Nuclear spin relaxation and molecular dynamics in ordered systems: Models for molecular reorientation in thermotropic liquid crystals

Observation of Angular Dependence of T1 in the Human White Matter at 3T

BACKGROUND AND OBJECTIVE

Multiple factors including chemical composition and microstructure influence relaxivity of tissue water in vivo. We have quantified T1 in the human white mater (WM) together with diffusion tensor imaging to study a possible relationship between water T1, diffusional fractional anisotropy (FA) and fibre-to-field angle.

METHODS

An inversion recovery (IR) pulse sequence with 6 inversion times for T1 and a multi-band diffusion tensor sequence with 60 diffusion sensitizing gradient directions for FA and the fibre-to-field angle θ (between the principal direction of diffusion and B₀) were used at 3 Tesla in 40 healthy subjects. T1 was assessed using the method previously applied to anisotropy of coherence lifetime to provide a heuristic demonstration as a surface plot of T1 as a function of FA and the angle θ.

RESULTS

Our data show that in the WM voxels with FA > 0.3 T1 becomes longer (i.e. 1/T1 = R1 slower) when fibre-to-field angle is 50-60°, approximating the magic angle of 54.7°. The longer T1 around the magic angle was found in a number of WM tracts independent of anatomy. S0 signal intensity, computed from IR fits, mirrored that of T1 being greater in the WM voxels when the fibre-to-field angle was 50-60°.

CONCLUSIONS

The current data point to fibre-to-field-angle dependent T1 relaxation in WM as an indication of effects of microstructure on the longitudinal relaxation of water.

Concepts and Methods of Solid-State NMR Spectroscopy Applied to Biomembranes

Concepts of solid-state NMR spectroscopy and applications to fluid membranes are reviewed in this paper. Membrane lipids with ²H-labeled acyl chains or polar head groups are studied using ²H NMR to yield knowledge of their atomistic structures in relation to equilibrium properties. This review demonstrates the principles and applications of solid-state NMR by unifying dipolar and quadrupolar interactions and highlights the unique features offered by solid-state ²H NMR with experimental illustrations. For randomly oriented multilamellar lipids or aligned membranes, solid-state ²H NMR enables direct measurement of residual quadrupolar couplings (RQCs) due to individual C-²H-labeled segments. The distribution of RQC values gives nearly complete profiles of the segmental order parameters S_CD⁽ⁱ⁾ as a function of acyl segment position (i). Alternatively, one can measure residual dipolar couplings (RDCs) for natural abundance lipid samples to obtain segmental S_CH order parameters. A theoretical mean-torque model provides acyl-packing profiles representing the cumulative chain extension along the normal to the aqueous interface. Equilibrium structural properties of fluid bilayers and various thermodynamic quantities can then be calculated, which describe the interactions with cholesterol, detergents, peptides, and integral membrane proteins and formation of lipid rafts. One can also obtain direct information for membrane-bound peptides or proteins by measuring RDCs using magic-angle spinning (MAS) in combination with dipolar recoupling methods. Solid-state NMR methods have been extensively applied to characterize model membranes and membrane-bound peptides and proteins, giving unique information on their conformations, orientations, and interactions in the natural liquid-crystalline state.

Diffusion-mediated nuclear spin phase decoherence in cylindrically porous materials

In NMR or MRI of complex materials, including biological tissues and porous materials, magnetic susceptibility differences within the material result in local magnetic field inhomogeneities, even if the applied magnetic field is homogeneous. Mobile nuclear spins move though the inhomogeneous field, by translational diffusion and other mechanisms, resulting in decoherence of nuclear spin phase more rapidly than transverse relaxation alone. The objective of this paper is to simulate this diffusion-mediated decoherence and demonstrate that it may substantially reduce coherence lifetimes of nuclear spin phase, in an anisotropic fashion. We do so using a model of cylindrical pores within an otherwise homogeneous material, and calculate the resulting magnetic field inhomogeneities. Our simulations show that diffusion-mediated decoherence in a system of parallel cylindrical pores is anisotropic, with coherence lifetime minimised when the array of cylindrical pores is perpendicular to B0. We also show that this anisotropy of coherence lifetime is reduced if the orientations of cylindrical pores are disordered within the system. In addition we characterise the dependence on B0, the magnetic susceptibility of the cylindrical pores relative to the surroundings, the diffusion coefficient and cylinder wall thickness. Our findings may aid in the interpretation of NMR and MRI relaxation data.

Proton and deuterium nuclear spin relaxation study of the SmA and SmC* phases of BP8Cl-d17 : a self-consistent analysis

A self-consistent analysis of proton and deuterium nuclear spin relaxation times in the smectic phases of a partially deuterated smectogen is presented here. Proton spin-lattice relaxation times T(1Z) were measured as a function of Larmor frequency over a range of 1 kHz to 300 MHz at selected temperatures. Deuterium spin relaxation times T(1Z) and T(1Q) were measured as a function of temperature at two different magnetic fields in the smectic A phase. The deuterium data provide dynamic parameters such as rotational diffusion constants and internal jump rates as well as the nematic order parameter S. The proton data are analyzed using a number of relaxation mechanisms, one of which is the molecular reorientation. It is found helpful in these latter analyses to use the nematic order parameter and to fix the contribution from molecular reorientations determined by the deuterium spin relaxation. The fits to the proton T(1) frequency and temperature dispersions by the remaining relaxation mechanisms such as layer undulations and translational self-diffusion will be discussed for the smectic A and chiral smectic C phases.

