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5 Electrophoresis, Diffusion, Scattering

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classes in polymer dynamic based
on George Phillies book phenomenology of polymer solution dynamics Cambridge University Press 2011
ends today this lecture is lecture
followers electrophoresis in conclusion diffusion and a few words on scattering
in any of that I'm professor at least this is still cost 590 said the phenomenology of polymer solution dynamics and what I'm going to be doing used to finish off today today's discussion of electrophoresis and then we will advance to the discussions began at what we did last time was to sample many of the individual measurements of the involved that gives information using electrophoresis ,comma how followers moved from solution the general objective and many of the things that used to say well we have experiments that were really don't discuss how we optimize separation processes however at the same time you're doing there because you were doing separation and looking at how whole of different probes traveled through a polymer solution when applying electrical field and therefore at the same time you're getting information on separation you're also getting information on the Apollo we did find a few interesting peculiar bits and pieces for example the interesting observations from part of the problem with the larger particles or West slowed down by the policy solutions from the small particles there you might propose to explain is that it is a reasonable explanation of the world .period larger particles experienced more Dreyer they also have more surface area more charge larger files and therefore large workers have more for some of the same time that's a fundamental issue interpreting like before it all of the accused parts of the chapters the skin for example are there are a number of people who studied what happens if you find an alternating electric field now if you just apply a simple easy field but it must be the case the charged objects that half the time going this way and half the time going that way and there is no net migration so you need some clever alternative way of measuring the motion of particles and Ken Schmitz and several other people discussed using interferometry light-scattering and measure the particles going back and forth by direct me however you can actually do In gel electrophoresis the use of alternating field directions to induce migration has actual substantial practical applications the reason for that is that it shall really goes to the horrors of the destruction as promised security here comes the DNA molecule but it happens to go down the path that comes to an end is stock I however if you back it up and try again if you're clever if you go back and forth back and forth the Alps hollow molecule all will find eventually find a hole and keep on going and therefore alternating feels allow you to do
things that straight-ahead does not but that's Engelbert has real structure it's the fact that you do not see this effect In Paula solutions at least I've ever seen any reference to the current market literature out there tends to suggest that Charles do not have the same obstructions they have permanent obstructions that solutions and solutions do not have those instructions so solutions and jails are really very good now we push ahead the section 3 . 9 page 73 and we will consider generalizations as to what we find experiment and the 1st generalizations it's shock always goes for a walk by my back to normal as the 1st generalization is that we can measure in light red ability and performance concentration the head and use more Alaska stretched exponential down if you look carefully at the data clearly plot communal versus come on at the end of the the I think if you look carefully at the measurements at very low concentrations all fine that things are not slow down as much as they are on the rest of her nonetheless the measurements lie on the solid lines say Figure 3 . 1 and this is because you really do see stretched exponential concentration but historically the statement there is a smooth curve I was
very surprised the reason was very surprising is that the people who were doing the measurements had a particular physical model in mind as to how policy solutions the it was the transient lattice model in which elevated concentrations but only at elevated concentrations of polymer solutions followers entangle and therefore if this is the concentration which entanglement 1st injured realize I don't really mean it's shot on from the that both here you start seeing saturation that was what was expected 10 below here you don't and if you believe in those models your expectation was that as a surprise surprise you see something else now view instead it has had advance notice of my book or by earlier review articles you would have known that when you study ,comma self diffusion were produced fusion or any of a variety of other related physical properties you seafarers life vests in which always slow each other down even at very low concentrations and he not found this result at all surprised on next following approximately speaking to have these parameters Calvin New and if you look around here or you look hot here you find that a single currency with the same parameters works all the way along if you thought that the mechanism of motion had a lot of warm down here and different for welfare well it things could rely on a smooth curve after all there's going to be something in the middle where if you thought it was 1 mechanism here different mechanisms there you expect the some region here and narrow with both mechanisms were working at the same time therefore you might see us move crossed over from down here and there a crossover it's sort of