19 Theory of Quasielastic Light Scattering

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19 Theory of Quasielastic Light Scattering
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30 (Lecture 2 missing)
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Lecture 19 - light scattering spectroscopy and the light scattering spectrum. George Phillies lectures on polymer dynamics based on his book "Phenomenology of Polymer Solution Dynamics" (Cambridge, 2011).
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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 lecturer
19 glossy elastic light-scattering Spektr Oscar B. and the light scaring Spec In any event today
we're going to finish off a discussion of call there's 1 little bit it's going to be postponed to later course and will take up a discussion of our home was elastic light scattering from on fall dead time money and I knew what we find out what we discussed :colon 1st of all we have a serious parameters place South Houston cooperation and mutual diffusion coefficient of the rotational diffusion coefficient and each of these perhaps some concentration pendants constant useful concentration calling fracture the important point I want to make is this constant is different from these 3 parameters but in point of fact if 1 knows reasonable calculations what can calculate what the slope is for all 3 parameters you get reasonable answers the statement get reasonable answers all tends to say that you understand what forces you could you could buy accident at 1 of these right but this parameter depends on the hydrodynamic interactions and also directed in very different ways for these 3 concerts and the fact that you can get all 3 of them right tends to say that you really do have an understanding of how hydrodynamic at work :colon if you look at the light-scattering spectrum of these systems and is actually true not only for the light scattering spectrum from a guy who modeled 1st system but also from a traitor system you find but the spectrum used by most there's is there's something that approximates Beinfest became world and there's something that approximates a slow decay now what is light scattering spectroscopy it looks for fluctuations in the concentrations part part if the concentration were absolutely uniform there would be white skin you get light-scattering because the regions where momentarily due to Brownian motion the fluctuations and therefore the regions were momentarily the concentration is unusually large foreign usually small it is the fluctuations of the concentration of particles that lead to the scattering of light and it is the relaxation of those fluctuations that leads to a scattering Spec no 1 thing that has to be remembered me doing this in more detail bitterness selection is that light scattering spectroscopy is driven by a single spatial 48 component of the concentration of particles and therefore you are looking at here is a lot of particles you were looking at here is "quotation mark wave fluctuation of of some sites also coincided with holds all different ways vectors are fluctuating at the same time but you all that light scattering picks out 1 of the 1 picks
out as determined by the wavelength of laser and by the scattering angles and that the picking out details the same as the 1st quarter were approximation a scary 6 so you say we have to build fast slow and there is going in automatic and totally incorrect written response which is to say that you're looking at particles moving over small distances in March this best completely and totally wrong the reason it's completely and totally wrong is the worst working at fixed humor the distance scale for particle motion to which you were says that is something like 4 is something like the inverse here and so the old times you were walking in motion at the same distance what you're saying is that on this distance scale there some fluctuations the transient and don't last very long and there some fluctuations there persistence the
particles of either packed up close together spread out made solution in which there is a low concentration of particles and whatever they're doing bolts slowed corresponds to the resistance fluctuations and advanced load corresponds to the transient population now you actually do particle tracking from college systems you can actually see somewhat what's going on and what you see corresponds to what is going on in computers and the way that is used for constant diet and structure in which the Oracle state together for a long time and don't move very rapidly and you also need your loss and you also have to provinces by direct observation and vertical trapping along which the particles move fairly rapidly but also in parallel to the the river by emphasized that no policy is not all boils speeches fears that you get trails in which the lead particles in rapidly and that all the articles following its weight so speak if you look at the Solver fluctuations even further slow fluctuation in recent fighting the diffusion coefficient and viscosity of both concentration camp but the product this fall is the concentration of so what we're saying is that all you do see not Stokes Einstein in infects even you colleges In addition to this we talked briefly about the concentration of and how tries discusses the aid and what we find is that lower concentrations there is a stretched exponential concentration there is then a crossover To empower the crossovers quite shocked how Coushatta well there are a few experiments were people managed to get experimental .period very close to here and it appears to be right at the intersection of 2 wants this towering region is a Powell this point encouraged where the viscosity provided by discussed the stalled is about tell also 5 and the volume fractions of the household .period toward the hole going to work different workers data the analysis showed that this transition is the announce the data art and literature from literature find the transition modestly different locations and it's not quite clear why 1 like proposes this effect is very sensitive to short-range interactions between colleagues and different samples gives slightly different results this point is very different from another point of here which is high volatile .period 1 and a household word you know about 50 and that is the concentration which according to computer studies that are actually quite old hot new stock performance by phases region in the system and since you were formed by phasing region while it's interesting ask what happens at the edge of the plight facing region all the statements of your formed by phases region undoubtedly use additional experimental calculator OK so we have discussed this with 1 of the last point I want to make himself or will briefly talk about in the apart from