Comparison of the dielectric and NMR results for liquid crystals: dynamic aspects

Critical analysis of the results of studies of molecular rotational dynamics in liquid crystalline substances with the aid of the dielectric spectroscopy (DS) and nuclear magnetic resonance (NMR) is given. Both methods are known to be sensitive to different aspects of molecular rotations: the polarization vector and the relaxation time τ(DS) in the case of DS, a tensor describing a nuclear interaction and the correlation time τ(NMR) for NMR method. Furthermore, both methods provide correlation functions with different rank values. A common basis for the comparison between τ(DS) and τ(NMR) is postulated. Several examples of the temperature dependence of the correlation times coming from the two spectroscopic methods are presented. Qualitative agreements of the correlation times were achieved in most cases.

Orientational order, molecular organization, and dynamics in mixtures of bent-core and rod-shaped mesogens: a 2H NMR study

Mixtures of a bent-core mesogen (ClPbis10BB) and a calamitic mesogen (6OO8), showing a nematic phase over the entire compositional range and one or two smectic phases (namely, SmA, SmC, or SmC(A)) below the nematic one over a wide concentration range, were investigated by means of (2)H NMR spectroscopy, exploiting selectively deuterated isotopomers of both mesogens. The analysis of (2)H NMR spectra recorded in the liquid crystalline phases on several representative mixtures gave information on the orientational order properties and the molecular organization within the phases as well as on the alignment properties upon application of a magnetic field. On the other hand, the analysis of (2)H longitudinal relaxation times (T(1Z) and T(1Q)) in 6OO8-d(2)/ClPbis10BB mixtures and pure 6OO8-d(2) allowed the influence of the bent-core mesogen on the dynamics of the calamitic one to be highlighted.

Dynamics of partially oriented L-phenylalanine-d(8) in the CsPFO/H(2)O lyotropic system via (2)H NMR relaxation studies

Dynamics of the l-phenylalanine-d(8) has been here investigated by analyzing the (2)H NMR spin-lattice relaxation times of this selectively deuterium enriched amino acid diluted in the cesium pentadecafluorooctanoate/water (CsPFO/H(2)O) lyotropic system both in the nematic (N(+)(D)) and in the lamellar (L(D)) phases. Information on the internal and overall molecular motions as well as on collective motions has been achieved by a global fitting procedure. The dynamic processes affecting this probe molecule reflect its particular conformational and interaction properties with respect to the lyotropic environment. The best reproduction of the experimental data is obtained by assuming free internal reorientations of the benzylic moiety, which results in diffusion constants of the same order of magnitude of the overall molecular spinning motion. Moreover, the contribution of collective motions (order director fluctuations and layer undulations) is estimated to be greater than that commonly observed by other techniques in lyotropic systems.

Generalized gaussian model for uniaxial rotational motion: application to the calculation of spectroscopic responses

An exact model aimed at describing uniaxial rotational motions, based on a rotational adapted Gaussian statistics, is presented. In its simplest form, it depends on only two parameters, an order parameter which can vary from 1 (perfect order) to 0 (isotropic diffusion) and a time-dependent correlation parameter rho which varies from 1 to 0 between initial and infinite times. This model yields closed form expressions for the correlation functions relevant to the main spectroscopic techniques (dielectric absorption, light and neutron scattering, NMR line shape, spin-lattice relaxation, etc.) for all values of the two parameters. According to the functional form postulated for rho(t), in particular forms decaying as power laws at long times, one obtains shapes for the spectroscopic correlation functions and spectra that are similar to those experimentally observed in a large variety of complex systems (liquid crystals, polymers, gels, and amorphous and glassy materials), especially in confined geometries, which often resemble "stretched" exponentials. A simple way to introduce time coherent effects through a modification of rho(t) is proposed. Examples of theoretical correlation functions and spectra are presented. Important remarks concerning the application of this model to the analysis of real data are made. This model is the rotational analogue of the Gaussian translational model developed recently (Volino et al. J. Phys. Chem B 2006, 110, 11217).

Chain dynamics in a chiral C phase by deuteron spin relaxation study

Molecular reorientations and internal conformational transitions of an aligned chiral liquid crystal (LC) 10B1M7 are studied by means of deuterium spin-lattice relaxation in its smectic A (SmA) and smectic C* (SmC*) phase. The motional model which is applicable to uniaxial phases of many LCs is found to be adequate even when the phase is a tilted SmC* phase. The deuterium NMR spectrum in this phase cannot discern rotations of the molecular director about the pitch axis. The basic assumption is that the phase biaxiality is practically unobservable. However, the relaxation rates can be accounted for by the tilt angle between the molecular director and the layer normal in the SmC* phase. The tumbling motion appears to show a higher activation energy upon entering from the uniaxial SmA into the SmC* phase.

Conformational dynamics of a metallomesogen studied by 2H-NMR spectroscopy

In this work we present a quantitative analysis of both quadrupolar splittings and deuterium Zeeman and quadrupolar spin-lattice relaxation times reported in the literature for two isotopomers of Azpac, an acetylacetonate derivative of the cyclopalladated 4, 4'-bis(hexyloxy) azoxybenzene. Azpac-d(4) is deuterated at the aromatic rings and Azpac-d(26) is deuterated on the alkoxy chains. The additive potential method is used to model the splittings, while the derived spectral densities are interpreted using the decoupled model in conjunction with the Nordio model. The two side chains are assumed to be noninteracting and identical in their conformations in order to limit the size of the transition rate matrix needed to describe correlated internal bond rotations in the chains. Rotational diffusion constants and internal jump rate constants are derived for this metallomesogen.