of the same as the transition lobbying careful not to use the word transition discussing this because I will say transitions and people will think phase transition well phase transitions are shocked if I take a block of aluminum and melt as its Iris solid or it's a liquid are melting is a complicated issue not fairly well understood however there is a sharp change in London and I say transition people think I mean a sharp change 1 concentration why don't have a theoretical model predicts that we just say we have a region here we have a region and we can resolve of mystery the middle but it and because we go from here to there you would police say that if this dynamics were different from that dynamics and might get the same functional form for the concentration because after all the same functional form comes out of differential equations that the detail physics but if you've got 2 different things going on you might think that health blew off to change as you get from someplace you someplace there well they don't if you found way back to section 3 . 1 you may remember that I mentioned scale scaling wall tells you do is proportional to the host city to be called wouldn't minus X has gotten a bad elements who sold beyond work and as the molecular weight of the Matrix all and therefore I go on too long long plot you might expect you believe this get straight line well if you put the data onto waterlogged flight you don't get straight you get smooth curves of course if I have a smooth curve like this and very creates a straight line themselves slowly it is always the case there will be some region where the straight line is tangent was moved her especially with the school's purveyors Wilson and the number
of data points along the smooth isn't incredibly here there was no reason to put an incredibly large number of data points on from the purposes of paper from there said however no matter what Slocum predicted within reason of fiscal year all you find there will be some part of their curve which is tensions here straight line an uncomfortable basic scientific knowledge and the word is falsified falsifiable is a basic property of scientific it means they make predictions the concreting enough that you can prove their role all How do do we know and scientific theories are true well there sources 2 sorts of things 1st of all there were few Chalmers effects and the model whatever you have to make predictions that predate lots of facts and are consistent with things the outside all falsifiable means theory makes predictions that made him a sense that you can tell they're wrong here might be lots of different theories that there are no longer on the predict more or less the same thing where you have to make some predictions which also is sufficiently concrete you can show incorrect the scaling predictions With longer here In the absence of a prediction as to whether Lopez like this here we're here to here on approach is not being falsifiable because the model does not predict the concentration reaching within there is opposed to see this behavior or if it doesn't make predictions that don't seem to be will get that there but if you want to have a scientific theory that has to have a property that makes reasonably free predictions and the predictions you are actually up and be shown to the untrue malls role In any event we not see scaling also the modeled after this the army 0 0 model predicts this is a general property of obstruction type models that if you have a very long polymers you does not merit the polymer molecular weight is they will slow down motion of the probes to the same extent because if you have a fixed concentration of really long polymers doesn't matter how long the colors of the holes between the chains the same size well and if you go back and look I give you a number of curves right slot mobility versus polymer molecular weight or fossil Bellizzi versus concentration and what is yet I don't necessarily use the axiom curves like that is that you increase the molecular weight of the matrix the latter Ferretti motions slowly there is a very strong piece of evidence that the obstruction or oxidant i models are entirely incorrect all they made a very concrete prediction and the very concrete prediction wrong OK through what else do you see well we can measure mobility is actually the same said that as long as the experimentally as you fill your capillary too With policy solutions some concentration you put in a lot on a whole bunch of probes the of different size you apply the old and weighed and as the probes travel they spread out and by the time they get to the far and capillary they're coming out at different times showing they have different abilities so 1 experiment gives you the mobility of a whole bunch of different approaches and what we thought while an impure water all these probes different sizes have the same mobility why well they have different charges and therefore the details of her and complicated they have different forces on them but they also have different hydrodynamic drafts the slowing down by the soldiers when they tried to do and those 2 effects exactly canceled and therefore if you look back