the reason we talked about proteins systems proteins along way there are highly monitored distributors the were charged "quotation mark wire routines church because they have the shortest route .period carboxyl after war and army also secondary and says primaries and carboxyl of hasn't can mark I analyzed here comes protocol on the saloon and the protons and finally to the young means a neutral pH of most of these things occurred if you go to the very essence conditions forced from comes down these if you go to a very basic conditions he insisted the probe comes off here and if you plot charge of protein molecules you get a smooth curve Of course eventually currently flattened out this everything sight ionized not the shape of the curve can be calculated with great precision using statistical mechanics and electrostatic you can use nuclear magnetic resonance to track for an identifiable 1 of these groups 1 at a time whether the group is neutral or charged and look statistical mechanics works you can calculate the charging her for with each group of protein molecules no structure and you can do their great state and so can calculate the skirt which is quite smooth all and you can get churches while having said that I suppose you measure the 2 light-scattering measured the mutual diffusion of proteins in solution we have proteins in solution and so on we get concentration fluctuations here
last there on the mutual diffusion coefficient describes the relaxation of the concentration greater follow what happens well the forces between protein molecules drive the relaxation of the direct actions for example screen electrostatic the hydrodynamic interactions political moves Cecile Way fluid flows surrounding solutions the address of proteins along you can actually calculated as we talked about 4 fears no what happens is that if you have proteins that are fairly highly-charged can start reducing salt concentration or you change the pH driving up charge the forces between the protein molecules increase brawl church same of forces are also on the net result is that the interactions drive off the the diffusion Co and you can't actually described this In terms of quality something and referred to the US my profession the drag coefficient which you can also get off line and then as I discussed last time the reference frame direction refers to the fact that the protein is reviewing this way influencing compressible simplest cases from the Internet is indicated for some of the soldier gets pushed the other way and this modest effect that actually calculus and said we can do this calculation all there is an interesting bit here there is an alternative form of this times used to describe a mutual diffusion of all macromolecules reviews the case the only 6 a sign fighters called the dynamic scaling like this is normal because of critical to if you have a mixture of 2 liquids the face seperate and you change the temperature and pressure enough you can often arrange things so that there's temperature and pressure beyond which the liquids or missile proportions right at the point where the 2 little sisters liquids become simple there is what is known as a critical point and the critical point the concentration fluctuations becomes very large and at the same time the concentration fluctuations because a lot of the diffusion slows down great and therefore what 1 observes is the dynamic life becomes longer life over which particle motions are correlated becomes longer and in this system correspondingly diffusion slows down indeed it slows down as tightly as the critical points approach In these systems precisely the opposite thing thinker it used to take the proteins and charged law were you reduce the salt concentration their interactions are made strong because the injury actions are made stronger and longer range as you do the things I just described the distance over which particle motions are correlated yeah increases yeah however at the same time that this correlation line for dynamic motions increases diffusion speeds off at speeds up the great detail deal for example there nice experiments by Guardian Benedek act and they have served up to a threefold increase in the diffusion coefficient of bovine serum albumin Water as they did various things to change the pH salt concentration calculating any increase cannot be doing calculations for a church system is not trivial however ,comma experimentally phenomenal logic will lead you make the interaction strong the repulsive interactions and therefore the diffusion coefficient goes up at the same time the correlation length for interactions goes up this also and therefore this summer this formula becomes a critical of his total is completely wrong as applied to macromolecules it gives completely physical impression of what is happening at the end of but the the 1 so that is there is the sort of thing we have found by dealing with "quotation mark diffusion coefficients and we're now going to push on to the next chapter we're not going to reject locked in the next chapter is about policy the last let the area and your mostly going and talking about what arrested light-scattering as applied to find systems that is we will have a system in which we can solve our leaders this goes on the citizens there's the abbreviation they don't have to put down the abbreviation the
notion is we have a mixture of him there are lots of which is more or less visible and the thing is drawing all its protest floor but they just as well be called and we studied the light scattering Inspector Trust there's we send in places like laser beam and here is an incident to where factor means life we observe scattering whose song angle there's no way that vector scattered light we can closet elastic light-scattering because the light was not changed frequencies significantly during well was part 10th 10 the frequency doesn't change so that two-way factors are equal in magnitude but .period different directions and the amount of IRA is this little from nowhere to think back to quantum theory of scaring Europe did you see the war approximation good will lose the support approximation accept Visa will bigger than the inside of protocol and 18 takes longer but the math is the Senate and therefore the Seattle field is proportional to solve scattering cross-sections and binary system scattering cross-sections the same for all the scary particles so we dropped out and is proportional to how bright the it's that life is make the incident brought light brighter make audiences feel he 0 largest gathering gets larger and analysts all were all part of the system he the guy's square miles 1 time they scattered case the IRA which is usually called a K final climb has been considered but the position of particles on time the reason I did take a look he is that that turning