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  • J. MICHAEL MCBRIDE: OK, welcome back.

  • I hope you had a good break.

  • Can you remember back to when we, before break, what we were

  • talking about?

  • The last thing we did was this gyroscope bicycle-wheel

  • precession to show what would happen to a nucleus that was

  • spinning in a magnetic field, or an

  • electron for that matter.

  • Just to rehearse it a little bit, remember the idea of a

  • pulse, a 90 degree pulse, that if you have a big magnetic

  • field-- the blue one there, really enormous--

  • and then the little magnet of the nucleus precesses at 100

  • MHz, for example, in a certain field.

  • And that gives rise to a constant vertical field, but a

  • rotating horizontal field from that one.

  • So the question is whether that rotating horizontal

  • field, which as you see it will be going back and forth

  • and back and forth, will act as an antenna

  • and give you a signal.

  • You should be able to pick up a radio

  • signal at 100 MHz.

  • Indeed, you should be able to, except that there's not just

  • one proton.

  • There are lots of protons, and they're in different phases of

  • precession.

  • So although they all add vertically, and you have a

  • substantial vertical magnetism from those, their horizontal

  • components cancel, so you don't see anything.

  • In fact, the energy is so small, of the interaction of

  • each of these magnets with the field, that there are ones

  • pointing the opposite direction, with higher energy,

  • almost exactly the same population.

  • Just a tiny, tiny difference.

  • But we'll look just at the excess.

  • Obviously, ones down will cancel ones up.

  • But if we look just at the net ones up, even they cancel,

  • because they're at different phases of rotation or

  • precession about that axis.

  • But you can do a trick.

  • We could consider that we're rotating with them, so that they

  • look like they're standing still.

  • And then in our frame we'll put on a little bit of a

  • magnetic field that's horizontal, a very weak field.

  • And now, as far as we can see, we don't care about the big

  • field anymore, because we've compensated for it by orbiting

  • around this thing as we're looking at it.

  • But what we see is that these will begin to process in our

  • frame around that horizontal field, so they'll do a slow

  • precession, all of them, in that direction.

  • So they'll be going like this.

  • They'll start here, they'll go there, then they'll go down,

  • then they'll go back, and then back up again.

  • But we're going to put on a pulse only long enough, of

  • this field, so that they go down to here.

  • That's called a 90 degree pulse, and they'll

  • rotate down like that.

  • And now forget the rotating frame.

  • They'll look like they're just pointing out toward us in the

  • rotating frame.

  • But if we go back to the real frame, the laboratory frame,

  • what we see is this whole bunch

  • precessing around the field.

  • And now as they precess around the field in the laboratory

  • frame, there will be a net horizontal field that they're

  • generating, a magnetic field.

  • And that will be the antenna that broadcasts a signal that

  • we can hear.

  • And what will determine the frequency of that signal

  • that's going to be coming out from going back and forth, and

  • back and forth or around?

  • What will its frequency be?

  • How rapidly are they precessing?

  • It says 100 MHz.

  • And what determined the 100 MHz?

  • The strength of this big magnetic field.

  • Remember, the more you twist on something,

  • the faster it precesses.

  • So we could make it 100 MHz.

  • If we had half as big a big field, it'd be 50 MHz.

  • Or twice the field, it would be 200 MHz, and so on.

  • So we get a signal that's 100 MHz radio frequency in

  • the laboratory frame, that we could detect with an antenna.

  • But in time it will relax.

  • This is a non-equilibrium situation when we put the

  • energy in to make it go down.

  • And in time it'll come back to equilibrium.

  • And that process is called relaxation.

  • And there are various things that control

  • how fast that happens.

  • But it will reestablish equilibrium, and it will be

  • very important later in the lecture about this relaxation,

  • and you'll see why.

  • So a 90 degree pulse makes the spinning nuclei, protons, or

  • C-13s broadcast a frequency that tells what their local

  • magnetic field is.

  • The higher the field, the faster they precess, the

  • higher the frequency.

  • Now let's first look at this as it arises in magnetic

  • resonance imaging, where the purpose is to locate protons

  • within the body using a non-uniform magnetic field.

  • Now, the idea of tomography is important here.

  • I've taken this from a Colorado Physics 2000-page.

  • So this is a slice through somebody's body, show their

  • rib cage, spine, and so on, and they're wearing some sort

  • of jacket that's opaque to X-rays.

  • And we're interested in finding what it looks like

  • inside, where these things are.

  • So what we do is we take X-rays, and send an X-ray beam

  • straight through and see how much gets through.

  • And we scan the X-ray from top to bottom, and see how much

  • gets through at every different x-coordinate.

  • So we do a scan, and it starts at the top, but oops, there's

  • something there.

  • And there's even more there.

  • And lots, then a little bit more.

  • And for when we hit the spine there's going to be quite a

  • bit, and so on.

  • But that's just a one-dimensional

  • picture of the density.

  • Now what we're going to do is take that same picture and

  • just smear it out to the right.

  • So that's the profile, top to bottom, or stomach to back, of

  • this particular slice through the body of bones

  • or whatever it is.

