Part 1 - T1 relaxation: definition, measurement and practical implications!

Nuclear Magnetic Resonance spectroscopy is based on the idea that some nuclei can behave as little magnetic bars (I spin number ≠ 0). In the presence of a magnetic field (B0) the nuclear spins feel a small torque for or against the B0 axis, which results in a net magnetization along the B0 direction (Figure 1). All the information that we can obtain using NMR comes from the manipulation of this net magnetization through the application of radio frequency (rf) pulses.

Figure 1: Representation of the net magnetization in the absence of magnetic field (left), and in the presence of a magnetic field (right).

If we first apply a 90° rf pulse, the longitudinal magnetization (Mz) will be flipped towards the xy plane (transversal magnetization). The signal detection in NMR occurs along the xy plane, however, it is a non-equilibrium situation, so the intensity of the detected signal will decrease over time due to relaxation. There are two types of relaxation, longitudinal relaxation (T1) and transversal relaxation (T2). Many mechanisms are involved in each kind of relaxation, this blog is dedicated to describing T1 in general, how it can be measured, and its importance in quantitative analysis.

T1 relaxation, also known as longitudinal relaxation, spin-lattice relaxation or relaxation in z-direction is the process by which the net magnetization returns to the equilibrium (along z axis) over time, and can be described mathematically, for ½ spin, as:

The method most commonly used to determine T1 is the inversion-recovery experiment, where first a 180° pulse is applied, so the magnetization goes from z to -z, followed by a time t (during this time the magnetization relax to z), and the final 90° pulse flips the magnetization from z axis to xy plane to be detected (Figure 2).

Figure 2: a) Pulse sequence diagram for the inversion-recovery experiment, and b) Graph of the relative intensity of the recovery magnetization (Mz) versus the time (t) for a sample of 40% H2O in D2O. The inversion-recovery experiment displayed was acquired using the Nanalysis 60 MHz.

Why it is important to know the T1 value? Its importance comes from the fact that it affects the relative integration between signals, since each nucleus (individual spins) in a molecule has a different T1 value, for quantitative purposes is mandatory to wait at least 5 times the longest T1 in the sample between scans in order to recover 99% of the equilibrium magnetization (Mz). The figure below (Figure 3) highlights how the delay between successive scans can affect the relative integration value. If you want to know more about qNMR read it here!

Figure 3: 1H NMR of furoic acid in DMSO-d6 acquired at 60 MHz with a) scan delay equal to 0 s, and b) scan delay equal to 30 s.

References:
* Chapter 4 and 9 from J. Keeler, Understanding NMR Spectroscopy (2nd edition, John Wiley & Sons, Ltd, 2010.)
* N. M. Loening, M. J. Thrippleton, J. Keeler, R. G. Griffin, J. Magn. Reson., 2003, 164, 321-328. 

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