Quadrupolar interaction description

If there is some molecular motion with characteristic times on the order of ICT sec, the NMR spectrum will no longer have the Pake doublet lineshape discussed earlier. For example, in gel-phase bilayers a perdeuterated lipid acyl chain will have a broad, relatively featureless spectmm, as shown in Fig. 3. These spectra do not lend themselves to easy analysis The molecular motion in the membrane is not rapid enough to be axially symmetric (see the description of the fluid bilayer below) on the NMR time scale but is fast enough to influence the average value of the quadrupolar interaction and thus the splittings of the individual labels. 

Here, Hz is the Zeeman term, Hq is the quadrupolar interaction term for nuclei with 1 1, Hd is the dipolar interaction term for nuclei with 1 = 1/2, Hs is the electron shielding term and Hj is the J-coupling term. Spin relaxations will be induced by the time fluctuations of these interaction terms. For example, H spin-lattice relaxation behaviour is dominated by Hq, whereas Hq mainly determines the relaxation process of the H or magnetization in organic materials. In some cases without significant contributions from Hq and Hq, the time fluctuations of Hs and Hj also induce spin relaxation for example, the magnetization of a carbonyl carbon with a large chemical shift anisotropy relaxes due to the contribution from the time fluctuation of Hs. Nevertheless, since the main interest of polymer scientists is NMR, we focus on the description of the relaxation process in this chapter. 

Quadrupolar Nuclei. - A geometrical description of the quadrupolar interaction has been presented. First- and second-order effects on all transitions were represented by quadrics and quartics. This approach allows a simple and exhaustive description of the Solomon multiple echoes the location of the echoes in the time domain, as well as their nature, is determined without calculation. Experimental evidence of multiple echoes in the case of an Al-O-P cluster is presented. In addition, the selection of double quantum coherences by appropriate phase cycling is presented. DAS and MQ MAS experiments are also described in this particular frame. 

For an ensemble of crystallographically equivalent nuclei with spin /, 21 NMR transitions take place. For most elements, the most abundant spin-active isotope is quadrupolar with half-integer spin. For these nuclei, spectro-scopists usually focus on the mj = 1/2 — mi = -1 /2 transition since it is not perturbed by the first-order quadrupolar interaction (i.e., to a first approximation, this transition behaves like that for a spin-1/2 nucleus, see below). Hence, an overview of the theory for half-integer spin quadrupolar nuclei is presented here. For a thorough description of the theory for the quadrupolar interaction, readers are referred to numerous texts and reviews on the topic. ... 

The chemical shielding, dipole-dipole, spin-spin indirect coupling or J-coupling, spin-rotation, and hyperfine couplings represent the major internal magnetic interactions. The quadrupolar interaction has an electrostatic character. All these interactions have a tensorial character, ie, are function on the ori-entation of the principal axes of the tensor relative to the direction of Bq. They are relevant for solid polymers below and around the glass transition temperatures. For polymer in solution or for soft polymers fast molecular motions average these anisotropic interactions to isotropic or residual values which can be zero. Detailed description of the properties of these spin interactions can be found in References 1-9. 

Because dipolar interaction is related to the intemuclear vector, which is the direct description of the molecular framework, the relation between the orientation distribution function obtained from a dipolar-DECODER spectrum and the molecular frame distribution is simpler than that from CSA-DECODER and quadrupolar-DECODER spectrum. One example of the 2D dipolar-DECODER experimental spectrum is shown in Fig. 19. The change of the orientation distribution caused by the deformation can be measured by the difference of the spectra before and after deformation. Of course, since the dipolar interaction tensor is always axially symmetric, the information content of a dipolar-DECODER spectrum is decreased. 

Electrostatic and induction energies are evaluated by multicenter multipolar expansions truncated at quadrupolar level, with an accurate description of the charge distribution and polarizability calculated ab initio at HF level on the monomer. The electrostatic interaction is then fitted by a Coulomb potential among two positive point charges on the hydrogens and two negative close to... 

The more recent ASP-W2 and ASP-W4 improve the accuracy of the description of multipoles, which is at multireference Cl level instead of MP2. All three potentials share the same form of repulsion and polarization term, the former using three sites with exponential functions while the latter is described by anisotropic dipolar and quadrupolar polarizabilities centered on the oxygen. Electrostatic interactions are modeled by a single-center (APS-W) or three-center (ASP-W2 and ASP-W4) multipolar expansion up to quadrupolar term for ASP-W and APS-W2 and up to hexadecapolar term for APS-W4. 

Lyotropic liquid crystal phases has been observed when l-Alkyl-3-methylimidazolium bromide (CnmimBr) was mixed with p-xylene and water. SAXS, POM, NMR and rheology measurements were performed to investigate the lyotropic liquid crystal phases. A lyotropic bicontinuous cubic phase formed in imidazolium-type ionic liquid (IL) system was found for the first time. The strong %-% stacking of imidazolium based ILs and their 71-cation interactions with p-xylene molecules have unique effect on the structural parameters.Description of NMR of quadrupolar systems using the Holstein-Primakoff (HP) formalism and its analogy with a Bose-Einstein condensate (BEC) system has been presented. Two nuclear spin... 

NMR relaxation data depend on dipolar ( N and C) and quadrupolar ( H) interactions on chemical shift anisotropy and cross-correlation effects. It is well known that the NMR relaxations can be written as functions of the spectral densities of the magnetic interactions, and this is the intersecting point between macroscopic and microscopic descriptions The spectral densities are calculated within the theoretical framework describing the dynamics of the system. 

For an accurate description of electrostatic interactions, it is necessary to take into account the polarization of the molecules due to the intermolecular interactions. Molecular polarizabilities and hyperpolarizabilities are introduced in the molecular mechanics for clusters (MMC) approach [30]. Several empirical or quantum chemical approaches exist to describe the molecular polarizabilities by atomic or site components [31-47]. The simplest model uses localized dipolar polarizabihties. Such a model can be extended to quadrupolar or higher order polarizabilities. Stone has developed the concept of distributed polarizabilities [36,42]. hi this model, each site of a molecule responds to the... 

Poniewierski and Stecki [245] combined hard Onsager spherocylinders with an attractive Maier-Saupe type quadrupolar potential. The Lenard-Jones interaction potential often used in isotropic phases with a repulsive term proportional to and an attractive part proportional to r" depends only on the intermolecular distances r, and is therefore not suited to the description of anisotropic fluids. A modification of this isotropic potential that accounts for the relative orientations of anisotropic particles has been proposed by Berne and Pechukas... 

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