over the year 3 . 2 you notice the these lines of starts at the top where the probe if you were probe mobility also is in the the process In polymer solutions at some point zone like this in which there is a stretched exponential growth size and then you hear crossover reading you have a very weak power loss and it really is a week it doesn't appear to be power although it might not be because you don't see very much of it and it's a fairly weak Powell and in this region the mobility changes very little with probe size do so if you trying do win lack frantic separation to all these things traveled about the same rate and therefore could not get separated very much so you can separations here is nicely and out here life is less interest I did however go I there you can also do the letter of the law as a function of applying electric field whenever we feel we all suffer from the community mobility as a function of electric field and in wheat fields the mobility is independent from the electric field that is the change the electric field and to increase if things go faster but it's a purely linear response so it's light stretches phrase there is a linear regime if you have a nice spring you you hear from law books on precisely and I have a amassing from the spring stretched and find all mass stretch work I have wire and I applied electric field there's current and almost lost 5 goalie applied voltage I don't I will ask the linear abrasion however if you take the electric field out there is a point at which you get a transitional and developed with nonlinear thinking and not hearing the mobility goes downstairs workday is so weak power and that transition is fairly sure similarly this transition is fairly sharp but it has to features the 1st feature is the position of the transition depends at least someone on concentrations fall concentrate not very much hard graft you'll see appears to be 1st 1 if you will .period there seems to be few points the year where there is a transitional regime where
you could actually clearly and on ambiguous we see that there's a transition that is you have .period serial line on the her you have points here why on earth and in between the points which really quite visibly city and so you have more complicated issue no 1 thing you might propose I can try testing is where it is that you have a mechanism that gives you this you have a mechanism that gives you that her and 2 mechanisms for editing and therefore if you have done fits a set of to use your going on all the time Paul the sum all of this straight up quite straight line this move her in the intermediate regions would have to rise up a bit and is possible if you were clever you can't find a better said a description of what ideas the book however as a practical matter since Sunday may be writing your own books but you should realize that at some point I hear you stop where things will never come to an end and of course there are people decide to write a book and holds perfect and they start when they're little more than you are and she 40 years later they claim they're still writing polishing the book but nothing ever gets complete you'd like to get things done the better In a way in the 3 it is possible that we will however all electric molecules that are not here the case like stopping startled and if we take to followers of the same year you discover the mobility of a linear polymer little melody and start all ,comma over very nearly the same yeah well all the big huge things they're being dragged through solution if I look at the little bit of Paul over here a little bit of polymer here they basically see the same environment next yeah the arms out here in this case that the way forward OK and therefore I say this to policy at the same total molecular weight because there is a total molecular weight at what separated all of the polymer here got knows there are pieces out there in some sense but it doesn't cure catch like it's worth the stretch like this so the tolerable regional little pieces of all moment of peace right here sees exactly the same environment whether it's on the Stockholm or a linear Paul therefore want now why is this your life might this be disturbed well if you weren't really low field region and the but if you were really love feels you will say the way it has changed and moved through solution Of course it is rampant .period the way I can move through solution Firefly an electric field D Is there move along its own life and wiggles back-and-forth somewhat because there's confusion but there are models and say this is the rare occasion model can move sideways he can only move by traveling all along its own lengths over this and this year and the year of did all this and this here and year yeah but the change sentiments here can sideways area that's the reputation of the motion now life this problem stop In the histories for offense .period called and it's stuck in a place where rectification works for example inside of solid across the chaps and there are changes all the changes around like this the only way this peace and in that way worse this To reach it In this to be tracked the ball well and now lot and sideways and after long has signed with the arm extended again you might realize this shortfall will be along these polishing the contract like this is statistically very unlikely and therefore if you thought this was the dominant change functions stock always will be almost immobile and polymers also under the external the answer is if you have a real cross-linked gel you can actually video microscopy watched the the stock holders the dread through polymer solution come after the service of the shell and crashed will hold because they hit surface they can penetrate again so they can sit there again do anything else the linear chains will they have work hard to find a hole in the and come along through linear a solution here a real challenge the bond going it's somewhat policy process in the Jets stock changed him in a real Chelsea Stockholm's polish solutions that's not true stock holders about moments later while there are also other mechanisms which would explain how polymers or movement and 1 mechanism reaction is here is the same charge politicians trying to move this way and is currently delays because wrapped around it is 1 of these neutral matrix of which for a lot the church Paula had pointed toward this way this followers were stopping partly somewhat attached to its so what happens is that this
