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8 Dielectric Relaxation, Part 1


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Title 8 Dielectric Relaxation, Part 1
Title of Series Classes in Polymer Dynamics
Part Number 8
Number of Parts 30 (Lecture 2 missing)
Author Phillies, George
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 10.5446/16234
Publisher Phillies, George
Release Date 2012
Language English

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Subject Area Physics
Abstract Lecture 8 - dielectric relaxation, part 1. George Phillies lectures on polymer dynamics based on his book "Phenomenology of Polymer Solution Dynamics" (Cambridge University Press, 2011)
classes in polymer dynamic based on
George Phillies book phenomenology of polymer solution dynamics Cambridge University Press 2011
today this lecture E is Life Church
a dielectric relaxation I'm
professor feelings and this is cost 597 but what you're going to do today is to start discussing dielectric relaxation which is actually a wonderfully useful experiment technique because it measures a substantial number of rare different variables all at the same time the same name but the general Moshe that was against constructed comparable general notion is we have college the polymer chain has a number of different features which we can actually measure using dielectric reluctance to let us look at a few features that all describe how dielectric relaxation cost and will finally get results the 1st issue we have just polymer change here and 1 thing you might ask as well how big is the several different ways of saying how how big 1 of the it is usually written little use the candidate and that the notion of the mental health effects here is simply starts at 1 of college came and went the other end college so we actually have a vector that tells us the distance between the 2 duets In a certain sense this tells you what is the orientation of polymer chains which way this chain .period now Of course if if you mentioned little factories running along the whole retained at different places the factors .period different directions but whether the Instinet vector doesn't tell you the total of all those pointing to you but also met him measuring I mean square site at length of the and effective and that gives you size they it doesn't give you the only side figure because there is no alternative sites for the year the radiance of gyrations part of the peace and what computers are G what we say a series of Polish and someplace in there it has a center of mass it has a point where it's uniformly balanced in each direction this is the average of the position of all the little beads of all and then reconstruct factors out from the center of mass each piece of the chain and we calculate for these little factors I was all told factors are associated the use that we calculate the average failure and that gives us the square foot radius of gyration you should realize that the radius of gyration it's not like the radius of the you have to here and I ask you what radius is year and the same person will say that the radius the sears the distance the outer will 1st all for polymer it's quite all its flexible there's a lot of empty space doesn't have a shout shop out of service so what is dollars to calculate the mean squared distance the average of square distance from based each beads and you get some it's sort of like but that is it's a distance that is much of the way out but it's not all the way out consistently are will be the chain of command and the way way out also if you tried to draw bounding surface around polymer it might be hearing work all so there are 2 estimates of how the chain about the change from which these chains sizes have 2 features are warriors "quotation mark the number of Apollo molecular weight more of these rare the longer the random oil is more or less stringent while the bigger the chain is going be and there is an entire field involved in studying how the changes relative to its molecular weight we get to that it later in Chapter I don't do invest details we get the 2nd issue that the use of both of these are also the functions component concentration they might ask why are they function as a Hall of concentration at all In the answer approximately here is the following if you look at all of the ran payouts called "quotation mark described space while a lot but some of them were discouraged because 2 component pieces of polishing get close to each other and you can imagine skin intact sketch hypothetical plants that do not exist in which court would have intersect itself go on through that's of course impossible so the payouts the per discouraged and those details since they can happen to have effect rather the absence has the effect of expanding Paul what they're supposed to put another call for 11 years the each polymer toil bumps into its neighbors and it behaves like so a polite person cocktail party intends to eliminate furthermore at high concentrations the whole solution is filled with uniformed all everywhere and the tendency of to repel itself that is to not have states in which Homer occupies the same place twice all this tends to be canceled by the other chains and the net result is the change shrinks so as positively plot the size of following versus polymer concentration we find that there some downhill consider I'm
