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NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

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When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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¹H NMR of Conformationally Flexible Molecules: Temporal Resolution00:52

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At room temperature, the chair conformer of cyclohexane undergoes rapid ring flipping between two equivalent chair conformers at a rate of approximately 105 times per second. These two chair conformers are in equilibrium. The rapid ring flipping results in the interconversion of the axial proton to an equatorial proton and an equatorial to the axial proton. Such interconversions are too rapid and cannot be detected on the NMR timescale. Hence, the NMR spectrometer cannot distinguish between the...
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The axial and equatorial protons in cyclohexane can be distinguished by performing a variable-temperature NMR experiment. In this process, except for one proton, the remaining eleven protons are replaced by deuterium. The deuterium substitution avoids the possible peak splitting caused by the spin-spin coupling between the adjacent protons. The remaining proton flips between the axial and equatorial positions.
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In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
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The earth's gravitational field produces a 'twisting force' perpendicular to the angular momentum of a spinning mass (such as a spinning top) that causes the mass to 'wobble' around the gravitational field axis in a phenomenon called precession. Similarly, the magnetic moment (μ) of a spinning nucleus precesses due to an external magnetic field directed along the z-axis. The precession of the magnetic moment vector about the magnetic field is called Larmor precession,...
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Generating accurate tip angles for NMR outside the rotating-wave approximation.

Christopher P Bidinosti1, Geneviève Tastevin2, Pierre-Jean Nacher2

  • 1Department of Physics, University of Winnipeg, Winnipeg, MB R3B 2E9, Canada.

Journal of Magnetic Resonance (San Diego, Calif. : 1997)
|November 26, 2022
PubMed
Summary

Accurate tip angles in low-field nuclear magnetic resonance (NMR) require careful pulse design. Strategies involving phase-dependent shifts and pulse timing can achieve precise control outside the rotating-wave approximation.

Keywords:
Bloch–Siegert shiftCounter-rotating fieldLinear rf fieldLow-field NMR/MRIRotating-wave approximationTRASE (transmit array spatial encoding) MRIrf pulsesrf transients

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Area of Science:

  • Nuclear Magnetic Resonance (NMR) Spectroscopy
  • Magnetic Resonance Imaging (MRI) Physics

Background:

  • Accurate tip angles are crucial for nuclear magnetic resonance (NMR) applications.
  • The rotating-wave approximation (RWA) may fail in low static fields with linear rf polarization, causing deviations in Bloch sphere trajectories.

Purpose of the Study:

  • To investigate deviations from expected Bloch sphere trajectories in low-field NMR under linear rf fields.
  • To identify strategies for achieving accurate tip angles when the RWA is invalid.

Main Methods:

  • Numerical simulations of NMR pulse sequences.
  • Low-field NMR experiments using 1H and 3He nuclei.
  • Analysis of phase-dependent Bloch-Siegert shifts and pulse timing effects.

Main Results:

  • Rectangular rf pulses show phase-dependent deviations, exacerbated by pulse transients.
  • Phase-dependent Bloch-Siegert shifts and optimized pulse timings can correct trajectories.
  • Bloch-Siegert shift magnitude depends on pulse shape and rf coil characteristics.

Conclusions:

  • Accurate tip angle generation outside the RWA in low-field NMR is achievable with specific strategies.
  • Consideration of pulse phase, timing, and rf coil parameters is essential for precise control.
  • Demonstrated experimental validation with 1H and 3He NMR.