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 (M_z) 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 (M_z) 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 (M_z). 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.