16 Yet More Probe Diffusion
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Title 
16 Yet More Probe Diffusion

Title of Series  
Part Number 
16

Number of Parts 
30 (Lecture 2 missing)

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License 
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
DOI  
Publisher 
Phillies, George

Release Date 
2012

Language 
English

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Subject Area  
Abstract 
Lecture 16  yet more on probe diffusion. George Phillies lectures on polymer dynamics from his book "Phenomenology of Polymer Solution Dynamics".

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Computer animation
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classes in polymer dynamic based on
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George Phillies book phenomenology of polymer solution dynamics Cambridge University Press 2011
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ends today this lecture E is lectures 16
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even more on probe diffusion I
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professor felonies and today I'm going to continue our discussion on optical produced Buchanan's followers we began with section 9 20 .period text which discusses specifically the very extensive series of studies of optical properties uterine hydroxy program selling books now there are several reasons why PCs interests of warning is that if you take age PC and 125 degrees centigrade in water which is good solvent and has something like 1 month as you approach was at least a pseudo very .period there is a distinct change in the solubility of material and other and other properties has been studied for example by Paul Russo about the reason we got into it originally was quite different namely the we started off doing what we're supposed to be straightforward studies to measure the diffusion of probes of different sizes will measure the viscosity of the solution we will look for Mount Stokes signing in the case and the fountain of knowledge and the anomalies as follows years of viscosity here's a concentration and here's stretched exponential concentration dependence as we saw the viscosity jacket that is the case here you most commonly find always at the time that we without this was since we don't turnover of measurements and some literature this is what you always solved but it's not like you always see instead urinalysis stretched exponential at about this point there's crossover and cross over to fight cleverly plotted this is locked in a long sea this was a power law and see some of that Europe together you the Elvis C do we hear stretched exponential concentration dependence all here we have power concentration there is a crossover of Carol and Quinlan was in my laboratory extremely extensive careful measurements of the shape of their fervor and particularly crossover .period lots and lots of ways and what we were able to do was conveyed to the measurement of lots and lots of points group neighboring groups of all 5 or 7 points to a linear quite erratic program gives you slightly less noisy data and you could get a slow well you can get the log data the whole city all along and what we found was the salt that's worth solve this curve is contained there is perhaps a little lot here and we want we didn't pursue waiting any more carefully but the important issues of the slope is at least very nearly continuous curves are very nearly continuous there is no crossover region whatsoever in which neither set of measurements plots there's just nothing there all to cheetahs some experimental and not accuracy so we have this procedure described this as a transition a solution Light is the solution .period region Melville life transition now we could have given solid name but we carefully chosen names that did not refer any of models were out of literature because we were making no claim that it was a transition of a particular sort predicted by particular theoretical models we also measured the intrinsic viscosity which is sort essentially linear slope viscosity versus concentration at all and this transition per se there concentration of natural movements about 4 as we saw on viscosity chapter tho you can find this transition perfectly respectable number of systems is not a freak due to the particular chemical nature of hydroxy probable cellulose however in different systems the transition occurs at a very different concentrations including C 3 5 Sierra fade hydroxy probable cellulose is a source of particular interest for the excellent reasons that the transition occurs at very low
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concentrations when the systems on very business and therefore the relatively easy to work will happen said we saw this transition and we were able to play this demonstrating continuity well there was some controversy as to whether it was a real problem and there were people who suggest loses some artifacts perfect known .period should fairly standard curves and power along a lot lot lot always gives you straight line History lined up in a stretched exponential all on a power loss lot of thought always gives you a smooth curve of nonzero curvature in straight line at least within experiment with accuracy have the highest this viscosity is memories of life we got up to she got up to 3 times as there were people were saying Well are you seeing Sheriff years instruments etc. etc. at the top end of the curve the times through the capillary discovered despite using the words words ,comma we find commercially the Florentines were for 5 hours so she could arrive early get everything set up be able to come back for lunch and then watch