  • Now the neat trick is that you rotate that,

  • rotate it by 15 degrees.

  • And now do the same thing again, and superimpose the new

  • one on the old one.

  • And now rotate another 15 degrees and do the same trick,

  • scan top to bottom and add it up.

  • And do it again, and again, and again, and again, and

  • again, again, again, and again.

  • And see what you got now?

  • When you superimpose all those, you get what it looked

  • like, the two-dimensional slice through the thing.

  • So that's called tomography.

  • If you can get a one-dimensional projection,

  • and do it in lots of different directions and add them

  • together, you can get the two-dimensional, or in fact, a

  • three-dimensional picture of what's going on inside.

  • So that's the trick that's used, except you want to do it

  • for protons, not for bone.

  • So we want to find protons in the body.

  • For example, let's find where there's fluid

  • water in the body.

  • So there's a body, and we put it inside this cylinder and

  • wrap the cylinder with special wire, that if we cool it to

  • liquid helium temperature is superconducting.

  • So essentially, we've made a big solenoid magnet that goes

  • along the body's axis.

  • Now, what will happen?

  • Well, suppose that field is 1.5 Tesla, which

  • means 15,000 Gauss.

  • A Gauss, you remember, is about the size of the earth's

  • magnetic field more or less, so 15,000 times as strong as

  • the earth's magnetic field.

  • So what will happen to the protons in there?

  • Well, they're going to precess.

  • And in that field, at 15,000 Gauss or 1.5 Tesla, they'll

  • precess at 63 MHz.

  • So if we put an antenna in there and give a 90 degree

  • pulse, we're going to hear a signal at 63 MHz.

  • Our radio will pick that up.

  • So we know there are protons in the body.

  • Surprised?

  • No.

  • The question is, where are the protons in the body?

  • Now here's an analogy to figure this out.

  • Suppose we had a cricket in this room, and

  • wondered where it was.

  • But I'm blind.

  • I can hear, but with only one ear, so I can't hear it.

  • I don't have spatial resolution with my ear.

  • How can I find out where the cricket is in this room?

  • Anybody got an idea?

  • Well, I have one bit of control over the room.

  • I can make a temperature gradient in the room, make it

  • cold in front and warm behind.

  • Suppose I can do that.

  • Now how can I find the cricket?

  • What?

  • Derek?

  • STUDENT: Crickets chirp at different speeds at different

  • temperatures. and different intervals.

  • PROFESSOR: You hear it chirping.

  • You count how many there are in 13 seconds and add 40.

  • You establish a temperature gradient and you

  • listen with a stopwatch.

  • And if you go to Snopes, you can see that this is not an

  • urban legend or a rural legend.

  • It's true that you can do that.

  • And they actually show this picture of Doctor LeMone from

  • Boulder, Colorado, who actually did this with

  • crickets, and showed that it gives a very good measure of

  • the temperature.

  • So if I could establish a temperature gradient from

  • front to back, and count for 13 seconds and add 40, and

  • knew what the temperature was, I'd know how far

  • from front to back.

  • What would I do next if I want to find the cricket?

  • I'd fiddle with the air conditioning controls and make

  • a temperature gradient from left to right.

  • I could even make one from top to bottom, and then I'd

  • know what its x-, and its y-, and its z-coordinates are.

  • So I could find the cricket that way.

  • So we're going to do the same thing with the protons in the

  • water in the body.

  • So back to the body here.

  • What I need is not a uniform field where all the protons

  • are going at 63 MHz.

  • I want to make them faster in some regions than others.

  • So what I do is I put two coils around this solenoid.

  • And in the one near the head, I make the current go that

  • way, which reinforces the field.

  • And in the one near the feet I make it go that way, which

  • subtracts from the field.

  • So now I've generated a gradient along the body.

  • And it turns out to be that what's actually used is about

  • 40 microtesla per millimeter.

  • So if I went, like, 25 millimeters, about an inch,

  • that would be 1000 microtesla, that is a millitesla.

  • So it'd be about one part in 15,000.

  • Or, pardon me, one part--

  • it's a millitesla out of a 1.5 tesla, so about a part per

  • 1000 difference.

  • So that means if I slice the body there or there, on the

  • first slice--

  • remember, there's is a gradient from foot to head--

  • so there we have the average.

  • 63 MHz is going to be a signal coming out from protons

  • that are in that first slice.

  • But in the second slice they're going to be at 63.05,

  • about a part per 1000, because there's a higher

  • field near the head.

  • And if I did another slice another inch or so along, it'd

  • be 63.1 MHz.

  • So if I had an antenna and could hear all these different

  • frequencies and how strong the signal was, I'd get a profile

  • of the proton distribution from foot to head.

  • So just like we did with the X-rays scanning down.

  • I now know how much water there is at different places

  • along the height of the body, or the length of the body.

  • What did we want to do next?

  • Matt?

  • STUDENT: You do it in a different direction--

  • PROFESSOR: So we want to make a gradient

  • in a different direction, so I stop the current in those

  • green coils and put on yellow coils with current going that

  • way, which adds to the big field on the right.

