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  • >> Sticks.

  • All right, but we're going to talk about spins today.

  • Not about sticks.

  • So I want to continue our discussion of the concepts

  • and theory behind NMR spectroscopy and again,

  • this is not going to be about math or anything to that extent.

  • But we're going to be thinking very, very qualitatively.

  • All right, so when we last left things we had said

  • that there are two spin states

  • for a dipolar nucleus like a proton or C13.

  • There's spin up and spin down,

  • and if you have an applied magnetic field there's a small

  • energy difference between the spin up state,

  • what we're calling the Alpha state and the spin down state,

  • what we're calling the Beta state.

  • And because that energy difference is

  • so small unlike IR spectroscopy or electronic spectroscopy,

  • UV Vis spectroscopy where the energy differences are very big

  • and all of your molecules are in the ground state,

  • here there's only a miniscule number of nuclei

  • in the lower state more than the number in the upper state.

  • We said if there are -- if we take 2 million protons,

  • out of those 2 million protons depending

  • on the applied magnetic field, it will be 50 or 80

  • or thereabouts difference in population.

  • In turns out that difference in population is going

  • to be extremely important because it is only

  • that differential population that's going

  • to be able to get us a signal.

  • All right, so if we think about things

  • in an XYZ coordinate frame, and I'll talk more

  • about NMR spectrometer in a second and how it works.

  • But imagine for a moment we have some coordinates,

  • so the X coordinate is coming out of the plane,

  • the Y coordinate is in the plane and the Z coordinate is pointing

  • up and we're going to have our applied magnetic field BNOT

  • pointing upwards.

  • That kind of makes sense.

  • These super conducting magnets are always vertical

  • because you've got this big pot of liquid helium surrounded

  • by a vacuum vessel, surrounded by liquid nitrogen,

  • surrounding by a vacuum vessel.

  • And, those small amounts of population,

  • that small differential of population with spin up is going

  • to give rise to a net magnetization.

  • Now, in other words a way to think about this is for most

  • of our cases we're going to have one nucleus pointing up,

  • one nucleus pointing down in their spin

  • and there's no net vector here.

  • Those vectors cancel each other out.

  • But for that small differential of access vectors you're going

  • to have some net magnetization along the Z-axis.

  • Now, the ay it works, when you apply a magnetic field is you

  • actually have those vectors that are processing around.

  • So in other words they are processing

  • at that resonant frequency, at the Lamar Frequency

  • at 500 megahertz for 117,500 Gauss magnet.

  • So we actually can represent this by saying okay,

  • we've got spin sort of pointing in every which way,

  • and I'll just draw two directions.

  • They're all processing around.

  • So remember, remember this is only the differential population

  • that we're worried about because already for every one

  • where you have one up and you have an opposing one spin

  • down those vectors are going to cancel each other out.

  • Now the other thing is they're not quite on axis.

  • In other words they're not like this.

  • It's like a gyroscope if you've ever hung it from a string,

  • the gyroscope doesn't --

  • who's hung a gyroscope from a string as a kid?

  • The gyro in physics lab or something.

  • The gyroscope doesn't hang vertically,

  • it kind of hangs off axis and goes around like this.

  • But if you think about it, since those spins are not bunched

  • up for every one that's processing

  • like this there's another one that's opposite it.

  • So in other words if were just like this you'd say,

  • oh there's a net magnetization along the Z axis

  • but also a net magnetization along the Y axis.

  • But there are other spins that are like this

  • and they're all going around.

  • So everything is canceling

  • out except the net magnetization along the Z axis.

  • All right, what I want you to imagine right now is

  • that we're going to place a coil along the X axis and we're going

  • to put energy into that coil.

  • We're going to apply a magnetic force.

  • And I want you to think classically

  • because the quantum mechanical thing is going

  • to be we'll flip the spins.

  • I'll show you that in a second.

  • But you have your net magnetization along the Z axis,

  • and think back to classical physics.

  • If I apply a force along the X axis, right hand rule and all

  • of that good stuff, we rotate our vector downward.

