EEVblog Electronics Community Forum
Electronics => Projects, Designs, and Technical Stuff => Topic started by: RoGeorge on August 21, 2021, 03:43:23 pm
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Trying to get a better understanding of NMR (Nuclear Magnetic Resonance), and thought an interactive macroscopic toy-model would help to grow an intuition about NMR.
If I understood correctly, it seems like a spinning-top toy with a bar magnet as its axle will be a very good macroscopic toy-model to represent NMR.
- first question, would such a model be accurate enough?
- if yes, does it captures all the NMR aspects, or else said does it miss anything important?
- are there any misleading effects existing in the toy-model only, and not present in the real thing?
For now I am just picturing a magnetized spinning-top toy, though a swirling spinning-top on a table would introduce some unwanted forces/interactions at the contact point between the spinning-top and the table. Thinking here about the circles described by the spinning-top on the table then the vertical self-stabilization. These effects are caused by the rounded tip of the sinning-top toy rolling on the table, and will not be present in NMR, yet these effects are substantial in the macroscopic model.
That reminds me of a very weird effect I "discovered" once, where the core of an electric motor was preferring to stay vertical instead to fall on the table, like this:
https://www.youtube.com/watch?v=Mz9a94I4rcU (https://www.youtube.com/watch?v=Mz9a94I4rcU)
(in case you wonder why on Earth anyone would do that, I was trying to "invent" a new type of holonomic drivetrain, with a ball on top of a rotating vertical axle, axle that is tilted to change the moving direction, like this: https://youtu.be/PrxRFqTLl3I (https://youtu.be/PrxRFqTLl3I) ;D )
Back to the NMR toy-model, maybe using a gyroscope suspended with a string would be better than a spinning-top on the table? But then the suspended gyroscope would get a precession move because of its own weight. Or maybe use a magnetized spinning-top but suspended somehow in mid air, either by a magnetic field controlled by a height stabilization loop, or by a jet of compressed air, IDK.
Any other ideas for a NMR macroscopic toy-model, preferably something to allow some direct interaction?
Just for the docs, quoting from the other topic where the discussion started, but would have have been offtopic to continue it there:
Not sure which NMR method is in discussion, but assuming we have a rotating battery to power the rotating instruments, will it still be possible to observe NMR?
Yes (in any NMR method).
In my naive understanding I am picturing NMR as a wobbling spinning toy, and in NMR we observe/measure that wobbling (the precession), though there's nothing really rotating inside atoms and there is no axle in an atom, so will NMR be seen as DC if we rotate the detector?
Yes, that's the classical model of NMR precession. The NMR signal is a rotating magnetic field, circularly polarized and rotating at the Larmor frequency.
In a stationary detection coil, we observe the NMR signal magnetic field induces a current, sine(Larmor frequency*time). And if we place a second stationary detection coil perpendicular to it, in it we observe a current cosine(Larmor frequency*time). (This is actually done by, for example, a "birdcage" coil, which has two physically orthogonal outputs. By measuring whether the phase difference between them is +90 or -90 degrees, we can determine whether the NMR precession is occurring at a positive or negative frequency, thus directly determine the sign of the nuclear magnetogyric ratio.)
If the detection coil is rotating, the current induced in it will be the difference between the rotation rate of the detection coil and the rotation rate (Larmor frequency) of the magnetic field (NMR signal) it is detecting. If rotating in opposite directions, this frequency will be higher. If rotating in the same direction, this frequency will be lower. If rotating at the same direction and rate, will be zero (DC).
This is exactly how an AC generator (an alternator) works. The rotor creates a rotating magnetic field, which induces a current in the stator windings. If it has multiple sets of windings, we can tell which direction the rotor is spinning by the phase difference between the currents from the windings. And if we were to begin to spin the stator in the same direction as the rotor, the frequency of the output current would fall. If the stator were spun at the same rate as the rotor, the output frequency would be zero (DC). So this is very simple. The rest of the universe is unaffected.
If yes, what will happen with the DC if we change the orientation of the spinning axle of the rotating instrument?