  • And then I put other coils over here, which the current

  • goes that way and subtracts from the current from the

  • field on the left.

  • And when I do that, I get a gradient from right to left.

  • So then I can do a slice and find out how water is

  • oriented that way.

  • And then I can put coils on the top and bottom, analogous

  • to these, and get a vertical gradient, and get it that way.

  • And in fact, by putting a certain amount of current in

  • all these coils at the same time, different amounts in

  • different coils, I can make a slice that goes in any

  • direction I want to, and find out how much is there.

  • So now in three dimensions I can do one of these

  • tomographic reconstructions, and get where the

  • water is in the body.

  • Now, much more interesting than that, which is itself

  • very powerful, is functional NMR, or MRI, magnetic

  • resonance imaging.

  • Where you locate protons whose signal strength is being

  • fiddled with.

  • So for example, we talked about relaxation, how fast the

  • signal goes away.

  • If you measured this for the different signals you were

  • getting, how fast they went away, then you'd know

  • something about a difference from one part of the body to

  • the other, that the protons in this part, their signal is

  • going away rapidly, whereas here they're not.

  • So you could get something about how the protons are

  • behaving, not just what their local field is.

  • So for example, blood oxygen level dependent or B-O-L-D,

  • BOLD imaging, you can do this.

  • And you get a spatial resolution of about one

  • millimeter, and a temporal resolution

  • of about two seconds.

  • So every two seconds, you can get where oxygen is in the

  • body, unusual amounts of oxygen,

  • Now, how is that relevant?

  • Because if you have cell activity, it increases the

  • blood oxygen supply, and that speeds the relaxation, how

  • fast the signal goes away.

  • So now, these are very weak signals.

  • So the way you tell something about them, is to take a

  • difference.

  • Where did we see a difference map before?

  • Do you remember?

  • Remember when we look for

  • bonds in X-ray, we look at the observed electron density

  • minus what you'd have for the atoms. That different signal,

  • tells you how it shifted for bonds.

  • Well, you do a similar kind of thing here.

  • You get a difference map.

  • Now, this is a bunch of different

  • slices through the brain.

  • And what's lit up is where there's relaxation.

  • That is, where there's oxygen, where the brain cells are

  • active under one circumstance, minus how active they are

  • under some other circumstance.

  • It's a difference.

  • So the brain is working harder when it's in one

  • state than the other.

  • Now, what are the two states?

  • It's the subject being shown donuts minus the signal when

  • the subject is being shown car keys.

  • So these are places where the brain lights up when it sees

  • donuts, but doesn't light up when it sees car keys.

  • Now, this particular subject had recently been fed.

  • And they did it also for someone who had not been fed,

  • who was fasting.

  • And their brain really lit up when they saw

  • donuts versus car keys.

  • So you can imagine that this is very, very popular with

  • psychologists and so on, people interested in brain and

  • all sorts of things, where you can use this trick of

  • differences to see where something's happening in one

  • case versus another.

  • So that's MRI, and, of course, it's not fundamentally our

  • business here to talk about MRI.

  • Except, we want to see things happening in molecules.

  • Now, why can't we do exactly the same trick with molecules

  • to find out where protons are in a molecule?

  • How do we know that something is here, rather than here,

  • rather than here in the brain?

  • We establish a magnetic gradient so that you get a

  • different field here and here, and you get different

  • frequencies.

  • And you can distinguish where it is in the brain.

  • What's the problem with doing that for a molecule, and

  • looking at different protons in molecules?

  • What's the difference between my brain and a molecule?

  • There are lots of differences,

  • but one of them is, that I hope my brain is an awful lot

  • bigger than a molecule.

  • So you can't establish a gradient big enough across the

  • small dimensions of a molecule, so that protons in

  • different regions will have different frequencies.

  • Within any one molecule it should all be the same field

  • for practical purposes.

  • So we can't do this trick, or can we?

  • So we want to locate protons within molecules.

  • And now we want to have, not a gradient, we want to have a

  • uniform field.

  • If we could make the gradient big enough, maybe that would

  • be useful, but we can't make it big enough.

  • So let's go the other direction and make it

  • absolutely the same everywhere, a uniform field.

  • Now, and then what we're going to do is listen until we hear--

  • and put up one of these pulses in-- and hear the frequency

  • with which these protons--

  • if there are protons there in the sample, we'll hear them.

  • Of course, most organic substances

  • have protons in them.

  • So it doesn't surprise you that as I scan

  • the magnetic field--

  • increasing the magnetic field, which changes the precession

  • frequency--

  • while listening with a radio that's tuned to just one

  • frequency, as I go along, at someplace I'm going to have

  • the right frequency.

  • And the protons are going to give me a signal.

  • Of course, if I had different nuclei in there that were

  • different magnetic strengths, then I'd get signals at

  • different places.

  • But I'm going to only look at--

  • only listen for protons.

  • OK, so there it is.

  • Bingo!

  • Protons.

  • Whoop!

  • Protons again.

  • Protons again.

  • There are different signals for protons.

