations at the time I speak I suspect this is going to be obsolete in that case what's the limitation of the technique is that if you want to let her house burglars do you actually have recorded the positions this is done on a large scale in many cases using video technology using video cameras and that if you do this you hit a limitation on their way to find right of a video camera were taking an image of the system but you can't take the image of the the system what 30 times a 2nd 60 100 times a 2nd on the other hand light scattering spectroscopy that article position information going down to the home certainly 50 years and then a 2nd time scale and routinely down from Microsoft still so you there's still some technical limitations but contracting is is really useful because you actually measured directly how particles now there is a historical theoretical basis for this which is 1 of the the ways in which describes vertical motion the logic from equation says he is very simple we have a vertical solution is moving experiences a direct force minus F B which in the original model was the stocks laundry goldfish will come from the problem with that said the particles is is also subject to what is called a brand for the death of 4 staff is not random in the sense there's no physical determination is due to the solvent molecules around the Oracle were interested in we can't see the solvent molecules directly so we don't know what that random force is going to be since we can't see all all molecules who travel from the hole only things can we predict what after 2 years of the sense we can predict what the songs gravitational force on will be for the next year so as far as we can measure directly to predict however it is and we can therefore use the random forced and the British forces to write on the walls and they have the means and made for a brand new part the random force in the lounge of all along has the important feature that provides value failure of the words of 1 side there is a need to no information whatsoever about the value of the forces of of forced fluctuates but the correlation side the forces is approximately 0 From this and a great deal of work described in my other books elementary lectures and statistical mechanics and there is becoming so video lectures on them now being used to from this and this weekend said she leaking calculate how the Oracle and we can calculate the particles displacements will on for all of one-dimensional component of random displacement say displacement along the x-axis probability of song displays the extra during the is proportional to leaders of minus Delta next where over in 1 dimension its according to see that yes well today any event that he wanted his use of calcium Pian del the next now proof that the formalism Gallician relies on 2 pieces and 1 of pieces called the Central Limit Bairam and the central limit theorem says that if you add a marginal random events the distribution of the song of the relevant events the statistical distributions Garcia so I roll won't die the 6 yen 1 2 3 4 5 6 will likely if I take a hundred dice and role there roll and the numbers I get the average idea for 100 diocese 35 is solved .period showing however during 35 350 100 times 3 . 5 however if I look at the distribution of dials the distribution of the song
Under rolls around there's a average 350 at 100 died I get calcium somewhere the other pieces of this which is just as important as the Central Weather is that this is what is known as a mark of process in Marcola of process is a process with no memory so that the velocity of particles all displacement of article over 1 piece at a time and the displacement over the next piece of time and the displacement over the 3rd piece of time all of correlated now obviously a very short time so this is not
Markoff process but over a reasonable time period it's in my book you can show them the behavior from on the way it is a mark of process and therefore you get this galaxy and distribution of displacements 1st time OK now having said that the event he will say Well we have this nice results you can find the result of local furniture horror the national total considerable number of e-mails and burned for a book on light-scattering then shows that well if you have a long way from members of to the displacement distribution tho it is Garcia and therefore light-scattering spectrum and I will write field correlation function here is some constants he used where they average displays that during time he this result is perfectly true for a system in which it was derived mainly a system in which the particle motions already Markoff there's no memory here and in which the direct costs of peripheral he is a highest at the where the slaughtering coefficient .period spheres but now the come from minor technical difficulties with this result the 1st technical difficulty which goes back home To the 1970 is that if you have Brownian particle intellectual but Brownian particle In his motion does not move at a constant speed constant direction its velocity is not constant subfloor is instead Brownian particles move like drug years I will not attend the front this much trouble from what and if you have particle moving within a regular speed through a full of probe and simply driven motion slot is not the correct what the correct form is that both unless graves a significant effort statistical mechanics back the 1970 uses a very nice papers about it you will go forward with the help of aluminum and shower there's a bunch of all