the experiment very successful nonetheless there were a bunch of people who did object to this and so we started doing probe diffusion indices and flying 129 dissipated .period out we actually do not the study a sea water and that was a great help because there were no longer things that have been filed in that some minor work all interesting data which was additional evidence that she the some funny here is decidedly in the and Jameson and what they did was put probe particles into hydroxy probable cellulose solutions and measured diffusion coefficient versus polymer concentration Our and 1 thing they deservedly others on victims was nonstop Science Society and behavior in the sense of probes diffuse faster relative to the solution viscosity involved a solution but fused relative to the viscosity of water water but they found something else something which previously we didn't see when we look at at our city which is at least a ridiculous said system B. versus concentration there was 1st a rather narrow actually quite narrow regions in which not much of anything happen and then Beyond that now region you very stretched exponential in concentration but there was this general and novelists region that's 1 of the several anomalies see probably confusion along with 3 entrance on case the only thing that Is the demonstrate there will sentences science programs as you increase the size of a pro particles as you may probe Oracle's larger and larger and calculated for each proposed the microbicide a city that is the current viscosity being satisfied the viscosity is calculated from the size of the program diffusion coefficient if you measure a you in these systems as you know a lot of trouble like proper city increased you may recall we look to other systems in which the opposite behavior and I truthfully do not have a complete explanation of why it's she not determined by the probe size but apparently it is the other thing that demonstrated when they also acknowledges is favors by Paul moved from of the graduate students was that if you have always said that this year's a safe you don't do anything the extensive survive and they activists however if you an assistant cases reacted may use tried that's 1 of which is a non ionic surfactants that is is a material which has a water soluble in water insoluble pieces and is electrically neutral if you can try to x 100 some modest concentrations you suppress Apollo binding the surfactants sticks to polystyrene spheres and states more firmly than the polymer
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does so you can suppress the poll OK so we can those results and now we skip ahead we say we're going to start studying this system and ordered discuss hearings start studying the system I have to take a flight to work in the tour involves factory current affairs now the 1st issue was this falls were doing light scattering spent trusted me what do we actually measured we send laser beams we have lot scattered out some directions the incident laser beam has a laidback incident scattered wave after case final what may have been to of is this visits Day is complied fully with land land being white wavelengths all and there's a scattering them gave final minus neutral in this case the virtue of K final minus the initials but this is the scariest vector it's the prevalence to waive the final minus the initial for this picture it's this way and the minds of drawing lines of constant faces the sensitive 5 loaded a "quotation mark a at end of our time finding "quotation mark wave in the system I'm not reducing income sign away I'm not compressing the particles I'm not pushing the particles along this is a mathematical cosigned with and I can then ask it's we're looking at 848 transform the density of frozen solution we no answer what the spatial
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components Aso K of the particles and solutions so there is a
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sufficient foreign component and I've been defined all use complex exponential says that "quotation mark something that gives me the scattering crosssection of particles and say after all they have scared away and there's something and but they're all the same selection factor is that last year really is there no farther their competitors in eye and got time there's something called for the position of all the pros and the scattering Volume III and there is a position of each probe and this is the case spatial for a component of the concentration of now if you actually do this experiment leaders some interesting complications for example were saddened this laser beams through the cell particles may all be equally good scattering .period but if you
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have a laser beam it has an intensity profiles left to right in made the naked eye to shine on wall quite stressed the uniform of light but in general is a case that a laser beam hasn't fallacy in intensity profile its brightest in the middle and then it gets to the sides of those fall as a result we are actually waiting all the articles the same way and there a very nice analysis right after all adviser George Benedict for example schools at all very carefully all of these questions and we can talk about this stuff and it's good OK well you know these particles of Brian particles and solutions so more already and therefore case station for a component of the concentration all the stations for a component party dependent on time and if I plot holders will always support the real component what they a function of time this season as a acts is random .period around ran very well but the Ramadan has feature and the future is as follows the