NMR field-cycling measurements of the Larmor frequency (nu) and angular (Delta) dependences of the longitudinal proton spin relaxation time T-1 for the nematic liquid crystals 5CB and 8CB allow a more detailed analysis of the underlying molecular motions than data available previously. All T-1(nu, Delta) dispersion profiles essentially distinguish three frequency ranges where T-1 is governed by either local field effects, collective motions (director order fluctuations), or rotational and translational diffusion of individual molecules or molecular groups, respectively. The angular dependence supports and extends previous conclusions about the significance of the order fluctuation term at low (kHz) and high (MHz) Larmor frequencies; in addition it is the basis for the disentanglement of local held effects, which involve Jeener's dipolar relaxation, and of the sophisticated rotational relaxation models suggested in the literature by Dong, Nordio and Void. It is found that Void's third rate concept gives the best explanation of the measurements. The results on the rotational diffusion processes essentially agree with deuteron studies from the literature, but also reveal clear distinctions with regard to the anisotropy parameter sigma, essentially due to the improved separation from the order fluctuation contribution.

Abstract In this paper we report the first molecular dynamics study combining fast field-cycling and conven-tional NMR techniques in a thermotropic liquid crystal of discotic molecules exhibiting an ordered columnar hexagonal mesophase. Using the association of these techniques we obtained proton T1 data over a very large domain of Larmor frequencies (ω/2π from 500 Hz to 85 MHz). The proton spin-lattice relaxation results were analysed considering the structure of the mesophase and the types of movements which are expected to influence significantly the relaxation rate, namely local molecu-lar rotational reorientations, inter-columnar self-diffusion and collective movements corresponding to bending and compression of the columns. We verified that these mechanisms dominate the relaxation respectively for high, medium and low Larmor frequencies.

We investigate the NMR relaxation of solvent nuclei in non viscous paramagnetic solutions, in the case where the electronic spin of the paramagnetic species is submitted to an internal hyperfine field H-hyp. General expressions of the intermolecular longitudinal relaxation rates 1/T-1 are provided, and three distinct regimes corresponding to an applied external field lower, larger and much larger than H-hyp appear, with three distinct linear laws for the relaxation rate 1/T-1 vs v(1)(1/2) ,, where vl is the nuclear resonance frequency. From each of these laws and mainly the third one, it is possible to derive the relative diffusion constant of the paramagnetic and solvent molecules without any model assumption for solutions with a rather high radical concentration of 10(-1) mol L-1. This is illustrated for a triglyme solution with new stable (NTMIOD)-N-15 free radicals at various concentrations. For this solution, T-1 measurements were performed at v(1) = 244 MHz, then at low and intermediate frequencies by the field cycling technique and finally in the Earth's magnetic field. From these results and from measurements of the solvent molecule diffusion constant by the pulsed magnetic field gradient technique, a determination of the diffusion constant of the free radicals is obtained which is compared with that obtained from a direct ESR measurement at low concentration. These data are used for the interpretation of the frequency and temperature dependence of the relaxation rates in this solution.

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Abstract The frequency dependence of the longitudinal proton spin relaxation time T1 was measured by field-cycling and standard NMR techniques at different temperatures in the liquid crystalline lamellar phases of bilayer systems, composed of lipids, nonionic surfactants, and lipid-surfactant mixtures. We show by our data analysis, comparing various motional models such as layer undulations (LUs) and relaxation by translational diffusion mediated reorientations (TR), that collective layer undulations with their typical T1~ν behaviour determine the low frequency T1 dispersion in both unoriented and glass plate-oriented bilayer systems. The angular dependence of the T1 dispersion for the oriented bilayer system supports these findings and provides a more critical analysis of the two dimensional self-diffusion than in unoriented samples. The evaluated fitting parameters of the LU model allows, together with the measured second moment of the proton NMR signal for the lipid, calculation of the bending rigidity ϰc for these bilayers at different levels of hydration. The obtained values of ϰc turn out to be too large compared with the literature. However, using recent LU models (B. Halle) which include the obvious couplings between neighbouring bilayers at low Larmor frequencies, the corrected ϰc of the fully hydrated membrane systems are comparable to those obtained from the standard videooptical experiments. Therefore proton spin relaxation measure-ments at low Larmor frequencies with the field-cycling technique are a suitable means to determine the bending rigidity ϰc of model membrane systems at low hydrations and of systems containing surfactants.

In this work we present the first study of molecular dynamics in the S-c and phi(h) mesophases of a liquid crystal of biforked molecules. This study was performed by means proton NMR relaxation measurements obtained at different temperatures in the studied phases, combining standard and fast field-cycling techniques in order to cover a large domain of Larmor frequencies (100 Hz-300 MHz). The experimental results were analysed considering the potential contributions of different relaxation mechanisms, namely local molecular rotational reorientations, self-diffusion and collective movements. The description of the contributions of the rotational reorientations and self-diffusion mechanisms are not quite different in the two studied phases. The main distinction in the molecular dynamics is found in the low Larmor frequency range dominated by the collective movements. While in the S-c phase this contribution can be described by the law characteristic of smectic layer undulations, the contribution of the collective movements in the phi(h) phase can be assigned to elastic deformation of the columns.