the 1st problems might worry all demonstrated if you have a particle little baseball's equations here's what you would of the calculated diffusion coefficient is the same as the diffusion way qualification again assuming Stokes however we have the other of some more technical obstacles the 1st technical obstacle is of course we're talking about complex fluids polymer solutions call solutions my concentrated myself systems you can come up with a very long list of and all the very long list of these have in wiry interest into complex will to welcome and insistently the fluids are Visco last thing the statement that fluids are disco elastic means stocks fell out of plot is possible you could rejigger of Boston s calculation to handle the state of the viscosity is frequency dependent and several other ways things it's going on however the important result is the system has memory if you have a history lesson fluids are thanks to the fluctuation dissipation here we can say we look at what we're calling random wars thanks to the fluctuations dissipation hero we can say program force is some function as some dependence on tousled random force was on and random force another time opportune correlated with each other and thus the wonderful description In my start to worry gee how the clientele is logic on is applicable How can I tell if I a system in which I can use this result and that is all or as opposed to a system in which I have fortunately there is a wonderful answer to this wonderful answer this is used but the thing that I knew that were you resolve its analysis of random motion it's an analysis of random walks the through this sort of the and the important answer is that if you have a Browning and Markelov process if you have a process through which the whole development leads to this result that is the same as the absolute mathematical certainty but the last year I respect the number light scattering spectrum is a single pure exponential if a light-skinned inspector is not a pure exponential then you are looking at something described by the simple logic on equation on this Place the distribution function is not a on simple simple that successive displacements are correlated but she is not determined by the mean square particle displacement and you actually have to know what you're doing someone getting hurt you might ask what do we do to replace along Giovanni equations and answer is there's an exact result was singing Torre fast once a known as the Maurice once fear of that is also covered in great detail in my book elementary lectures statistical mechanics this is an exact results and its house you what happens next course evaluating it makes correctly universal trip but him try announced that she there's this question of what is going on and you have to realize that there is something of an intellectual life in the old class hiding here and people who say Garcia wanted money equation will West on likely to be correct their solitary insects and know what's wrong and followers of the endowment from the extremely experiment works works are the 1st of which is the most favorite after my home said it was offers all the paper as a society is noteworthy is a superb illustration of professional ethics namely I have listened to the names because the paper has to 1st of and there is even a footnote telling people virgin forest authors and equally deserve credit for their incredibly important piece of work and what they did was to particle tracking of Portland for 3 home when 6 months from Sears
and a look in a series of solutions and I started out OK located the experiment were no less looking something like a quarter or more glycerol they also look In solutions of active as solutions of active fashion please captain Paloma rises and makes along threats have indeed if you're trying to work with a lot of problems will will do so under all sorts of different conditions and controlling the polarization the trip and what they actually did was to measure not talk about the manager that displays the distribution at different times now that we're doing this with particle tracking and limitation of were doing it with particle tracking doing computer and I want you to give analysis of images these days is that the alarm the number of measurements you get out is a bit less than you would get out of here were doing Bossier elastic quite scary and some of the there's a certain amount of signal-to-noise question which obviously worked very hard on the important result is that P and Delta with expertise the spheres of protein solutions which is very badly so I don't variations on the endowment tests he is not a Palestinian in Delta well it since we believe that Polish solutions going west and that's not a a big surprise if you understood the underlying theory that would begin immediately obvious results there's absolutely no reason to to expect that was you don't act all the core issue is that Florida has Gallician behavior the Central Limit remote do it for you you also need a system had been Markoff processes its motions in this U.S. OK so we not Garcia this was not the only other experiment to move on I look at this there is also another nice verified said in the Oval Office is looking into the same sort of thing sand and of all you also look to sell the excess where there are a lot of times and what they found the Belgian March 5 Delta next where your roses of power in time and power in Haiti a is less than 1 that is you have won the described as solvent is used to a set in which both and said it's