Classes in polymer dynamics

Classes in polymer dynamics based on George Philly's book phenomenology of polymer solution dynamics, Cambridge University, Press 2011 and today this lecture is lecture 1 course introduction welcome to physics, 597 D. I am professor Billy's, you can reach me my WPI email address that you will, however, do better emailing me at home. Much of the time we have questions there, I haven't hand out its downstairs. We will end class slightly early and go down to my office, and I will give you the handout with the class schedule. The handout also discusses presentation of research papers in terms of footnoting, citing references properly and that sort of thing which sense your graduate students, you should more or less know, and it's mostly a friendly reminder. As I say, this is an advanced graduate class. The objective of the class is to discuss how polymer schoolin solution you take away from a course like this as much as you put into it, and as long as you do a respectable job and get the appropriate grade um. Having said that, we are primarily based on reading my textbook phenomenology of polymer solution dynamics, there's also a supplemental volume, which is the complete numerical tables which probably do not need to buy for this course. But if you were doing research, you'd find quite useful okay. So what are we going to do the course is 28 lectures. As I said, there will be reading assignments. I don't plan on having a midterm or a final. It is not the sort of course that lends it to. What can you right now or say in an hour and a half? It'S it's the sort of thing where you're going to pick up a great deal of information, but writing useful questions would be a little discouraging for everyone. So what do we do? Well, we start out saying here's how to speak. It'S a polymer molecule. It is a long springy molecule if it's in a good solvent, that's a polymer molecule in the solution. On the other hand, if you have a polymer molecule in the poor solvent, it will fold up in some sort of fall now that what looks like a fairly well-organized ball, and that is because it is the most important set of polymers in pure solvents. It'S a protein water is poor, solvent for proteins, most proteins. They form up and form very compact structures, very ordered structures as opposed to oh, this is polystyrene in benzene, a very dangerous solvent. You want to be careful of it um. This is polystyrene and benzene. It sort of forms a large, open, coil large. Well, if we look all of the way in on the structure fully styrene, you have something I'll give you the organic structure and that the benzene ring, and here we have an organic molecule and the trick is the polymer has all of these subunits and it repeats A very large number of times so this polymer chain is very thin. But if you measure along here it's very long now, polymers don't have to be very long. This sometimes gets lost and if you just have one or two or three monomers, we might say Oh lid, over meaning m small instead of polymer, but that is a distinction without much of a difference. If you think about things, you will also realize that something has to happen in each of these ends or you'd have dangling bonds free radicals. That would be very bad. So what are we going to do in the course we are going to discuss how polymers move in solution, and then we are going to discuss a few other related topics. So having said this, what are we going to do? Well in a certain sense, we are piece of the course retraces, the history of polymer solutions. If you go back to Oh 1910 or 1920, people knew about modestly large organic molecules, say tetrasaccharide, and there was some supposition that was about as large as molecules could get. Um people didn't know about proteins. Proteins were assumed to be association. Colloids, like gold collides, the amino acids were stuck to each other people who there were amino acids and proteins, but the structure was completely random and it was just things that stuck out of solution. We now know that approach is completely wrong and it is in the 1920s that several people worked out. Experimentally, but polymer molecules are actually very large molecules, much larger than the organic molecules that were known at the time and their properties. Their solution properties arose because they were very large, a solution properties, the conspicuous solution, property at the front end was viscosity and is, if you have water in a glass and pour tip the glass over pores. If you dissolve polymer in water, we've got a fast food chain, milkshake, something that does not or at all and in some cases it does not pour at all, because it's had mixed in significant amounts of hydroxypropyl cellulose inert, very long-chain, polymer ball. That runs up the viscosity. The resistance pouring will be much more precise on this, as the course goes on. So how do we, or how did I organize the course well, the organization of the textbook is not the historical organization with studied what well it's an effort to do things in the somewhat logical manner. Well, I tried, and so we actually will start out talking about driven motion of polymers and driven motion. That is, we have this polymer solution, their polymers. This is a little less magnification, but there's a polymer molecule. We apply some external force F on the polymer molecule and it moves and we can measure how fast it's moving. There are two sorts of ways to do this, and one is the centrifuge and centrifugation has actually been used significantly to study, polymer molecules and the other on which there is a huge literature. Not precisely pointed in our direction is electrophoresis, so we'll start out talking about driven motion. We will then do an excursion there cup of there couple of chapters in the book that are really side, excursions that I could have stuck in any place, and sometimes it wasn't quite clear - word put it in, but the side excursion. What we'll talk about next is quasi elastic light, scattering spectroscopy, for which I give you just the abbreviation, and that is a scattering method. Now it's actually a somewhat complicated scattering method. We will talk about