Quadrupolar nuclear electric quadrupole moment

Extraframework cations are needed in anionic zeolites for charge balance, and for several zeolite topologies their locations are well investigated [281, 282]. Different cations have been investigated by solid state NMR in the past with different NMR properties and different project targets. We restrict this section to a tutorial example on sodium cation motion in sodalite and cancrinite structures [283-285], 23Na has a nuclear electric quadrupole moment, and quadrupolar interaction is useful to investigate jump processes, especially when they are well defined. 

NMR spectra of quadrupolar nuclei are influenced by the interaction of the nuclear electric quadrupole moment with electrostatic field gradients generated at the nuclear sites by asymmetric electron distributions due to chemical bonding. To a first order... 

To understand the varied chemistry of the aluminas, techniques need to be developed for studying the surface independent of the bulk. Structural and dynamical aspects of the surface do have their origins in the bulk, but the specific details delineating the surface will be different. Clearly it would be advantageous to apply the same surface selective CP methodology developed for the silicas [12-16] to the surface of the aluminas. Before addressing this particular point, however, we need to consider the feasibility of the experiment. Are the aluminum atoms at the surface indeed observable by NMR methods If surface aluminum atoms are observable, we must then recognize that the spin of interest, Al, is not a spin-1/2 nuclide (/ for Al is 5/2) hence Al has a nonzero nuclear electric quadrupole moment. Cross-polarization from protons to a quadrupolar nucleus presents the experimenter with another layer of complication in compari-... 

Besides the magnetic dipole moment, nuclei with spin higher than 1 /2 also possesses an electric quadrupole moment In a semiclassical picture, the nuclear electric quadrupole moment informs about the deviation of the nuclear charge distribution from a spherical symmetry. Nuclei with spin 0 or 1/2 are therefore said to be spherical, with zero electric quadrupole moment. Quadrupolar nuclei, on the other hand, are not spherical, assuming cylindrically symmetrical shapes around the symmetry axis defined by the nuclear spin. Within the subspace I,m), the nuclear electric quadrupole moment operator is a traceless tensor operator of second rank, with Cartesian components written is terms of the nuclear spin ... 

The quadrupolar interactions occur when I > and arise from the interaction of the nuclear electric quadrupole moment eQ with the non-spherically symmetric electric field gradient at the site of the nucleus due to the electronic charge distribution of the atom or molecule... 

The relaxation of the quadrupolar Xe nucleus is predominantly due to the interaction between the nuclear electric quadrupole moment and the fluctuating EFG at the nuclear site. The origin of the EFG contributing in a solution is, however, still partly an open question. Various models, both electrostatic and electronic, have been developed. The electrostatic models assume the EFG to be due to solvent molecules represented by point charges, point dipoles or quadrupoles, or a dielectric continuum. In the electronic approach, EFG is considered to be a consequence of the deformation of the spherical electron distribution of Xe. The deformation arises from the collisions between xenon and solvent molecules. It is obvious (evidence is provided, for example, by i Xe NMR experiments in liquid-crystal solutions, and by first principles calculations) that neither of these approaches alone is sufficient. In typical isotropic solvents, the Xe ranges from 4 ms to -40 ms. 

O, Na, and Al) and arises from the interaction of the nuclear electric quadrupole moment qQ with the electric field gradient eq produced at the nuclear site by a nonspherical charge distribution around the nucleus. The quadrupole interaction is usually characterized by the quadrupole constant e qQlh and asymmetry parameter rj. The magnitude of the quadrupole interaction is such (up to several MHz) that it completely dominates the spectrum for most quadrupolar nuclei, even in the case of H NMR, which has the smallest quadrupole moment. 

Use of H-NMR for membrane studies is based on the fact that deuterium nuclei, with spin 1=1, have an electric quadrupole moment. It originates from the asymmetrical charge distribution in the nucleus. In the presence of an external field gradient, which is almost always the case for (deuterium) atoms in molecules, the different orientations of the nuclear spin experience different interaction energies with the quadrupolar field of the environment. 

Nuclei with spin quantum number I > can possess electric quadrupole moments. The nuclear quadrupole is directly coupled to the nuclear spin and the electrostatic interaction dominates the nuclear spin relaxation. The quadrupolar interaction is simply the first non-vanishing term in the Taylor expansion of the electrostatic interaction between the charge distribution of the nucleus and that of its surrounding. It can be expressed as a direct product between the nuclear quadrupole tensor and the electric field gradient (EFG) at the nucleus [6]. 

In addition to the interactions which broaden the sohd-state NMR resonances of spin-1/2 nuclei, the electric quadrupole interaction considerably decreases the resolution of the spectra of quadrupolar nuclei (spin />l/2). These nuclei have a non-spherically symmetrical distribution of nuclear charge and possess an electric quadrupole moment, which interacts strongly with any electric field gradient, created by the surrounding electron cloud, at the site of the nucleus. In the tensorial Cartesian form the quadrupolar Hamiltonian is... 

In many ways the information available from NMR studies on these two isotopes is complementary. Although 14N is by far the more common, in natural abundance, it has an electric quadrupole moment while the less abundant 15N nucleus does not. Thus the l4N nucleus has been more frequently used in chemical shift studies on natural abundance samples as well as in quadrupolar relaxation investigations. The larger magnetogyric ratio of the l5N nucleus, together with its sharper lines, renders it more suitable for studies involving spin-spin coupling constants in addition to those on the less efficient nuclear relaxation processes. 

For all nuclei with spin quantum number I S 1 an electric quadrupole moment exists that couples with the gradient of the inhomogeneous internal electric fields that are created by other charges in the system. " The quadrupole moment and the magnitude of the electric field gradient (EFG) are given by eQ and eq, respectively. The strength of the quadrupolar interaction is, therefore, dictated by the molecular or crystalline environment, and is denoted by x = the nuclear quadrupolar... 

In nonspherical nuclei (/ > i) there exists a nonzero quadrupole moment for the nuclear charge density that contributes to the quadrupolar term (fourth term) in Eq. (1). In the expression for the electrostatic interaction energy for the nucleus in the potential produced by the electrons, the electric quadrupole moment of the nucleus is coupled to the gradient of the electric field at the nuclear site. This field gradient is, of course, due to the electrons. In diagonalized form one may write... 

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