not a Garcia there's no important inside on if you go through the literature you will find bunches of experiments under the title Michael reality where people actually assume that EU Delta expertise calcium I all the techniques which simply assumed ousting behavior in a fundamental way as opposed to saying they're going to assume that there was something quite different doesn't really rely on that but all of the techniques that really rely on the assumption that the Delta next season calcium dulled X on the outcomes of those methods are the invalid because the underlying ground assumption is incorrect maybe patched up well clarity and lot of but now that is categorically said the series of meetings Dolomite Arriola and let's see Procter & collaboration In and who else she said and the a series of other references in the text of what they do if due to the sort of the same name sense to expand and wants to say here is political and it has a displacement Delaware water and we can look at war example Delta wants where the and on the way here and the other is said to have used his heart valves along delve too and if the 2 articles moving we can look at please cross-correlation across correlation is the displacement metaphorical longer times of the displacement of particles from Europe during the time the and and subject this varieties across the huge object these are all the factors the conversation is legitimately and our product has surprised some of the the to in the general case could be described as a prostitute Spencer and hands on the this place between the 2 particles he added the this fall unless the system you might discover there is difference were found now we discussed at some way we can mean square displacement here and therefore we pretend this is diffusion coefficient we can extract from some sort of microscopic stuff we can also going here this is all this is a different diffusion coefficient crossed cancer however the same general analysis that extract from here on other microbes viscosity 1 over the viscosity and then the month Constance and he can extract from each of these Micro viscosity the interest in doing this is that if you go ahead and do this twice well there 2 people there to key features warriors there is a time or frequency it's here that is the apparent microbes viscosity and the Times said the as measure and this corresponds to to the system having some standards In dynamic storage models and the Gold Pride a dynamic lost modules so you have to model I moved both of them and what comes out of this well the 1st thing that comes out and say he's the essence of frequency and viscosity the considerably more precise ways Jack and the information is that this is sort of you what this is new to the area you on over years you to the 2 viscosity these Odai equal to each other the ratio could have a difference which is a factor of 2 factor 3 so that this are city so elastic properties from the central part of the government to particle correlations not thank you also find recent system was studied the 2 horrible promised us that he is something like quite close to the macroscopic viscosity liquid West very interesting Of course there some complications I said that staff Scott I mean
you viscosity measures if you actually get a 3 Armeta of boxes some size and measure fluid flow over distances you see with the naked eye OK needed firm of Crocker and series of others at the core issues they what it's called 2 particles reality and having gone like a reality they infer viscosity that actually did something else so that it's sort of you read the paper very carefully in knowledge that others as they crossed diffusion developed serious crossed the answer and the prosecution intends to track the the policy-making venture which can unseen has reduced crime fighters dynamic interactions between pairs of spheres but there is a power series in 1 over the distance to various powers the OSI intensive recently term others interesting implication of this is to cut back to very late cost so this is the media studies Crocker and any other people on board a library all of there is pretty experiments were going to look at all Michael reality again we're going to look again at the sentimental scale was a wonderful experiment by going to assess what they did was take a long ball so there is a long haul and what they do is to attach to the long ball a bunch of time over the wall for his little particles are attached to various points along the chain and therefore you can see the change where it is and you're taking pictures of you and you can watch the chain moved and 1 of the Beyond the convention center of mass closure we say I don't look at this piece the change and this piece of the chain has emotional component paralleled the character of and perpendicular to the paralleled for and this season the change area piece by the way has parallel component to the perpendicular component costs for perpendicular outpointing completely different ways in different places along the chain of events they are very cleverly test all these speeds I concede course outline of where Cheney is and I haven't found the parallel and perpendicular points in each place along the chain the club and I can now measure a parallel diffusion coefficient and they'd perpendicular diffusion of may actually do experiment