change is this away it's like putting your column In some very soft you raised for and the new rules fall off before yes well that's going on in principle it linear Stockholm which moved the ball solutions and since this little area here doesn't care very much about the stock it does lead to the picture of the linear and stop all miners could move at about the same speed From day 1 of the questions the cultural entire background which chance winning people also how it managed to the retraction while the arms were moving through diffusion they do random motion yes so 1 of the random moments like this and it's of course a random but there is some statistical likelihood that it's always curled up spontaneously and have to had to wait for this to happen spontaneously none will correctly said if the art is really lost nearly all arms you don't expect the arms be able to curl up like this very often and in fact the prediction is that the mobility of the starch falls exponentially with the length of the yards exponential philosophy really OK I know it was a very good question OK let us show that has and was forced to the three-day at 15 on page 76 group there is 1 of the things you can say is I have this picture at least this function describes the measurements were and 1 of the questions I can sensibly asked is well parameters doing something at least vaguely intelligence so we're sitting on page 76 and what I have done is to take the parameters of the new and they also and new these are different for different size probe so what I have done is to apply health as a function of probes eyes to the sort of question is do I get something resembling a smooth curve do I get something that looks as tho it could in principle allowed the physical theory on why simply get hatch and the Hashim or sending the message that idea again is smooth curves the theory that fit data but they're really telling you when and well you actually see smooth curves I have fondness this for several different polymer matrices and if you look up from the bottom to the top you notice that as the concentration of the matrix is change the current thrift in a systematic manner all were BH they are ensuring young at component molecular weight is changed I said concentration if you change the molecular weight of Calder you get somewhat different person that's sort of what you would reasonably expect now are there are people who moved all the people who tried Analyses of this or that the truth in terms of hall there is an extremely effective literature offer was worth reading was not told of the plagues often sold by the name of 2 of the and was not very systematic studies and electrophoresis and cross-linked jets and in Crosslake jails the our reputation and pangolins obstruction models were quite respectably well and there some very nice papers in for example the use reviews of modern physics called correctly me to carry shows how homeowners moved through generals and guess reasonable agreed however he doesn't briefly very very briefly discuss solutions saying that all it seems fair to say that present theoretical understanding of Holly electrolyte separation and 72 polymers solutions rather unsatisfying work experimental data appear display very smooth evolution of mobility across the entangling transition which cannot be accounted for by an existing models and then of course but that the yes DNA fragments can be separated polymer solutions well below the entanglement concentration um it's a surprise such a result was believed to be impossible within the framework of the existing theories since few always art entanglement then exist theories that these people were using the word only theories even better than didn't predict what you actually found experimentally OK so we have now shown through and I have discussed policy options and electrophoresis of all now I'm going to push ahead discussed something else question section 112 it is trying to intervene in this legislative program and that it was found that the OK the issue this fall electrophoresis substantially but not completely works there's also this electoral most electrophoresis words because you were applying electrical force on the Palma's you try and separate if the polymers were not Polly electoral rights if they were not sure there would not be nearly as much force now that would not be 0 worse because the dielectric constant inside the home Paula chain is different from the dielectric constant water and therefore if you applied electrical field gradient you can call us things to move because they become have served as a
service charge and the service charge can interact with the field gradients as called by electrophoresis on the other question you might ask however is supposedly the background polymer instead of being neutral were also charged with you vendors separation wall that might sound the slightly more the question but in fact there is a literature history based on solid Fugate and that is if you were sitting doing this chapter to critical separations of several species in the polymer matrix is probably the case of polymers not exactly density managed soul and therefore you were running the experiment and the species trying separator following up through but you're matrix ,comma is also willing and so it it turns out for example the matrix Paula is moving faster than the separating species it still manages slowdown remote all by analogy that it should be possible to do electrophoresis and a solution that contains church polymers makes the very serious complications of which is that if you have all these charged objects and solutions and applying electric field you get feeling and Headingley used all sorts of complications from what so as the answer is yes you could do what might find
