NMR macroscopic toy-model to interact with - Page 1
Forum section: electronics / projects

author: RoGeorge
author_rank: Super Contributor
timestamp: August 21, 2021, 03:43:23 pm
content: 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:(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)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:Quote from: Rod on August 21, 2021, 06:34:26 am

author: Rod
author_rank: Contributor
timestamp: August 22, 2021, 02:13:20 am
content: Quote from: RoGeorge on August 21, 2021, 03:43:23 pmFriction. 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.Quote from: RoGeorge on August 21, 2021, 03:43:23 pmRelaxation. 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 herehttps://mri-q.com/bloch-equations.htmlQuote from: RoGeorge on August 21, 2021, 03:43:23 pmYes, 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_fieldThese 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_LaboratoryAnother way (CW NMR) has been discussed herehttps://www.eevblog.com/forum/projects/diy-nmr-(nuclear-magnetic-resonance)-spectrometer/Quote from: RoGeorge on August 21, 2021, 03:43:23 pmSaving 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 enoughfor 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 explainshttps://onlinelibrary.wiley.com/doi/abs/10.1002/cmr.a.20142

author: ezalys
author_rank: Frequent Contributor
timestamp: August 22, 2021, 02:31:07 pm
content: 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.

author: Rod
author_rank: Contributor
timestamp: August 23, 2021, 09:02:44 am
content: Quote from: ezalys on August 22, 2021, 02:31:07 pmNo, radiation loss does not contribute to the free inductiondecay(FID). It is a precessing magnetic field, but it's notradiatingor 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  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 1025seconds—about 108times 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 suchusefulclassical 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!