so how going experiment what they were well the 1st thing they found was a very short time technical displacements parallel entered data about the same but if you wait a while and look at significantly longer times the parallel displacements the ran rather than parallel and the perpendicular displacements and somewhat slower than the general displays I should stress the timescales on which these observations you being made are much shorter scale on which this column all of the terms of the rare occasion has escaped from the and moved to look at it sigh over here so we're looking at measurements are still fairly short timescales however what we find is the parallel motion is faster than the perpendicular and this is actually a prediction of models on short timescales you may have global trade motion in it's fairly affects others however another piece of text namely if you look at parallel motion you can extract from the perils of using old used for microbes Wisconsin and the micro viscosity is something like water management larger sold us areas there is a microburst City in there but the polymer on sentiments do not think they are moving through the plains although they think they're moving through something that is quite resistant to the motion when they heard the experiment called on microscopically is an experiment that would be wonderful cheeses computer technology issues if could be carried out in user emotion after very long time and France 5 5 lectures over time discovered that that of the long but didn't seem to have been done on time and Bruce Arena OK let's look at another store and the other experiment we will look at Butler and was developed .period was to look at diffusion the motion In the end a solution that DNA Solutions always almost biotechnology stocks were from polymer physics standpoint there's something very important there are a number of the NAC Europe that brains and they can be quite large this along the largest state welfare was greater than on what times tend to form base there the Raiders all essentially totally modern dispersed and thanks to modern biotechnology value the rain and ,comma the Sharia during exactly wants to get a linear polymer whose molecular weight is identical to call 1 part 5 1 apartment and 6 from probably in certain hydrogen him with something all animals but the rain and these who were exactly the the same molecular weight exceptions no opinion polls as having said that I hope cable we will not do so here my reality in these systems I think concentrations in natural immunity only about 6 fortunately are however what they found Was that microbes of ratings system that related to my staff you many years of elevated concentrations the ratings system was considerably less sophisticated by several people now the reason this is a solid interest is that there are a theoretical treatments of rates it is always possible to find those theoretical treatments for some brilliant but they not yet implied this system because the system is not concentrated but what this city tradition saying is that we hear chains have loads of motion for example translation along the the whole way they're not usefully available during all polymers and therefore the viscosity of the rain solution ought to be considerably larger than the viscosity of the solution only hear chants such behavior has never been there historically when you talked about bringing polymers so there were always objections well the ratings Ramos instead of being pretty picture I've drawn the tangle not and ran so I think apparently is fighting its own tail that students who flew around itself on the could be to have rains there were all sorts of devices you discuss synthetic With biopolymers these objections were in invalid we biopolymers units as a result of the waiters synthesized there essentially 0 and came for or change are all wonderfully monologues 1st personnel no linear chains based in there too furthermore there you can do a lot from my process being the sea rains they found various objects you see rains don't see balls and therefore with greater certainty we can say we actually have a brings polemicist its modest 1st it's not concatenated doesn't have all those nasty criticisms that have been made and this is a legitimate tested the system of the invasion that he wished his staff that he had been taken to the some higher number last experiment it anyway was stable the system were not talk about the agreement were worth to all and we're looking at need for life which is a natural product and we're looking at diffusion of objects through wheat collided then she hears and very odd results come out quite solid and 1 result is that we have station had 10 is the measure of the osha problems through the solution in different parts of solution you can sort out their regions where the properties of the liquid a bit if on 1 hand saying well as a qualitative descriptions about him directly the result regions which are relatively fluent their regions with particle pollution work slowdown Jerusalem said it buy but those of you who were familiar with the pupils of glass and other recent work on glasses may realize that I describing from his solution can be had homogeneous shoot well no it's not and the implication is that you might as well as look at the last piece of the experiment and I say pride they looked at the series concentrations of 150 gram leader the 400 grams of India and 250 grams per liter the delved X displays the distribution function of calcium and on the ground earlier this year will be dealt with varied definitely not GE this system it's a liquid but it's not homogeneous it's the of what we're looking at Kittelson last model which proposes the glasses they occasionally herds