some interesting challenge what's happened without challenge other question a professor of English at ease the next chapter Washington that this year she has any of this that suggesting that in the shares sending out OK I will briefly comment on issues the notional shares standing is as follows the policy if you put most polymers in most solvents the viscosity of the solution goes off the measure this but at the same time parallel plates have want them this way and the other 1 stationary and you get a force you have to to find the optimal with respect to the lower 1 anyway asked how you managed to hear complaints and not worry about the answer 1 plan the other place I'm looking at a cross-section of the circle shaped like cold I wrote a conical objects with respect to flat object and she at this point congress coming out of the water a ever that's the players is sitting there and therefore there is no velocities 0 in this direction here there is a velocity substantial in this direction of here and this year 1st that except these 2 1 only here coming out of the water .period and so this topic is moving its long-distance business stationery and the it the would take velocity but I have to apply worst hit the upper plate however if I have shared the there's also something to hold on to their international players don't walked have more info I have shared that I increase the velocity of the upper plate the forest is not increased linearly that is the apparent viscosity of political with the resistance to motion falls I the upper play faster and faster and so I parked the car viscosity systems of VS 12 you could contact with a simpler way monitoring the whole philosophy .period you get monolog was a lot of personal life there and there is a low share region of which viscosity is independent of how the tests no place and if she want to play sufficiently faster this falls off it's over it's over last year shares but the year thickening you see something like that well the notion it's because you objects very fast so solution at least asked relative to the distances between them and the neighbors 1 explanation for the behaviors you see is what you were getting share and the current velocity of the apparent viscosity medium falls because the particles of movements of its sufficient effects wide we say thinning gray hair thickening well there is 1 of the reasons for the users like you have and the plot as a function called concentration the viscosity of the solution and we thought it was over the mobility and his father Dreyer article fields and we get 1 of the viscosity and we had the effect her worker mobility and water over the mobility and sold Italian Polish increases the viscosity of law but also increase resistance particles would finally the same amount this behavior where the viscosity does not help particle mobility is actually quite uniform other questions before I put on Chapter 4 of which would mean that there is no time for that small molecules to be act I don't think it's all of us well the to stressed you question the 1st I have not yet been who have called for if the object is 1 very strongly the holders because it refused to get out of the way the object and Paul the motion of the police's what they would be if the object of their environment is not carried safely through to follow molecules along forced out of way and emotional polymers here moving object becomes very different emotions have if the object from that's then the 2nd part of the terms of the responses there is also what is known as a nonlinear viscosity where you Europe for example applying each year and you suddenly changed their and so we were rotating disk quickly and you suddenly slowed down how fast you're moving in the polymer solution has noticed that you've changed how fast you win the rotating object and respond to the check and it takes a while for the polymer solution to respond and was discussed go over the value that corresponds to the motion Basson nonlinear viscosity is discussed in chapter working over OK the last thing I wanted but this part of the about light skin now Chapter 4 were actually has a bunch of pieces in and I'm only going to focus on scattering pieces that I don't talk about the details chapter I also talk their share your about diffusion and swords in the future I will talk about that 1st I also talk about methods for calculating diffusion calling particles were going to skip because it's very remote from professional interest in the
calculations are actually fairly interest however having said that when that let us 1st of all the questions but I do the original experiment goes back remembered saying to fish who started out for example putting a drop of ink water and measuring the His spread out through the water tank and he eventually but problems fixed and fixed swallows the fusion currents of factors all material and some direction although there isn't 1 of them JKX :colon wondering was Constance B. diffusion coefficient and the diffusion coefficient multiplies concentration gradient so the concentration is uniform there's no net loss more than however if I have more Oracle's here and you particles the there is a net diffusion current that tends to make the concentration gradient go away now the exterior variation of face wall as well this is exactly like forays result from the diffusion of heat except instead of observing the diffusion of Winchester which was a method of chemical element used chemical element that was no isn't such a thing opt instead of measuring the diffusion of Houston we're measuring the diffusion of pain and instead of having a temperature gradient was said to the concentration of is well we have concentration gradient of what we would now say is a real chemical sources works were treated well however the advantages for workers