includes interference between staring from 1 article not it includes body interference because the scattering volume in a typical experiment may have focusing England's here you have clapping after years of involvement there is a region in which you were collecting scattering which might be 100 miles from the crossed it is surely less than 1 mm long the light the visible light you're using a laser it has coherence line kilometers typical experiment across this distance the visible light is coherent and therefore you can see interference between scaring from different parts it's another way to interpret this picture is to say this is a Michaelson interferometry each of the molecules acts like a little mirror you have a very large number of key teeny tiny tiny little malt Maris and there and the intensity of the scattered light is determined by the interference of the interference as the particles move the amount of interference changes and so does the intensity of the skin like and so on said the intensity of scattered light is going to very honorary longtime states was
Bertelsmann don't there but how you characterize and the answer is that we veterans scattering spectrum here is the spectrum of scary light it is both theoretically and experimentally more convenient to work primary frequency domain but the time domain the the frequency domain it's a matter of forays there basically the time and frequency domain are obliged to give you the same information are knows this is kind of call the spectrum take the intensity of the scattered light scattered 1 year were there at times the it has indeed some players you lost power we multiplied yet the at over lot separate times and we end up with something I've been notationally system in which Indiana the scattering spectrum is only permitted by the time separation between the 2 for well OK so we have the intensity the intensity is proportional to the square of the field and so he wrote the intensity is out her feet the field you would get a four-song fortunately there's a physics and here is the system is a very big here is the distance over which particle positions emotions are orally it's a very small as a result you have invested over terms with 4 particles in and you have a reasonable number of terms in which 2 the particles are within the same volume but the number of terms in which you have to particles of the same
volume is huge relative to the number of terms this is the 4th power near the number of terms that puts for particles and 1 as a result this object is dominated by 2 particle terms and we can write destined to the EU's equal to the world of constant today and there is something called she wants you on the leading candidate to symbols staring back and I water between where calls the energy 1 of humanity's dynamic structure fair here it's also known as the intermediate scattering function and she wants to see equal to what he people called and when use all particles in the system all capital and I am going to bowl song because the 1 of and the use of the product of 2 of those so there an easy 0 square and health where all of particles of the same so they have the same scattering Alpha's clears scattering process he said the allies you distance from house my I a and that sometimes called the years seeing interference between Paris apartments now you have to be careful because this song includes an equal standard terms and case using 1 Article 1 time and the same particle with different time but also includes an not hold in terms of which you looking at 1 Oracle 1 time and a different article 2nd so this is how she wants is related article there are also here to answers a and B. on the constant a is normalizing there she goes through literature you'll discover that lots of people who were happy to "quotation mark normalizing effect the difference it doesn't matter assault within reason how you quote the normalizing their because it's a constant but constant has no effect on the final weekend of this function the only place where it matters a bit what you're doing is that if you say I have some external means of calculating and he fought in the war value for orders relies so your value it has often been used this object was inside the house was this object he hated 0 2 and 0 times Howard T. plus how come to the wall and there's some quantity that you reach times era and if you put it the wrong normalizing constant data some minor hazard messy yourself all these long term limit how to measure the long term limit value their devices that actually calculates score this I suspect this is actually also correlation function the function of the variable one-time variable of 2nd time you see that In the correlation functions he is a function of the times separation will you can actually measure these experimentally the complicated machines doing that In a few actually do this then do this application are you can measure out a very long time since December that spectrum goes out becomes a constant during long time other methods of calculating constant should be withdrew worthwhile objects they can actually measure this directly and when you measure it directly certain fluctuations in Norway here that was repeated their view measures directed that points gets trick that so you were actually measure the died structures but the dynamic structure Gregor the slated to terms so he wanted to continue to the people he wanted ask the visitors this summer the authority of Tiananmen structures because the there won't be those who you really think about and you know the other partners this thing all I can we say about the south of the city parks where they come from they both come from this the whole self the south part of firms which have the hold on so you're looking at the same particle to this is state terms Oregon chosen with and is not now you might say she did not have the right to be a whole pile on the same terms yourself terms and the answer is yes there are already a lot more distinct terms and herself however however In the South distinct characters what has to be case is that particles down and can have started out a brand of printer close to each other and because if they are their positions the 2nd said start time are on correlated with the halfway across the system from each other the to turn the 2 positions are uncorrelated and contribution to the distinct determine averages 2 0 why both the 2 particles are out here they could be out here or they could be half a wavelength closer and those 2 states about her very nearly equally likely because of way for particles away far apart from each other at all while particles are being way far apart from each other alone the contributions to this object average 0 we have a particle can only particles near neighbours contributed distinct part of the correlation function while the number of nearest neighbors serious fall 3 12 whatever and therefore this term the and not holding and the South termed the and equaled and