scattering detail because there are a lot of uses of scattering and materials of x-ray scattering light scattering for molecular weight, determination, we'll talk somewhat less about the details of how fuzzy elastic works, and then we start talking about having them driven motion. We'Ll start talking about things that are actually thermal motions: well, mostly thermal motions, and we do this well first, we will talk about single particle and then we will talk about collective motions. Now, when I say single particle motion, that is perhaps a little imprecise. So let me fill in it in a bit more detail, we'll start out by saying: okay, we have a polymer solution, here's a polymer, but it's not hovering in the vacuum. For all these solar particles and the solvent molecules are very important. If you want to say there is a solution here, and so it will start out by talking about solvent mould motions which come out to be considerably more complicated than people thought 20 or 30 years ago, and then having done solvent motions, we will push ahead to Discuss what are called segmental motions that is segments - you have a big long, polymer chain. The polymer chain is made of little pieces and there are several techniques that let us reach in and look at a single piece and ask how that piece moves just a second. I'M going to close the door, those are segmental motions. The third piece is really named by a technique. It'S dielectric relaxation, the issue in dielectric relaxation, is that if you apply an electrical field to a molecule, it can move, it gets shaped and change its orientation. Can change at high frequencies? There are other issues that come in, and so, if we have this hurting molecule here, there is a vector from one end to the other end to end vector and we can measure how long it is and we can measure how its direction changes due to the Diffusion of the polymer molecule, I'm just really giving a sketch. If you find some of this unfamiliar we'll be doing it much more detail a little bit. Finally, single particle motions: we will be talking about self and tracer diffusion self and tracer diffusion. Yes, we have our polymer chain here, it's in a fluid, it's more or less free to move. Well, that's not exactly true, because the solvents get in the way other polymers oils get in the way and therefore the rate at which a polymer molecule can move it and through solution is affected by its environment and the simplest experiment you can ask is well. We will identify one chain and we will so-to-speak label it by painting it green. You actually have to be a little more clever than that, and because we have labeled this one chain, we can watch the one chain move relative to the entire background. The reason we are two names here is that the chain we're watching could be identical with its neighbors, except that we've labeled it or it could be different from its neighbors. So we have a chain of one species and we have surrounding polymer chains of a different species. If everything is the same, we're talking about self diffusion, if they're different we're talking about tracer diffusion. Finally, single particle motion: we will talk about probe diffusion and that is actually one of the larger chapters of the book. So what are we going to say about probe diffusion? Well, what is it first of all? So here is our polymer change and we are going to drop into the polymer solution, something that is not like a polymer at all and the representative object. There are several variations. You'Ve got choices here is a colloidal sphere and fear. Does Brownian motion just diffuses through solution it diffuses through solution, just in the same way that a polymer does? However, that's obviously not a polymer coil. It'S rigid its spherical typical case and when we measure the diffusion it moves of the sphere through the polymer solution. We get experimental information out, okay, we now get another excursion and I think it will start the excursion over here and the excursion is colloid dynamics. You may assume that we're going to come back and cover all of this in a lot more detail, but I've, given you a course outline okay, what is a colloid? A colloid is a microscopic or nanoscopic particle. It'S produced by any of a wide variety of synthetic methods. The simplest colloidal particles are spheres and colloids in liquids are stable. That is well considering that we are having the blizzard or your blizzard or earlier what we say. In any event, a colloid sphere, a typical value, ammeter, might be a radius might be 200 angstroms and because it for a typical thing, we're going to talk about, we are in water or some neutral, solvent. If we're in water. These things are charged one way or the other, and then that result is the colloidal suspension is stable. The Brownian motion is such that the particles don't settle out of solution. You can also get client suspensions that aren't stable at all. If you take beach sand and stir it up in water, it will float some distance above the certain surface of the bottom of the pond. But if you wait, a bit sand will settle out. Colloidal particles are very small, they don't settle and they have dynamics. In fact, colloidal particles have more or less all of the same dynamic properties that polymer chains do. They can do all of the same motions in all of the same ways more or less. The one exception is right here. Segmental motion, colloidal particles are rigid. They don't have internal motions, and this means in certain senses, they're very simple. The other features of colloidal dynamics, though, which is important, is it the forces between colloid particles and solution, and the forces between polymer chains and solution are basically the same there in a solvent, and that has a whole bunch of consequences called hydrodynamic interactions we'll get that Later and they can't move through each other and as a result, there are a whole bunch. All not only are all of the experiments that you two on one or the other the same, but there ought to be some similarity if the forces are the same. The significance of this we'll get to later in the course um: okay, that's colloidal dynamics, and now we will go back