because you start forming Harare genius regions which are in some sense vitrified resist both will here's the experiment you're seeing direct OK so much for his work on life but it's a struggle that we have another section In the next section of the paper book we're going to talk about truth life from reality whether 1 by her life reality as opposed to a diffusion and a migrant viscosity from future we were going to experiment with from taking the Saskatchewan we find in the of of foreign after we discovered portable has associated Velocity ft such things as final possibly worse than we velocity all this is a real viscosity measurements in the sense we're actually applying an external force assist OK all watched experiments studying this all example of people on the Camelot what is bound to apply force to the system and this can be done they did something terrible flight work and they will use of motion and they ask OK what happens to for example the means square displacement at long times for what happens displacement of fire appliance forced on and both of these were found that the for a song about the retorted that is a long time these laws so that when they apply force and in response the displacement increases power long time but not immediately and the usually measurements in what you sort of expect from a fluctuation station argument the diffusion experiments show the same behavior enabling him to be a free maybe some power required OK 1 can also series papers but such things as busloads fears that bigger and bigger and bigger there is sometimes hand-waving argument can be made here there is sometimes a hand-waving argument the 4 small spheres you might expect Stokes Einstein's equations fail what a small means means small relative to solve a light scale on specified with oppression have really skiers trip to the really big spheres the food outside looks like being and therefore say they can waivers if you make this big enough you will see stocks I decided that fuses and threatening behavior well that doesn't appear to be the case the experiment is not an issue go large particles removed definitely do not over to my viscosity green metal stocks OK there are also a series of other experiments also put a few names are Guard polish and so there is a series of experiments which Real Michael reality is not what we have the Saskatchewan Oracle forces applied viscosity is inferred and what found his life custody and he is not all the same the sassy measured experimentally and if you look at frequency well that doesn't help OK so what is the importance of the result let's step back a bit you remember at mentioned possible particle with a life of reality in order to fight a radiology and people said Michael viscosity overtime looking correlations among Oracle's was saying this stuff to the America's Cup publicly troops after that that probably well gathered from discussing their next stop :colon area mainly can work on my was tacitly but there's an interesting issue here is who really the source that on the basis of part of the deal Wisconsin Minnesota their real life real reality experiment using pieces about distance sales does not equal command staff resources and therefore the diffusion discussed the 1st moral reckoning you can see the fact that he to be a macroscopic viscosity she was that parliament should provide proper starts at the 3 diffusion might viscosity agree with the real reality experiments made on the same distance scales father is an interesting issues here there is still under investigation .period we don't advance peace original advanced to shelves for the most part this book is not discussed troop jets by Trujillo jail I mean he had a lot users and the long visas are covalently cross-linked so essentially all purposes those are permitted bonds and you have the best work the book does not cover true jails great nonetheless the do look at it a little bit and we can make a few observations about the 1st observation is that true to all time concentrated solution made from jail is a science filter that is true gel really does let small particles through and really just 5 word-for-word schools so they cannot enter on this experiment is real physical results as the basis of Gelber mediation chromatography since I was an undergraduate column more years ago overnight size the there is the result from gels although the real or followers solutions size filters they married church margins small particles to different extents and modestly however particles of all sizes passed on solutions they can test jets for all of small particles their solicitor 5 forget all on how the diffusion coefficient depends of solution properties and you still get they stressed that the exponential stretched exponential has concentration exponent which is slightly less than the 1 that has size exponent which is for the problem which is about three-fifths the EU should realize this all of problems with the small enough to get the holes if you presented a large object its strength was not through OK Tom Morris said experiments this year although this case could be felt as collaborators that went about 20 their day although the least we can talk about the it envelops work and Corey issue as less a 10 mom model how objects move within set and there's 2 sorts of issues and what is looking if you didn't know that there is a concentration dependence and the other is 1 thing look at Bologna for very small particles of the diffusion coefficient when asked what the effect of the system on very small particles