  • Not all protons are equivalent.

  • Now, the difference here, between this signal and this

  • signal, and how big the magnetic field is, is very,

  • very small.

  • It differs by only that fraction,

  • 2.48 parts in a million.

  • They're almost exactly the same.

  • But they're a little bit different, just parts per

  • million different.

  • Now, when this was discovered it was an annoyance for the

  • physicists who were mostly interested in things like

  • measuring how strong the magnetic moment was, how fast

  • the precession was for protons.

  • But they put something in there that has protons and

  • they find out there are different protons.

  • Which one is the real proton?

  • So they called this the chemical shift, because these

  • differences had something to do with a chemical

  • environment.

  • But this was a gold mine for chemists, because since the

  • beginning people have been--

  • since 1850, at least-- people have been interested in

  • chemical structure.

  • But the only way they could do it was convert one molecule to

  • another, count isomers--

  • as we discussed last semester with Koerner, and so on--

  • and try to use logic to figure out what structure would be

  • consistent for these various transformations, chemical

  • transformations.

  • And, of course, then there was X-ray, which really did show

  • where atoms were.

  • But here's something that could work in liquids.

  • Not everything can be a crystal.

  • So this looked really, really promising.

  • Now, this sample was ethanol.

  • Now, what do you think the three different

  • signals are in ethanol?

  • Well, one must be the OH.

  • One must be the H's of the CH2, and one must be the H's

  • of the CH3.

  • Now, doing such an experiment requires that the field be

  • very, very uniform, because if, as you go from one part of

  • your sample to another, the field changes by a couple

  • ppm, then the methyl protons in this part of

  • the sample will appear the same place that the CH2

  • protons appear in this part of the sample, or the OH does in

  • this part of the sample, even if the gradient across the

  • sample is only a part per million or so, a couple parts

  • per million.

  • And that's one of the reasons these peaks are not

  • infinitely sharp.

  • One of the reasons they're broad is that the field isn't

  • perfectly uniform.

  • But it's very good.

  • It's within a fraction of a part per million.

  • Now, in the late 1950s, as it says here, chemistry

  • departments began buying commercial NMR spectrometers.

  • This one was called the Varian A-60, and it's the one I

  • learned to operate.

  • And they had to have fields that were homogeneous enough to

  • determine molecular structure.

  • So they had to have fields that were different, that

  • didn't vary by more than a small part of a part per

  • million, so that you could tell things about chemical

  • shifts and spin-spin splittings, which we're going

  • to be talking about in the rest of this lecture.

  • But, of course, these things were expensive and many

  • different people were using them, so it was a challenge to

  • keep the field homogeneous to obtain sharp lines.

  • Now, there were knobs in there that you could turn the

  • current to coils, to cancel a gradient in one direction or

  • another, or another, or another.

  • And most of them were hidden behind that door, and the door

  • said on it, Do Not Open.

  • Because someone who knew what he was doing came in at the

  • beginning of the day and turned all those knobs just

  • right, so the field was very uniform.

  • And if anybody else came in and twiddled them, then the

  • next guy to come in was really up a creek.

  • So do not touch these gradient knobs.

  • In fact, there was one there, the y gradient, which would

  • have its own special sign, Do not touch this.

  • Now, this was fine, but across New Haven... or across the Long

  • Island Sound here, you see the smokestacks of Port Jefferson

  • and the medical building at State University in New York

  • at Stony Brook.

  • And there was a physical chemist at Stony Brook who

  • fiddled with them.

  • His name was Paul Lauterbur.

  • And in 1972 he would take over this machine every night, and

  • he'd just wreck the field homogeneity.

  • And, of course, late at night before he left, or early

  • morning, he would turn all the knobs back, because he was

  • really an expert at NMR. But the reason he did this was to

  • establish gradients in different directions so that

  • he could locate--

  • he had a sample tube, and he filled it

  • with D20, not protons.

  • And in it he put two capillary tubes that had water in them.

  • So he did exactly the kind of experiment we

  • were talking about.

  • And in Nature in 1973, he published this, where he

  • scanned vertically and got this, scanned horizontally and

  • got this, scanned at 45 degrees or -45 degrees and got those,

  • and could find out where these water samples were inside D2O.

  • And he called that zeugmatography, but the name

  • didn't catch on.

  • But the good news was that 30 years later he got the Nobel

  • Prize in Physiology or Medicine, for inventing MRI.

  • And that's what he worked on the rest of his life.

  • So it was a chemist who invented MRI.

  • So there are lots and lots of magnetic resonance

  • spectrometers.

  • And I already showed you some X-ray diffractomers around,

  • which have put classical structure proof by chemical

  • transformation, the kind of thing that we talked about

  • Koerner doing,

  • and even IR, mostly out of business, although there are

  • still things for which IR is as good or even better than

  • NMR. And, in fact, there was a Yale--

  • before I came here, there was a organic chemistry professor

  • who was in the field called natural products, where the

  • job was to take something that came from nature and figure

  • out what its structure was.