to polymers. I started by saying we'll study driven motion. Then we will study single particle motions or small pieces of particle motion, and now we get to collective motions and by collective motions. I am referring to the notion that we have polymers in solution and they have properties that arise because there are multiple polymers and they interact with each other, and the property is determined by the fact there's more than one polymer. Their simplest example going to plot concentration of polymer versus position, and we have process known as diffusion, so concentration position. We get something like this. Yes and what happens if you have something dissolved in water and the concentration is not the same everywhere. Well, if you sit in wait a long time, the stuff will transport from the low concentration regions up away and the high concentration regions, and it will transport. So, after a while, in most cases, the concentration becomes uniform, the classic freshman chemistry example of this, which is fake, is that I take stand in the front of the room and I open a vial of perfume and spray of that around and we sit and wait And after a while, the folks in the back of the class have no problem spelling the perfume. If I use enough of it now this process of what I, what I just described, you is actually not diffusion. Diffusion is a very slow process in order to get gas moving across a room. The sort of yard scale motion. Well, the reason for that is: there's air circulation. There'S convection people are moving and have set the air into motion and so you're actually seeing a different transport process than you were told in freshman chemistry. However, on a microscopic scale, a very small scale, diffusion is very important and what happens high concentration. Low concentration is that in regions where there's a concentration gradient DC DX, you get a current J, the stuff flows. Well, it doesn't really flow the molecules move and due to their thermal motions, they rearrange and when they have finished arranging you have um in the end the concentration becomes uniform. So we will talk now you say: didn't we talk about diffusion before didn't we talk about one chain moving through others? Yes, I brought that up earlier. However, there are two different sorts of diffusive processes. There is what we call self diffusion, which is just one shame. Moving through a uniform background, and then there is the diffusive process we are talking about here, which is mutual diffusion, which is lots of chains moving, because there is a concentration gradient DC DX in general. These two diffusion processes are not the same. Now I say in general because if you're in very dilute solution, they become practically indistinguishable. However, so that's diffusion, but there's some other collective properties. The first collective property that we talked about is viscosity symbol is the Greek letter ADA and the viscosity is the resistance to pouring the larger the viscosity. It is the harder it is to get something to pour smaller the viscosity the more easily something pours. Then, beyond viscosity we have what we call linear visco-elasticity. The issue in linear viscoelasticity is well. We say, there's a resistance to pouring so I have, for example, a tube. I apply a uniform pressure to one end and there's a flow rate down the tube. However, I could also, instead of saying, instead of applying a uniform force, I could apply a time-dependent force. For example, I have some type and the liquid is Cle acid. It'S just sitting there. I now turn on the pressure, apply pressure and there's a transient while the fluid starts moving and comes up to speed for simple liquids um, you turn the force on and the fluid starts moving more or less immediately, except it may be compressible for a polymer solution. Life is more complicated, polymer solutions behave is that, though they have little Springs and be more precise, as time goes on, and so, for example, I draw a sketch. We are looking in from the side. There are two flat plates and if this were simply water - and I oscillate one plate back and forth so it's moving back and forth. There is a force on the lower plate and if I simply take this plate and displace it a distance very quickly and stop, there is a very briefly force on the lower plate with polymer solution. If I take the upper plate - and I displace this sideways, there is a force on the lower plate and the force on the lower plate has an extended lasts over an extended period of time, and it has a complicated time. Dependence when we get to this it'll become more clear. That'S a linear fiscal elasticity! Why do we call it linear? Well, that's true, but there's another reason to you're right, but there's another reason and the other reason is suppose I displace the plate sideways. Suppose I displace the plate sideways again. Each of these displacements on the of the upper plate creates it's a friction effect a force on the lower plate, and each of these two forces depends on time and we ask what is the force on the lower plate, given that I've displaced the upper plate twice At two different times - and the answer is its linear - the force on the lower plate is just the sum of the force due to this displacement, but had happened by itself and the force due to that displacement. If it had happened by itself. Okay, that's what English, and why do you bother to call it linear and the answer is: there's also nonlinear visco-elasticity and there are two sorts of nonlinear viscoelasticity. There are classical experiments and then there are more moderate, there's a set of modern experiments which are really fundamentally different from the classical ones. What do I mean by a classical experiment that shows nonlinear visco-elasticity? Here'S a tub that contains a polymer solution or a liquid someone and I put into it a stir bar and I rotate the stir bar. Well. If I do this in freshman chemistry lab, the stirrer is spinning, the liquid is spinning and the liquid is pushed up against the sides of the vessel. If you have ever used a mixed master at home, you've seen this effect in action. Now we want to replace the Orthodox liquid with