Beyond Structural Elucidation - Introduction to qNMR Part III - Relaxation Delays

In this blog, Part III of the qNMR series, I will be addressing relaxation and why it's important for quantitative nuclear magnetic resonance (qNMR) experiments. If this is your first time reading about qNMR and would like to know more, please check out our other posts where you can find a general introduction to qNMR as well as information for the types of calibrants available for qNMR experiments.

I’d like to start by giving a brief overview of the ¹H NMR experiment. In the absence of an external magnetic field, the magnetic moments of the ¹H nuclei in the sample are equal in energy and are randomly oriented resulting in no net magnetization. Due to their intrinsic property, the magnetic moments of the ¹H nuclei will split into two orientations with different energy levels in the presence of an external magnetic field, either in the direction of the external magnetic field (denoted as +½ in the figure below) or against it (denoted as -½ in the figure below). Magnetic moments that are oriented in the direction of the external magnetic field will have a lower energy while the magnetic moments oriented in the opposite direction will have a higher energy. ^[1,2]

Figure 1. Left) Illustration of the magnetic moments in a sample with and without the presence of an external magnetic field. Right) Energy levels for the 1H nucleus with and without the presence of an external magnetic field.

At room temperature it is seen that both spin states are almost evenly occupied. However, since a lower energy state is indeed more favourable, there are slightly more nuclei in the +½ state, resulting in a net magnetization in the direction of the external magnetic field.^[2]

The crux of the NMR experiment is the excitation of the ¹H nuclei into a higher energy state. This is performed by supplying energy, in the form of a radiofrequency (RF) pulse, that is absorbed by the ¹H nuclei. This RF pulse will knock the bulk of the magnetization of the sample from the z-axis (in this frame of reference the z-axis is in the direction of the external magnetic field) into the xy-plane where an NMR signal can be detected.

After excitation by the RF pulse, the excited nuclei will start to relax back to its ground state. Unlike other spectroscopic methods, the excess energy will not be released in the form of a photon. Instead, the nuclei release their energy to neighbouring atoms via collisions, rotations and electromagnetic interactions. ^[3]

There are 2 major types of relaxation processes in the NMR experiment, spin-lattice relaxation, also known as T₁ (relaxation in the z-axis), and spin-spin relaxation or T₂ (relaxation in the xy-axis). For this blog post I will focus solely on T₁ relaxation times.

Figure 2. Schematic showing the relaxation of magnetization after a 90° pulse. Relaxation in the z-axis is represented by the grey arrow while relaxation in the xy-axis is represented by the orange arrow. [4]

As described by equation 1, the T₁ relaxation time can be defined as the time it takes the z-component of magnetization to reach ~63% (1 – e^−t/T1) of its maximum value (B₀); where B_z(t) is the amount of magnetization reached at time t, B₀ is the maximum amount of magnetization in the z-axis, and t is time. There are several factors that affect T₁ relaxation times such as nuclear magnetic dipole-dipole interactions, electron dipole relaxation, and electric quadrupole relaxation.^[5]

Now that I’ve covered the NMR experiment and relaxation, you might be wondering how this all relates to the qNMR experiment. While regular NMR experiments rely on more qualitative and semi quantitative data, qNMR experiments require precise quantitative data. If all the ¹H nuclei have not fully relaxed before the next RF pulse is applied, only a fraction of the total excitation can occur. This will lead to decreased signal intensity and result in inaccurate integrations. In extreme cases of insufficient relaxation, the signals might not be observed at all. It is therefore vitally important that sufficiently long delay times are used for qNMR experiments. Based on the formula above, it is recommended that you allow the ¹H nuclei to relax for at least 3-5 times the T₁ relaxation time to allow for the bulk of the magnetic moment to relax back to its equilibrium. For regular NMR experiments, delay times are often set to less than 3-5 times the T₁ relaxation time with little to no consequences on the resulting NMR spectra.

How do you determine T₁
One of the most common methods to determine the T₁ relaxation time is the inversion recovery experiment. The reason why it’s called an inversion recovery experiment is because the signal is initially pulsed with a 180° pulse resulting in an inverted net magnetization. This inverted magnetization recovers at a rate corresponding to the sample’s T₁. After a specific delay time (tau), a 90° pulsed is applied and the NMR signal recorded. To obtain the T₁ relaxation time, a series of inversion recovery experiments are performed with different tau times. The intensities of the NMR signals are then plotted vs. the delay time and the T₁ relaxation time can be extracted from the resulting curve.^[6]

This pulse sequence comes preloaded on our NMReady-60PRO to allow for T₁ relaxation time to be determined in an easy and hassle-free manner. Hopefully this blog post has been helpful for you to understand NMR relaxation times and why it’s important to qNMR experiments. If you have any questions about conducting qNMR experiments with the NMReady-60, please don’t hesitate to contact us.

References:
^[1]NMR Spectroscopy Theory https://teaching.shu.ac.uk/hwb/chemistry/tutorials/molspec /nmr1.htm# (accessed May 23, 2019).
^[2]NMR: Introduction https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_ Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/ Spectroscopy/Magnetic_Resonance_Spectroscopies/Nuclear_Magnetic_Resonance /Nuclear_Magnetic_Resonance_II (accessed May 23, 2019).
^[3]Wink, D. Journal of Chemical Education 1989, 66, 810.
^[4]NMR Relaxation http://chem.ch.huji.ac.il/nmr/techniques/other/t1t2/t1t2.html (accessed May 23, 2019).
^[5]T₁ Relaxation Measurement: The Inversion-Recovery Experiment https://apps.carleton.edu/ curricular/chem/assets/Inv_Rec_Expt_IconNMR_4_21_2015.pdf (accessed May 23, 2019).
^[6]Relaxation in NMR Spectroscopy https://www.chem.wisc.edu/areas/reich/chem605/ (accessed May 23, 2019).