  • So after we apply a pulse, I'll just say a pulse.

  • If here's out net magnetization,

  • when we apply an RF pulse our net magnetization moves along

  • the Y axis, and so I guess if I want

  • to actually represent it I'll just say XYZ,

  • and I'll say here's our net magnetization.

  • And as you'll see in a moment we're going

  • to have continued procession.

  • And again, if you're worried about the fact that all

  • of our vectors are not lining up, that they're all processing

  • like this, just think as I apply a pulse

  • and drive my magnetization from the Z axis onto the Y axis,

  • the vector sum is right along the Y axis even though there are

  • some that are like this, I drive it down.

  • They're countering each other.

  • There are some like this, I drive it down.

  • They're countering each other.

  • And so our net magnetization ends up a long the Y axis.

  • Does that make sense?

  • All right, lets come back to our spins to see what this means.

  • So, the way I was trying last time

  • to represent this very small difference

  • between the Alpha state and the Beta state was

  • to show some vectors, some spins pointing up in the Alpha state.

  • And some spins pointing down in the Beta state,

  • and to try to represent this miniscule difference

  • in population what I did for the purpose

  • of my drawing was I drew 6 with spin up in the alpha state and 4

  • with spin down in the Beta state.

  • >> [Inaudible] nuclei right?

  • >> Those are representing exactly the spins

  • of individual nuclei.

  • So in other words, if we had a mole of --

  • or more realistically if we had a millimole of CHCL3,

  • proiochloroform [assumed spelling] in our NMR tube,

  • what this would represent would be the different,

  • the nuclei of the hydrogen there and we would have out of

  • that millimole of nuclei we would have a small access

  • in the Alpha state and they would all be processing.

  • All right, so if we apply an RF pulse, and now I'm going

  • to be a little bit specific, if we apply a pulse long enough

  • that it's what's called a 90 degree RF pulse or a pi over 2.

  • That's just radians and degrees, your choice

  • and they get used interchangeably.

  • What that does is it equalizes the population of Alpha

  • and Beta state, so I'll represent

  • that by 5 spin up and 5 spin down.

  • And this situation is exactly the situation that we have

  • at the end of my little drawing

  • over on the left-hand blackboard.

  • In other words here's our net magnetization.

  • And so the key is now we have no net magnetization spin up,

  • no net magnetization spin down,

  • but the very important point is we have the net magnetization

  • focused along the Y axis.

  • It is not diffuse, it is not pointing in all directions.

  • We actually have net magnetization in the XY plane.

  • And if we apply a longer pulse, a more powerful RF pulse,

  • so again I will represent our 6 little arrows

  • and 4 little arrows representing our differential populations

  • of the Beta state.

  • If we apply a more powerful RF pulse,

  • what we call a pi RF pulse

  • or a 180 degree RF pulse I can invert the population.

  • In other words I will represent that by 4 arrows pointing up

  • and 6 arrows pointing down.

  • And if I want to draw that on my diagram,

  • can anyone tell me what I do with my net magnetization

  • on my little XYZ diagram at this point?

  • >> Down.

  • >> It's going to point down, exactly.

  • All right, and this is the damming thing.

  • Well, one of the many damming things

  • about NMR spectroscopy is no matter what you do

  • with your pulses you are limited to the difference in population

  • that occurs between the Alpha and Beta state,

  • and later when we start to talk

  • about 2D NMR spectroscopy we're going to learn about one

  • of the common techniques now, which is to go ahead

  • and have polarization transfer.

  • Now, think about what I said before

  • in the equation relating the Boltzmann Distribution

  • to the energy difference.

  • And remember how the magnetogyric ration

  • for carbon was a quarter the magnetogyric ration for protons.

  • That means that roughly the Boltzmann Distribution is going

  • to be a quarter as big on differential population

  • for carbon as it is for protons.

  • So when we get into techniques like HMQC,

  • which is a two-dimensional technique one of the tricks

  • of this technique is to transfer the larger

  • but still miniscule population difference

  • from proton to that of carbon.

