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Introduction to Fast Field Cycling (FFC) relaxometry

The Fast Field Cycling (FFC) NMR relaxometry technique

Fast Field Cycling 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.

FFC NMR relaxometry is the only low-field NMR technique which measures the longitudinal spin relaxation rate, R1=1/T1, as a function of the magnetic field strength over a wide range of frequencies using only one instrument.

The information obtained from T1 is connected to the molecular dynamics of a substance or complex material. The technique is particularly useful in revealing information on slow molecular dynamics which can only be carried out at very low magnetic field strengths.

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 reorientation and diffusional dynamics of molecules);
  • Identification of effects connected to crosslinking 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;
  • Separation of slow and fast motion relaxometric components in polymers (inter-chain and intra-chain interactions);
  • 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.

The NMRD profile

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 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.

FIG 01: The NMRD profiles of a foodstuff before (black squares, unspoiled) and after it has expired (red dots, spoiled). Stelar in-house data.

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.

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

FFC technique

FIG 02: schematic representation of the field cycling technique.

FFC NMR relaxometry requires a small amount of a solid or liquid sample (enough to fill a standard 10mm NMR tube to a volume of around 1 cm3) with no other form of preparation required.

The Stelar wide-bore magnet is able to accommodate larger samples such as rock cores or even small animals. The Stelar relaxometer works by fast electronic switching of the magnetic field from an initial polarizing magnetic field (BPOL), where the equilibrium of nuclear magnetization is attained in about 4T1, to a field of interest (relaxation field; BRELAX) at which the nuclear spins relax to the new equilibrium state with a characteristic relaxation time constant T1.

After a delay time, τ, the BRELAX is switched to the field of acquisition (BACQ) and the NMR signal is detected after a π/2 RF pulse (fig. 2).

Fast Field Cycling NMR relaxometry: a technical explanation

FIG. 3: NMRD profile for bovine serum albumin in water at 200 mg/mL.
Picture provided by Prof. Robert G. Bryant (University of Virginia, USA).

FIG 4a & 4b: The relaxation dispersion profiles for cross-linked bovine serum albumin samples at different compositions shown in semilogarithmic (a) and log-log (b) presentations.
Picture provided by Prof. Robert G. Bryant
(University of Virginia, USA)

Fast Field Cycling (FFC) Nuclear Magnetic Resonance (NMR) relaxometry is a measurement of the nuclear spin-lattice relaxation rate constant as a function of the applied magnetic field strength that provides a unique characterization of the local molecular dynamics of molecules over a wide frequency range. The spin-lattice-relaxation-rate constant (1/T1) characterizes the time dependence of the approach to thermal equilibrium for the nuclear spin magnetization if it is perturbed from equilibrium in a magnetic field. The process involves an exchange of energy between the nuclear spin energy and the other degrees of freedom in the system collectively called the lattice, even in a liquid.

This energy exchange requires photons of energy corresponding to transitions between the nuclear spin energy levels that are a linear function of the magnetic field strength. The fluctuations that cause the coupling derive from molecular motions in the system ranging from vibrations at the highest frequencies to global fluctuations at the lowest frequencies. Varying the magnetic field strength varies the frequencies sampled by the relaxation rate measurement. By varying the magnetic field over wide ranges, it is possible to map the power spectrum of the fluctuations from a few kHz to hundreds of MHz corresponding to a time scale range from tens of microseconds to hundreds of ps. Incorporation of a paramagnet in the system permits exploration of dynamics to the sub picoseconds domain. One may think of nuclear magnetic relaxation dispersion (NMRD) as the magnetic analog of dielectric dispersion; however, NMRD has the distinct advantage that one generally has no difficulty identifying the origin of the motions that drives spin relaxation.

The solid curve in fig. 3 is a “fit” to the data assuming a single rotational unit (monomer). The fit fails because the solution is severely aggregated. As a consequence of the aggregation, the inflection point is shifted a decade to lower Larmor frequencies corresponding to much larger rotational units than a monomer, and the dispersion is broadened which reports through the rotational correlation times the distribution of apparent molecular sizes. The weighting of the contributions to the NMRD profile is proportional to the rotational correlation time, thus, the larger aggregates make a much larger contribution to the relaxation rate constant than the smaller ones. The dispersion is predominantly a power law in the Larmor frequency for the rotationally immobilized protein cases or very large aggregates (fig. 4).

Practical difference between a fixed field magnet and an FFC relaxometer

FIG 5a: 1H NMRD profiles of three different weight distributions of polyethylene glycol (PEG) melts. Data produced from in-house studies at Stelar. Samples kindly provided by Dr. M. Fleury, IFPEN, Paris.

FIG 5b: NMRD profiles of BTPI as a function of salt concentration.

FIG 5c: NMRD profiles of starch samples with differing water content.

A FFC relaxometer, such as the Stelar SPINMASTER or SMARtracer, is a specialized system with a low field magnet which is able to electronically switch the magnetic field strength required, from a few kHz up to the maximum magnetic field strength allowed by the magnet (up to 42 MHz 1H Larmor frequency with the 1 Tesla magnet) and which is able to overcome the limits of the NMR signal-to-noise ratio at low magnetic field strengths.

A standard fixed field magnet measures the relaxation rate constant 1/T1 with the limitation that it is unable to change the magnetic field strength of operation and thus is only able to measure 1/T1 at a single magnetic field strength. Fixed field time domain instruments generally operate in the range of 2 – 60 MHz. The FFC relaxometer is able to measure 1/T1 at very low magnetic field strengths (down to a few kHz) which is of particular advantage as many molecular processes occurring in the range between nano-seconds and milliseconds (slow molecular dynamics) are very difficult to measure at higher magnetic field strengths.

In the following we show three examples. The NMRD profiles in fig.5A, measured with a Stelar FFC NMR relaxometer, show three different weight distributions of polyethylene glycol (PEG) melts (blue squares 8,000 Da, black squares 20,000 Da, red squares 35,000 Da). This demonstrates how the ability to measure nuclear spin relaxation over a wide range of magnetic field strengths, and especially at very low magnetic fields, can be of advantage. It would be difficult to distinguish between these three different polymers at magnetic field strengths higher than 0.1 MHz. In fig. 5b it is shown how protein aggregation can be investigated using FFC. NMRD profiles allowed to study BTPI (Bovine Pancreatic Trypsin Inhibitor) self-association as a function of pH, salt type, salt concentration and temperature.

FFC method sensitively detects stable oligomers without being affected by other intercactions. Looking at the NMRD profiles in fig. 5B, it is evident that it would be difficult to distinguish between the different samples at magnetic field strengths higher than 5 MHz.

In fig. 5C it is shown that applying FFC to starch samples it is possible possible to distinguish between samples with different water content. The difference between samples is not detectable for field strengths over 10MHz.

Technical difference between a fixed field magnet and an FFC relaxometer

The key difference between the fixed field experiment and the NMRD experiment is that the NMRD profile provides a test of the theory used to interpret the data in terms of the molecular dynamics in the system. Rotational motions are a simple example.

The relaxation rate constant may be written for relaxation induced by rotational Brownian motion as:

The measurement of the field dependence characterizes the rotational correlation time, τ, as well as the strength of the coupling, B2, driving relaxation. However, one does not need to know B2 to extract the dynamical information because it derives from the Larmor frequency dependence entirely.

In the fixed field experiment, the Larmor frequency, ω, is fixed. In this case, to extract τ, one needs to know B2 accurately. Further, there is no test of the assumptions in the theory for the fixed field measurement, but in the NMRD experiment, if the theory is inappropriate, it will not faithfully fit the NMRD profile.