problems the way the call it was gathering intensity particularly March like this 1 or this this is so far was the start of each of those moments and recorded what happened at later times given the 1st started on the scared life is very bright after all that's what happens when case let's face it when they get longer and longer time and this the 1st curve at a different time and so forth and if we get a really bomb but I say look for this practice I have heard because this is the 1st allaround but I'm saying the average I out of here now what I actually do take the average so that instead of saying will just wait for these offenses here this 1 failure instead of doing their I calculate what is called the intensity intensity correlation involved and so I wait will look at every single possible starters moment and we will wait every single started moment by tolerate light is the fun of it careful readers will notice I am skating over to form part of you do not critical and a light is particularly dear well here's the average the intensity minus the average intensity is found negative numbers that lives this verifiable applied by starting number minus the energy density that closes curve so tributes and positive way net result of all this discussion
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I've captained measured using light scattering suspect trusted me after I skip over some substantial details dash measure 88 0 T I've been measured time correlation involved in the constant for the case station for component concentration this object to polls he warned and function of a yeah next year it's function of time although it is not actually exactly what you measure directly experimentally experimental invasion of measuring square this happens stretch of from the other nite results this you're measuring directly Al concentration relaxes in time notice this object is only a function of time difference between 1st measurements on secondment from and that's because you're looking at an equilibrium system which is Will the subject this time is that it's a question what signed that's how we will find out well when the simplest analysis is said say these are all large along the way Asian behaving particles follow the logic on the way to do it Brownian motion and if you believe that you would think he warned of a unique by plane and offers replaced OK with you humans same variables it's going to be the reason minus the a square feet you could also say for Browning and particles in with with no memory meaning Water Street closed this would be easy minus flair next clearer the police have a duty to and always claiming a regiment of means square particles displays now burying danger that In the process what I just show you which you can find burning cross beautiful applies to particles in liquid that has no matter how great a label that is not sole lasting for example it applies to things that are not polymer solution there is a very simple test known use their own and those of their own tells you where is he in history that is the equation is true if this is true there is a lot law versus from tendencies straight line if you don't the straight line this result but recently published the correct result general result replaces and instead Texas where you you had enough of this very complicated although only which involves told even moments of displaced distribution Peter now you might ask how how much we have to away modest 1st fears water from his former and the answer is the series of fighters 1st European mixture of polystyrene series sizes so that the spectrum is less than that fuels this warm already gives you totally Wakil answers with means where displaced due the people I have warrant it's not an exponential decay we have occurred while this year experiment was all over and we would like to analyze current and the strike and reduces measurement the dynamic structure too few parameters so what do we do while 1 of his decisions almost straight line and right How would you describe it almost straight line will as you and has an initial and as a 1 that I firmly ruled that ties your power series and you are measuring areas of the world for sent chunk of this works very nicely however you run into a problem the problem did not exist 30 years ago with court the measurement schemes area because the surveillance schemes period you only covered bowl 2 orders of magnitude tea with modern instruments of the color of the Warriors satirist management time history the problem is the electorate it does this and since takes plus infinity doesn't work at large ,comma values and say we will be this fight on putting in lots of lots of terms and of course is the on Taylor series convergence with know this method works but may not terms that means to alternative to I Barbara was saying we want you to the other 2
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there is we will eventually also a power series insists that the lead term really is an exponential and we will use these things described deviation from simple exponential all of this works much better because the exponential always dominates all and therefore you can be sure is that those voters 0 alongside so the basic correct behavior has been stopped now there is 1 minor complication if you're reading this this straight to loosen curve you can use linear least squares in the face of course you have to be careful because when came along river of function during our function and the air all of the Arab farmers in absolute size from about the same old awaited her but when you take the logarithm of the function so Her looks like a straight line you work the size of the year award and he must use this point is not mentioned in any text this