and there's a great deal of experimentation .period and the net result of all of this is to say partly by the fact that the actions of is that you have made the interior the cells and the Saudis along brand names and actually used profits salt from all particles and the next thing With the long things are smaller and all of this is to be fair and smaller more American that also have to diffusion but not in the same way the make our matrix national and so this very pretty said experiments says we can construct physical models that are all made of materials we understand and the diffusion of behavioral problems can be shown to be the same as the diffusion behavior within the itself with and sort out of not very beautiful piece of this but the belt buckle now such section of of the chapter which was rejected by the original draft of the manuscript was much longer except in in the United States scrapped and this section we're going to talk about hence the name my girl reality and the reference here he is in the series of experimental methods to assume that I really need to that if we're looking at appropriate solutions to top the light scattering dispatched from all right in front of the correlation found you see that miners and other appears areas mean squared Place for work on time as we have seen going back to the experiments of and as we can see directly neighborly if you look at the system this specter are not pure single exponential this assumption has 1 basic problem is what as resulted experimental Analyses that rely on land now experiment with a few exceptions Our unreliable in their determinations of what's going on now there is some very clever accession 1 of the very clever exceptions it's an experiment for partial it's light-scattering experiment except what was due on was use a diode laser gave us life was laid .period Brett whose correlation length I could see was extremely short that is if I look a lot like that come out of Malaysia series points the light is more or less but not quite monochromatic however Friday look at the faces the series points over a very tiny there is life here tells me the face life here but if I go out any distance of all the phases of life here face life there are independent of each other what's the experiment with consequences that politicos and scaring off foreign if the 2 models are separated by sort of distance the face of life here in the face of life there are independent from each other can and there's no interference there's no way to tell the relative motion articles with 1 exception life is going in through window we have some of part the Treasury post the last and now the Aronoff last service and we have staring off Oracle's family close to the the service close enough that they are within the correlation life politely .period correlation online service and the lights scared by these few particles and the like scared by the window are coherent and you get interference and you can then look at the motion of a few particles are very close the windows so this is very useful for example you may have a basically through the solution don't White solution regular light scattering is disappointing notwithstanding the paradigm coincidence spectroscopy and related that or light scattering spectroscopy is disappointing but the progression technique is theoretical analysis of corporate hour all last year amended his fusion of particles close to window however progression when all very careful to emphasize what they basically they're talking in the future particles Over a very short time in which there are only looking at the lead from this hypothetical exponentially the leading lady near-term behaves the way it's supposed to be really does give you mean square despite all the difficulties arise if you try carry out over this so there is this very pretty experiment it really does these nice things and it works how can they the experiments with passion to all you're limited little limited to happen how far out of time to get to work we have reached the end of the chapter at soldier after except for a summary summary is we have to look at diffusion of problems from policy there has been enormous literature on probes and all the solutions and that enormous literature is mostly on communicating with the so-called micro reality literature based on program here on so as to literature something not talk to each other much of however we're going to be talking about the article probe diffusion literature optical including some of the techniques like particle traps on the 1st point we can say is that if the measure the fusion using lights there and find the source of the cases and was the reality of there also stretched exponential the 2nd behavior and on the green and where there is somber regime which is usually quite limited in which you do not see this behavior but that after you leave the regime behavior emerges on the theory that sort of thing seen this study in detail and hydroxy probable cellulose Is that on page you also get multiple loans that used several relaxation is going on at the same time in the same system system managers to do this is a little less clear is clearly don't do it off United for foreign trade purist whose value is the here and what applied to Eric Balfour who as a function of molecular weight for each fall in light of the waiters concentration independence measure a whole series of concentrations and get out of that number is Calvin and news which corresponds to what molecular weight will be used to from longtime stands for