  • But again, what's damming is you never can get away from the fact

  • that out of 200 million --

  • out of 2 million protons at 500 megahertz there's no way

  • to exceed that I think I said 81

  • out of 2 million population difference with the exception

  • of some very specialized techniques that involve

  • for example unpaired electrons and free radicals or xenon atoms

  • for that matter, and special optical techniques.

  • All right, so we have our differential population

  • and we know that if we apply a pulse

  • of the right length we can drive that population

  • to have a net magnetization in the XY plane.

  • Now let's take a look at how we get a signal

  • out of the spectrometer.

  • All right, and again we have a coil and I'm going to represent

  • that coil as being along the x-axis.

  • That's a little bit of an over simplification.

  • And now we have our net magnetization in the XY plane.

  • And as I said, it processes and so I'm trying,

  • of course it's hard in three dimensions.

  • I'm trying to represent this as procession in the XY plane.

  • I'm trying to represent that with a curvy little arrow

  • but what I'm really saying is you have your net magnetization

  • and it's moving around, those vectors are moving around

  • and we'll just take a single nucleus like chloroform.

  • It's processing at the frequency,

  • we'll call it V, call it new.

  • So like at 500 megahertz sometimes it's called the

  • Lamoure Frequency.

  • So for example at 500 megahertz for a 117,500 Gauss magnet.

  • NMR spectroscopy was actually discovered by the physicists

  • and rejected by the physicists because they figured

  • that there would be this universal property of a proton,

  • of how fast it processed in any given magnet and we --

  • when we come next time to the concept

  • of chemical shift we'll see that the frequency,

  • the magnetic field that the proton field is modulated

  • by the nature of the molecule, by the environment

  • in the molecule hence different types of protons process

  • at different frequencies.

  • Chloroform processes at a different frequency that TMS,

  • the CH2 groups of ethyl alcohol process

  • at a slightly different frequency than the CH3 groups.

  • These differences in frequency are very, very small

  • but they were upsetting to physicists

  • because psychics figured this has to be universal property

  • of protons and when they saw it varied by magnetic environment

  • in the molecule they gave it the contemptuous term

  • "chemical shift" [laughter].

  • Anyway, so okay.

  • So what happens if you have a coil

  • and you have a magnet rotating in that coil?

  • Think back to your physics.

  • Well eventually you'll have -- we'll get to relaxation

  • but right now lets just imagine--

  • [ Inaudible Speaker ]

  • Anyone ever done this again, as a kid?

  • Where you take a magnet and you spin it in the coil?

  • [ Inaudible Speaker ]

  • An electric thingamajigy.

  • [Laughter] a current.

  • Yeah. Yeah, we get a current in the coil, and this is the basis

  • for all of this stuff.

  • So while the nuclear generator are working hard

  • in San Onofre making steam,

  • what they're basically doing is turning a magnet inside a coil.

  • In practice it's done with armatures and wires,

  • but it is the exact reverse of a motor

  • and the simplest motor you can make involves taking a coil

  • and taking a magnet on an axel and putting

  • in alternating current in.

  • And the reverse, when you spin a magnet inside a coil you get an

  • alternating current, and so the current looks something

  • like this.

  • On the X-axis I'm going to plot voltage

  • and on the Y-axis I'm going to plot time.

  • And an AC current is simply the voltage oscillates

  • in a sinusoidal fashion.

  • So we get this cosign wave and it goes on.

  • You can call it a sine way if you want,

  • and technically I guess I should be at the peak

  • of my wave right here.

  • But what that's saying is as the magnetic --

  • as the vector is like this is relation

  • to the coil your current comes to a --

  • your voltage comes to a peak and then

  • as it gets along the negative X-axis you come down and it gets

  • to the negative Y-axis and it comes up

  • and for the 117,500 Gauss magnet we're going ahead

  • and having this coil,

  • the frequency be 500 million cycles per second.

  • It has to be in the XY [inaudible].