who might be sent to the problems of the world there are 2 sorts of experiments American tried 1st of all I hear is a solution those things following his space in between Seoul and underdevelopment and find warlords and I'm the candidate himself away so I can observe the motion that 1 molecule relative to its background and I discover at least at long times that means where distance traveled is linear and ,comma proportional to Constance B. that is the diffusion coefficient however this diffusion coefficient is the sum of just south worst single forest but if you future of it the reason it's called single particle diffusion coefficient is that we're just measuring the motion of this long horrible relative to a uniform back that's all but how do you intend particle over actually lots of different ways to do it 1 thing you could do was to chemically modified Oracle to take at actually died died to with the simplest thing to do is to watch the dice spread out solutions a more complicated version as saying well if I have guy hit very hard with laser Poles dialog through the composers and I bleached dyed white and I can produce and solution of a bunch of songs straight lines where there is very little time left in between there is stuff and then I can measure how fast those zones this year old discusses piece of very thin new used to say I'll take a small varies from falling and I'll observatory microscope and that illuminated with a very bright light every so often and I will tell you how many dilated particles you maybe there are in the volume and on and I will also measure how long it takes for that moment to change because it emerged that number to change 1 of these particles of various Borland yesterday refused to the edge of the volume and had rest solution so why do these measurements and from these measurements I can determine the diffusion coefficient the tail another way to do this calls on what is called pulsed field gradient nuclear magnetic resonance we will see this technique going by us on a few occasions suffice to say this is a technique that uses an important measure how long it takes have Oracle spinning their particle to move a certain distance from solution but the rest of the way do the I could do this diffusion
measurement by emulating professor Dr. thick and what Prof. Dr. face it hasn't said I will produce a solution that we think profits of and therefore the about in molecules here there were a few working molecules out here but there might be solved by the water .period glasses with certain the figure and therefore plot concentrations 1st position I see something that looks like this and I can ask a lot happens as time goes on answers and goes on particles over here on the application that the office particles over Of the erection of what many particles or and particles here whatever the solid is it's concentrated they see each other and jostle each other and try to shove each other down here concentration gradient will show jostles obviously it oversimplified and 1 of the late sections Chapter forgoes considerably more prosaic however the important issue is but I had a few encourage users share which is the diffusion current but they describe and as the is and the summer mutual worked here if you don't want to the mutual diffusion coefficient describes the relative motion to articles solution he clearly didn't think calculations for saying it distracts the motion of particles down at concentrations greater than the mutual review on but the important result let's get this is a fight flocked to the area part of the city 1st concentrating too the call the US and South diffusion coefficient falls along side increased concentrations particles as they just get in each other's way on the other hand for the mutual diffusion coefficients through 2 affects 1 which is the particles in some sense to get in government and the other is they tend to to push on each other and push each other away from each other and therefore mutual diffusion both all arises there so I might impressively with increasing concentrations the uniform those of the self and mutual diffusion coefficients are not gay that you will find people using other terms in the literature and 1 of the terms this is the collective refusal told the collective diffusion coefficient is just the mutual diffusion of you will also find he was the product of a whole new energy-efficient homes things are introduced using diffusing through each other and unfortunately as far as I can tell some people being mutual song he himself and this term is not always used to complete consistency ball single officer consistent most people very good about them but if you read the literature you find a half-dozen papers which say introduced Fusion you have very very carefully with the experimental method is what they did in order tell what they're talking about all Southern diffusion coefficients analysis a few words about him the it has undoubtedly have someone get off the ground but when Seattle light X-rays or whatever OS scaring his very uniformly used in the study objects to physics materials science the thing doing scattering can be described as a way but the thing to do in this scheduled could be applied to commit the X-rays which is basically same life much shorter wavelength you can use agreement New France because we don't promise they all have the same speed and momentum and make it work neutrons behave like away you can also use the area with the electrons so you have all these choices of things for which gathering