very important issue due functional manipulation of data prior to taking yes you should realize who worked here worsening after weighted least squares and my thanks to the hard work of 1 of the major natural she 40 years now by the way do crack where to win this is well understood your alternative however is same the actual data points the Arab words on the data points either all the same size good 1st approximation or not quite the same size and we can calculate what they are and we moved nonlinear least squares that stretch and parameter and the nonlinear swears they needed was based on the simplex I brief pause but there are 2 completely unrelated groups of mathematical studies based on a curve fitting using the simplex algorithm and 1 is linear fitting very large linear matrices that goes back to the lorries and the other is functional parameter optimization it's a completely different approach but hiding in the middle is something called a simplex which is a mathematical objects and so we can do this and we can extract parameters let's paradise to great extract parameters and the questions and which parameters you extract instruments there's another Janise tries to shirk out work extremely well the other guys choice is based on saying was looking at a long long long want the truth launch the annexes carrots that looks like their positions you actually find little more like this and they often have later relaxation now vessel limits imposed by was elastic white skin and limited posed by causing elastic like scary is a light scaring spectrum does not contain a lot of independent free parameters that because basically looks like a decaying exponential knows what is called the old clothes however :colon back some decades I didn't set of numerical simulations of the ESD question from any independent free parameters lightscattering spectrum have so we generated various sorts of spectral mixtures and this and that the only thing and we said we will have additional correlated has 128 million EUR space channels war 250 lost space channels of channels out here forever part of the year what state the length of the part well that's not say we have put reasonable corrections because all the channels saved with medicine must reveal the most he said and there is no BS luckily alone will human once it's as good as any other things proceed and we will it fit to 2 2 you know was thinking what reaction time were 3 Cumulus working alliance and eventually we have fixed the spectrum within the city lawyers rate was 2 1 got description of respect within the signaltonoise ratio you have extracted all of the information that is hiding in any will use a certain number of parameters to do so now maybe you have a spectrum from that looks like and if you were very clever turns out there is specific functional form but only has 2 parameters for bottled water parameter that this is weird curve because you have outside information but if you have no outside information if you must use the general thing for all you can determine how many distinct parameters are in there the answer is well can how wide spectrum is because of the musical noise ratio is as a practical matter all signaltonoise ratio 1 thousands and thousands are about as good as you can get its digital you can get much better than analog mentions all Weiss the signaltonoise ratio there is no lights on his her there is a signal which is the amplitude it's 0 the same lights ratio is the ratio of the template to 0 2 the amount wiggle and with this sort of Red Lodge signaltonoise ratio and especially has lots of features that
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are well spread out me profit feature every 2 workers many of you will pull out of 6 to 8 parameters if you work hard and you cannot take parameters the rights and has all the parameters there are now what is the importance of saying only 6 3 8 may be worth regions of the state brain suppose you hear some spectral fitting at the Andean reports 20 parameters gardens 50 parameters you can be sure of 1 thing Muslims parameters are totally not our total nonsense the parameters are all correlated with each other
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and the number of independent parameters in measurement is the same Cesar A. that I found using cumulus and analysts you cannot do better than that and that its report more parameters of this well you can't we would say that's just the way things are OK so I thought well functional Williams of well what the answers was a stretched exponential in time and in some cases when you distraction as source those that if you have 2 of these the severity of samples that prior to the meeting their private you choose your own parameterization us stretched exponential analysis since that the interceptors sort off by itself there effectively 1 2 3 4 5 parameters the soul of the students on constraints in India and all the rest of so next 5 parameters you have 3rd stretched exponential 80 parameters even that 3 balls were separated out of 6 to 7 hours wanted to which in fact they are in some cases so we actually were able to do spectral lines that are and what happened when it did so well I suppose the 1st thing is asked what these parameters to of hitting here you could defining characteristic time and the characteristics of Powell it's something like favorite of mine has told me there is instead parameterize and things like this to program arises the minus the you'll have to pay if there's a time and it really does have a right to units of time and if you do the math discovered the data beta like this and so there's some sort of characteristic times describes the relaxation what they said was slogans is this strike the way in a