  • [ Inaudible Speaker ]

  • That comes from the pulse that we apply, so remember we have

  • out net magnetization along the Z axis.

  • We apply a pulse that pulse drives the magnetization

  • into the XY plane along the Y axis and we get procession.

  • That pulse is equalizing the population of Alpha

  • and Beta states and doing

  • that is basically making same number spin up, same number spin

  • down but it's directing them together in one way,

  • and in practice when you apply pulses they actually come

  • in fours.

  • So for those of you who've run a spectrometer --

  • how many of you have run a NMR spectrometer?

  • And you do number scans as equal to four or eight or 16.

  • That's no accident because we are actually doing what is

  • called phase cycling, which means in order to cancel

  • out artifacts we first do --

  • we do a set of four experiments or eight experiments.

  • You first do a positive X pulse for example,

  • then you do a negative X pulse, then a positive Y pulse,

  • then a negative Y pulse.

  • And then we average them all together

  • and that reduces artifacts.

  • So this big problem with all of this is we're dealing

  • with really miniscule signal and so the killer

  • in NMR spectroscopy, we've got very few nuclei

  • that are available, we've got very small magnetic vectors,

  • we get very small signals and the whole key is how

  • to get enough signal out of there

  • over all the noise that's coming

  • so that you don't need an entire NMR sample, NMR tube full

  • of pure sample and you can take just a few milligrams

  • or less compound in your NMR tube.

  • So if I want to give my very, very simple diagram

  • of an NMR spectrometer; so you have a solenoid.

  • A solenoid is just a coil in which you have electricity.

  • It's a super conducting coil.

  • Super conducting so that you have the electricity flow

  • forever and you don't have

  • to keep putting more electricity in it.

  • To do this you have a cold and liquid helium.

  • In order to minimize the evaporation

  • of the liquid helium you have a vacuum around it.

  • That's a Doer vessel and if you have a vacuum thermos

  • for your coffee, it has that.

  • But in order to further minimize the loss you have

  • that Doer contained in liquid nitrogen and a second Doer

  • around there because liquid helium's expensive

  • and you don't want to replace it that often.

  • So you have your solenoid and then you have your NMR sample,

  • and an NMR tube, and then you can think of it as your coil.

  • God this is a horrible drawing [laughter].

  • So your coil goes to an amplifier.

  • So this is just like a radio at this point.

  • Your coil goes to an amplifier

  • because you're getting a miniscule signal.

  • Who's ever opened an AM or FM radio and looked inside of it?

  • So the first thing you see is some sort of metal coil,

  • right, on an armature.

  • That coil, one of them is tuned for the AM frequencies

  • and there's a different one tuned for the FM frequencies,

  • or if you have a stereo and you have one coil that's your FM

  • antenna and one coil that's your AM antenna.

  • Obviously none of this is internet radio.

  • So anyway, you have two different coils.

  • That comes back to what I was saying before about having --

  • remember I mentioned broadband detection and the proton coil?

  • So in general different coil shapes work well

  • for different frequencies, and so one coil's on the inside

  • and so if we are doing proton NMR it's best

  • to have your proton coil on the inside.

  • If you're trying to get the best carbon NMR, in general it's best

  • to have a coil tuned to carbon's frequency.

  • Remember they differ by a factor of four from the inside.

  • Okay, so then for modern NMR, what you do is you go

  • from an amplifier we're going to go digital.

  • So after you get a signal, the signal is analog, after you go

  • to the signal in order

  • to process it we're going to digitize it.

  • That simply means convert it to bits and bytes.

  • So in other words instead of having a voltage here that's,

  • you know, 1.007823 millivolts you're basically going

  • to convert your voltage to binary

  • and say that's 110011 etcetera.

  • So we go to an ADC or analog to digital converter,

  • and then that goes to a computer and to a printer.

  • And for those of you who've run an NMR spectrometer you probably

  • know the command RG, receiver game.

  • Who's heard that one?