  • And the way to do it, in those days, was to do these chemical

  • transformations and try to make it from something or make

  • it into something whose structure you knew.

  • So these were great puzzles, and it was

  • really a big operation.

  • But when NMR came along, he abandoned organic chemistry

  • and took up fundamental research on quantum theory.

  • And in fact, later he became a professional studio

  • photographer.

  • He was just wiped out by NMR coming along, which is the way

  • people know structures now.

  • We haven't really talked about that much, about how people

  • knew-- we've talked about different structures, but not

  • really how people figured them out, except

  • when they used X-ray.

  • But this is an even more common way of determining

  • structures routinely, is spectroscopy.

  • And in particular, nowadays, magnetic resonance

  • spectroscopy.

  • So a couple of years ago I took a tour through the

  • department and took photographs of magnetic

  • resonance spectrometers to show you here.

  • So across from your lab you may have noticed this door

  • which says Chemical Instrumentation Center, and it

  • says warning over here, about magnetic fields, so if you

  • have a pacemaker, be careful.

  • And you go inside there, and some of these have now been

  • moved since I took the pictures, but you see these

  • things sticking up like here, and here.

  • And if you go around, you see these big cans, WARNING:

  • strong magnetic field.

  • Here's another one.

  • Here's another one.

  • That's a 500 MHz spectrometer.

  • Here's a 500 MHz spectrometer.

  • Here's a 600 MHz spectrometer.

  • Here's another 600 MHz spectrometer.

  • And out in the courtyard, behind your lab, there's this

  • special little building that was constructed specially for

  • a big magnet.

  • And it has this one, which is an 800 MHz spectrometer,

  • which turns out to be 8 to the third power.

  • That is 512 times as sensitive as a 100 MHz

  • spectrometer, not to mention other advantages that we're

  • going to talk about below.

  • Now, why is it 8 cubed?

  • It's because of the Boltzmann factor.

  • Remember, this signal comes because there are more that

  • point with the field than against the field.

  • We only see the difference between those two.

  • And if you have a bigger energy difference, you'll get

  • a bigger population difference.

  • So you get an eightfold factor from that.

  • But the energy quantum that you're dealing with, in going

  • from one level to another, becomes eight times as big.

  • That's an advantage in your signal.

  • And the sensitivity of the electronics, when it's eight

  • times bigger, is also better.

  • So all these things go together to make it 500 times

  • better, and even more than 500 times better when you consider

  • what we'll talk about soon, the chemical shift advantage.

  • So that's why one pays the big bucks to have a

  • machine like that.

  • Here are just some others that I took around.

  • And now by the cross hall there, next to your lab when you

  • walk down there on this side of it, there's a room that has

  • electron paramagnetic resonance spectrometers.

  • So this is a much smaller magnet, not one of these big

  • liquid helium cooled things.

  • And the reason is that this is to study free radicals, which

  • have magnetic electrons.

  • Mostly electrons come in pairs and their magnetisms cancel.

  • But in certain molecules, free radicals, there's an odd

  • electron, whose magnetism is detectable.

  • So this is to study free radicals.

  • And the electron magnet is 660 times

  • stronger than the proton.

  • So you don't need such a big field to make it precess.

  • So you can use just 0.3 Tesla instead of several Tesla for

  • electron paramagnetic resonance.

  • So there are two of those spectrometers.

  • And in fact, we don't have one of these, but there's now

  • commercially available a 1000 MHz spectrometer, which

  • is 23.5 Tesla.

  • And at the Florida State University National High Field

  • Magnet Lab, there's a field that's pulsed

  • that goes to 45 Tesla.

  • And it's a national lab.

  • You don't pay to use it.

  • But you have to have a great experiment to be assigned time

  • to do things there.

  • So there are lots of these things around.

  • Now let's go back and see why it's so good.

  • OK, we have these three signals, and as we said, we're

  • interested in which peak is which set of protons.

  • Now, how do we know which is which?

  • Can anybody see a way of figuring out which is the CH3,

  • which is the CH2, and which is the OH?

  • Any guesses?

  • Yeah.

  • STUDENT: The size of the peaks.

  • PROFESSOR: Ah!

  • If you have twice as many protons, there should be twice

  • as strong a signal.

  • You measure the strength of the signal by how much area is

  • under it, by integrating it.

  • So if we measure the integrals, we see they're in

  • the ratio of 1:2:3, so it's clear that that's the 1,

  • that's the 2, and that's the 3.

  • Now, we couldn't do this in IR, because we had these

  • normal modes,

  • an had for example, C=O.

  • And remember, as the C=O vibrated, something else

  • vibrated at the same time, and other things, and they could

  • cancel or reinforce.

  • So the signal intensities were very, very different for

  • different groups.

  • But here the protons are all essentially exactly the same.

  • They differ only by a part per million, or a few parts per

  • million, so the intensities are proportional to the number

  • of protons, because the difference is so subtle.

  • So you can count protons by the area under these peaks.

  • That's what it says here.

  • The number is proportional to the number protons because

  • they're so similar, not like IR peaks.

  • Now, how can you use this?

