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NMR Theory, Relaxation and Precession 
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#1
Apr412, 07:56 AM

P: 4

Hello everyone, I'm having a really confusing time trying to get my head around these concepts, so I will try to explain what I can...
So, in proton NMR we have nuclei that can be in either spinup or spindown states. Nuclei align with an external magnetic field but precess. (This precession is more towards the z axis?). Applying a second, othogonal magnetic field at the precession frequency (Larmor), will cause the precession to go in the xy plane (Im not too sure about this either  sort of like a spinning top completely on its side if i can visualise it). When this happens, the nuclei can switch between states. Because of the small difference in states (Boltzmann), this can be seen via absorption at a particular RF. So is spinlattice relaxation when the precessing goes from xy plane (spinning top on it side) to the z plane (spinning top is now perpendicular to the surface)? And where does spinspin relaxation fit into this  from what I understand, its when spins of different nuclei don't correspond to each other. How is this different to T_{1} relaxation? Thanks for any help! 


#2
Apr412, 11:25 PM

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PF Gold
P: 2,081

You are mixing up quantum and classical pictures of NMR. I suggest sticking with the classical picture (which has no concept of states) and stick with classical. The spins align with B0. An applied RF field B1 causes the spins to precess and increases their polar angle theta (angle away from the z axis) continuously as long as B1 is applied. The spins end up in the xy plane only if B1 is turned off when they reach theta=90°. As they continue to precess in the xy plane, a signal is induced in the pickup coil. If B1 is left on longer, the spins precess down to 180°, that is, the magnetic moment is opposite to B0.
Spinlattice relaxation describes the transfer of energy from the spin system to the lattice. Following a 180° RF pulse, the spins are pointing along z but they relax back to +z through this mechanism. Spinspin relaxation doesn't remove energy, but it changes the local magnetic field such that spins following a 90° become decoherent (neighboring spins no longer track each other). This causes the signal to disappear. 


#3
Apr512, 12:14 AM

P: 10

Precession cone from xy plane to z axis is spinspin relaxationT_{2}(exchange of energy b/w nuclie spins) after 90^{o} pulse applied to spin system.
This T_{2}relaxation is insuffecient to detect practical useful decaying signal, but when 180^{o} pulse is applied, in which magnetic moment will take initially z axis direction, spinlattice relaxationT_{1}(exchange of energy with suroundings"atomic vibrations or molecular tumblings") takes place. So, this is the practical technique(MultiplePulse FT): We start with T_{1} process(180^{o} pulse) then applyT_{2} process(90^{o} pulse) after approperiate delay time(magnetic moment in +z direction) then the entensity of signal will be proportional to magnetic moment! repeating this several times gives us our lovely spetrum by computer 


#4
Apr512, 03:37 AM

P: 4

NMR Theory, Relaxation and Precession
Why does precession at θ=90° allow the nuclei to from spinup to spindown? I understand more, but I just wish to clear some stuff up and remove confusion which is frustating. Anyway thanks guys! 


#5
Apr512, 05:36 AM

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P: 3,596

It is not so easy to understand this emission in the picture of photons getting absorbed or emitted. The main point is that the phase of the electromagnetic wave is due to the superposition of states with different photon number (just like the angle of the magnetic moment in the xy plane depends on the phase of the superposition of the up and down states). To get a classical picture you have to consider both superpositions of spin eigenstates and of photon number eigenstates. 


#6
Apr512, 06:18 AM

P: 4

PS. what do you mean by nonvanishing expectation? 


#7
Apr512, 06:59 AM

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P: 3,596

However if you are willing to forget for some time on what you know about spin up and down, NMR can be understood to a large part in purely classical terms: http://en.wikipedia.org/wiki/Bloch_equations 


#8
Apr512, 07:05 AM

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#9
Apr512, 03:35 PM

Emeritus
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PF Gold
P: 29,238

There is a very old thread in which some of these issues have been discussed:
http://www.physicsforums.com/showthread.php?t=42814 Zz. 


#10
Apr512, 04:40 PM

P: 4

Thanks ZapperZ (and everyone else), I think I was mixing up quantum and classical too. The explanations helped as well.
I have another question now regarding T_{1}...When we say that the states become saturated is it that all the spin states are in the higher energy state? Because if we lowered the temp to 0K, wouldn't nearly all of the spins be at the lower state? Secondly, I read this online here I was also looking at some lecture notes and another thing which caught me was linewidth. The lecture says that line width is largely independent of field strength. But on another of the notes I was reading online, it mentioned that T_{2} and T_{1} have an effect on line width. Is this correct and if this is, doesn't field strength have an effect on relaxation? Again thanks a lot guys, it has cleared up a lot but replaced it with more questions! 


#11
Apr612, 08:26 AM

P: 485

Saturation refers to the situation when the populations of each state have been equalized. If you apply enough strong pulses continuously, the populations will equilibrate. If you read the discussion that was linked earlier by ZapperZ, you will note that ZapperZ mentions the situation at T = 0.
It may help to think about what T_{1} is  it tells you how long it takes for the system to be restored to its thermal equilibrium values. It has to interact with its surroundings to do that, as you just perturbed it with the RF pulses of an NMR experiment. The sample is in the presence of an incredibly strong static magnetic field that runs along the zaxis. Fluctuations along the zaxis are most likely going to be quite small when compared to the static magnetic field. Remember, for a 14.4 Tesla magnetic field, the proton Larmor frequency is 600 MHz  that means in one second, it precesses 600 million times about the static magnetic field. For something to be "spontaneous"  at least in a practical sense  would mean it occurs prior to a single precession. I don't know what other notes you've been reading, but I can certainly say the following. In principle, at least for a simple enough system, one can show that the Lorentzian peak width at halfheight is inversely related to T_{2}. Of course, in the lab, things can be more complicated  there can be effects from imperfections in the static magnetic field, magnetic susceptibility of the sample, and I believe related instrumental issues whose details I am not remembering at the moment. Clearly, in certain cases, the two times can be basically the same magnitude (I'm thinking of quadrupolar nuclei), and relaxation becomes extremely efficient. Otherwise, you're going to have to point us to these other sets of notes you've been reading. 


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