not yet telling you what trend but in fact there was considerable theoretical work this 20 years 30 years ago and what people said time was the local concentrations of nothing much will happen this theory and that elevated concentrations the radius of gyration with and oratory Square would be reported to the scene minus 4 and I should emphasize that is a particular theory and it was not based on experiments but it is a particular theory really does exist and there is considerable work don't test there was also considerable work that had also been done already but did tested people didn't realize there were the sorts of measurements out there we have West but if you want to ask Well how do you measure the size of of all the 3 sorts advances and 1 as neutron scattering which requires a big atomic reactor in some extremely expensive instrumentation another in a series of light-scattering which bought easier and cheaper In the 3rd answer to his use legendary Indian number measures a slightly different variable is dielectric relaxation however I'm starting out by commenting and simply saying that there is this interesting question how big change but there are other things you can ask about policy changes in that chain and 1 thing even ask is if I had volunteered poetry has an end to end and the question we can ask is what happens to that and and vectors time goes on both polymers sitting in solution it's floppy like over boiling and therefore as time goes on the ends of the chain will with respect to each other and the 2 sorts of things you can imagine and what is that you can imagine this kind of on the hands-on executives long or short and it's certainly allowed do that the 2nd thing that can happen in years but the end of the year and change the direction in which its point because water and the polymer has rotated with respect to the US now when I say rotation you have to be a little purple and I think if I sell sell you this is a new racer and its rotating its rotating as a rigid body and all parts of the eraser stay in fixed positions with respect to each other yes they also said that the frigid bought you think that freshman physics it's a rigid body and you can write to rotate the rotational velocity of parts areas if you take me away there and here is the it is far from lost fulminated that make look familiar from freshman physics in a long time so OK so that's rigid body rotation of Homer does not not a rigid body however there is a rotational motion which you can actually measure at through and so is time goes on if we had this is supposed to to be the initial In the end factors time is Europe and we think that's not product that would the end and factories the as time goes on the vector for guess which way it's going it's like fluctuates and this quantity on the average look at lots of all change is going to change in particular well it could be the vector gets smaller and it could be a factor gets shorter there is a nice mathematical result will skip over which guarantees this object once we average of the case and a very long time so the vector was originally like this at long times it could be pointing in any direction with equal probability and this function the phase out on the Net :colon well it doesn't have to be prepared if it's pointed like this time on and like they have it's time to this summer's becomes negative not drawn to win by parallel that but would be the product of 2 perpendicular factors and there'll be some likelihood that it's comeback has parallel with each of the main thing is all the possible directions and lights along the lines are equally likely and therefore when you average this averages 0 yes we get she worked and we say about this well 1 thing we can do is to say thing vaguely resembles an exponential it doesn't have to be exactly that that is the word exponentially the fighting atypical time on which dysfunctional relaxes we plotted this fall showed bruises time and there's some typical time on which thing relaxes now relaxes simply as an exponential it's very easy to say with sensible definition of relaxation time if the relaxation function is more complicated you have alternatives it is quite critical which alternative fall so far so good the certainly introduces a analysts is a function of time and there a function of time I characterize the shape the function can actually measure now we are going to take a mass steps and this is a master Pozo who revel in reality or response that is if
I say I have something that is a function of time I can equally said I will do the measurements a series of frequencies and I'll have something that is a function of frequency and so for example I take the mechanical disco elastic band case I have blocked and I'm impressed with what and this is some soft objects not block the fight compressor the 1st thing that happens is that I have forced pushing back however I said the force disappears fades because the option these objects is soft and gradually changes shape and some of my profound changes and compress the object was measured the cost of the object put him back as a function of the time I get some sort of relaxation however I would also say what I will do his own thing the object between 2 plates and I will take the offer played and I will shape the overflight of them like this yes well I do this very very very low frequency the object always changes its shape as I there is basically no longer there may be frictional resistance or not but if I changed things very slowly this push back the car on the other hand provided the same emotional over the same distance and high frequency there will be a response for and the response forcefully have to parts there will be an interface and there will be out of phase part yes so and because there is an interface pop in and out of phase part on the interface part basically behave as a part the object behaves like Sprint said so in that sense of yes the House face part 19 rephrased part out of phase part says that there is frictional resistance and therefore there is lost and for the dielectric responses recalls epsilon crime and excellent doubled from and this is the I'm lost for words this is the dynamic part by going on the air for the important issue is that instead of looking at something in time domain I could look in frequency domain they might ask is it useful to do both and if you have a perfect instruments the the answer is no all of the information you have time domain you also have the frequency domain and vise versa furthermore called promises to relations and promised crime relations held it tells the tells us that these 2 parts I said there is an invasion response and there is an phase response of the system these 2 are not independent if you know at all frequencies you know the other the reason this is true