  • What you're doing there is basically saying, okay,

  • we want to have -- we want to fill up, have as big a number,

  • if we had an eight bit to analog converter,

  • in other words eight digits of zero

  • or one you want your biggest signal to fill up that thing,

  • to be as close as possible to 11111111,

  • whatever, eight one's is.

  • But if it's bigger you're going to saturate it

  • and then you're going to get all sorts of artifacts and clipping.

  • But if it's too small, if you're representing your maximum signal

  • by 00000111, then by the time you're

  • down t very small signals you just don't have the digital

  • capacity for it.

  • So that's what you're doing when you're adjusting receiver game.

  • Okay, so that's my pigeon diagram

  • of an NMR spectrometer and what's happening.

  • And as I've said, it's more complicated

  • because we have coils in all four directions

  • and you're going positive X to negative X and so forth.

  • All right, the big advance which of course is accepted

  • as ubiquitous in NMR is the Fourier Transform.

  • And I can guarantee all of you are going to be able

  • to intuit what this is with zero mathematics.

  • I've nothing against math, but there's incredible power

  • to being able to actually understand stuff rather

  • than calculate it.

  • Extras needed back here?

  • All right.

  • I'll give you the simplified version then I'll explain a

  • few details.

  • But let's start with the simple version.

  • All right, so this is a cosign wave corresponding

  • to a procession at one cycle per second.

  • In other words, every second we go around once.

  • If we take this function and Fourier Transform it we end

  • up having an amplitude axis and a time axis,

  • and what the Fourier Transform does is converts the time axis

  • to a frequency axis.

  • So we still have amplitude and now we've gone

  • from time to frequency.

  • And so if I write a little graph, 0123, I can represent --

  • God that's lousy and uneven.

  • I can represent the Fourier Transform

  • as a peak at one hertz.

  • One cycle per second.

  • And to a first order

  • of approximation that's all there is to a Fourier Transform.

  • It is taking that oscillation

  • and saying what's the frequency of the oscillation?

  • So if I take this second graph here

  • and we Fourier Transform that,

  • what's the Fourier Transform of that second graph?

  • A peak at two hertz.

  • Now if you've ever looked at your free induction decay --

  • we'll come to FID but you collect an NMR spectrum,

  • you see that wiggly thing.

  • That wiggly thing is the free induction decay.

  • That's what's going into your coil at each cycle.

  • If you've ever looked at it it's not a simple sign wave.

  • It is a simple sign wave if you only have one type of proton.

  • So if you do it on pure CDCL3 that has a little CHCL3,

  • and not a lot of water,

  • not a lot of TMS you'll just see a sign wave that decays

  • and I'll tell you about that in a second.

  • But normally what you see is something

  • that has more complications to it.

  • And so here what I did literally, this was just done

  • in Excel as an example,

  • is I took our one cycle per second graph

  • and I took our two cycle per second graph

  • and I added them together to get this red curve.

  • And so if we take the Fourier Transform of this red curve,

  • again we get frequency.

  • I'll just represent that as 0123 etcetera.

  • But now the Fourier Transform is going to be a peak at two hertz,

  • or peak at two, and a peak at one.

  • In other words, basically what's that saying is

  • that this is just the super position

  • of a one cycle per second current

  • and a two cycle per second current.

  • And obviously in an NMR spectrum

  • in which your ethanol may have four peaks for the CH2 group

  • and three peaks for the CH3 group it's going to be a heck

  • of a lot more complicated than that.

  • [ Inaudible Speaker ]

  • Parts per million is like cycles per second and more specifically

  • if you have 500 megahertz per session then you're going

  • to have 500 hertz as one ppm, a 1,000 hertz is two ppm

  • and 1,500 hertz is three ppm.

  • And if you have 300 megahertz per session,

  • if you have that 70,000 Gauss magnet I talked

  • about last time you're going to have 300 hertz is one ppm,

  • 600 hertz is two ppm, 900 hertz is three ppm.

  • All right, now I'm not exactly playing honest with you.

  • Because if you have a frequency at a certain --

  • so remember, this is amplitude and time,

  • and the Fourier Transform transforms the time axis

  • to frequency axis.