a viscoelastic polymer solution and we start seat. We stir again rotate the rod and we get rod climbing what is rock climbing the solution, climbs up the rod. The reason the solution climbs up the rod is that there is a pressure in the liquid justice there's a pressure in water, but because we are in a non system that has a nonlinear viscoelastic affect the pressure. Instead of just being a number becomes 10 a 3 by 3 matrix and the pressure in different directions is not the same, and if you act, because if the liquid is being sheared well, polymers can do this normal liquids, don't very much so that is nonlinear viscoelasticity Um and I have now gone through a sort of run over rather quickly, all of the topics that we're going to talk about. Ok, so how are we actually going to talk about them? Well, this is a course. It says so in the book title on phenomenology phenomenology is a study of what happens experimental ii, and so we look at experiment and we let the experiments lead us to an understanding of how liquids work. Now this isn't just a blind use of experiment of there are several competing models, theoretical models for how polymer solutions behave and, as you will discover, as I lead you through the course. Some of the models are good and some of the models make predictions that are consistently wrong and we will charge through, but we will be mostly focused not completely on what the experiments are safe, um. The way we will do that as a practical matter for a fair part. The book has all of these wonderful figures in them and I will point you with the figures and I will draw sketches on the board, but my expectation is actually for once bring the textbook to class because we will actually be using it. So I can point it the figures and you will have them in front of you and if you want to take notes, you don't have to try to sketch a graph with 200 data points on it. You'Ve got the graph and you can make notes on it, and you can see very clearly exactly what the data looks like. So, for once, you will actually be bringing your books to class and you will be getting some use out of doing so, as I recall, being an undergraduate. We never actually did that, but this is a different sort. Of course. Ok. So I have gone over all of these methods and they all are used to study polymer solutions. A rational question is well: where does this whole discussion fit in with the broader study of polymers and under different conditions, and where does it fit in with the other books that I can pull out of the library which you are going to be doing, because I Said the course is going to be based on writing research reports. Now I realize a few of you may not have English is your native language, and I am willing to be quite forgiving on that, though I will correct, because you know, one of the reasons you come to a foreign country is to learn how to speak. The local language, the other reason for doing the research reports is this - is a grand research class and you're going to be exposed to the primary literature. Ok, there are lots and lots of books on polymer solution and dynamics, and if you read them - and you read enough of them - you eventually notice what is not discussed. So let us start out with sort of graph of concentration and we start out at approximately zero, and here is the test tube and there exactly one polymer chain in it. That is as the diluted polymer solution as you can get at the other extreme. We have something that is all polymer and nothing else now the reason I bring up all polymer and nothing else, a polymer molecules, many of them not all, but many of them, if you heat them off and isolate them from air. In some cases, if you a melt, you have polymer and it's melted just the way as if you take iron and heat it up in a blast furnace, you get liquid iron. Well, if you take polymers and heat them up, you get liquid polymer and if you look at a lot of books, there is a considerable study of dilute solution and there is a considerable discussion of melt properties and if it were a sixteenth century European map carefully. Be labeled here be dragons or something equally probable and there's sort of a gap, and if you are not reading carefully, you don't realize there's a gap. It'S just that there is a discussion of dilute solution properties. There is a discussion of melt and everything in between is compressed to a couple or four pages. There'S a rational reason for this. If you are doing industrial processing in large numbers of classical cases, you're doing something like injection molding, you take the liquid polymer, you push it under pressure into an object of some shape which receives it. You worry about little details like getting the object plastic out when it's cooled off and thus melt properties have important industrial or if you want to prepare thin plastic sheets, the things you use for kitchen wrap well you're doing film casting you start out with the liquid. You start out with the polymer and somehow you spread it out into being a film. Therefore, melt properties are very important at the other end over here. Why would we care about dilute solution properties and the answer? Is you have a polymer? It has a length. It'S a number of repeat units, but another way of saying that the polymer has a length is that the polymer has a molecular weight and you know about molecular weight. So we can have water and its molecular weight is 18 dolphins and you have a polymer. It has a bunch of repeat units, and it has a molecular weight, except the molecular weight of a polymer might be Oh 300 thousand or a million. It has become interesting for scientific reasons to prepare polymers of what historically would be viewed as huge molecular weights and people can produce polymers of molecular weights of Oh 30 million or whatever. Then, of course, there is this huge field of research known as biotechnology, where people want to study. Dna'S DNA is a polymer. It has a very complicated structure, which I would not care to try to draw on the board during one class except by cheating, and the important issue is the molecular weights. You can get up there and be huge like 10 to the 9. Some DNA's are