As first discussed by Pincus and by Blinc et al., fluctuations of the director in a nematic liquid crystal should lead to a characteristic square root dependence of the nuclear magnetic relaxation time T, of a liquid crystal on the Larmor frequency of the considered nuclear spin. The significance of this process in nematics and of related mechanisms in smectics is violently disputed in the literature, essentially because standard NMR spectrometers do not allow a sufficiently broad frequency variation. In this Chapter we first illustrate the present capabilities of field cycling methods to perform frequency dependent T, measurements over a range from about 100 Hz to 10 MHz, and then review the results of proton and deuteron spin relaxation dispersion measurements for numerous nematic and smectic liquid crystals. As a rule it is found that director fluctuations are clearly observable by the relaxation rate only at low Larmor frequencies, i.e., far below the standard megahertz regime.

NMR field-cycling measurements of the deuteron spin relaxation dispersion T1(nu) for the fully deuteriated nematic liquid crystal 4-n-pentyl-4'-cyanobiphenyl (5CB-d19) over a broader Larmor frequency range (nu almost-equal-to 10 kHz to 30 MHz) than reported so far in the literature basically confirm the magnetic relaxation mechanisms previously observed by frequency dependent proton spin studies of various nematogenic molecules, namely collective nematic modes of the director field in the kilohertz regime, and anisotropic reorientations of individual molecules (mainly self-diffusion for the protons and mainly rotations about the long axis for the deuterons) in the megahertz range. Within the experimental error limits such a model allows a self-consistent interpretation of the available deuteron and proton T1(nu) results for deuteriated or protonated 5CB, respectively. In particular, the magnitudes of the measured order fluctuation contributions are in approximate accordance, i.e. within a factor of less than two, with theoretical estimates from NMR line splittings and the relevant material parameters. More exact and more extensive deuteron studies are needed to locate the origin of the observed minor inconsistency.

As first discussed by Pincus and Blinc, order fluctuations of the director in a nematic liquid crystal should lead to a characteristic square-root dependence of the nuclear magnetic relaxation times T1 of the considered atoms on the Larmor frequency v, i.e. T1 - v 1/2. The significance of this process is violently disputed in the literature, essentially because standard NMR spectrometers do not allow a broad frequency variation sufficient to separate different dispersion laws reliably. Using a newly developed field-cycling NMR spectrometer with a fast switchable 1.2 T detection field and fast Fourier transform data processing capabilities, it became possible to extend previous proton relaxation studies to selective frequency dependent deuteron T1 measurements in the range between 500 Hz and 7 MHz for various deuterated nematogens (PAA-d6, PAA-d8, PAA-d14, MBBA-d6). Compared with previous proton results in the same frequency range, the relaxation dispersion of the deuterons at identical sites is relatively small in all studied samples, and unlike the proton T1 the deuteron T1 does not show a fully developed square-root regime. However, the process is clearly detectable at medium and low Larmor frequencies between about 5 kHz and 500 kHz, where the Pincus-Blinc model dominates the proton spin relaxation. Thus the first deuteron field-cycling measurements support the previous proton results that nematic order fluctuations are not visible by T1 at standard high Larmor frequencies in the megahertz range.

Using a novel field-cycling spectrometer with a fast switchable 1.2 T detection field and fast Fourier transform data processing capabilities, frequency dependent selective deuteron T1 relaxation measurements were performed for several deuterated nematic liquid crystals (e.g. PAA, MBBA), and also for some deuterated solutes in a nematic solvent (e.g. p-xylene in MBBA), over the broad Larmor frequency range from v ≈ 400 Hz to 7.5 MHz 1). Compared with previous proton relaxation dispersion work of the same non-deuterated systems, the longitudinal deuteron relaxation time shows a remarkably small dependence on the frequency, particularly above v ≈ 20 kHz, and it does not clearly reveal in any case the square-root law contribution T1 ~ v 1/2 to be expected from collective molecular reorientations, and well-established by proton studies. The strongest variations, namely by factor of up to 10, occur typically below 20 kHz, where the Zeeman and quadrupolar energies of deutoron spins become comparable.

The theoretical magnet-coil optimization formalism described previously 1) has been extended to calculate a still stronger and more homogeneous (105) low-inductance (6 mH) copper magnet with a maximum magnetic flux density of 2.4 T for fast field cycling NMR, where field switches of the order of milliseconds are necessary. These calculations were combined with a novel, computer controlled coil cutting technique from copper and aluminium tubes, which allows us to produce much narrower gaps between the conductor windings (0.1 mm) and a more precise sawing path (0.01 mm) of the sophisticated coil geometry than in our original construction. The cutting procedure was successfully tested on a smaller 1.4 T system, and the final magnet is under construction. It will considerably improve both the signal sensitivity and the spectral resolution of selective frequency dependent relaxation measurements of deuterons in difficult systems, like liquid crystals 2).

Abstract The frequency dependence of the longitudinal proton spin relaxation time T1 was measured by field-cycling and standard NMR techniques in the nematic, smectic and reentrant nematic mesophases of the reentrant liquid crystal 6OCB-8OCB. The results clearly demonstrate that, in contrast to conclusions reported in the literature, the underlying relaxation mechanisms are the same for the nematic and reentrant nematic order, but different in the nematic and smectic phase. In particular, at low frequencies the nematic and reentrant samples reveal a square-root dispersion profile (T1,~ ν½) characteristic for nematic director fluctuations, whereas the smectic samples show a dissimilar and only very narrow dispersion step. It can be attributed to a linear relaxation time increase (T1 ~ v1) expected for smectic-type order fluctuations. The experimental data are described and discussed in terms of four molecular processes, namely nematic or smectic order fluctuations, self-diffusion, rotational motions, and a resonant proton nitrogen coupling.

A mathematical formalism is described which allows the design of the most effective geometry for homogeneous, fast-switchable field-cycling magnets. The method minimizes the electric power needed to produce a flux density B subject to constraints on the homogeneity and effective volume. It was used to build a low-inductance 1.2 T coil for fast-field-cycling NMR experiments with protons at 50 MHz and with deuterons at 7.5 MHz. Driven by a 25 kW MOSFET switch the field turn-on and turn-off times can be adjusted to less than 0.4 ms. Data for a projected 2.4 T coil, which will extend the field-cycling range to Larmor frequencies of 100 and 15 MHz, respectively, are also given.

A fast electronic field switch is described for field-dependent NMR experiments (relaxation dispersion, zero-field spectra, cross relaxation, etc.), which makes use of high-voltage thyristors and transistors (GTOs, MOSFETs) and thus allows production of cycles of the magnetic flux density B with much shorter transit intervals to the maximum field level than instruments previously reported in the literature. The switch controls a 3 kW power supply and gives dBdtmax = 6 × 102 T/s for Bmax = 0.21 T; a projected extension of the device to 50 kW driving power will increase either the maximum switching rate or the maximum field level by one order of magnitude. The performance of the switch is by measurements of the proton spin relaxation dispersion of samples with rather short relaxation times, namely in the millisecond range. Also shown are proton zero-field spectra of such systems, which cannot be obtained by means of the recently reported, inherently slow mechanical cycling devices because of the presence of fast longitudinal relaxation processes.