acceptance of hard to see why it's truly is the I say at times 0 disclosure of blocked them the forest looks like this in the negative times there is no response the statement that the title response he has a functional form positive times and is a 0 native times constraints with these can have look like I'm not really told you have OK so I think when I wanted to make was that you can have a response which you may actually meant you go to party but now income dielectric materials In the 1st question is what is going on so that we have to heard her little place yes and we have put in charge of 2 plays here and we asked what voltage we put on 2 place to get shot there's several ways of asking the same question you could also apply voltage ask what current law all this if you think way that this is roughly fresh freshman physics class however suppose I take 2 plates and molecules in the space between the legs of effective what happens well-being may be the case but the molecules somehow have parts with charges moved in detail what I mean by parts it and as a result the charges are oriented please indicated yes well there oriented as indicated in inside in the middle of the year minus by lost and nothing is happening this is electrically neutral because innocence and lost groups right next to each other is elected political parties however at the 2 services here molecules and there will be a line of molecules here minus groups of guests and there will be a line of molecules here the Foster groups against surface In order to get the voltage difference to be the same as well the minuses and pluses are canceling and that the same voltage between the 2 places I have to larger charges 2 plates it if you actually seen as yesterday you look inside integrated circuit or circuit boards see things called capacitors and the point of capacitors that something stores charge all of the fact that you have a material that polarizes like this between 2 plates mean that means that the capacitor Concerto store much more charged than used to be the if there's material was not there and the question is that the bad news is that took you choose generative day died in the book recounted that mold the question is where the the guy calls come from and there at least 3 major sources and all talk about that in a few seconds OK now the question is is this a large effect yet Trojans have hypothetical won fair and passed out when I was an undergraduate 1 fairy capacitor would have filled a significant part of this room likable rear wall thanks to modern materials polarized much better and varied capacitors now something that you can actually pick up and walk off with it's a huge capacity and the typical capacitors you see electronic circuits are micro variants of Pico variance in size to really tiny but if you wanted a nominal 1 unit capacitor thanks to materials you can now get their recent sizes OK for how get those guys OK having died calls there's resources things that can happen the 1st issue which happens in almost any material this is a material there are balanced and and has a nucleus which positive charge in electrons which negatively charged and it may also be the case that you have covalent bonding in the electrons overlapped with neighboring
atoms and if you apply electric field you move the electrons in 1 direction and some very tiny step and move the nuclei in the other direction some very tiny extent and you have done something with the electronic states and the position of the electrons inside a mail and you polarize the mayhem and this if you have a solid this is what I have just shown you is the most common source of polarization this polarization effect does not change very much until you get up to very very high frequency because you to saying that will apply oscillating electric field the electrons and very easily moved back and forth with respect to the nuclear and that continues to be true until you start to approach the infrared and optical frequencies which lifestyles change however the important issue is 1 thing you can is to In the electrons around we're going to talk about however about liquids in was the jewel of the effects but there is a file folder and statistical biopolymer like protein and biopolymers have features that they fastened church groups to the services part for example the gap year carboxyl yesterday and it may be like this what about hydrogen this is an organic acid were made life there and that's what it looks like it is less polarized protons hydrogen ions protons nothing on the front of the floated off into the water now suppose I fly and electrical field will 1 of the things we protons let go on and go off and water found again great frequency and 1 of the things that happen is the prompted on the water over there and now this is neutral because the Tigers in there and this is negatively charged because at Wallstreet age was a hydrogen ions protons and we certainly have the case that we can remove the dipole moment of the molecule charges on the surface surrounded by moving protons around hydrogen so the hydrogen ions can move and furthermore if this is a typical by former it has service charge inside of positive and negative and the service charges like this 1 but for violence of the kind of prevailing charge thousands solution now which I on attracts depends on what's available in solution the important issue is that if you can molecule and you track outer islands there's a cloud of charges surrounding each molecule and this charge into something called defined streaming to the contestants of devised screening is you something solutions data the the it's got lots of native currently intends to attract positive ions the service and if I sit out here and how use the electric field I couldn't balances month and I asked how much charges in there and the answer is negative charges are apartment canceled by positive charges and out here this object looks as tho it's much more we can well the final electric field the extend of hold positive charge 1 way and then shot the other way with respect to its positive charges and that all is I have created a dipole see positive jurors hear negative charges there that is I get dipole moment out of this thing because I have stretched the ion the offers that out something else unfortunate of going on at the same time namely the freedom will visit induced