much smaller in molecular weight, but you can get absolutely huge more of molecular weights and an important issue is remember: we're using melts to do in steelwork. Well, the properties of the melt are substantially determined by the molecular weight of the polymer and and the distribution of molecular weights, because palmer's aren't all the same size and the easy techniques for measuring polymer molecular weights work in dilute solution. And so, if you are sitting trying to do, industrial processing you're, also very interested in dilute solution properties, because that's how the batch shows up on a truck you'd like to know what the molecular weight really is and dilute solution measurements get you there. Well, that's fine, except there is this big region in between, and the interest in this course is mostly in the big region in between the region which is non dilute. What do I mean non dilute? Well, here's dilute there's only one polymer chain. I put more polymer chains in, as I put more and more polymer chains in the viscosity of the solution, starts to go up and eventually the polymer solutions start the polymer chains start getting each other's way. They interact with each other. They keep each other from moving or something well they or something is the point on this course and therefore we get to non dilute solutions. Now I sort of drawn this with wines. That'S fudge, because really you have something that's continuous here. You have one polymer molecule in solution to Avogadro's number, but there's continuum of solutions on the other side. In some cases you have a continuum through to the melt. That is, you have a solvent. You have a polymer and, as you make the polymer concentration higher and higher and higher, eventually you get to the polymer and the polymer is a liquid that doesn't have to be that way. The other thing that could happen is you run the concentration up and up and up, and you hit a solubility limit and above the solubility limit, you have a solution, a saturated solution and second phase. You have a solid polymer, because at that temperature you can only put a certain amount of polymer into the solution as Fikes a dissolving sugar and water. You can dissolve a certain amount of sugar in water, but at some point it just won't go in anymore um. The complication of charge of being able to do this, if you say it's a polymer melt if they have to be fairly warm and if it's fairly warm or hot, the vapor pressure of the solvent may be very high and you may get boiling instead of the Effect, you want now another way to do this, though here's the melt on solid, there's a solvent and what I can do is to start putting in individual solvent molecules of some sort and they're just traces. Solvent molecules spread out in that polymer. The polymer is almost certainly an amorphous solid, not a crystal, and now we've put mala extra molecules in. Why would you do that? The little things are called plasticine, the plasticizers so to speak, typically lubricate the motion of the polymer and, as a result, you can, by dissolving small molecules in an amorphous polymer. You can change its properties. Is that anything right? It'S an additive correct! If you have recurrent tires or a good example of this, it's in the PVC Editors duty that farmer buys. Ah, yes, you have a polymer cart classic car tires. The additive was carbon particles, another example. If you have seen teflon tape that you use to put seal joints, a real purity Flon actual Teflon is very brittle. If you try bending it, it would just shatter. So you add plasticizers to the Teflon, and now the Teflon gives you this nice smooth tape, which is the despair of plumbers, because it means that amateurs like me can fix joints around the house and an emergency. However, teflon tape actually works and it works because the plasticizer solution may be a solid solution and, as you add, more and more plasticizer, you move this way and in some cases you can move continuously into a non diluted blood dilute solution. Okay, let us clear this off on the first chapter or two of the book and the introduction list a bunch of additional references on polymer solutions and their properties. Ah, they are. If you look at them, you will find the topics they cover are a subset, a somewhat restricted subset of the properties I talked about, and in many cases the focus is very much more for very sound historical reasons on melt properties rather than solution properties. Nonetheless, there are a lot of other references out there and it is worthwhile for you to look at them. I will ask, though, that if you get from two books in the library that you read them in the library, so your fellow students can find them. I didn't put the whole library on reserve. I suppose I could have okay, so I have described this and we now come to the gene. What is known about this, and why did I bother to write book and this comes through theoretical models that I will occasionally invoke, but except in the very last lecture I will not be discussing and then great detail. Oh so, let's start out this done and if we have dilute solutions we have polymer chains and they move and they have properties such as diffusion. And if you say I have a chunk of a polymer chain here, moving it sets up awake in this awake, like the wake of a motorboat drags the water route or solvent along or along, and if this is a little piece of polymer is moving the neighboring Solvent is dragged along well if the neighboring solvent is dragged along. This piece of polymer here is also grabbed along, and so, if you have polymer chains moving through a liquid, each piece polymer chain has what is known as a hydrodynamic. A solvent mediated force that it creates on its neighbors. The solvent mediated force is described by something known, as the Oh seen. Tensor from tensor is a threatening word, but what it really means is here's the point in the liquid. I apply a force on liquid. The force is a vector over here if I'm patient, the liquid, not very patient ball, but slightly patient. The liquid responds by moving with the velocity V and V and F, are not parallel. Well, how do i, how do I mathematically set up something that