Relaxation

In most spectroscopic techniques, how the energy absorbed by the sample is released is not a primary concern. In NMR, where the energy goes, and particularly how fast it “gets there” are of prime importance. The NMR process is an absorption process. Nuclei in the excited state must also be able to “relax” and return to the ground state. The timescale for this relaxation is crucial to the NMR experiment. For example, relaxation of electrons to the ground state in uv-visible spectroscopy is a very fast process, on the order of pico-seconds. In NMR, the excited state of the nucleus can persist for minutes. Because the transition energy between spin levels (discussed earlier) is so small, attaining equilibrium occurs on a much longer timescale. The timescale for relaxation will dictate the how the NMR experiment is executed and consequently, how successful the experiment is.

There are two processes that achieve this relaxation in NMR experiments: longitudinal (spin-lattice) relaxation and transverse (spin-spin) relaxation.

In longitudinal relaxation energy is transferred to the molecular framework, the lattice, and is lost as vibrational or translational energy. The half-life for this process is called the spin-lattice relaxation time (T1). Dissipating the energy of NMR transitions (which are tiny compared to the thermal energy of the sample) into the sample should not be a problem, however T1 values are often long. The problem arises not in where to “send” the excess energy, but the pathway along which the energy is released to the lattice. Contributing factors to this type of relaxation are temperature, solution viscosity, structure, and molecular size.

In transverse relaxation energy is transferred to a neighboring nucleus. The half-life for this process is called the spin-spin relaxation time (T2). This process exchanges the spin of nucleus A with the spin of nucleus B (A mI = -½ ® +½ as B mI = +½ ® -½. There is no net change in spin for this process. Inhomogeneity of the magnetic field or the presence of paramagnetic materials can be a large contributor to the value observed for transverse relaxation.

The peak widths in an NMR spectrum are inversely proportional to the lifetime (due to the Heisenberg uncertainty principle) and depend on both T1 and T2. For most organic solutions, T1 and T2 are long enough to result in spectra with sharp lines. However, if magnetic field homogeneity is poor or paramagnetic material (such as iron) is present the NMR signals can be broadened to the extent that the signal is destroyed or unusable.

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