but the underlying demand is always the same we have whatever is coming in and whatever is following in the described as 1 that so here is wave pressed was waiting to see young Ocean Beach and accept the traveling waves and very uniforms and waste coming this from objects were scattered in all directions however we're going to have offered here in the great distance the factor and attaches only going "quotation mark collect the light this scary exactly ports now picture of drawing sheets in waters that actually in order for this to work to make this distance has this fall rather small guest relative to this this is the more so than 1 meter lap scattering from different objects scattered light or whatever its head off that way and white race almost parallel to to each other the government so we're doing scattering we collect scattered light electrons were where the skin on the next thing we say on which a single Seattle forward Tuesday with 1st Werder born approximately when we did said brands he added whatever we say the idea here is the incident light coming in and the reactors use stuff going back yes this this this life is quite head this is very big why does America well like going this way could also be scared off Adams and have offered different directions and be riskier and if I'm sitting here with my captured in addition to the single scary like the 1 that is only scary wants is staring strong Lacy Dole's scare light scattered bodies and triple scared and then masses of mathematics nowhere end so what we're saying is we're looking at some of the solution that is almost transparent so almost all of the light goes through and only a little thing like scared off the side and that's what we do can I wouldn't approximation of we say volunteers a reference and this a 1 of these particles of pollution is the origin of the coordinates and like that marches along this path and that has phase year-round when it gets to the water of like what turns along like this test here sets off while they are on the bench against the detector while had travel faster yes as light moves its phase changes and because a lot longest path travel that means when it gets to the detector is not the same as the face of this fight what happens if you combined to light rays monochromatic light rays having new faces interference yes if you think back to to freshman physics maybe you taking laser and you shine through open handkerchief works piece and a laser beam goes to bunch holes and get this remarkable pair spectacles and dots and lines on the wall because the light rays they act coherently and sometimes they had constructively light bright and sometimes they are destructively and lawyers did you well that's fine what we like to to do it it is the man that tells us what the change in phases but on condition that what we know is what we say it is as the light moves take a snapshot of 1 incident what we the light years traveling in this is direction has what is called the waiver a initial carrier international points in the direction is moving and it has meant to the fight over land of life you don't hear someone is going to have landed has way affected the final I mean it's going that way and a final as wavelength from high over land that I had implicitly put last approximation I capital and alas approximation is the initial waiting for the final leg of 1 in gallery are saying that is the lightest scaring off this objects so must be some momentum transferred with the energy that is transferred to this object is extremely small the energy transferred this object is very small and therefore I approximately the 1 here and 1 there is evidence that wave well it appears to me that I was and therefore I will finish this discussion next time in addition Art in the legislature will get started on Objective 5 the chapter 5 discussed the motion solvable molecules and other small
Schiffsklassifikation
Schaft <Waffe>
Messung
Hohlwelttheorie
Windrose
Gel
Polymerlösung
Diffusion
Diffusion
Übungsmunition
Computeranimation
Teilchen
Schiffsklassifikation
Elektromigration
Luftstrom
Satzspiegel
Spiralbohrer
Gleichstrom
Trenntechnik
Ersatzteil
Feile
ALEPH <Teilchendetektor>
Raumsonde
Messung
Aufschmelzverfahren
Mechanikerin
Maßstab <Messtechnik>
Festkörper
Ladungstransport
Cross over <Teilchenoptik>
Schwächung
Leitungstheorie
Zylinderblock
Schärfen
Kopfstütze
Pfadfinder <Flugzeug>
Kristallgitter
Molekülmasse
Bahnelement
Klangeffekt
Theodolit
Pager
Konzentrator <Nachrichtentechnik>
Kaltumformen
Relativistische Mechanik
Hydraulischer Aufzug
Rauschzahl
Diffusion
Stoßdämpfer
Übungsmunition
Flüssigkeit
Kernfusion
Matrize <Drucktechnik>
Buntheit
Modellbauer
Rosa
Fliegen
Stromausfall
Masse <Physik>
Konfektionsgröße
Linearmotor
Ladungstransport
Tiefgang
Satz <Drucktechnik>
Leistungssteuerung
Leitungstheorie
Woche
Prozessleittechnik
Trenntechnik
Kette <Zugmittel>
Spannungsänderung
Molekülmasse
Schleifwerkzeug
Raumsonde
Klangeffekt
Theodolit
Kaltumformen
Konzentrator <Nachrichtentechnik>
Kraft-Wärme-Kopplung
Licht
Elektrische Ladung
Druckkraft
Handy
Nassdampfturbine
Schwarzes Loch
Satzspiegel
Eisendraht
Gummifeder
Jahr
Source <Elektronik>
Matrize <Drucktechnik>
Modellbauer
Buntheit
Ersatzteil
Brillouin-Zone
Papier
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Potenzialausgleich
Schaft <Waffe>
Messung
Magnetisches Dipolmoment
Gagat
Anzeige <Technik>
Closed Loop Identification
Kugelblitz
Mechanikerin
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Metadaten

Formale Metadaten

Titel 5 Electrophoresis, Diffusion, Scattering
Serientitel Classes in Polymer Dynamics
Teil 5
Anzahl der Teile 30 (Lecture 2 missing)
Autor Phillies, George
Lizenz CC-Namensnennung 3.0 Unported:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/16231
Herausgeber Phillies, George
Erscheinungsjahr 2012
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Physik
Abstract Lecture 5 - more on electrophoresis; diffusion; a bit on scattering. Professor George Phillies lectures from his book "Phenomenology of Polymer Solution Dynamics" (Cambridge, 2011).

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