says I have a vector as the input I have a vector is the output and the two vectors aren't parallel to each other. If they were parallel, it would be easy. Freshman physics case is F, equals MA the force factor and the acceleration vector are proportional to each other and they're parallel. So M can just be a scalar a number here. However, the two factors are not parallel, and the question is: what do we do to generate? One that one vector out of another - and the answer is and T is a 3x3 matrix and if you think way way back some of you it's way way back in time. You saw vector, multiplying a matrix and it gives you another vector out and G. That is the Oh seen tensor and the reason it's a tensor we have to use it is that the output vector before the velocity of the liquid is not everywhere in the solution. Parallel to the force, now you might say, gee. Aren'T there symmetry constraints? Oh, there are a whole bunch of constraints. I said force flow, but over here on the other side, the factors of wide should be a mirror image. We are not going to do this sort of math issue with a lot of detail. I'M going to talk about phenomenology, not about theory for the most part. So if you want to talk about dilute dilute solutions, you can do calculations on single polymer chains and if you do with calculation on a single channel, there are number theories. There'S one two Kirkwood and riceland: there is another one due to grouse and third, due to Zim the rouse and Zim models are actually quite similar and they actually do. Calculations like this and the objective of the calculation is well. We have a polymer chain, we put it into a liquid, for example. How fast can the polymer chain diffuse? What effect does the polymer chain have on the viscosity of the liquid? If I take the polymer chains and I make a longer use two different polymers for that, actually, if I compare two polymers of two different lengths at the same cut wave concentration, how do they affect the viscosity of the solution? And the answer is why these theories are done. The viscosity is proportional to M molecular weight to some power, but it's not first power at some lower power, and we can do actually do theories like this. So that's dilute solution. However, if you try to take these dilute solution theories and compare them with melt properties, you find the melts show a bunch of things that the dilute solution models do not, for example, they show visco-elasticity. I will do a much more detailed sketch of viscoelasticity at a later time. They also show pure thinning shear. Thinning is much easier to draw. We have two parallel plates with a liquid in between I move the upper plate at some velocity V. I clamp the lower plate in position, so it doesn't move and I ask how much force I need to apply to move the upper plate. Alternatively, this is hurting analyze. Theoretically, I take a pipe and I push liquid down the pipe, and I ask how the flow rate determined is determined by the applied pressure. Well, if I have a Newtonian fluid water, Newtonian fluid it has a simple viscosity, ADA and um. The force that is developed is proportional to the viscosity and it's determined by the velocity and by this distance the force is determined by the velocity gradient. Oh, I better be a little careful with my image labels here. This is the direction Z that is the direction X. I have liquid moving in the X direction, but the velocity depends on the height Z, between the plates, so down here at Z, equals 0. The liquid is touching the stationary plate not moving and, as I move up this way, the liquid is moving faster and faster and is eventually speed B and the force is determined by this constant and the gradient dvx BZ. If I push the plates closer together and keep the constant V is constant, this distance Delta Z is smaller, so the gradient is bigger and the force is bigger and, in a certain sense, you've all seen this. If you try to push a liquid through a small pipe at some rate, you have to push further than if, if you're going through a big pipe okay. Well, that's a Newtonian fluid. If you have share feting traditional symbol is Kappa. Greek K is DV, X, easy and a dot. The viscosity is a function of the shear rate, so if you start things flowing more rapidly, the viscosity good. Well, I better drop Aventine, eyna Kappa and what happens is this is actually a log plot, because the shear rate can be changed by a lot. But at some point the shear rate rolls over and if you share the liquid faster, you see shear thinning the liquid flows more easily than it would at zero shear. There is also shear thickening um. Once upon a time that was controversial, there were people who denied that there was such a thing as shear thickening. But in fact there is a shear is shear thickening and you have liquids that are happy to flow if you don't push on them to lard. But if you push on them hard, they don't quite turn into a solid, but they thicken up a lot very concentrated starch. So some of them have this very strange property. So, in any event, we talked about this because if we go to the melt, we have a property described as visco-elasticity. The flow of the liquid is not what you would have expected from dilute solution descriptions just alone for a long time. It'S shows up industrially, whether you care about theory or not, namely you try, for example, doing injection molding and all sorts of odd things can happen um and then the nonlinear effects, which are even stranger, come in and you are trying to get this industrial machine to Work all these weird things are occurring. A challenge for a very long time was that you had dilute solution theories that were known from 30s and 40s, but they certainly did not describe any of the things that occur in concentrated solution. And so there were a number of very different theoretical efforts to explain what was going on. This is not a theory course, so I am NOT going to do the theoretical calculations I mean I could. I think most of you would find this not to be why you were wanted to be here. Some of you would find it why you wanted to be someplace else very quickly, um. However, I should give a little sketch of the theory, because