It is well known that Liquid crystalline compounds with a cyano terminal group can present-peculiar polymorphisms in particular different types of smectic A mesophases and a reentrant behaviour for both nematic and smectic A mesophases. In this work we study by proton NMR relaxation the influence of these features on the molecular dynamics of the compound 4-cyanobenzoate-4'-octylbenzoyloxyphenyl (DB8CN Sym) in its nematic (N), partial bilayer smectic A (S-Ad), reentrant nematic (N-re) and reentrant smectic A (S-A1) mesophases. Standard and fast field-cycling techniques were used for our spin-lattice relaxation's study over a broad frequency range of 6 decades (200 Hz up to 300 MHz). It was found that the molecular dynamics in the nematic mesophases is rather different from the molecular dynamics in the smectic A mesophases. However, the reentrant aspect present in both nematic and smectic A states is not associated to a major difference on the molecular dynamics of the nematic and reentrant nematic or smectic and reentrant smectic A mesophases. Order director fluctuations and rotations/reorientations are the most important relaxation mechanisms in the nematic mesophases in the lower and higher frequency Limits, respectively, while self-diffusion has a very small contribution to the overall relaxation. As for the smectic A mesophases, self-diffusion and rotations/reorientations are the predominant relaxation mechanisms for frequencies above 20 kHz. The collective motions, which for these mesophases have to be associated with layer undulations with the frequency law T-1 similar to v, are only important to the spin-lattice relaxation on the low part of the frequency spectrum (v < 10 kHz). The inclusion in the relaxation study of a contribution from the cross-relaxation between protons and nitrogen nuclei improves the quality of the 1/T-1 data fits in both kinds of mesophases. The combined study of the molecular dynamics in the N, S-Ad, N-re and S-A1 mesophases of DB8CN Sym reveals that it is necessary to consider one more contribution to the relaxation in the analysis of the 1/T-1 data in the S-Ad and high temperature N mesophases. This contribution is associated with a dynamic process of dissociation and recombination of molecules in groups that could be present in this kind of systems as predicted in the literature to explain the layer thickness detected in the S-?(Ad) mesophases. The characteristic time for this process was estimated.

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.

A proton NMR method is described which enables rotational flow and viscosity measurements of low molecular weight nematic liquid crystals (NLC's). This is achieved by an extension of the common NMR field-cycling technique, namely by fast electronic switching of both the external magnetic field direction and strength. In thermodynamic equilibrium, the director of an NLC with positive diamagnetic anisotropy (DELTAchi > 0) orients parallel to the external magnetic field. Thus a change of this direction causes a reorientation process of the molecules to align to the new equilibrium, which in low viscous systems in contrast to polymer liquid crystals is rather fast and hence requires fast field switching. We have studied systematically this response as a function of the initial field rotation angle theta0 relative to the director for some homologous NLC's of the n-alkyl-cyanobiphenyl (nCB) series. It is shown that there exists a critical angle theta(cr) in such a way that for theta0 < theta(cr) the director rotation is homogeneous and only controlled by the rotational viscosity gamma1. For theta0 > theta(cr), however (e.g. in the case of 5 CB theta(cr) is almost-equal-to 85 degrees) the viscoelastic behaviour is more complicated because of a coupling between flow and director gradients. The analysis of the alignment process by the changes of the proton line spectra also allows to determine the Leslie viscosities alpha1, alpha2, alpha3, alpha4 + alpha5, and the average Frank elastic constant KBAR by a single measurement.

Abstract Proton spin-lattice relaxation studies were carried out in the SA and S*C phases of the liquid crystal CI IPNOC using both conventional and fast field cycling NMR techniques. T 1 dispersion curves were obtained at two different temperatures for each mesophase covering frequencies from 102 to 3 × 108 Hz. In both mesophases the T 1 data can be described assuming the presence of three different relaxation mechanisms, namely local molecular rotations, molecular self-diffusion and collective motions. The self-diffusion constant D 1 was evaluated for several temperatures and the activation energy associated with the diffusion process was obtained. The expected contribution of the soft-mode for the spin-lattice relaxation could not be separated from the contribution of other collective motions. The correlation times associated with the rotations around the molecular long axis and with the fluctuations of this axis were evaluated for both the SA and the S*C phases.