authorities vaguely the same slots there is a specific exceptions and the specific exceptions tracer experiment In tracer experiments we we have a background influence could be a polymer solution invisible polymers mixed with some things we do not see and dropped into their are dying bird the particles that are doing scattering are almost always very far apart from each other and because they are almost always very far apart from each other the position of terrorist particles terrorism scares are uncorrelated as a result of the Treasury conditions South Carolina it gives us a sense essentially all of the contributions he and same German would you looking correlations positions Paris gallery avatars very nearly 2 0 this is how traces the fusion experiments get on .period get back to us so tracer nations the distinct terms of panic all said the same terms than you then ask Well what information does she she 1 S and G 1 the give us about the system the title of the information the coroner's is there is a probability distribution and this is the distribution of tracer particles of interest will take a step Delta hex during time t well this object from Brownian particles in the simple sold is calcium Delta Ex if we polymers system we find that we're doing traces find G 1 this specifically not not devote all his flock of long the Angie although it is not on the mobile and correspondingly reduced their for the year Delta expertise is not without seeing something more complicated however the South distribution function the south part of the dynamic structure factor gives us the likelihood that a given Oracle will take a step Delta expiry time the now actually inverting the spectrum to get dealt requires that you do need to be dependence on cue for a series of water use on the requires that you have high-precision measurements and what you can and will be positive even moments of averaged over the even moments of doubt that the odd moments averaged 0 that's cemetery but you can measure the even moments at least and even measured only by doing so he wouldn't pendants any serious at any time you want to you could actually get get approximately information about this function of particles are not high life becomes less was less safe a finer details you on what he saw this is for the likelihood of a particle would displace some distance adults or during times of the year actually is modulated by the position of all of the particles insisted here is a list is a list of targets were part 1 is tolerable who is out article I guess I call hold on all the particles in the system the time the he also tells that he is equal to the average overall starting positions so there's the return on our overall started positions of all particles and there is the old Delta the party and there is a list of all started and there is a need to find a space of the Federal Energy dryness and normalizing factor I and Battersea the actually don't see softest virus distribution function talks about and this is in terms of where all the stories positions are widely starting position their long years of particle and at times 0 5 if no other information it's more or less equally likely to move in any direction on the other hand at times 0 through 3 neighboring over here and the particles all repel each other the steps standards turned into those motions bounced back on these steps the enhanced and therefore vital to the information about all of particles are a kind of 0 I'm giving you information about what steps this 1 part of article interest like with status lightly over the time the well there's a fair amount of Frank and it turns out that the same part of correlation function is determined by the probability of a particle warned states that and find the best and it's determined in Perth 5 the vector From particles interested to 1 neighboring particles during time the because through the PTI are 1 here many where Jones Westward and this effect is firm which comes out of the the the International here Saturday that the probability of displacement during the time the these 2 station for a transformed complicated on distribution followed with respect to the position of modern variable they might gee meant that go away by going to small you and the answer is that if you go small you if you really go small you the cheese got wall 0 and have not yet started to decay you can look at the initiative's slow all she longed self she won distinction can look at the initial slopes of these 2 functions that
civil kind has calculated and if you do that you discover this object contributes substantially to how fast relaxations the of OK so that is a discussion of whites can expect roster and now we chug ahead we're going to apply this holders and if the client hold solution there is a problem complicate this here a call to reduce what if you stare at 1 of the following you can get interference between light rays scatter from different parts of the same but as long as the ecologists fear that interference block
modulates the intensity of scary .period but it has no effect on the time the law because any interference happens you the sphere doesn't change fired rotates fear is just that there is scaring from different parts Sears for Holloman life is a little more of so many years ,comma loyalists on the same scale as we bread would let break trumps along with after all of these years has all year and we have a light rail shrubs along guests here and scared off words texture and she Palmer's flexible that means that as time goes on abroad as they have Apollo toiled in the shape of of the new share this pieces now we're here here I the reaches the factory has a different path for as a result of the internal motions of polymer contributed to the tiny tents scattered light in order to do that this assistance has to be sort of comparable politely if Paula tradition of this scale just talking like that the radius of gyration if the Paula radius of gyration is much smaller than the light like that is virtually guaranteed that there is much less than what Paul can change shape the interference doesn't change that is almost 0 the distance from here hearing years time he relative to White Wave .period so like scare from here and from here on it's all about the the same thing however you make really big poets because you can make a really big falters then as the polymer changes shape you get contributions time dependence that see however because of time frames I am out of time today and therefore it next lecture will continue to discuss how this affects contributes the light skin from Paul but that's it for today where does


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