Ouch! Now my head is really spinning! :scared: Hmm... :popcorn:
All the imaginary spinning we've done above is only of the detector, around the axis of the magnetic field produced by the NMR magnet, which defines the axis about which Larmor precession occurs. Whether the magnet has rotated or not, its magnetic field has remained static; we have rotated around it. So please clarify the question: by "rotating instrument", do you mean (1) rotating only the detector (NMR probe), or (2) rotating both the detector and the magnet (the entire instrument)?
If (1), then the detector, if still spinning at the Larmor frequency, will see two magnetic fields, both at the Larmor frequency and whose magnitude is proportional to the sine of the angle between the two axes: one enormous (produced by the magnet), and one tiny (the NMR signal).
...and if you've ever pushed a conductor into a magnetic field of several Tesla, and felt it push back (due to the induced eddy currents), you can imagine what's about to happen... a huge current will be induced, quickly heating the conductor... converting the energy of the entire magnetic field into thermal energy in the detector, which becomes a rapidly expanding ball of plasma. Poof! Ende gedankenexperiment!
If (2), then the result depends on how quickly we change the orientation of the magnetic field.
If the change is slow compared to the Larmor frequency, the NMR magnetization simply follows it. This is called an "adiabatic" process (termed "adiabatic" in that it does not change the spin temperature by inducing transitions between NMR spin states).
If the change is fast compared to the Larmor frequency, effectively instantaneous, the NMR magnetization does not move during this change, but suddenly sees the magnetic field appear in a new direction, and simply begins to precess about it. This is termed a "nonadiabatic" process.
Both have been done in the laboratory (but by switching magnets on or off, not by rotating them). It is called an "adiabatic demagnetization in the laboratory frame" experiment. It has been described in many papers and several books. A very clear description is given by Melton and Pollack, "Condition for adiabatic passage in the earth’s-field NMR technique", JMR 158 (2002), 15 [url]https://ur.booksc.eu/book/4940715/42cb27[/url]
([url]https://ur.booksc.eu/book/4940715/42cb27[/url]) In its Figure 2, the (a) nonadiabatic, (b) intermediate and (c,d) near-adiabatic cases are depicted. This is simple classical magnetodynamics, more easily understood in a rotating frame of reference, although we detect it in the stationary laboratory frame of reference.
...and the analogous experiment can be done with rotating magnetic fields, "adiabatic de- or re-magnetization in the rotating frame"... but that's enough for today! :phew:
How did we get here from oscilloscopes, anyway? :-//
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- are there any misleading effects existing in the toy-model only, and not present in the real thing?
Friction. A gryoscope spins more slowly as it winds down, causing its precession angle to increase as well. NMR precession is frictionless; it continues at a constant angle and frequency.
- if yes, does it captures all the NMR aspects, or else said does it miss anything important?
Relaxation. Felix Bloch's introduced this precession model of the NMR phenomenon in his original paper, adding relaxation to it. This is such a delightful and physically insightful paper, you would surely enjoy reading it. It's available here https://mri-q.com/bloch-equations.html (https://mri-q.com/bloch-equations.html)
Any other ideas for a NMR macroscopic toy-model, preferably something to allow some direct interaction?
Yes, actual NMR precession! It's relatively easy to observe in the Earth's magnetic field, thanks to a brilliantly simple design by Carl Michal, "A low-cost spectrometer for NMR measurements in the Earth's magnetic field" https://www.researchgate.net/publication/230972230_A_low-cost_spectrometer_for_NMR_measurements_in_the_Earth%27s_magnetic_field (https://www.researchgate.net/publication/230972230_A_low-cost_spectrometer_for_NMR_measurements_in_the_Earth%27s_magnetic_field) These and similar instruments are used in many undergraduate teaching laboratories; see for example Mann et al. "Earth's Field NMR Spectroscopy in the Undergraduate Chemistry Laboratory" https://www.researchgate.net/publication/336369074_Earth%27s_Field_NMR_Spectroscopy_in_the_Undergraduate_Chemistry_Laboratory (https://www.researchgate.net/publication/336369074_Earth%27s_Field_NMR_Spectroscopy_in_the_Undergraduate_Chemistry_Laboratory)
Another way (CW NMR) has been discussed here https://www.eevblog.com/forum/projects/diy-nmr-(nuclear-magnetic-resonance)-spectrometer/ (https://www.eevblog.com/forum/projects/diy-nmr-(nuclear-magnetic-resonance)-spectrometer/)
- first question, would such a model be accurate enough?
