Liquid crystals spin Hamiltonian

The frustration effects are implicit in many physical systems, as different as spin glass magnets, adsorbed monomolecular films and liquid crystals [32, 54, 55], In the case of polar mesogens the dipolar frustrations may be modelled by a spin system on a triangular lattice (Fig, 5), The corresponding Hamiltonian consists of a two particle dipolar potential that has competing parallel dipole and antiparallel dipole interactions [321, The system is analyzed in terms of dimers and trimers of dipoles. When the dipolar forces between two of them cancel, the third dipole experiences no overall interaction. It is free to permeate out of the layer, thus frustrating smectic order. 

Recent solid state NMR studies of liquid crystalline materials are surveyed. The review deals first with some background information in order to facilitate discussions on various NMR (13C, ll, 21 , I9F etc.) works to be followed. This includes the following spin Hamiltonians, spin relaxation theory, and a survey of recent solid state NMR methods (mainly 13C) for liquid crystals on the one hand, while on the other hand molecular ordering of mesogens and motional models for liquid crystals. NMR studies done since 1997 on both solutes and solvent molecules are discussed. For the latter, thermotropic and lyotropic liquid crystals are included with an emphasis on newly discovered liquid crystalline materials. For the solute studies, both small molecules and weakly ordered biomolecules are briefly surveyed. 

Anisotropy of the Spin-Spin Coupling Tensor. - In NMR experiments performed in anisotropic liquid crystal (LC) phases or in the solid state, the anisotric part of an indirect nuclear spin-spin coupling tensor J appears combined with the direct dipolar coupling D. The NMR spin Hamiltonian appropriate for spin 1/2 nuclei in molecules partially oriented in uniaxial LC solvents can be written in the high field approximation as... 

Structural studies by NMR in liquid crystal solvents are distinguished by several special features the matter of time scales, spin Hamiltonian symmetry and connectivity, and the influence of the liquid solvent phase. 

Two types of rigid media have been employed in hyperfine studies supercooled liquid solutions or powders and single crystals. The anisotropy in the g and A tensors produces anisotropic line shapes in the ESR of supercooled solutions that can be analyzed to deduce the spin Hamiltonian parameters that will produce such shapes. In practice, line shapes... 

In principle, NMR spectroscopy in liquid crystal solutions, or in other situations where the molecule can be oriented, allows the measurement of elements of the spin-coupling tensor other than the simple isotropic trace. Unfortunately, this anisotropy enters the NMR Hamiltonian in exactly the same fashion as the corresponding dipolar couplings that are also observed in anisotropic media and hence cannot be measured separately. Thus, estimation of this anisotropy relies on any deviation between the observed dipolar coupling and that calculated from geometrical considerations. In principle, the coupling tensor can also be asymmetric. 

Spin-Hamiltonian parameters of Tm nuclei at liquid helium temperatures in TmBaiCujOs, crystals... 

The observed nmr-spectra in uniaxial liquid crystals may be described by the following effective spin Hamiltonian [40, 45]... 

The averaging of nuclear spin Hamiltonians under rotations may be easily studied when it is expressed in terms of irreducible spherical tensor operators, TL,m and In liquid crystals, the main interest is in time averag-... 

Electron paramagnetic resonance (EPR) measurements for actinide ions are usually made at liquid-helium temperatures in order to lengthen the spin-4attice relaxation time (Tj) so the resonance may be observed [7,8]. Consequently information is obtained only about the ground crystal field state and possibly the first excited state. The spectra are interpreted in terms of an effective spin Hamiltonian ... 

In partially oriented systems (in liquid crystal solution or in strong electric fields) only linear combinations of tensor elements, such as — or Jaa — Jbb + Jcc)l may be obtained. The spin Hamiltonian for partially oriented molecules, spectral analysis, determination of NMR constants, and results from many applications have... 

In previous chapters we have seen that the Hamiltonian describing a nuclear spin system is considerably simplified when molecules tumble rapidly and randomly, as in the liquid state. However, that simplicity masks some fundamental properties of spins that help us to understand their behavior and that can be applied to problems of chemical interest. We turn now to the solid state, where these properties often dominate the appearance of the spectra. Our treatment is limited to substances such as molecular crystals, polymers, and glasses, that is, solids in which there are well-defined individual molecules. We do not treat metals, ionic crystals, semiconductors, superconductors, or other systems in which delocalization of electrons is of critical importance. 

For an ensemble of nuclei with spin / > 1/2 experiencing no quadrupolar interaction, such as in an isotropic liquid or a crystal with cubic symmetry, the equations describing the time evolution of the density matrix under action of static and RF magnetic fields are a natural extension of the / = 1/2 case. The Hamiltonian contains only the Zeeman and RF terms the effects of RF pulses are described by rotations of the spin operators around the transverse axes in the rotating frame, whereas free evolution corresponds to rotations around the z-axis. 

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