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NMR Spectroscopy

Learn the fundamentals of NMR Spectroscopy as it delves into the origin and behavior of nuclei in a magnetic field. Discover the properties of nuclei with spin quantum numbers, spin orientations, and the effects of radio frequency on NMR signals, relaxation, and equilibrium. Gain insights into angular momentum, magnetic moments, and bulk magnetization in this comprehensive guide.

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NMR Spectroscopy

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  1. NMR Spectroscopy Part I. Origin of NMR

  2. Nuclei in Magnetic Field • Nucleus rotate about an axis -- spin Nucleus bears a charge, its spin gives rise to a magnetic field . The resulting magnetic moment is oriented along the axis of spin and is proportional to angular momentum m = g p • : magnetic moment p: angular momentum g: magnetogyric ratio

  3. Nuclei in Magnetic Field • Spin Quantum Number I a characteristic property of a nucleus. May be an integer or half integer # of protons # of neutrons I even even 0 odd odd integer 1,2,3… even odd half integral 1/2, 3/2, 5/2… odd even half integral 1/2, 3/2, 5/2…

  4. Nuclei in Magnetic Field • Properties of nucleus with spin quantum number I 1. An angular momentum of magnitude {I(I+1)}1/2ħ 2.A component of angular momentum mIħ on an arbitrary axis where mI=I, I-1, … -I (magnetic quantum number) 3. When I>0, a magnetic moment with a constant magnitude and an orientation that is determined by the value of mI. m = g mI ħ

  5. Nuclei in Magnetic Field • In a magnetic field B(in z direction) there are 2I+1 orientations of nucleus with different energies. B0: magnetic field in z direction nL: Larmor Frequency

  6. Nuclei in Magnetic Field • For I=1/2 nucleus : mI = 1/2 and –1/2

  7. Nuclei in Magnetic Field

  8. Nuclei in Magnetic Field

  9. Nuclei in Magnetic Field

  10. Nuclei in Magnetic Field

  11. Nuclei in Magnetic Field Distribution between two states

  12. Nuclei in Magnetic Field

  13. Nuclei in Magnetic Field Magnetizaton The difference in populations of the two states can be considered as a surplus in the lower energy state according to the Boltzmann distribution A net magnetization of the sample is stationary and aligned along the z axis (applied field direction)

  14. Nuclei in Magnetic Field Two spins All spins  Sum Ho parallel anti-parallel Bulk Magnetization excess facing down

  15. Effect of a radio frequency p 1. equilibrium DE ap H1 hn = DE hn = DE 4. release energy (detect) 2. pump in energy p p 5. equilibrium 3. non-equilibrium ap ap

  16. Effect of a radio frequency

  17. Effect of a radio frequency

  18. NMR Signals

  19. Relaxation- Return to Equilibrium t t x,y plane z axis 0 0 Longitudinal Transverse 1 1 t t 2 2 E-t/T2 1-e-t/T1 8 8 Transverse always faster!

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