electrical current in the evening and this creates all sorts of interesting experimental issues we're going the main generations always I have to file folders and Polly electrolyte College where the violence not in solution the 2 would additional mechanisms for getting a dipole moment what is it you around the pile of protons where water solution and the other is to distort the IOC vise OK now this process will not continue to was high frequencies as the processes involved in lot the electron polarization why not because if I flipped the electronic field back-and-forth is a fairly large objects not tiny like electrons and they take a lot move back and forth and advised flips the electric field fast enough they sit here and say I don't have time to move so they don't operate at higher and higher frequencies this effect was wh OK now I don't know most the last sort of dialect moment you and we do it without going to the 1 that matters for styrene polymers suppose I have a molecule that I'm going to phrase this in terms of organic molecules doesn't have to be there if I have organic molecules for example I tell you what worries some work again yet routines this is what's called polyester that's an Astor polyester means you have a whole bunch of these linked together the way you synthesize them all or most typically perform respond to synthesize them and if you drop it into water and heated up you can break Fiesta ponds and greater there thanks to its polyester and the important issue although it this accident this is furnaces hydrogen whatever in each added to some extent is electric positive or electric negative and tries to attract electrons from the neighboring gaps now it doesn't attract them completely it's not like sodium chloride where chloride Mauritania strips of electron off sodium in their positive charge vary in their native charge there fate a version well however it goes to the Senate and therefore the electrons in the oxygen tends to be negatively charged with respect to to the that's also true his oxygen about his wife while the hydrogen and carbon are much less significant than the oxygen but there is some tendency for each molecule and each bonds have stifled the dipole moments are affixed fixed fight quantum mechanics fireflies electric field of any reasonable size the electrical field has a very very little effect on the cycles may create a solid I but it doesn't change very much how big this it's not a lasting solution you can create polarization how you create authorizations you take them all at the very line work and you rotate molecules of what is now facing 1 this and if you physically rotate the molecule 1 way or the other and the wrong way but you can actually online the dipole moments and polarize the liquid by aligning the Is this a large effect will yesterday sooner water water at low-frequency worry online titles as dielectric constant around the on the other hand
if you ask what is the only part of the In the end of the year I'm not trying to remember which just quoted things and I know :colon blank will undoubtedly companies whose classes of however on if you repeat the same experiment in the visible and asked What is the index of refraction water following . 3 this will cut income combined with the work in any of the main issue is at low frequencies you can line up those water at high frequencies to kids and if you are asked to what extent is if you measure the dielectric constant the students cost depend on which the unit's of if you measure the dielectric constant low-frequency to get 1 answer and is the frequency goes the dielectric constant falls for it's what you find in the optical just display some the Americans and their said we can line up molecules molecules have died forms we now go go back to start Meyer New Rama I discussed 3 sorts of motion now wired all sorts of emotions interesting suppose I have some organic molecules and structure of not giving interviews and has signed through and through and the president even rotating well if every if this object is perfectly symmetric has mirror symmetry it will not have died alone but there are many organic groups that do not have nearest cemetery around every access and therefore there 3 sorts of stuff on dipole moments with the 1st of all the standard group To some extent his hold only focal C which is perpendicular to his axis this doesn't mean the whole dipole moment .period way means the dipole moment has component is a very also have components that way With this type of this component relaxes by reorientation around this bond which is a very fast process so this this process opposite very high free there was this whole kind of group they have a type acceptance cycle face in that way and that the whole world can only be read last where it's not the the same as being delivered by rotation like this you may say Yukon River rotate like that means there's no can't rotate life that's attached to fall more than half of the year I attended group you can rotate around this bond around this axis only like this this whole thing then only rotate back and finally filed with the monomer they have that title with long with bonds lot change that In order for there to be and that Moeller along the chain back backbone there's symmetry requires start with polyethylene theory he has assembled his you can get yes on he on which way it does the dipole moment .period well the answer is this is message saying so there's no reason to prefer 1 direction or the other yes and therefore they're not there can be no then died alone surprises Idaho and and I thank the 2 sides agreed his arm the well now in this direction and that direction are obviously different yes and this fund and have a viable unfortunately there is problem they Is there are images that so this and that are going to cancel along the back they have component perpendicular to the back of memories of our current of the attaches Europe they are squished flat .period How will we be there it said yesterday this Parliament and look the company coverage yes so landings it's not about 180 degrees so the debts let me drop picture but I am not wrong all-star cast so there is a factor like this and the fact of life that the component called volunteer at songs 0 there will however be perpendicular to the back and that contributes to the title be relaxing yes see that so on and so following European the bond angle doesn't matter contributed to last Friday's contributions the not too I think somehow let get something going on Iraq and the answer is need some follower whose structure of the world's most life that mandate nice example is here's polyester the
