A Treatise On NMR

My first week of NMR (nuclear magnetic resonance) research has consisted largely of researching what I will be researching. More specifically, I have been developing theoretical and practical background knowledge in which to ground my research. As such, my work has consisted of two parts: learning what buttons to push, and why to push them.

The “what-buttons-to-push” portion of my work has largely consisted of hands-on work with the spectrometer. In the first week, I learned to quickly configure the NMR probes used to make measurements. This process involves inserting a sample into the probe, inserting the probe into the magnet, and connecting a multitude of wires to the probe. In order to obtain a proper reading, a data filter is attached to the probe: this filter ensures that the proper frequency is feed to the amplifier, which boosts the signal before it is sent to the digitizer, which converts the data signal into a Fourier transformable spectrum (more on this below). I have also learned how to use the lab’s Topspin spectrometer software, and can perform basic scans with the magnet.

The more important “why-to-push-them” portion of my research has consisted of a large amount of reading. Specifically, I have been using volume three of Douglas C. Giancoli’s Physics for Scientists and Engineers to get a basic grasp of the quantum mechanics involved in NMR spectroscopy, and Eiichi Fukushima and Stephen B.W. Roeder’s Experimental Pulse NMR: A Nuts and Bolts Approach to obtain a practical understanding of how the quantum mechanical world impacts these NMR procedures.

To briefly (as to avoid boring more humanities-inclined readers) summarize this information: all atomic nuclei have quantized amounts of angular momentum (or “spin,” as it is called). These nuclei also have magnetic moments proportional to their angular momentum. In NMR experiments, samples are placed in a probe, which consists of multiple capacitors connected to an inductor (which is basically a coil of wire) in a high-power (17.6 Tesla), static magnetic field. The magnetic moment of these nuclei align with the magnetic field. A high-power, “square” radio-frequency (rf) pulse, which contains a wide distribution of different frequencies, is applied perpendicularly to the static field. The magnetic moments of the sample are reoriented by this pulse, and actually begin to rotate about the static field at a nuclei-specific “Larmor frequency.” These rotating magnetic moments, however, cannot stay in their new, higher-energy excited state, and begin to shift back to their original orientation. The decaying magnetization vectors induce a voltage in the inductor coil, which is then digitized and converted into a free induction decay (FID) plot, a sinusoidal amplitude versus time graph of the sample’s decaying magnetic moments.

This process, seemingly complicated, is simply measuring the magnetic responses of atomic nuclei to an applied magnetic field; the basic idea of the phenomena can be greatly simplified via analogy. Consider an opera singer positioned in front of a wine glass. The wine glass vibrates at a specific resonant frequency; when the singer’s voice is at the same frequency, constructive interference increases the energy of the vibrating glass, causing it to vibrate faster and possibly shatter. If the opera singer were to gradually increase the frequency of his voice, a microphone placed inside the wine glass could be used to measure its vibrational response to the opera singer’s applied frequency; in this way, the resonant frequency of the glass could be determined. The process becomes trickier, however, when attempting to measure the resonant frequencies of several hundred glasses. Each glass could be measured using a single microphone and a single opera singer, but this process would take far too long. Instead, the resonant frequency of each glass could be measured simultaneously. Instead of using a single opera singer varying the frequency of his voice, a choir could be used instead, with each member singing at a slightly different frequency. Using this multitude of singers, a multitude of frequencies can be produced at the time. Each wine glass would then respond to one of these many frequencies, and would vibrate at their resonant frequency as a result. Using a specialized microphone, the net vibration of all the glasses could then be recorded; this net recording could later be analyzed to determine the resonant frequency of each glass. This means of measurement is the essence of NMR spectroscopy: in NMR, the choir is the square rf pulse, the wine glasses are nuclei, the microphone is the probe’s inductor coil, and the FID plot is the recording all of the glasses resonating together.

The true power of NMR, however, does not become apparent until the FID plot is processed using a Fourier transform, a mathematical process that converts the amplitude versus time FID plot into a spectrum, a plot of amplitude versus frequency. Recall that the “square” pulse used to excite the magnetic moments contained a wide distribution of frequencies. Each of the many nuclei in the sample responds only to its nuclei-specific Larmor frequency. Once excited, the magnetic moments of the nuclei rotate at this Larmor frequency, which is reflected in the sinusoidal FID plot. The Fourier transformed amplitude versus frequency plot thus displays the relative amount of nuclei that respond to certain Larmor frequency, which allows researchers like me to make inferences about the sample’s molecular structure.

As before, this idea can be simplified by means of analogy. In terms of the previous operatic illustration, the Fourier transform is the analytically process by which the recording of the many wine glasses (the FID plot) is used to determine the resonant frequency of each individual glass (the amplitude versus frequency plot).

In the next several weeks, I hope to become more familiar with interpreting these Fourier transformed spectra, and to be using my theoretical and practical knowledge of NMR to analyze the structure of Scandium-based piezoelectric materials.

Comments

  1. gkbryant says:

    Glad to see I’m not the only person on here with tendencies toward the circumlocutory. Regardless of the treatise-length, your project sounds interesting. I look forward to seeing the results of your piezoelectric research beyond theoretical concepts. Hopefully that probe will come back fixed soon.

  2. pgyanev says:

    Very handy wine glass example – your instinct for the ‘humanities’ is very much intact. For someone who has worked with NMR before, this post still managed to refresh my perspective on a mechanism I thought I had in the bag, so to speak. Keep up the good work —

  3. William Adams says:

    I already had the basic idea of what NMR did, but this actually explained to an extent how it worked. What, if anything are you hoping to find in the spectra you will be looking at?

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  1. […] amplitude plot using a Fourier transformation.  (For a better explanation of the process, check this post.) The nuclei’s return to equilibrium, known as “spin-lattice relaxation,” does not happen […]

  2. […] amplitude plot using a Fourier transformation.  (For a better explanation of the process, check this post.) The nuclei’s return to equilibrium, known as “spin-lattice relaxation,” does not happen […]