Energy dipole-quadrupolar

The first attempt to develop a statistical model of the cholesteric phase was by Goossens who extended the Maier-Saupe theory to take into account the chiral nature of the intermolecular coupling and showed that the second order perturbation energy due to the dipole-quadrupolar interaction must be included to explain the helicity. However, a diflUculty with this and some of the other models that have since been proposed is that in their present form they do not give a satisfactory explanation of the fact that in most cholesterics the pitch decreases with rise of temperature. 

In Eq. (8-7), which is Coulomb s law, the charges are to be aeeompanied with their signs. Because of the high-order reciprocal dependence on distance in Eqs. (8-11) and (8-12), these quadrupolar interactions are usually negligible. For uncharged polar molecules the dipole-dipole interaction of Eq. (8-10), which has the dependence, is the most important contributor to the electrostatie potential energy. 

The 7Li resonance in zeolites is also difficult to interpret, even though the quadrupole moment is much lower. Lechert et al. (227) believe that the 7Li linewidth is controlled by the dipole-dipole interaction with 27A1 nuclei in the aluminosilicate framework. According to Herden et al. (232) the increase of 7Li frequency from 9 to 21 MHz does not affect the second moment of the spectra in zeolites Li-X and Li-Y, which means that the quadrupolar interaction is small. The second moment was also independent of the Si/Al ratio. The mean Li-Al distance calculated from the van Vleck formula was 2.35 A. Small amounts of divalent cations reduce the movement of Li + considerably, with the activation energy for this process increasing from 30 to 60 kJ/mol. 

The dielectric constant is a macroscopic property of the material and arises from collective effects where each part of the ensemble contributes. In terms of a set of molecules it is necessary to consider the microscopic properties such as the polarizability and the dipole moment. A single molecule can be modeled as a distribution of charges in space or as the spatial distribution of a polarization field. This polarization field can be expanded in its moments, which results in the multipole expansion with dipolar, quadrupolar, octopolar and so on terms. In most cases the expansion can be truncated to the first term, which is known as the dipole approximation. Since the dipole moment is an observable, it can be described mathematically as an operator. The dipole moment operator can describe transitions between states (as the transition dipole moment operator and, as such, is important in spectroscopy) or within a state where it represents the associated dipole moment. This operator describes the interaction between a molecule and its environment and, as a result, our understanding of energy transfer. 

The mechanism is distinguished from dipole-dipole relaxation in two ways. First, it does not require a second nucleus in motion the quadrupolar nucleus creates its own fluctuating field by moving in the unsymmetrical electron cloud. Second, because the mechanism is extremely effective when the quadrupole moment of the nucleus is large, T can become very short (milliseconds or less). In such cases, the uncertainty principle applies, whereby the product of A " (the spread of energies of the spin states, as measured by the line width Av) and Ar (the lifetime of the spin state, as measured by the relaxation time) must remain... 

Besides the elastic and the electric torques the so-called flexoelectric (or flexo) torques on the director play an important role as well. Their effect on pattern-forming instabilities in nematics is the main issue of this chapter. Flexotorques originate from the fact that typically (in some loose analogy to piezoelectricity) any director distortion is accompanied by an electric flexopolarization Pa (characterized by the two ffexocoefScients ei, 63). From a microscopic point of view, finite ei and 03 naturally arise when the nematic molecules have a permanent dipole moment. But also for molecules with a quadrupolar moment, finite ei and 63 are possible (see also Chapter 1 in this book ). Flexopolarization has to be incorporated into the free energy P n) for finite E. It is not surprising that this leads to quantitative modifications of phenomena, which exist also for ci = 63 = 0. Though, for example, the Freedericksz threshold field Ep is not modified, the presence of flexoelectricity leads to considerable modifications of the Freedericksz distorted state for E > Ep- ... 

Solubility of Homopolymers Polyethylene (PE) is a semi-crystalline and nonpolar hydrocarbon polymer. Because of its apolar nature, this polymer is practically insoluble in SC-CO2 in conditions as harsh as 110°C and 2750 bar [4]. The interchange energy is then dominated by quadrupolar-quadrupolar interactions of CO2. To promote dipole-quadrupole interactions, the progressive introduction of fluorine atoms onto the polymer backbone has been studied through poly(vinyl fluoride) (—(CH2—CHF) —), poly(vinylidene fluoride) (—(CH2—CF2) —), and poly-tetrafluoroethylene (—(CF2—CF2) —) (see Figure 13.1). 

As already shown, the total NMR Hamiltonian, from which the spin energy levels are obtained, is the sum of terms representing the Zeeman (Hq), chemical shift (Hcs)< dipole-dipole coupling (Hdd), and quadrupolar (Hq) interactions for nuclei with spins greater than V . 

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