  • Here was one of the very first uses of a subtle organic

  • chemistry question.

  • This was an advertisement by the Varian Corporation in

  • 1955, who were trying to sell those machines I showed you,

  • that the guy over at--

  • Paul Lauterbur messed up the field on every night.

  • So this was 20, the use of integrated

  • intensities in structural analysis.

  • So there's a question of the structure of C7H8, whether

  • it's this or this.

  • And notice that those two are related to one another,

  • because if we shifted the electrons like that, one would

  • go to the other.

  • So you could imagine them going back and forth by an

  • electrocyclic reaction.

  • And the question is, which is it really?

  • Well, you could try to figure out by chemical

  • transformation, and people did that.

  • So which is it?

  • Well, let's try ozonolysis.

  • Now, do you remember what happens with ozonolysis and

  • then oxidation?

  • You cleave C=C double bonds and make carbonyl groups there, an

  • acid, make a carboxylic acid group when you add the H2O2.

  • So these would give different products.

  • Notice that on the left, you would cleave three bonds, on

  • the right, you'd cleave only two double bonds.

  • So on the left, you would get that diacid. On the right,

  • you'd get the diacid that has two more carbons.

  • Now, in fact, that acid on the right was known.

  • It's called cis-caronic acid, and that's what you got.

  • So what's the conclusion?

  • The conclusion is that the structure must be B, not A. So

  • that's a classical structure proof by chemical

  • transformation.

  • But here's a completely different way

  • of going about it.

  • Take the NMR spectrum and count the protons.

  • So the group on the left there are protons that are attached

  • to double bonded carbons, and on the right, to

  • single bonded carbons.

  • And now, notice that the compound B has

  • four of each kind.

  • But compound A has six of one kind and two of the other.

  • And if you integrate, you find that those

  • ratios are 2.9:1, 3:1.

  • So which is it?

  • It must be A that you're taking the spectrum of.

  • That's the one that's 3:1.

  • So it must be that that's the structure, but then how do you

  • explain this misleading chemical transformation?

  • It must be that there's an equilibrium between these two

  • things that lies to the left, so when you take the spectrum

  • that's the stuff you see, that's most of the material.

  • But it's not as reactive with ozone as the

  • stuff on the right.

  • So that little bit of stuff on the right is what reacts with

  • ozone and gives the product.

  • So the chemical transformation was misleading.

  • And this is the kind of thing that made this Yale natural

  • products organic chemistry professor pull out his hair

  • and become a quantum chemist, and then a studio

  • photographer, that you couldn't do what he was

  • trained to do anymore.

  • So spectroscopy took over in determining structure, and

  • we're going to talk a little bit about how you do this.

  • Now, Chemistry 220 website has a bunch of NMR problems.

  • There are 40 problems there, and I took this from one of

  • them and fiddled with it a little bit.

  • And in fact, let me just see, I think I left an extra--

  • well, I'll go through here and--

  • there's going to be an extra slide in here.

  • So we can integrate.

  • And see that there are 2 and 3, and 3.

  • So we know that the 2 must be that CH2, but there are two

  • CH3 groups, one is one and one is the other.

  • That's at low resolution, where the

  • field isn't so uniform.

  • But if you make the field really, really uniform, if you

  • tweak those knobs just right, so that the peaks don't get

  • broadened by having different fields in different parts of

  • the sample, and in fact, spin the sample, so that a given

  • molecule actually is going around and sampling different

  • parts to average the field, to make it even more uniform,

  • then you see this thing with sharp peaks.

  • So it's the same 3, 3, 2, but they look a

  • little different here.

  • So the peak width is about three parts per billion, and

  • that's just, as you see, a single peak there.

  • But this next one is a little different.

  • That's a triplet, 1:2:1.

  • So that's one of those CH3 groups, but which CH3 group?

  • Oh, pardon me, I got it backwards.

  • This was a CH3 group, and it turns out to be this one.

  • This CH3 group is split into three, and it's that one.

  • Now, why is it not a single peak?

  • What's different?

  • OK, well, that splitting is 0.029 parts per million.

  • I obviously blew it up in order to be able to see it

  • clearly here.

  • And this is a 250 MHz spectrum.

  • So it means that splitting, the difference in frequency,

  • of protons in one environment or the other, is 7.3 Hz.

  • And it's exactly the same there, 7.3 Hz.

  • Now, if you look here, that's a quartet.

  • And those are 7.3 Hz as well.

  • Now, what's that last signal, this little

  • tiny one down here?

  • Well, notice that the solvent is CDCl3.

  • Now, why would they pay the bucks, the big bucks, to get

  • deuterium rather than just using normal chloroform,

  • CHCl3, for a solvent.

  • What would it look like if the solvent were CHCl3?

  • You'd have an enormous peak from the solvent, that

  • hydrogen of the solvent.

  • It would wash out the other things.

  • So you make it deuterium.

  • But it's not 100% deuterium.

  • There's a tiny, tiny amount of protium in there.

  • So that tiny signal comes from a little bit

  • of CH3 [correction:CHCI3] in the solvent.