I will occasionally invoke the theoretical model concepts, so I'm going in few of them, and the first is what is known as the entanglement idea. The entanglement idea is to in particular you might build bracele, I'm not going to give you a detailed history. The notion is here is a polymer chain. Here is another polymer chain, looping around it and or polymer chains get close to each other. They can get wrapped around each other now. This is not a covalent bond. However, if you don't work, wait very long. If the notion is, if you try to pull this chain this way and that chain that way, the chains aren't physically bonded, but it's like untangling. Two pieces of all the string that are round web wrapped around each other. They tend to stick even though they're not fastened and entanglements as an idea tended to explain the viscoelastic effects. That is, if you have two chains, if there very short, they really can't not help each other. But if they're long enough, those the chains are wrapped around each other somehow lasts a long time and behave as though you have, if not a cross-linked gel, something that on short timescales, behaves as a gel. And so the notion is the polymer chains. Can somehow not each other up, and this contributes to the behavior in the melt in dilute solution? It does not contribute because here's chain it's dilute the other chain is over there and since there are way of far away from each other, you don't get effects like this very much. The next idea, which refers to the fusion mostly are a series of models known as augstin by oxygen bottles. Oxygens, the fellow who worked about and the notion is, you have polymer chains and they look like a lattice in the simplest model. There are lattice of toothpicks and they're all toothpicks with short pieces of wood are all jumbled together and if you are something trying to diffuse move through this lattice, you have to find a hole that is big enough for you to get through. You have a diameter D, the hole that has a size H and if you want to get through D, has to be less than H now. That is not exactly correct, but this is the starting point of these models and the models that explain why. For example, if you try to measure diffusion in a polymer solutions suppress and now we push ahead - and there were a series of models - do in particular again whose French, theoretical, physicists and other people of his school and the models are called reputation. Scaling - and I am NOT going I'm just giving you a very slight sketch of what is going on so you're aware there are theoretical models which we're going to talk about the more detail and later lectures. The idea of reputation is, let us start out by talking about a real gel in which we have lots of polymer molecules and they're all covalently bonded to each other. They'Ve been welded together chemically where they cross make real covalent gels polyacrylamide with cross linkers. Does this and we will now put in a single polymer chain a long chain and we ask how the polymer chain can move through the gel diffusion and the answer is it's obliged to move parallel to its own length? If we have a piece of it here, it can't move sideways very far because it runs into the gel. That'S why um there is a child's toy known as a jungle gym, so bunch of steel pipes that are cross-linked in three dimensions and you can sort it so to speak climb through it. If you're a small child, the pipes don't move, and so you have to move through it one step at a time. Okay. Well, this is a random jungle gym. This is a very long snake-like object and reputation, and the polymer chain can only diffuse parallel to its own length can move backwards. You can move forwards, it cannot move sideways. That turns out to be a rather powerful restriction and put on top of that. We then impose the notion of scaling which actually comes out of critical for the a theory, and it's proposed, for example, that the diffusion coefficient well, it will depend on the molecular weight of the polymer. The larger the polymer is the slower it moves. It will depend on the concentration of those that gel the more gel is in the way the slower the polymer moves, and then there will be powers like M to the X e to the Y. Those powers are what are called scaling exponents and the notion is, you do a whole bunches of experiments and the relation between say, diffusion coefficient and molecular weight or concentration of the gel or whatever is, if you put it on a log-log plot. It'S a straight line. This is these: are power lines, that's scaling. Well, I talked about it for gels and the radical extrapolation is to say that a polymer solution basically behaves like a gel. This is the vision proposal and therefore, whatever we see for we can use the same theoretical arguments with some minor qualifications and Corrections and improvements, and we can predict how polymer as we move in the solution, and the main statement is that, if we are in constant Concentrated polymer solution and the degenerative polymer chains can only move back and forth along their own chain, contour, okay, and when we do calculations and predictions, we say there should be scaling laws being predicted and what the theory does is to predict these exponents. Of course, it also does something else. It says that if I plot log the against the log of concentration of polymers, I should see power log on a log-log plot. What compare laws look like someone must know this, the straight lines, if you take the power law and you put it on a log log plot, it becomes a straight line. Well, it looks like a straight line. Many observe D proportional to see the X log D is proportional half log Z and therefore, if I do a plot of log D against log C, I get a straight line whose slope X is this exponent? Let'S the models claim, it is the claim. I promise you that, and there is a very extensive set of calculations on this um. However, there is a little difficulty. A little difficulty is called experiment and if you actually do bunches of different experiments and cover large ranges of concentration and molecular weight this that the other thing and you look plot - do log-log plots. There is a