  • If this goes on forever then you end up with a line

  • of infinite sharpness.

  • What actually gives rise to the sort

  • of peak you see is something at this frequency but that dies off

  • with an exponential decay.

  • And so when you Fourier Transform a cosign wave dying

  • off with an exponential decay you actually get something

  • that looks like an NMR peak and I'm not a great artist

  • but I will try my best

  • to represent the shape of this peak.

  • You have little wings coming out

  • and this is what you call a Laurencin Line Shape.

  • A Laurencin is just a mathematical function

  • that corresponds.

  • Its Y equals 1 over 1 over X squared plus 1,

  • and you'll later one see I have a simulation program

  • that actually incorporates this we'll get to play with.

  • However, the main point is peaks are not infinitely sharp

  • and this doesn't go on forever.

  • The reason this doesn't go

  • on forever is what's called relaxation.

  • So there are two types of relaxation.

  • There's longitudinal relaxation, sometimes called spin lattice.

  • Sometimes you'll also refer --

  • see it referred to as T1 relaxation.

  • And what this involves is re-equilibration

  • of the Alpha and Beta states.

  • My transfer of energy to thermal motions in the sample.

  • Now, easy way to think about this is

  • when we applied our pulse we drove our magnetization

  • down into the XY plane.

  • In other words what that means is we took the Alpha

  • and Beta states that were in the Boltzmann Distribution,

  • a natural distribution to be in a magnet and we forced them

  • to an unnatural distribution.

  • But eventually due to spin lattice relaxation your nuclei

  • flipped their spins back to these -- to the Z axis.

  • Or flipped their -- the population returns.

  • And now you see why you have an exponential decay.

  • It's a half-life process.

  • Any given nucleus has a finite probability

  • of having its spin flipped back to the natural population states

  • and so that's like radioactive decay.

  • That occurs with a half-life.

  • It's called the relaxation time

  • or more specifically the T1 relaxation time.

  • So that gives rise to our exponential decay.

  • That gives rise to our exponential fall off.

  • Now, there's a second type.

  • T1 relaxation is a little more important

  • in small molecule NMR spectroscopy

  • but there's a second type

  • of relaxation that's also important.

  • Transverse relaxation, sometimes called spin relaxation,

  • sometimes called T2 relaxation.

  • And what transverse relaxation does is involves interaction

  • of spins with other spins in the sample leading to an unbunching

  • of spins in the XY plane.

  • [ Inaudible Speaker ]

  • Unbunching of spins in the XY plane.

  • So interaction with spins of other nuclei leads to unbunching

  • of spins in the XY plane.

  • What does that mean?

  • Well remember, I said when we applied our pi pulse all

  • of our net magnetization was along the XY plane

  • and all the spins of the same type are processing together.

  • But if they unbunch, if due to getting tickled by other nuclei,

  • some process a little faster and some process a little slower.

  • I'm talking now for one type of nuclei

  • like the hydrogen and chloroform.

  • What happens to the net magnetization from that vector?

  • So look at where the vectors are starting

  • to cancel each other out.

  • We're still in the XY plane.

  • In other words out population of Alpha

  • and Beta states hasn't been perturbed.

  • We still have that none Boltzmann population

  • from the initial pulse where it's in this case

  • for pi pulse; 50% up and 50% down.

  • But now we're losing our focus in the XY plane.

  • As they unbunch our magnetization gets smaller

  • and smaller and our signal falls off.

  • And so through these relaxation processes, through T1 relaxation

  • and through T2 relaxation we have a falloff in our peak.

  • In our intensity.

  • And so we get a line that has a width to it.

  • All right, there are two concepts

  • that are closely related.

  • One concept we saw is the whole idea

  • of the Fourier Transform gives rise

  • to a peak with a width to it.

  • But the other thing is that line width is related

  • to the uncertainty principle.

  • So we could always go ahead and blame quantum mechanics.

  • And just of the uncertainty principle

  • as you've probably heard it is that you cannot know

  • with exact accuracy both the position

  • and the velocity of an object.