  • So the 90 degree pulse makes the spinning nuclei broadcast

  • a frequency that tells their local magnetic field, in a

  • uniform field.

  • Now, there's the big uniform field.

  • But what the nucleus sees is an effective local magnetic

  • field, which is, of course, the big field-- that's mostly

  • it-- but little, little tiny differences due to the

  • chemical environment.

  • And let's see how we do it.

  • OK, just to back up at first, you could make the applied

  • field inhomogeneous, as an MRI.

  • And then the field can be, for example, 2 Tesla, 30,000

  • Gauss, with a gradient of 4 Gauss per

  • centimeter for human samples.

  • And if you have a tiny thing, you could

  • make a bigger gradient.

  • So for small animals you can get 50 Gauss per centimeter

  • and do the imaging that we talked about.

  • But in chemistry it's different.

  • In chemistry, you make it really homogeneous, so the

  • only differences come not from where the proton is in the

  • sample, but from where it is in a molecule.

  • And now we're interested in a molecular field that's added

  • to or subtracted from the big field.

  • And mostly it's subtracted from, as you'll see.

  • So these molecular fields then tell you about the molecular

  • environment, these tiny shifts.

  • So there are two sources of these local magnetic fields,

  • besides the enormous big field that you put on.

  • One is electrons orbiting.

  • Now, the electrons come in pairs that tend to orbit in

  • opposite directions, so they tend to cancel.

  • But there's a little bit of excess, for reasons we don't

  • need to go on to, of one orbiting over the other.

  • So you get effects from electron orbiting.

  • And the magnitude of this shift is about 12 parts per

  • million for protons, or 200 ppm for carbon,

  • the range of values you can get from that.

  • Which is-- so this is grossly exaggerated.

  • It should be only parts per million of this, not, you

  • know, like a 20th or something like that, or a 10th.

  • OK, so one thing about the environment is how many

  • electrons are around doing this orbiting?

  • The other thing is there are other magnetic nuclei nearby

  • who have fields, too.

  • So if you're this proton, or listening for this proton, its

  • field is not only going to be the big field, not only what's

  • coming from the electrons orbiting, but also what's

  • coming from other nuclei that are in the vicinity, being

  • oriented either this way or this way.

  • OK, and those we measure in Hz, and you'll see why we

  • measure one in ppm, and the other in

  • Hz very soon.

  • So anyhow, when you add all those things together, you get

  • an effective field.

  • And that's what determines the frequency of the signal you're

  • going to hear.

  • So first we're going to talk about the chemical shift, what

  • happens from orbiting.

  • So electron orbiting gives this little red B, but the

  • reason the electrons orbit is because of the applied field.

  • And the bigger the applied field,

  • the bigger the orbiting.

  • So that says the red field is

  • proportional to the blue field.

  • If you spent the money to get a bigger magnet, you'd get

  • twice as much orbiting, so the red would be twice as big.

  • So that says that what you measure then is a fractional

  • thing, because it's not a standard difference.

  • It depends on how big your magnet is.

  • If you make your magnet twice as big, the shift is twice as

  • big, the red field is twice as big.

  • So it's a fraction of the big one.

  • So you measure it in parts per million, in a fractional unit

  • rather than in an absolute unit, like an energy unit,

  • like Hz.

  • OK, so here's a scale of parts per million.

  • Let's see what different values we have. Now, the

  • standard that's used it's called TMS, tetramethylsilane.

  • Now, why use such a weird molecule as your standard?

  • Well, it's a small molecule and it's volatile.

  • So you can add a drop to your sample, but you can easily get

  • it out again if you want to recover your sample, because

  • it evaporates easily.

  • Now, it has four CH3 groups, but they're all identically

  • situated, so it will just give one peak rather than a more

  • complicated molecule, so that's good.

  • But the thing that's really special is that the silicon

  • is, being a metal, is partially plus, and the methyl

  • is largely minus, which means there are more electrons

  • around the protons, which means

  • there's a bigger shielding.

  • This B is bigger than it would be if there were fewer

  • electrons around.

  • So it shifted all the way to one end of the spectrum, so it

  • doesn't overlap other things that you might

  • have in your sample.

  • So you have a standard, then, that you can use with high

  • electron density around the protons, which defines 0.

  • And now, you get another peak from your sample, and see

  • where it is compared to this.

  • For example, if you have a carboxylic acid, the H on a

  • carboxylic acid is way what's called downfield.

  • Why?

  • Why is it very different from the hydrogen in TMS?

  • Anybody see why the COOH hydrogen might be different?

  • The environment of it?

  • The OH is electron withdrawing, especially with the carbonyl

  • group on it.

  • So the electrons get sucked away from the hydrogen.

  • You don't have as much of that red shielding effect, so it's

  • shifted way down to the other end.

  • So on the right, it's said to be shielded.

  • That is, the electrons around the proton cancel the big

  • field, but only a teeny bit of it, only a

  • few parts per million.

  • And it's called upfield, and it's also a place where

  • there's high electron density.

  • And it's called a low chemical shift.

  • This scale is the chemical shift numbers, and that's

  • defined as zero, so it's a very low number.