teeth is here so the song titles here which has some signs and as I hold there that I hold there and this is the same as that of the animal there is some along the back home has not been 0 it errors OK so if you select the right call and unfortunately the world list of the Great Wall is not as large as you might like it is the case that if you select the correct polymer the dipole moment along the backbone has out other cases where it would be interesting dipole moment is close to 0 for example DNA double-stranded DNA dipole moment is the unsurprisingly 0 because to add 0 well so what can we do with this His scholarship and that each group of monomers gives us time all moment that flights along the chain and if you get out here if the wall on the to music titles including the suit 3 and if you add up the dire warnings of pieces and all factors that all life paralleled change when you have them all the other factor but has to be parallel the end the effect it does not have to be equal to the end and vector and starters the units at different businesses a distance times chartered survival this is just the distance but the sum of all the little dipole moments passed hat too a vector is parallel To Be and to have that furthermore ,comma mode is more or less the have some floppy bits so that for example 1st the the molecule title and that there is little collectors has no title that there's Rudy unit with dipole moment another flocking there so long as the whole molecule has died moments it must be the case like this 1 is no originally reported some of the dipole vectors that is if I move the ending and that will move the check to follower apart I have changed the ending and that the stretched and at the same time I must have lined up the Stifel sold molecular title it so what do we do with this well 1st we can take our polymer solution for the dielectric apparatus and we can ask on how much does it contribute to the diet the owner dielectric increments all of these the material between capacitor what happens to the capacitors measured the contestants faster and more frequency and the answer is here to replace the capacitors tells me how much charge items from plates to give and the larger the guide calls Fico small light poles between Place to really big guy falls between flights as citing increased the dipole moment molecules between plates the extent to which the molecules reminder of guess what might increase the capacity of its capacity yes and there is a rigid mathematical relationship such that I look at the dielectric increments the change in dielectric constant material we've played since I polymer and that is linearly proportional to this plot and square which is clearly proportional to the mean square and and that's why and what I have to say the bullying Oliver have 1 invigoration of the molecule as another configuration 3rd followed way stretched out so it given time each molecule has a different dipole moment the molecules all moves of dipole moments change but on the average which is always see low-frequency at contributing to the masses pasta and corresponding to that contributing quality that's proportional to the average mean square and an so that is the very 1st thing we can do we can see with dielectric constant the 2nd thing we can do that as we can apply electric field between plates an oscillating field and if we apply an oscillating feels is of all of that is tied and and and there if I lived the electric field In order for the molecules to home contribute to the dielectric constant it has to get itself turned and that takes a while and if you ask how long does it take well there's force on molecule toward which some force that induces rotation for there is also a frictional force because these things trying to move from solution added the ratio of the
driving force for the frictional forces tells you how fast things move that sort of freshman physics and freshman physics so we usually talk about a person jumping out of an airplane opening parachute and there is a force of gravity down and there is a 4th during worse off and during forced all proportional to how fast persons falling in the office that's true if you actually are doing this with real life parachute dynamics in freshman physics we usually talk about very low-speed motion would would not get conventional operations and it's only linear however whether is square is worse off than is determined by the velocity costs down reality had the worst of all voters wears Real Americans and the worst of realities it is courses and this is the thing down by the acceleration however few jump from any reasonable high you Terminal Velocity your velocity is constant the four-year acceleration is 0 and therefore the square and holes In the head of the the square root of the machines will have actually I'm sure there were about parachutes it's not something I'm practically interested in all but the 1st day of the rounds of I haven't said that the important issue is you applied driving force and really there's a relaxation rate which is determined by the ratio of the driving force 2 a resistance add the larger the resistance the slower motion the longer it takes things to get around very and if I apply a driving force of the exercise and I change the frequency will find very low frequency even very slow motion Watson rotate type if I'm height at sufficiently high frequency these things notices supposed to start switching places but they have hardly moved at all for the electric fields which side the operation it hasn't the solution of the sometimes election so it can be a factor the polymers well let's see the solution will have several relaxation some of them correspond to motions of Paul we are measuring those times directly so it's the same time on the they'll also times that are not related to what is doing the related same solvent is doing the things that the solvent is doing occur at much higher frequency and therefore those things happen very quickly in old with see at all OK so we actually can do these experiments and we can actually measure the size of pall overs we change its concentration and that leads us to figure 7 . 