certain sense that is to the is long this is a simple accident and I'll send a lot lot I have straight 1 year's data is not lost the current deviates from a straight line and they bail is less than Wall of deviation from his life back data greater than all of the deviations life back we usually as I recall we almost never saw beta graded on and what you're saying is that this curve in the boss transforms his exponential and beta telling you what range of exponential Studio representation come their discussion of the parameters to Friday asked why don't you Austrians for respect the answer is class transforms our poems small amounts of Norway's lead to huge areas transform a fundamental limitation of worldclass transforms and there's all this I can't make that all dated he says there is you may a smaller or larger than 1 the range of exponential is transformed changes however although if you actually try finals exponential here him OK so we chug ahead can we get from the work that was done in my life that I made for 2 and then what can we say about that well this factor it's something worthy of the final status of of the data and they beta both depend on polymer concentration and they both because on Paul molecular weight if you fall on the set of the same scale UC concentrate their they UC concentration dependence is an oddly somewhat limited range of concentrations of molecular weights to the act we saw the of by the dissolution of the had stretched exponential concentration dependence we all know we did do some investigation later in some investigation on how on staring and the answer is they are Over the square was Constance were correspondingly faces for use where if you think back to simple diffusion you hear the finest beat the square feet and Fairchild correct Hughes squared leads you squared and now we did find her systems in which as you make the scattering bacteriological larger so you look at diffusion shorter and shorter distances because he was won over a distance is to make you larger and larger meaning looking at motion shorter and shorter distances faded headed on Hughes as I recall typically increased and therefore if you actually get true measurement of diffusion of different on different lines scales you could see how was the last day of the year was heard to experiments OK we also fell future took time about aboutface balanced out this howled for over a year for worst fears power over data was approximately in the concentration they might say this is Stokes unsigned behavior will it's really sumo Stokes unsung behavior because power was not a diffusion of yeah OK now let us struck again in favor of the of the major part of the work in the end there was 1 or 2 and it was not by funerals lessee drive down the faculty at Cleveland State Arturo about a dozen papers out of his PhD thesis so in some sense he most successful applications to what type WilliamsSonoma national chains .period University in Taipei well he had used much more limited technology period he did very well too on what's for less than it was doing extremely systematic studies of probe diffusion hydroxy probable cellulose is change the polymer concentration you change the probes are dead you use a lot size of Provence he didn't limited studies several molecular weights after all some point their stopped he introduced a radically new method of analyzing spectrum found all sorts of results OK result 1 less Mexico's result number 0 he found that in general dispatch probes that from the Bible there were 2 models there was not involved for which data was approximately 1 told Sharon that and there was another mode in which data was significantly less than 1 that were asked which we call wrong about we didn't quite figured this out 1st time we did the experiment at 1st we saw
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the the 2 modes will hold fast and slow and fast and slow were both characterized by fate of which approximately speaking gives you an initial slow after however if you take the on Net beta smaller what happens when it becomes flattened out current mortgages they most wanted here is betting on less than 1 yes well making the mode broader and broader yesterday morning and initially slow to get and that means the Broadmoor we call all its last true however most people confronted with the specter of life this this is the status of the profit motive this and depending on what basis did that identification doesn't necessarily bring through directly because the thing that has to do with this the battle is this slowly the quite and I result is determined as you go through the doesn't have that actually on this topic and papers papers of the alliance is you go through the papers on this you discover that's very interesting ,comma terminology changes and life becomes a bit complicated but provided few read papers in reverse order you were better off and then you have this the papers restoring a lack of all of the states that what John Hammond said they liked the final 1st in India is looking fail because the sharp fall exponential in the ongoing the plot that for this year's size will get curves for different concentrations and column what can we say well the variable constantly 0 concentration we get something flat as we increase the concentration what would have find the euro area's such fundamental science for small spheres nothing happens to fails to increase polymer concentration this is figuring out there and 3 so you may increase ,comma concentration this year's just keep confusing but there is lot of time and above all but you discover that the concentration dependence becomes extremely Florida the there's a lot of of concentration years intermediate concentration and higher