Nuclear magnetic resonance of liquid crystals

1. Quantitative Description of Orientational Order: Rigid Molecules.- Looking for a complete description.- A simple case: cylindrical molecules in a uniaxial phase.- The effect of symmetry.- Ordering matrix.- Orientational order parameters for more complex phases.- Connection with experiment.- Non-uniaxial phases.- Cartesian treatment.- Summary.- References.- 2. An Internal Order Parameter Formalism for Non-Rigid Molecules.- The internal order parameter formalism.- Observables for a molecule with one internal rotor.- Limiting cases.- Relation to Emsley-Luckhurst formalism.- Multi-rotor molecules.- Summary.- References.- 3. Molecular Field Theories of Nematics: Systems Composed of Uniaxial, Biaxial or Flexible Molecules.- The Maier-Saupe theory.- Biaxial molecules.- Flexible molecules: orientational order parameters.- Flexible molecules: the thermodynamic properties.- References.- 4. The Landau-De Gennes Theory of Liquid Crystals.- Landau theory of second order phase transitions.- The Landau-de Gennes theory of nematics.- Pretransitional behaviour.- A molecular approach.- References.- 5. NMR Spectra in Liquid Crystals the Partially Averaged Spin Hamiltonian.- Macroscopic alignment.- Spin Hamiltonian.- Spherical tensors.- Magnetic interactions in cartesian formalism.- Dipolar coupling.- Nuclear quadrupolar interaction.- Anisotropy of the shielding tensor.- Indirect couplings.- References.- 6. Studies of Solutes with Internal Rotors.- Theory.- Approximate methods.- Applications.- Molecules with a single locked conformer.- Molecules with two planar equivalent conformers.- Molecules with non planar equivalent conformers.- Molecules with two or more conformers.- Molecules with methyl rotation.- Molecules with ring puckering motions.- Conclusions and perspectives.- References.- 7. Molecular Structure from Dipolar Coupling.- The basic equations.- The procedure of structure determination.- Differences between spectra of isotropic and of oriented molecules.- Relations between direct couplings and molecular structure.- The computer programs for structure determination.- Types of molecules studied so far.- Basic theory for vibration corrections.- The continuum of directions with Saa = 0 in oriented molecules the Saa = 0 cone.- The use of satellites for increased sensitivity.- The use of satellites in underdetermined cases.- Possible structure precision.- Limitation of structure precision due to anisotropy of the indirect coupling constants.- Limitation of structure precision due to correlation.- Vibration-rotation coupling.- Mean-field deformation.- Limitation of structure precision due to complex formation: the two-site approximation.- Summary.- References.- 8. On the Orientation of Small Molecules in Anisotropic Solvents.- Theory.- Dipolar couplings.- Quadrupolar couplings.- The hydrogen molecule.- The methane molecule.- External field gradients.- Solute-solvent interaction mechanisms.- References.- 9. Diffusive and Collective Motions in Liquid Crystal Phases.- Molecular motions in liquid crystals.- Motional processes and spin relaxation.- Correlation functions.- Projection operator techniques.- Choice of the projection operator.- The formal derivation of the diffusion equation.- Explicit form of the diffusion equation for cylindrical molecules.- Solution of the diffusion equations in liquid crystalline phases.- Side-chain dynamics.- Collective motions.- References.- 10. Density Matrix Formalism for NMR Studies of Liquid Crystals.- Basic theory.- Free precession.- RF pulses: flip angles and phase shifts.- Multiple quantum coherence.- References.- 11. Nuclear Spin Relaxation.- Theoretical framework.- A case study: one spin I = 1.- Relaxation calculations.- Relaxation measurements.- Instrumental requirements.- Results for systems with a single deuteron.- Sample rotation.- Multispin systems.- Deuterium.- 13C-H relaxation.- Other nuclei.- Conclusions.- References.- 12. Multiple Quantum NMR in Liquid Crystalline Phases.- The averaging of magnetic interaction tensors.- Multiple quantum NMR.- Time domain cross sections.