  • To put it in other terms the longer you can make a

  • measurement the more accurately you can know the velocity

  • or the longer you make a measurement the more accurately

  • you can know the angle of velocity.

  • That's the same ideas in infinitely sharp line.

  • If I have something processing and we can watch it forever,

  • we can know that this is processing

  • at 500.0003215 cycles per second.

  • However, if you only get to look at it

  • for a little bit you say well it was moving fast.

  • It wasn't moving at 100 cycles per second.

  • It wasn't moving at 1,000 cycles per second.

  • It was somewhere around 500 cycles per second.

  • And express mathematically what we get is

  • that Delta nu times Tao is equal to 1 over root 2 pi.

  • What this is, is the -- I'll call this the half line width

  • and you'll see why in a second.

  • And this is -- Tao is the half-life of the spin.

  • And so let's come back to our Laurencin line shape

  • and let's come to some hypothetical idea.

  • So remember we're talking frequency here.

  • All right, so our hypothetical ideal is this is the

  • hypothetical exact frequency.

  • But the point is if we can't measure the frequency exactly

  • because we're not measuring it for infinitely long,

  • because the frequency is -- the line is relaxing,

  • we can only tell well, it's somewhere around here.

  • So you get a peak that has some width to it.

  • And this is our Delta nu and from your point

  • of view what you often think of and what I think of when I look,

  • is this is what I like to call the line width.

  • In other words it's sort of at half height.

  • In other words it's 2 Delta nu.

  • Because here we're saying well it's within plus

  • or minus Delta nu of this center value but we can't tell exactly.

  • Here I look and I say, okay, this line is fat.

  • All right, so what does that mean?

  • If we have a Tao equals 2 seconds that leads

  • to Delta nu is equal to 1 over root 2.

  • Root 2 pi is equal to .11 hertz.

  • That's .22 hertz line width.

  • If I have Tao, and this is of course seconds,

  • if I have Tao equals one sec then Delta nu is equal to one

  • over -- well, I'll just skip the equation here --

  • it's equal to .22 hertz is equal --

  • and that's .44 hertz line width.

  • Now the relaxation of protons typically occurs on the order

  • of one or two seconds.

  • So there is a real theoretical limit

  • to how sharp your peaks can be.

  • Because that theoretical limit is going

  • to be determined by the relaxation.

  • Carbons are funny because they relax more slowly

  • and there the reason that you end up not having big peaks

  • for quads are always going -- your quandrinary carbons,

  • your carbon yields and carbon [inaudible] active are always

  • very short is because between pulses you don't go ahead

  • and have full return of magnetization.

  • >> Oh, how [inaudible] spin?

  • [Inaudible].

  • >> No, you don't have control of it.

  • I mean you have a little bit of control.

  • If you remove paramagnetic --

  • if you add paramagnetic impurities then --

  • which we actually do in experiments

  • like the inadequate experiment then you can increase --

  • you can decrease the half-life.

  • if you remove paramagnetic impurities for example,

  • if you by freeze pump [inaudible] degassing remove

  • dissolved oxygen which is paramagnetic from your sample,

  • you can decrease T1 relaxation

  • because remember it's the interaction of nuclei

  • that flips the spin and so you have oxygen as paramagnetic.

  • All right, so the point is exponential decay leads

  • to line broadening and if you have a little bit

  • of exponential decay like so, then you get a sharp line.

  • If you have a lot of exponential decay you get a broader line.

  • So these are both of Fourier Transform.

  • Yeah?

  • >> Do we reduce the fact of the other species

  • by aligning those nuclei's up?

  • >> You can do various tricks.

  • So, in the case of molecules

  • that have very restricted motions like solids,

  • T2 relaxation becomes critical and in the case of solids

  • to get good spectra you have to spin the sample at what's called

  • "the magic angle" to reduce relaxation, T2 relaxation.

  • So there are little tricks.

  • But for the most part relaxation isn't a problem.