1 which is a few pages into the chair and 1 of the year's 7 . 1 hours shows you 1st of all is the size of the polymer the look mean square lined the and and vector as you change the concentration of always around and so when you find there is a means wears size where contribution to the dielectric constant that's the same thing going for polymers given the where giving us the Bible as a function of concentration we actually directly what is called dielectric increments constant the contribution always dialect monster liquid but with some work shows that dialect in is linear you mean square size at the end and what you see in setting yourself .period warning this fall and tracts as you increase the concentration concentration now the contraction is not incredibly big we get up to 600 grams per liter or not quite 6 that's 50 percent fall more than 50 % solvent that is extremely concentrated that's not dilute solution all and doing so we get to the on the size of the polymer from home 20 in the scribe units sound like aid so we've made this very dramatic change in the polymer concentration and the polymer science has only gone down a bit the notice however if you look at the grass practices he boasts small color concentration and as you get out the larger concentrations the contraction affects slows down OK well we can reasonably ask say that's a very nice we see that the thing is contracting of what is how was contracting what can we say about the form of contract and the answer that schools over those points tells you that means square radius is some of the town's trade please equaled mean square radius is 0 and functional performed needed the minus constant concentration will power and this functional known as stretched exponential we talk about earlier in therefore we have is shrinking process which carries on all the way out more and over the observed rained out to about 600 we have a smooth curve and we have data points lying on top of a small group there is something else we can we can also measure the rest of the year said .period 1 we have that here a relaxation time the relaxation time tells us how long it takes for a polymer molecules arranged like me to rotate through some typical of some technical angle we've applied we switch the direction of the electric field reviewing this co-signed and the molecules respond by rotating yes a version of and so are the more resistance the solution is to mold stop-motion B Lorena is time is going and what observed time bridges concentrations saying this is the same home actually it's the same experimental apparatus the same time measuring both of these measures both of these simultaneously just series captain series concentrations is the time increases sort of like that and there is a slope which can be measured and there is the behavior of Argentine and when we combine these 2 we get a concentration results concentration of all this result can again be written in the form of timed his home 0 even "quotation mark seated that is you can say that time increases when you see the smooth curves that you see in last 7 . 1 b and the data lies on a smooth curve U.S. gene once the foreign-investment her and the answer is the form of a smooth curve he is the 1 that I brought his time his farm houses and then we have the exponential and constant a new constitute I but I'm doing something about there is the size of the policy concentrations the divided by the size of the policy concentrations 0 this is a quantity has mentioned 1 it's the ratio of the radio I have to concentrate and this is raised through and then there is the In the years now raise the 1st house that is there is a concentration dependence for the relaxation time analysts determined by the size of the whole chain the end and vector sizable tract this is approximately wife and then there mind you no there is a low concentration here which is effectively a dozen low concentrations of writers as how have 0 1 plus a C but there is a deviation specifies that controls over red going off straight there is a deviation of the curve familiarity and the deviation is exactly determined by the size of the intact all now if you think of the Polish areas having to rotate the wave with water the statement that the kind knows all his popular humans not very surprising because if you have sphere rotating waters here I will water and drag force for rotation goes as human radius size sphere but with me resistance in the office of the chief the form part of the work force of street kids in this at the end thereof the of 3 areas the world only areas radius square yes however the answer is the Torah the resistance force closes the queue and I'm trying to think fast hand-waving explanation the answer is the yes there's this area that is going up or square but if I am trying to pull something distance or out at a certain angular speed the generates grows because I further out from the center and so you end up with our humor and GE home so there's something depends on radius but however on the same track if you increase the polymer belongs to him they start out base is you increase the polymer concentration they're getting smaller and therefore the ability the the ability to contribute to rotation resistance is going down because the radius is going down we are able to do this measurement because well we can measure not only the dielectric increment gives us the means we're size we can also measure my and we can measure relaxation time cannot win we can measure stone frequency domain how long it takes for molecule to forget which way it's and and vector was initially .period we have characteristic time scale to measure that figure 7 . 