Liquid crystalline compounds containing a cyano terminal group often exhibit peculiar molecular organizations of their mesophases. In this work we present proton NMR relaxation studies, performed by means of standard NMR and fast field-cycling NMR techniques, in the nematic (N) and bilayered smectic-A phase (S(A2)) of 4-pentyl-phenyl 4'-cyanobenzoyloxy-benzoate. The field-cycling measurements were used to clarify the relaxation behaviour in the low Larmor frequency range, where conventional techniques are not applicable.Self-diffusion and rotational reorientations are found to be the essential relaxation mechanisms at MHz frequencies in the smectic mesophase, while the contribution of collective modes appears only at lower frequencies in the kHz range. In the nematic mesophase the order director fluctuations mechanism dominates the relaxation dispersion up to 10 MHz, where the rotational reorientations become important, with minor corrections from the self-diffusion process. The agreement between the experimental findings and model fits could be improved by an additional relaxation mechanism in the kHz regime, ascribed to the interaction between protons and fast relaxing quadrupolar nitrogen N-14 nuclei. Though all four processes are present in the nematic and smectic-A2 phases, the overall T1 frequency dependence is quite different in the two cases. This behaviour is discussed in terms of available theoretical calculations of the proton relaxation dispersion in liquid crystals, and it is also compared with data known from other cyano compounds.

Molecular dynamics studies were carried out in the S A and S * C mesophases of the Ferroelectric Liquid Crystal Val.DOC by means of longitudinal proton spin relaxation dispersion. Fast field-cycling and conventional Nuclear Magnetic Resonance (NMR) techniques were used to obtain the frequency dependence of T 1 covering frequencies from 102 to 3 × 108 Hz at two different temperatures in each mesophase. The T 1 dispersion in both mesophases could be well modeled by the proposed dominant relaxation mechanisms, namely collective motions, molecular self diffusion and local molecular rotations. A Soft mode contribution to the spin-lattice relaxation could not be singled out from the contribution of other collective motions. The diffusion constant D ⊥perpendicular to the director was obtained at all temperatures studied and involves an activation energy of about 35 kJ/mol. Effective correlation times characterizing the average molecular rotations around the long axis and fluctuations of this axis, respectively, were evaluated; their temperature dependence agrees with an Arrhenius type law with activation energies of about 50 kJ/mol.

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.

Abstract The Larmor frequency dependence of the proton spin relaxation time, obtained by means of the fast field-cycling NMR technique, has been used to study the 14N quadrupole coupling constant K and its asymmetry parameter η in the nematic and smectic phases of some liquid crystalline azoxybenzenes (PAA, BAB, HAB, HpAB), cyanobiphenyls (8CB, 9CB, 11CB) and oxycyanobiphenyls (9 OCB). Due to fast molecular reorientations, the effective quadrupole coupling constants are relatively small, whereas surprisingly the asymmetry parameters are rather large. The temperature dependence of both K and η within the mesophases, as well as their discontinuities at the different mesophase transitions, can be interpreted by the anisotropy of molecular rotations. It is found that temperature effects are significantly more pronounced for the (biaxial) smectic-C phase of the heptyloxyazoxybenzene (HpAB) than for the (uniaxial) smectic-A phase of the various investigated cyano- and oxycyanobiphenyls. As a rule, η turned out smaller in the smectic than in the nematic state, whereas K has similar values in both phases

Abstract Field-cycling and standard pulsed NMR techniques have been used to study the frequency dependence of the longitudinal proton spin relaxation time T x in the crystalline estradiol compound (+)3,1,7-ß-bis-(4n-butoxybenzoyloxy)-estra-1,3,5-(10)-trien or BET, which is a mesogenic material with a chiral molecular structure. From the measured Larmor frequency and temperature depen-dences we conclude that, at low NMR frequencies in the cholesteric phase, T1 reflects in addition to the relaxation process familiar from nematic liquid crystals (director fluctuation modes) another slow mechanism theoretically predicted for cholesteric systems, namely diffusion induced rotational molecular reorientation. These relaxation processes are not or much less effective in the crystalline and glassy state, where they are frozen. Also the high NMR frequency relaxation dispersion strongly differs between the cholesteric mesophase and the not liquid crystalline samples. This is interpreted by a change from essentially translational self-diffusion to rotational diffusion controlled proton relaxation.

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 longitudinal proton spin relaxation time T1 was measured over a broad range of Larmor frequencies w in the nematic and isotropic phases of the liquid crystal Hexyloxyazoxybenzene, deuterated on the benzene rings (60AB-D8). All the measurements were made on a Fast Field-Cycling Spectrometer [1]. Our analysis also takes into account T1 data from the literature [2].

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).

The 14N quadrupolar coupling constant K and the asymmetry parameter η of the nitrogen sites in some nematic and smectic liquid crystals (alkyloxy-azoxybenzenes, cyano-biphenyls, oxycyano-biphenyls) have been studied by means of the Larmor frequency dependence of the proton spin relaxation time T1, which reveals the presence and asymmetry of nitrogen bonds by small dips in the 1H relaxation dispersion profile. Both the steady temperature dependences of K and η within the mesophase ranges, as well as the strong discontinuities of these parameters at, phase transitions, can be interpreted by changes of the anisotropic molecular rotations. It is found that the temperature effects are significantly more pronounced for the biaxial smectic-C phase of the heptyloxy-azoxybenzene compound (HpAB) than for the uniaxial smectic-A phase of the Investigated biphenyls (8CB, 9CB, 90CB, 11CB), and also compared with the results obtained for these biphenyls and some azoxybenzenes (PAA, BAB, HAB, HpAB) in the nematic state.