Skip to main content
Chemistry LibreTexts

1.10: How do T₁ and T₂ relaxation affect NMR spectra?

  • Page ID
    77767
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    The decay of the FID corresponds to the loss of intensity of the macroscopic magnetization vector in the xy plane (called the transverse plane) by a process called spin-spin relaxation (or transverse or T2) relaxation. T2 relaxation occurs when a nucleus in a –½ spin state transfers its spin to a nearby nucleus in a + ½ spin state, and vice versa. Since T2 relaxation occurs through mutual spin flips, the energy of the system is unaffected, it is an entropic process. In terms of our vector model, T2 relaxation corresponds to a loss of coherence or dephasing of the magnetization vector. The recovery of magnetization along the z (longitudinal) axis (aligned with Bo) to its equilibrium position occurs by a process called spin lattice (or longitudinal or T1 relaxation). T1 relaxation occurs through interactions of the nuclei with the lattice (or the nuclei that surround our sample). Lattice motions at the same frequency as the Larmor frequency stimulate the magnetization in the higher energy – ½ spin states to lose this excess energy by transferring it to the lattice via a process called radiationless decay. Since T1 relaxation involves a loss of energy by the system as the spins return to their equilibrium populations, it is an enthalpic process. These relaxation processes are first order processes characterized by the relaxation time constants T1 and T2. The width at half-height of a resonance is inversely related to the T2 relaxation time of the nucleus, w1/2 = (πT2)-1. Because the magnets we use are not perfectly homogeneous, there is a secondary contribution to the line width that comes from magnetic field inhomogeneity. Therefore, the apparent spin-spin relaxation time constant or T2* observed in the FID includes both the natural T2 relaxation time of the nucleus as well as the effect of magnetic field inhomogeneity, w1/2 = (πT2*)-1. If you want to know the real T2 value for a nucleus, a special experiment, called the spin echo can be used.

    Exercise \(\PageIndex{5}\)

    What are the resonance line widths of nuclei that have apparent T2 relaxation times (i.e.T2* values) of 1 and 2 sec.

    The effects of T1 relaxation are more difficult to observe directly, because it corresponds to the return to equilibrium populations following the pulse. However, if several FIDs are coadded, as is usually the case in NMR, and if the time between successive pulse and acquire steps is insufficient for complete T1 relaxation, the resonances in the resulting NMR spectrum will be less intense than they would otherwise appear. Because quantitative NMR measurements rely on resonance intensity, understanding the effects of T1 relaxation is very important for obtaining accurate qNMR results. Therefore this subject is treated in greater depth in the Practical Aspects section of this module.


    This page titled 1.10: How do T₁ and T₂ relaxation affect NMR spectra? is shared under a CC BY-NC-SA 2.5 license and was authored, remixed, and/or curated by Cynthia K. Larive & Albert K. Korir via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.