1 which is also from results of the Duchy at all is a 100 killer insists Paul supreme and benzene call so that actually only a single system you're looking but we will talk about Cisse Polly Supreme great deal because his Polly I Supreme has a key feature namely as a pall over whose structure can be written as ABC ABC NBC so it hasn't dipole moment .period long it's on their response tray if the molecule were just symmetric .period polystyrene all there would be no polystyrene from armored scales a b it's symmetric there being no dipole moment along the line and if you get these measurements you wouldn't see it sees folly I Supreme has the nice features but it does have a dipole moment points along the backbone and therefore you can see from the back of rotating and which is what we're seeing here start II show couldn't find safety caution of benzene is is an extremely nasty percentages if you ever feel temptation to use it you want to be quite respectful of the the well that's sensible OK let us push ahead figure 7 . 2 and in Figure 7 . 2 we talk about the same Hall who sold and so we're talking about the same polymer and the Apollo assist Polly I Supremes and the top solids for advancing which is a good soldier and I are saying which is not now I we care about solving well the notion of solvent quality is that if I have the very qualities that I have polishing and if the polymer isn't good solvent each Mama would rather interact with solve them with another model and so there is preferentially tendency for monitors to move apart from each other so they all have sold next year however the proposal as we had off and was sold horses were sold you're going to get there are there and we 1st get to the center of the whole thing .period traders sold as a little misleading because most solids really are only faded at a specific temperature and higher at lower temperatures there better or worse than fate but there come to attack region where tolerance not here where is interacting with polymer next to it another on bomber and this effect of the Paul of the policy subunits not being able to get to the same place the same kind of cancels that resulted is the change trend and we don't worst the shrinks considerably however there is a consequence of being famous all manner of goods sold if I run off the concentration of polymer and dissolved the parliament changed sees neighbors and since the monomers wanna stay apart from each other by oversimplifying vastly Paul a change in the insolvent and directs the fate of solvent the college Mamas don't care whether the touching on modern were sold so I have is when I ran up the concentration and went on behalf 3 it was it's a constant corrected doesn't care and there were no favors solving the size of the polymer does not change as you change the concentration that is an oversimplification the reasons oversimplification is you eventually get to the point where you would have to be polymer these on 3 chains close to each other at the same time the effect of the solvent the fate solvent is to cancel the interaction of Harris of when you get to the point where are triples of monomers you no longer have necessarily cancelations and therefore in concentrated in really concentrated all the solutions things can change Monday Monday's let's go back to that of expression ,comma the time expression I wrote them out the relaxation time some constant AA radius concentrations Group radius had the 0 and it really is very close to the previous concentration however he as is the case of does not contract is you need to use concentration this is civil exponential if I lot sending long scale as is seen for example in Figure 7 . to be that's the right hand figure you under-17 large-scale define what theirs this isn't doing anything I will see an exponential on a semi log scale I will see a straight line when solvent because the trainers contracting if I thought how Brazil instead of seeing a straight line policy something that rules over well that's exactly what happens if you look at the the 2 lovers sets of points of 2 fairly high concentrations I said it breaks down eventually the Allman measurements also show that you get either pure exponential stretched exponential until you get up to help the concentration there's not there's another way to break this tho I haven't thought about fact of the famous solvents on hold oversized and that's true for large chains we're very short changed there is not much effect on size of changes all quality because Paul doesn't often bend around to run into itself and so over a very short chains you would expect this object the independent concentration and if you look at the 2 sides to bottom curves and 7 . 2 b you see 2 straight lines OK the that wealth that's saying the Solomons quality effect is about what you expect all right what we've done today is to discuss dielectric constant measurements I have said a little bit but not very much about how this works I have made the point that because we can do dielectric constant measurements and dielectric response measurements we can measure the mean square size of Paul with and we can also measure in addition to the mean square size we can measure the typical relaxation time these 2 quantities are related are there were vast Nova and researchers who worked on this and that she we all this you go back far enough to find papers by Stuckmeyer yes all and I have not given all of those who try put those finery and drop from on the blackboard all the citations in detail in the text OK we're out of time players dismissed
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