  • Proton NMR, it's a good thing because it allows you

  • to repeat your experiments, and that brings us to the next

  • and I think perhaps the last thing that I will talk about.

  • And as I said, carbon NMR can be a pain because it --

  • the relaxation is so slow that it makes your peak small.

  • All right, so the last thing I'll talk

  • about is signal averaging.

  • Now, I've already hinted that you have this notion

  • of phase cycling and that your really have to do experiments

  • in sets of four or eight with the exception

  • of certain pulse field gradient experiments that I'll talk

  • about later that reduces phase cycling.

  • This becomes important in 2D NMR.

  • But you go to all the trouble to synthesize a compound,

  • make up an NMR sample, you collect the spectrum;

  • it's no big deal to collect date

  • for a minute instead of for five seconds.

  • So that's not a big deal.

  • But the big problem that we have, as I said,

  • NMR is a very insensitive technique.

  • You have a very low signal.

  • You're not fighting the low signal.

  • What you're fighting is the noise

  • and we talked about the cyroprobe.

  • The cryoprobe the other day, doesn't increase the amount

  • of signal but it does decrease the amount

  • of noise, electronic noise.

  • Think of noise as static.

  • You tune to an FM radio station that's far away,

  • you hear a lot of static.

  • Doesn't occur on internet radio because it's all digital.

  • But you tune to a station that's far away there's a lot

  • of static.

  • So what can you do?

  • The static is random, so if you go ahead

  • and collect repeated signal you can average it out.

  • The signal to noise varies as the square root

  • of the number it scans.

  • In other words if I collect more data I get more signal to noise,

  • but the noise is going up as well.

  • It's just going up randomly.

  • So in other words, if I go from 16 scans

  • which is a very reasonable number,

  • to 64 scans I don't quadruple my signal to noise,

  • I double the signal to noise.

  • And so if you're collecting a C13 NMR spectrum

  • and you've got a lot of noise you say, oh well if I go ahead

  • and I want to make my spectrum twice as good I've got

  • to collect data four times as long.

  • If it's midnight and you've been collecting since 10:00 pm,

  • know that your spectrum's only going

  • to get a little bit better, only 1.4 times better

  • if you wait till 2:00 in the morning.

  • If you wait till 6:00

  • in the morning it's going to get twice as good.

  • If I double the concentration I'll also double the signal

  • to noise.

  • So I'll say 2X.

  • So again, I'm sitting there at midnight and thinking, my God,

  • I don't want to be sitting here till 6:00 am.

  • I run up to the laboratory, I dump more sample in my NMR tube

  • and now by 2:00 in the morning I have twice as good A spectrum.

  • So that's the general gist.

  • There are a number of other aspects.

  • I think I gave us a reading in Claridge that I'd

  • like you to look over.

  • There are a number of other aspects

  • in Fourier NMR Spectroscopy including digital resolution.

  • But suffice it to say, right now we collect data

  • for a few seconds, the data is becoming

  • as your signal is falling off like so.

  • We have more noise here relative to signal so we don't want

  • to collect data forever.

  • So in the end we strike a compromise.

  • We collect for a few seconds, we average the data,

  • we perform a few mathematical operations to smooth it

  • out because the Fourier Transform of a truncated signal,

  • if I just truncate my signal the Fourier Transform actually looks

  • more like this where we have a couple of wiggly things

  • around the peak so we apply weighting functions.

  • That's called the exponential multiplication.

  • We apply weighting functions so you don't just truncate,

  • you actually drive the signal down so

  • that you get a better line shape

  • and you can read a little bit more about that in Clairedge.

  • All right, we'll pick up next time talking

  • about chemical shift and at that point we'll start to talk

  • about differences between different types

  • of protons within a molecule. ------------------------------fa4c97f04076--

>> Sticks.

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ケム 203有機分光法.講義08.NMR分光学入門、第2部 (Chem 203. Organic Spectroscopy. Lecture 08. Introduction to NMR Spectroscopy, Part 2)

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    Cheng-Hong Liu に公開 2021 年 01 月 14 日
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