  • And it's also low frequency, because we have lots of

  • electrons relatively big value here.

  • There is very small, relatively small, magnet

  • effective field, relatively small.

  • So a low precession frequency, not such a big field.

  • By contrast, the OH is called deshielded, downfield, low

  • electron density, high chemical

  • shift, and high frequency.

  • Now, if you have a proton that's attached to a normal

  • carbon, not one that's attached to silicon, which is

  • giving electrons away, then it comes around 1, or

  • between 1/2 and 2.

  • And these were found just by putting different known

  • samples in and seeing where the peaks came.

  • But if you have oxygen, halogen, or nitrogen attached

  • to the carbon, in the same way that silicon donated electrons

  • to carbon, these electronegative atoms take

  • electrons from the carbon, which take electrons from the

  • hydrogen, which make B smaller,

  • which shift it downfield.

  • So in that region, between 2.5 and 4.5.

  • If the carbon, to which the hydrogen is attached, is

  • itself attached to a carbon, not to one of these

  • electronegative elements, but that carbon has oxygen on it,

  • then the oxygen is sucking electrons from carbon, from

  • carbon, from hydrogen, so it's shifted down a little bit.

  • So a hydrogen on a carbon attached to a carbonyl is in

  • between there.

  • If you have a carbon attached to a double bond, it's shifted

  • down still further.

  • Now, why should a hydrogen attached to a double bond be

  • different from a carbon with a double bond, be different from

  • a hydrogen attached to a carbon with only single bonds?

  • What difference? Mimi?

  • STUDENT: The pi bond?

  • PROFESSOR: It's not the--

  • well, actually, to tell you the truth, it probably is the

  • pi bond, but that's not the explanation that people

  • usually give.

  • What other difference?

  • What difference is there in the sigma system?

  • Lauren?

  • STUDENT: Hybridization?

  • PROFESSOR: Pardon me.

  • STUDENT: Hybridization.

  • PROFESSOR: The hybridization, right?

  • This is an sp squared, more s, more electron withdrawing.

  • Whereas these carbons are sp cubed, so as you pull

  • electrons to the carbon, away from the

  • hydrogen, you shift down.

  • That makes sense.

  • In fact, this, you might expect, would be the same.

  • It's shifted even a little further down.

  • All these things were discovered empirically, just

  • by putting known samples in and finding

  • out where they come.

  • And then an aldehyde is, you won't be surprised to hear, is

  • still further down, because it has the oxygen-- it's not only

  • double bonded, it has an oxygen pulling away.

  • So all these things more or less make sense, in terms of

  • electron withdrawal, or donation to the hydrogen.

  • But in fact, it's a little more subtle than that.

  • Now ROH is funny, because it can come at lots of different

  • positions, depending on concentration, and depending

  • on temperature.

  • Why would concentration have anything to do with it?

  • Why would it have come at a different place if

  • you had more ROH?

  • Lauren?

  • STUDENT: The hydrogen bonding between molecules.

  • PROFESSOR: If you have hydrogen bonding

  • and that affects the chemical shift, the higher

  • concentration, more hydrogen bonding, higher temperature,

  • less hydrogen bonding.

  • So OH comes at lots of different positions depending

  • on those factors.

  • But you can already see from this, that if you take a

  • spectrum and see peaks in different positions, you can

  • try to say, aha!

  • This looks like it has hydrogens that are just

  • attached to carbons that are all single bonded.

  • It has hydrogens on double bonded carbons, blah, blah.

  • You measure the integral and see how many of each kind

  • there are, and you can then do puzzles, like the ones in that

  • web page that I mentioned, to try to figure out what

  • structures are.

  • Now, let's see if you've learned from this.

  • Where should you expect the hydrogen that is attached to

  • the carbon of an acetylene?

  • Where would you expect it to come?

  • What's special?

  • Noelle, you got any idea on this?

  • What's special about it?

  • STUDENT: The triple bond.

  • PROFESSOR: Can't hear.

  • STUDENT: The triple bond.

  • PROFESSOR: The triple bond.

  • So now, how is the triple bond going to affect things?

  • STUDENT: Hybridization.

  • PROFESSOR: It will affect the

  • hybridization, in what way?

  • STUDENT: Will it be deshielding?

  • PROFESSOR: It'll be sp.

  • It'll be an sp hybrid, which is more electron withdrawing,

  • than sp squared, than sp cubed.

  • So it should be pulling electrons away, deshielding,

  • as you say, because the electrons are shielding, so it

  • should shift to the left, compared to the double bond

  • ones, right?

  • Wrong.

  • It actually comes up there.

  • So there's more to it than what we're saying.

  • Now, what is this more to it?

  • Unfortunately, the clock has run, so you're going to have

  • to wait for tomorrow to find that out.

J. MICHAEL MCBRIDE: OK, welcome back.

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B2 中高級

22.醫用核磁共振成像和化學核磁共振 (22. Medical MRI and Chemical NMR)

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    Cheng-Hong Liu 發佈於 2021 年 01 月 14 日
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