difficulty. You'Ll, essentially never find any straight lines. You see smooth curves, okay um, however, the smooth curves have a form, Oh comfort, upscaling. First, we will look at say the diffusion of a polymer chain through a solution and that's simply a representative transport coefficient. I could talk about viscosity or bunches of these other things, but here is an example: it's the diffusion coefficient of the Silk single chain and, as you increase the concentration of other chains, the diffusion coefficient slows down and it's supposed to slow down this power law. This is not what happens and we will spend much of the course where I will show you the de step. The diffusion coefficient flows as some 0 e to the minus alpha. That'S a constant C to the noon. That'S another constant! This is a functional form. Those stretched exponential - that is the it's an exponential, but the argument C of the exponential has been raised to some power new um. That was first found more or less empirically, mostly by me, since I was the one doing that particular chunk work and if you come up with a form, an empirical form. What you find is people are saying: well, that's very nice, but um there's no theoretical basis for it, which is a polite way of saying you better find the theory that predicts this, because otherwise people won't believe you, and that would be the last lecture of the Course, the hydrodynamic scaling law, okay, we have gone through, and I've said something about polymer transport properties and the ones we're going to talk about - and I have said a fair amount about at least a bit about what each of them is. I talked very briefly about theoretical models that make predictions there's actually going to be a lot of theory, inter woven with the course it's going to be presented, mostly in terms of results, as opposed to here's a calculation, and you can use it to do more calculations Yourself, so we're going the course in that sense is going to be descriptive a little bit more than it's going to be formal theoretical. The one large exception to that is when I talk about scattering, but scattering is something that is extremely useful, even if you're doing a solid aluminum and you study the crystal structure with x-ray or neutron scattering it's the same scattering theory. Well. So, where does that leave us in terms of what we're going to do? What I would like you to do for the next time? Let'S see next meet next Wednesday is, I would like you to go in and I would like you to read reasonably carefully. The first chapter and the introductory couple of four words and introductions: they actually contain important things, and I would like you to read the first chapter, which gets you through page nine, and I would then like you at least, to have looked after too so read carefully. Chapter 1 and at least skim chapter 2. Now there will be bunches of things that are sort of referred to that I don't describe in detail in the book because to some extent the book was written for people who have some background in polymers and it may be. You are going to hit a fair amount where you off to do your own reading, so that, for example, when you skim chapter 2, you will find a reference to good fullness of solvents and for solvents and theta solvents, and you would be sensibly advised when you Hit something like that do some sort of internet search or whatever the Internet makes this incredibly easier than it was when I was a graduate student and see that you could leak and see what the topic is and get some information on what is being discussed. So I say this is an advanced graduate course. What you get out of the course will very much depend on what you put into it. If you just do exactly what I say in terms of reading of, it will be true, but there will be a lot more that can be obtained if you do some more searching, also, which is much much infinitely easier than it was 15 years ago. For example, you hit chapter 2 and I say all of this can be traced back to the paper by launch of on and Rhonda less on theory of sedimentation of probes. Well, that's a footnote. You don't even have to walk over to the library anymore, to pull it off. The ship find the volume hopefully on the shelf. You can simply pull it down off. The internet you'll have the paper and you can see what they talked about and when you are doing the reading assignments, I will tell you, for example, the first one will actually I'll tell you what the first reading assignment was. It will be on electrophoresis and it will be take a year of the journal. Electrophoresis pull out the papers that are similar to the ones we talked about. That is only a small fraction of them and see what they say or could be used to study. That is not the same as what you studied already or seen in the book and I'll go into much more detail on what that means. But it'll be a literature, search and it'll be the sort of literature search where you know about where to look. But there will be a whole lot of wonderful paper, superb papers that have nothing to do with the topic you're interested in, and I will give you some hints for finding the ones that you should care about. Ok, so I have two minutes left and the question is: why did I bother to write the book and the actual answer is there have been this very long period going back from 85 to about 2000, where I had had a dispute with some of my colleagues As to what the experiments actually said about palmar dynamics and they would say well, you should look at this or you should look at that. So I looked more or less at everything. This is a. I won't claim. I found every paper, but I looked at more or less every sort of experimental measurement and then I added the colloid discussion and and we will discover what the colloid discussion you cannot find in any. I added the whole discussion on electrophoresis as a probe polymer dynamics, and you will not find that anywhere else because essentially now there's wonderful studies of electrophoresis for a long time. My contribution is saying you can use it to understand polymer dynamics, as opposed to biochemistry so that is roughly where we are
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