concentrations and the curves are moving away from each other for large spheres but not small spheres there is a long there's a boundary that separates small and large spheres and it's something in the range of 50 per cent of the leaders which is about the time that the widest size this year will fall was it's not making characterized the size of small oil in several different ways and therefore if you don't want push to the too being interesting of the important issue is that was a boundary between small and large group behavior furthermore during went over moderate ranging concentration 2 see area of about 8 and all that range this boundary it was concentration now wasn't exactly independent concentration is a limitation going out certain Oliver's years sizes and anything that happens between 1 sphere size in the next year size can't really see you someone in the world by straddling a person can't really see it and so someplace between 50 and 18 years sevenyear aiding the enemy years something happens and if you wanted to tell me this on our scale concentration the Titus if that's the best the change contracting because of the train struck you couldn't tell however there are a number of models of all say the policy and there is a typical distance like that all now the depending on several issues like the soldier quality polymer etc the exact powers there is there but it's Scientologists even the minus expert at some someplace in the range of 3 workers already observed range of concentrations the boundaries of very high considerably it's very definitely does not relative to concentration dependence you get mesh tight series of boundaries clearly not 1 of these messed things because it doesn't its location doesn't depend on concentration day that part size the also that concentration that its implicit here and on aligned vertically displace collected once a year and parameters at different concentrations in Graf said they have in their direction and what happens well in Europe if you look at that the actually work parameters sitting here and we mean for example that the Justice and various body parts were looking at large spheres and we will not the suit of relaxation around the and we will look at the associated with program they were and what does he find well from March years faded shrubs along it is close to independent concentration and you really have to call off 5 years and then there is a sort of dramatic change here you can also look at Baylor and there is always the continued to fall into about same about remaining in the 2nd part of your desire and there was this and about 5 grams per liter the behavior of the probe's changes vary dramatically the behavior of the problems on in terms of what is concentration dependence you have 1 behavior in the solution white regime and you have a 2nd quite different behavior Malaita regime Westernized as we now know about the probe diffusion of the solution where we saw the viscosity of the solution lies in our life transition and at the same place we saw solution like melt like transition viscosity we see a transition the diffusers behaviors here and thus we have a 2nd best set of measurements basically completely independent 1st and we see the same trend we see a transition at the same concentration lastly use light scattering spectroscopy to verify the experimental planes Quinlan myself but there is a solution like well like transition in this polymer Poland concentration on during did 1 other thing 1 of these continue doing this was and what he did it starts with a simple and federal the T 0 2
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was vanity you know minus the hammer created equal to on the inverse as Anaheim 0 insists he the mixture of gamblers even the finest in the white analogy with this equation please don't say so the average Indiana 1st yes for an hour intervals 0 to 60 sea he began a career for lead minus the biggest Solomon the animal to the minus and postwar that is what you take something but if you take a decaying exponential integrated overall behind you get the of relaxation rate is never solve exponential all the average and if you take the ball is a guarantee that moment you get moments of Indiana unsuspected ways District that's spectrum of a pure exponential isn't an arbitrarily came back from she that means Britain solve exponentially and therefore we can be finding characteristic it's universe relaxation rates by shaking she and integrating over time I the same thing here and the onset of looking I'm downloading moments strategy this is the opposite of all of those human along by the data because of the cumulative being look at the initial and encourages the Taylor series expansion around 5 0 so in a certain sense you're focusing on shore the moments because he gets bigger and bigger focus on long now you might say experimentally that's going to be a little tricky the reason it's going to be a little trickier since insist on going out not to be a problem he goes out to infinity and the suspect measurements of the spectrum of very large times on noisy so computing moment looks difficult How we be fixed the answer is we take the actions that we think the speck of a will function that describes the spectrum accurately namely source friendships and we extract a data and the data on 2 and outlook to another thing about the date for teaching moments and now in the individuals not numerically would do the internet rules analytically and if you do these you get always office factory the moments are extremely reproducible and are quite stable and even do moment analysis close factor during the war To date all you can do manically upbeat on universe has a value yes Dear and function of Walter Wallstreet along