FFC NMR relaxometry is a non-destructive low-field magnetic resonance technique which is performed in the range of a few kHz up to around 100 MHz, depending on the instrument (unlike FT-NMR spectroscopy which tends to work with magnetic field strengths from 200 MHz upwards). The information obtained is connected to the molecular dynamics of a substance or complex material through the measurement of the nuclear spin-lattice constant 1/T₁ over a large range of magnetic field strengths, which is carried out on the same instrument (relaxometer). The technique is particularly useful in revealing information on slow molecular dynamics which can only be carried out at very low magnetic field strengths. For a more detailed explanation see Fast Field Cycling NMR relaxometry (section below) and Relation of NMRD to molecular dynamics.

Examples of important molecular dynamics information which can be obtained through FFC NMR relaxometry:

• · Characterization of rotational dynamics
• · Determination of thermal activation energies
• · Identification and distinction between different molecular dynamics e.g. solid/liquid dynamics, fast/slow dynamics, inter-molecular/intra-molecular dynamics
• · Characterization of surface exchange effects with solvents and other small molecules
• · Characterization of porous systems and local diffusion effects
• · Characterization of translational diffusion in bulk and geometrically restricted environments
• · Identification of the presence of paramagnetic substances
• · Evaluation of MRI contrast agents (electronic relaxation, kinetics of exchange, coordination number, correlation times in the spectrum of re-orientation and diffusional dynamics of molecules)
• · Identification of effects connected to cross-linking in polymers
• · Separation of slow and fast motion relaxometric components in polymers (inter-chain and intra-chain interactions)
• · Separation of amorphous and crystalline contributions in solids
• · Determination of aggregation states of complex biomolecules such as proteins
• · Exploration of relaxation of interesting nuclei, such as ²H, ¹³C, ⁷Li, ¹⁹F, ²³Na, etc.: structural information connected to the presence of a particular nucleus at a specific molecular site may be obtained.
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The magnetic field dependence of 1/T1 of any given substance or material is shown in the graphical form as a Nuclear Magnetic Resonance Dispersion (NMRD) profile. The NMRD shown below shows the different profiles of a foodstuff before (black squares, unspoiled) and after it has expired (red dots, spoiled).

NMRD Profile

Data produced from in-house studies at Stelar

The relaxation rate 1/T₁ of a substance or material will tend to change when there is a variation in molecular dynamics, which may be caused by the following:

• change of state (e.g. solid to liquid; phase changes in complex systems such as liquid crystals)
• concentration changes (e.g. effect on aggregation states of biomolecules)
• temperature changes
• viscosity changes
• cofactor interactions such as sulfur-polymer coupling or plasticizer effects
• paramagnetic impurities

Changes in the relaxation rate, 1/T₁, of a substance or material, are sometimes not evident at single magnetic field strengths, but when studied over a wide range of magnetic field strengths, as with FFC NMR relaxometry, changes are easier to identify as they are often more visible with the NMRD profile, especially at the lower magnetic field strengths.

Relation of NMRD to molecular dynamics

Molecular dynamics are generally rotational or translational motions that are modeled as small angle or small step translational jumps which occur randomly in time. The random functions of time are usually characterized by a time correlation function that characterizes the conditional probability that if there is a particular orientation or position at time t, what is the probability at time (t + τ) later? For Brownian rotational diffusion, the correlation function decays exponentially:

Where B² is the strength of the coupling modulated and τc is the correlation time for the molecule to diffuse approximately one radian. Nuclei are relaxed by the transition induced by these fluctuating fields at the Larmor frequency (single quantum) and twice the Larmor frequency (double quantum) spin flips. What motions are important depends on the magnetic field strength experienced by the nuclei. The more intense the fluctuations are near the Larmor frequency, the faster the spins relax. The frequency dependence of the fluctuation intensity, i.e., the power spectrum or the spectral density, is the Fourier transform of the time correlation function. For rotation this becomes,

Which to within a constant has the form

Thus, the Nuclear Magnetic Resonance Dispersion (known as NMRD or MRD) maps the Larmor frequency dependence of the spectral density function that is related directly, by the Fourier transform, to the time correlation function characterizing molecular motions. Any motion that causes changes in the local fields contributes to the relaxation process including rotation, translation and chemical exchange among different chemical or physical environments.

A critical feature of NMRD is that it is possible to map spectral densities as low as 5-10 kHz which corresponds to a time regime in the vicinity of 30 microseconds, i.e., well into the range of chemical exchange events. Variations of the method permit exploration to lower frequencies. See also page on Frequently Asked Questions.

Acknowledgement: Thanks to Prof. Robert G. Bryant (University of Virginia, USA) for providing some of the text for this section.