options exulted .period firefighters said 5 over Werder manager at Tuesday fairly nice lines also depends on molecular weight power on the reason I show the deck strand measurements 1st is that historically these were the 1st measurements in which on 1 hand the met the values of Alpha and weren't very noisy and on the other hand in the world hold onto different molecular weights and see red linear behavior here there is also were to be similar behavior in which goes from out of off 6 school same molecular weight range and you see a veteran the parameters have fairly clean all molecular weight has which is why it should have expected given the theory actually met head on OK ,comma another piece USA experiments against Hamburg so I think it will work we will also Alpha against molecular weight these are the probes and polystyrene solve they medicine fairly sure all hours earlier Wyoming and then you have the straight line and waits for was on a straight line all the point the experiment was to test theoretical calculations and there is still 1 of of the reasons theoretical calculation of health is of interest is that for these fears and polymer oils which beaches quite small there are no free parameters in law model actually gives Sonoma out not with fitting for him and 1 of the leaders of the longest of the new plans very satisfactory because it was that direct test of can we calculate interactions between probe molecules and polymer boils and always solutions and the answer was a rare definitely up we can't figure in 1914 by continues this and over for Ron polymers with a wide range of life base if a lot of resistance and yet they take much 1 the of peculiar no way at the bottom of a liar a couple of points where the polymer isn't fair ball violent serial number lines around the diagram for a ball with a well-defined structures and so far lines serial we on this graph we did putting in it's actually molecular weight we plotted as tho it were a threat was random Paul of someone Villanueva molecular weight that he would give us a brand loyal over the size of the essential and those points 6 right on point OK what else to meet you we discussed a lot comparison travels in the work place is the real shelling across and held signs filter I really doesn't know what the total time objects that are bigger rules had a homer solution is not the size of the older its effect on tumbled promptly because someone on the size probes but even if you have a really big particles they can diffuse through polymer solutions we also emphasized the power the 2 "quotation mark the pipe thus is a very complicated story here but we in general finds delightful viscosity is the same as of the text that will almost solutions to through all the way from the promise will fall as a solution to a very small and micro viscosity and The Man from viscosity are pretty much close to each other you're varieties tests of the so-called lingerie ,comma Brundle as picture which was derived for suffered humiliation at the hands of the original authors of this being their people who apply this diffusion her absence is not quite feared original work on unless the original picture before research patient was that this should be solved from minus any concentration of power for all sides to power following the molecular weight power 0 loss on his cereal the salt viscosity solution with us if we want all solution is much more more viscous Water Safety assassinated solutions 50 years or 20 Boise this German concentrated polymers solutions disappears Russo has given a very pretty tests are where and looked at the floor label best friends such part of it various followers solutions the final concluding this term is useful but they didn't get the gold very high viscosity Aidid's top of Europe was heard to say the important piece here as a conclusion 1 way of stress if you take fear of what plans there should be an end to 0 beat Penn State is the resistance of polymer solution particle diffusion sedimentation should be in the head and molecular weight and the basis for their use of hearing home solution and fall fuels varied work now goal is say cut the molecular wave followers and by splitting while it is possible that I will go and suddenly I made holds twice as big by cutting hole there but of polymers are routinely being if I have molecular weight of polymer have clear very small lower Cox there very marginal these hypothesized gaps through which claimed progress and almost none of the guests have called cut the side To and therefore work asked the but In terms of this picture would be expected be independent Paul like very well the probe diffusion is quite sensitive to the matrix molecular weight that was pretty graph that showed helpful of bruises here and we saw quite strong I would like them 5 states working birth all and the reason for it must be his picture of probes as advancing through always solution by looking for gaps is incorrect instead presumably happens in former solutions is the probe was advanced the polymer chains move out of its way to interact with that then move along with probe because the strong hydrodynamic interactions and therefore all the probe vertical followers solution was not look for holes between the changed because chains are anchored to specific spatial coordinates the free will and because the freedom to this pictures simply incorrect but it that's it for today and we have reached the end of Chapter 9 will discuss something else the next lecture


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