Saving your first question for last, as it is a deep question, one deserving a far deeper answer than any my shallow understanding can provide.
umm... accurate enough for what purpose? Gyroscopic precession can be a useful model for visualizing how the macroscopic nuclear magnetization interacts with external magnetic fields. It is a very useful metaphor for certain aspects of NMR. Spin echoes and many related 2D NMR and double resonance experiments can be visualized with it.
But this model of NMR as classical precession is broken in many NMR experiments, such as multi-quantum NMR, or NMR of nuclei with spin >1/2. The reason is that the nuclear spin is not a classical phenomenon, but a quantum mechanical one. Just as, while the classical wave model of light is wonderful for visualizing refraction and diffraction, it utterly inconsistent with the photoelectric effect, the blackbody radiation spectrum, the spectrum of a hydrogen atom, etc. These reveal the true nature of light as discrete quanta of energy, photons.
So we mustn't become too enamored of this metaphor to believe it accurate for all aspects of NMR. Even the classical electrodynamics model of the NMR signal as "nuclear induction" arising from this "nuclear precession" is not a true model of reality. It is useful in many ways, yet may be misleading in others. NMR actually arises within the mysterious realm of quantum electrodynamics (QED), as David Hoult explains https://onlinelibrary.wiley.com/doi/abs/10.1002/cmr.a.20142 (https://onlinelibrary.wiley.com/doi/abs/10.1002/cmr.a.20142)
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Sorry what do you mean that the precession continues frictionlessly? I mean technically there’s no mechanical friction but there’s radiation losses that result in the free induction decay.
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Sorry what do you mean that the precession continues frictionlessly? I mean technically there’s no mechanical friction but there’s radiation losses that result in the free induction decay.
No, radiation loss does not contribute to the free induction decay (FID). It is a precessing magnetic field, but it's not radiating or losing energy.
Why does it decay? Spin-lattice relaxation limits the lifetime of the spin states (measured by a time constant T1). Spin-spin relaxation causes an irreversible loss of phase coherence (T2). Magnetic field inhomogeneity causes an additional loss (T2*) which is reversible (and is refocused in the Carr-Purcell pulse sequence). These result in the observed decay, at a rate of 1/T2* > 1/T2 > 1/T1.
You are correct: if we place a conductor (observation coil) in the alternating "free induction" magnetic field created by the phase-coherent nuclear spins (the nuclear magnetization), and extract energy (an NMR signal by Faraday induction) from it, the resulting loss of energy acts like an additional relaxation mechanism. It is called "radiation damping", but might better called induction damping or eddy current damping.
In absence of these relaxation mechanisms, the NMR free induction would continue... virtually forever.
As David Hoult explains on page 202 of the paper cited above "...the signal produced in [any] NMR spectrometer must be due to spontaneous emission. However, it must be a very strange kind of spontaneous emission: [in 1954] Bloembergen and Pound computed the half-life of an NMR excited state that one should expect to be associated with this relaxation mechanism. For a proton in a magnetic field of 10^4 oersteds [1 Telsa], it turns out to be 1025 seconds—about 108 times the estimated age of the universe.’’
See Hoult's appendix A-2 for details.
The point of Hoult's paper is to reiterate that NMR "induction" is actually not classical Faraday induction at all. The nuclear magnetization creates only a near field, but no far field, no electromagnetic wave. The terms "nuclear induction" and "spin precession" are such useful classical metaphors that we may be misled into thinking they reflect reality... but they do not. So we use them carefully, and don't stretch them too far... lest they break!