with the divided by wasn't divided by later they are best that's for 1 morning she can actually do these it's an average time approximately at this point the heroes with him right in the eye and said helium neon ladies which on a lot places we have done ion wages which could give us a lot Our people had already gone light lightscattering from policy solutions a lot and it occurred to us that we can do studies of the spectral loans of hydroxy proposal cellulose itself we are looking at your age in see in water and the correlation with the and there are no problem what do we we found as long as it is fairly low concentrations factor of vinyl and we can characterize the 2 moments but as he from a low concentration walked to higher concentrations there is a time which was about 6 grams per liter of many maybe with various factories gets you to the lower end of the plot follows referred to him plot the relaxation rates of what happened well below concentrations relaxation rates of pure color even traits that's not surprising the following changes to tell each other they don't like overlap and so low concentrations as you had increased Paul concentration of hydrodynamic gets stronger the repulsion is get stronger faster diffusion coefficient for these relaxation break increases and then get out some concentration which is about 6 straight and it's 6 grams per liter solemnly the 3rd fears and the 3rd mode is very small the 2 moments out here fairly concentration by the 3 modes 1st by about 10 timescale leaders in this because the models separated by timescale see 3 Belgians spectrum reasonably reliable in August won't have time with this tale which is traded on the 2nd so signaltonoise on it's not very good because if you run all day you know sample very NyAlesund C 3 modes the transition let the 6 grams per liter it's something fairly close to concentration at which you go from solution lies about what since it's not clear who see it's very small exactly when it 1st appeared on you would hesitate to say that should transitions are exactly the same spot at least I would hesitate to say so 0 so what happens well we can do a series of different measurements they are of the 1st thing is get a C 3 involves here you seem old structure in the diffusion of problems but we can see say quite firmly these 2 1st not the same as the 2 problems I might think along reason you see to apropos probes on trained by polymers and his followers during problems a long time to see the polymer diffusion reflected the probe refuse any probe relaxations sort of right time scale however the concentration because users of promos and all the following molds were opposite as you increase quality of radiation the Palmor relaxations occurred more and more rapidly and I'm a lot more rapidly but clearly more more assuming increased polymer concentration the trial motions are slowed down so even know you were seeing events happening on the same time scale the
1:01:47
measurements conclusively refute the idea that you're seeing entrainment directs the probable part if you were familiar with the old literature you can find people speculated there was such a thing as in training the speculation was based on the observation that all you see things happening on that same time scale even tho the theoretical calculations don't give any hint of how you could get in training all programs that we would again OK this philosophy results do all of that sort of thing I said was that he was pleased that the store Wesley measurements indicate that there is a fundamental point scale in the cities and the land like scale as it happens about probe ,comma reason generators the 1st was transition that something like this he said many years in problem behavior between small probes and large worlds the Senate however there are a few more of these all supposed to measure the relative on 2 Sharon loans they changed staring the relative amplitude 2 the depends on scattering angle and you can say amplitudes cross intensity you save ratio was about 1 and it is wanted a particular value of to Italy crossover occurs when the universe was about 7 set the you can also go in and say Well that's very nice I mean you could also look at the case here the broader mode relaxation rate as a function of and discover that a small fuel over large distances the MLB is fairly constant at about lot meaning it is the best this again but larger you relaxations have more rapidly and the crossover in human workers about the universe about 15 minutes I would not get all off said is whether this Over the same or different offers volume of letters equality is the interesting part of the you know September whether it's supposed to be all right 81 . 2 summer during their 2nd this isn't sharp you only have a certain amount of of measurements certainly really accuracy but there is 1 more thing you can do it but you compare and worlds of Paula and the pros yes and what happens if you look at the intermediate relaxation rate probable the 3 Baltic fast intermediate slope if you look at the intermediate there is a concentration of of which this is concentration events to onslaught more work when is this occur the makers of approximately the timescale of Provence in media world becomes greater than the timescale of hauled into the mold that is probably intermediate mode slows down with increasing involvement concentrate the only time scale and I said that was the time scale Robles guessing along with increasing polymer concentration the inverse the timescale of polymer becomes faster with increasing fall all concentrations to the you there is a concentration at which the 2 timescales slick and now the timescale of promo is slower than the timescale of Paul will be talk talking about the intermediate means only the last very interesting In and eating at the crossing point depends on the concentration of the probe size however if you have role that is about 15 on the news large the point at which the protein is tall and how timescales