- Projections of two dimensional spectra.- The complexity of the multiple quantum spectra of an oriented chain.- Multiple quantum NMR experiments on oriented chain.- Spectral simulations.- Discussion.- Conclusion.- References.- 13. Dynamics of Molecular Processes by NMR in Liquid Crystalline Solvents.- Dynamic 1H NMR in liquid crystals.- Ring inversion in s-trioxane.- Bond shift in cyclooctatetraene.- Bond rearrangement in bullvalene.- Dynamic deuterium NMR in liquid crystals.- Ring inversion of cyclohexane.- Ring inversion in p-dioxane.- Bond rearrangement in bullvalene.- Ring inversion of bridged perinaphthalenes.- Dynamic lineshapes in liquid crystalline solutions.- Dynamic lineshape for I = 1/2 systems.- Application of group theory.- Dynamic lineshapes for I = 1 nuclei.- Summary and conclusions.- References.- 14. Discotic Liquid Crystals and their Characterization by Deuterium NMR.- Chemical structure and classification of discotic mesophases.- Deuterium NMR in discotic mesophases.- Uniaxial discotic mesophases.- Alignment in a magnetic field.- Molecular order parameter.- Chain conformation in the mesogen.- Biaxial discotic mesophases.- The Drd mesophase.- The Dt mesophase.- Discotic mesophases as solvents.- Molecular translational diffusion in discotics.- References.- 15. Measurement of Orientational Ordering by NMR.- Rigid solute molecules.- Choice of interaction.- Dipolar coupling.- Quadrupolar splittings.- Comparison with theoretical models.- Non-rigid molecules.- Location of axes.- Local ordering matrices.- The ordering of alkyl chains.- Comparison with theory.- Non-rigid solutes.- Carbon-13 studies of orientational order.- Conclusion.- References.- 16. Determination of Biaxial Structures in Lyotropic Materials by Deuterium NMR.- Analysis of the spectral patterns.- Hexagonal phase.- Ribbon phase.- Ripple phase.- Discussion.- References.- 17. Phase Biaxiality in the Cholesteric and Blue Phases.- 2H NMR spectral patterns.- Distortion and spatial modulated diffusion.- Blue phases.- Discussion.- References.- 18. Phase Biaxiality in Some of the Smectic Phases.- General theoretical considerations.- SG phase.- SC phase.- Discussion.- References.- 19. Orientational Order Parameters and Mechanisms of Phase Biaxiality.- Ordering in uniaxial phases.- Ordering in biaxial phases.- Biaxial mechanism of the cholesteric phase.- Biaxiality from rotational freeze-out parameters.- Discussion.- References.- 20. Amphiphilic Molecules in Lyotropic Liquid Crystals and Micellar Phases.- Relevant aspects of NMR.- Order parameter curves.- Infinite lamellae in lamellar phases.- Infinite cylinders in hexagonal phases.- Spheroids in micellar phases.- Oblate spheroids in nematic phases.- Discussion.- Comments about the thermodynamics.- Conclusion.- References.- 21. Structure of the Hydrophobic-Hydrophilic Interface in Lyotropic Liquid Crystals: Counterion Binding Studies.- Theory of counterion quadrupolar splittings.- Sodium-23 studies.- Non-ionic surfactants.- Charged surfactants.- Potassium-39 studies.- Effects of water content and temperature.- Effects of solubilization of alcohols.- Effects of hydrocarbons.- Chemical equilibrium model of counterion binding.- Comment.- References.- 22. Solubilizate-Bilayer Interactions in Lamellar Mesophases.- Solubilization of alcohols.- X-ray diffraction measurements.- 2H NMR measurements.- Solubilization of hydrocarbons.- X-ray diffraction measurements.- NMR measurements.- Comparison of bilayer thickness as calculated from X-ray diffraction and 2H NMR measurements.- Distribution of hydrocarbon solubilizates in the bilayer.- Response of the bilayer structure to solubilizate.- Appendix 1.- X-ray diffraction measurements.- The partial molecular surface area.- Appendix 2.- The calculation of the effective length of a hydrocarbon chain from its order profile.- References.- 23. NMR of Liquid Crystalline Lipids in Biological Membranes.- Some characteristics of biological membranes.- Deuterium NMR spectra of membranes.- Acholeplasma Laidlawii B: a simple biological membrane.- 31P NMR of membranes.- Synopsis.- References.