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whereabouts saying plus the transition concentration and so if you use probes of this interesting widescale size the program will follow remote intermediate worlds about elements not say timescale at seaports and so we have a bunch of completely unrelated seemingly ways extracting a length scale from data and these data are consistent saying the interesting white is about 15 Indiana years and the length scale does not cure all concentration 1500 metres is about the size of intact all chain and a certain sense it makes sense this is a significant length scale namely that means that these things always being Pearl Necklace Hall will be there on the same change must stay attached to each other and therefore there is a wide scale is about the size of the whole polishing change over which the on infinite timescales must altogether because the crew family bonded to each other OK I have had this social pressure on the wound 2 more sections and 1 of the sections will do this all about the fund called correctly aligned with his party based on the work of the ground and solid it is true and what they did is measure South diffusion single particle diffusion of but they did something important managers will probably futile publication for an honest to goodness pro partly sold this year they also measures a tracer diffusion coefficient of polymer of polymer chains going through the same polymeric nature that is unless something called they used a virus called directly apologize to you and we confront the polymer with facilities for years we confront the matrix following the the fall of oil and we measured the diffusion of these 2 very different objects through the same matrix question about the news of the world go you mean how do you tell your looking at the nation's follow 1 and not this will you are looking for you that you arrange things that you have a matrix polymer and you have a problems following the end of the 2 profit to the Matrix Pro Bowl Marguerite different molecular weight and scene of some of the alternative method of doing the same experiment the the fluorescence relaxation will have following week In which case had all major of the fears of fluorescent molecules police so the sound different ways of doing the experiment what they found Wells if you have war fears but the it is very emotional for March spheres with motions of traces of similar size yeah radios about what is worst fears have changed the slowdown in about the same amount but you can also look at small spheres and you could look at Matrix followers I'm sorry probe also the of tracer changes in and the growing this year's increased concentration of Matrix program year what does and measure the diffusion of and how to the concentrations of which they then "quotation mark what happened to those fears 1st slow down by about 10 fold in the small major exchanges are slowing down by about 300 people I said they would probably change for slowdown by everyone that is the matrix is far more effective at slowing down traced should change name is slowing down spheres they also continue the
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increasing concentration of places on for years and found that if you increase the latest concentrations of UMassLowell probes fears by the affected 300 also brilliant used for matrix concentrated not from the standpoint of on ratification time models this is an extremely alarming result warming results but here it is the alleged transient seen Landis transient Gerald I apologize to all you and other apologies headfirst takeovers based here it is obliged to move law and therefore Paula because it contains head carafes and actually modes of both this year and not and someone forget it the polls Alaska fairly small you once more prolific polymer change what being the here that's exactly the opposite of what time now you can say it will you go out for a concentration and if you
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went out far enough and concentrations of your last pollinators really the only thing you see is the opposite we came however insisted on reducing the opposite behavior increase concentration of 1 of 2 things that have happened the 1st thing that would have happened that is was theirs following and the polymer chains sulfur fusion casts not necessarily please stop change but has to roll over so that the chains using the attitude to the other alternatives the probes slowdowns out and suddenly they crashed into stock and crossed to review the matrix the approaching so Tracy use these were both the sudden deviations from the French exponential behavior as some might call concentration well that he and therefore even you can say France Brown and challenges to go foreign often concentration and therefore the switch the Fagan of foreigners in order for the switch to the current something would have hired to be concentrated in the hands of skiers were concentration dependence raise changed there would have been crossover in their behavior concentration the ends of sort that has never been seen before and since then has never been seen before the reasonable inferences it doesn't exist and therefore there is no way you can say there is such a crossover but if you saw it the ground we are almost exactly how much time we have reached particles trapped in the next lecture I will discuss particle trapping as a method of study motion almost until then classed as this