Chemical shielding anisotropy relaxation

When l l, the above gives the so-called cross-correlation functions and the associated cross-correlation rates (longitudinal and transverse). Crosscorrelation functions arise from the interference between two relaxation mechanisms (e.g., between the dipole-dipole and the chemical shielding anisotropy interactions, or between the anisotropies of chemical shieldings of two nuclei, etc.).40 When l = 1=2, one has the autocorrelation functions G2m(r) or simply... 

When r s, one has interconversion between operators Br and Bs, and Rrs is a cross-relaxation rate. Note that the cross-relaxation may or may not contain interference effects depending on the indices l and /, which keep track of interactions Cyj and C,. Cross-correlation rates and cross-relaxation rates have not been fully utilized in LC. However, there is a recent report41 on this subject using both the 13C chemical shielding anisotropy and C-H dipolar coupling relaxation mechanisms to study a nematic, and this may be a fruitful arena in gaining dynamic information for LC. We summarize below some well known (auto-)relaxation rates for various spin interactions commonly encountered in LC studies. 

In order to discuss the origin of these terms we need to allow the spins to have anisotropic shielding tensors. Molecular tumbling in solution makes the chemical shielding in the direction of the external magnetic field a stochastic function of time and acts therefore as a relaxation mechanism, called the chemical shielding anisotropy (CSA) mechanism. The Hamiltonian for each of the two spins, analogous to Eq. (5), contains therefore two... 

A second important mechanism for fluorine spin-lattice and spin-spin relaxation is produced by the chemical shielding anisotropy (CSA) [13, 14, 21, 71]. The magnetic field experienced by a nuclear spin depends on both the electronic structure of the molecule and how easily the electrons can move in the molecular orientations. In addition, the CSA depends on how the molecule is oriented in the magnetic field. Like spin-spin and dipole-dipole interactions, the CSA of small, rapidly tumbling molecules will be an averaged value (the chemical shift). However, these tumbling motions cause fluctuations of the local magnetic field that lead to relaxation. Also slower reorientation, or an environment that restricts the molecular motion, will result in broader lines due to CSA. 

The application of temperature-dependent line shapes and the measurements of second moments in more complex organic solids like polymers followed soon after. Even nowadays, this simple method still has its place in the characterization of materials like solid polymer electrolytes where the line widths and Ti relaxation of the charge carriers provide information about their mobility that can be correlated with the electrical conductivity of the material. More detailed information can be obtained from cases in which the interaction is well defined, i.e., when an anisotropic single-spin interaction dominates the spectrum. Typical cases are the chemical shielding anisotropy (CSA) and quadrupolar interaction for which the theory is well developed. 

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. 

Significant contributions to spin-lattice relaxation are dipole-dipole interactions (DD), chemical shielding anisotropy (CSA), spin-rotation interaction (SR), scalar coupling (SC), and electron-nuclear interactions (EN). Contributions from each mechanism to the relaxation rate = 1/Tj are additive (eq. 6). 

Lithium-6. Wehrli (79) has investigated carefully the relaxation of natural abundance Li in aqueous LiCl. (3.9 M). At 25°C, 86% of the relaxation rate is dipolar ( Li- H), falling off to 48% at 100°C. The nondipolar contribution to Li relaxation exhibits a maximum at ca. 40°C, pointing to the presence of spin-rotation relaxation. Thus, by estimating upper limits for the quadrupolar, for the chemical shielding anisotropy (negligible), and for the dipole-dipole ( Li- Li), Wehrli could provide the individual contributions (80) (Table 20). Wehrli also studied... 

Spin-lattice relaxation rates for cadmium in organometallic compounds have been measured for neat dibutylcadmium (13) (T 0.2 sec - 5 sec Temp = 228 K Bq = 2.1 Tesla) and dimethyl-, diethyl-, and dipropylcadmiura (15) (T = 3.5-0.6 sec Bq = 2.35 Tesla). From NOE measurement, neat dimethylcadmium experiences no dipolar relaxation (15). Mechanisms contributing to relaxation are thought to be chemical exchange and chemical shielding anisotropy however, their relative importance has not been published for these compounds. 

Cadmium relaxation in Cd-EDTA complexes have been measured at 2.3, 4.7, and 9.4 Tesla (34). The dipolar contribution dominates at low field strength and chemical shielding anisotropy at high fields. A third, frequency independent, contribution is also measured. The data are consistent with a 1.1 x 10 sec correlation time for the low pH form. Relaxation rates and NOE of Cd-cyclohexanediaminetetraacetate at 2.3 Tesla are also dominated by the dipolar mechanism (32). 

Relaxation of the cadmium-tetraphenylporphyrin pyridine adduct studied by Jakobsen et al. (28) is strongly dominated by the chemical shielding anisotropy mechanism. Even at the moderate field strength of 4.7 Tesla ( Cd 44 MHz), this mechanism is responsible, within experimental error of 10%, for all observed relaxation (T = 28.5 sec). 

Recent improvements have increased the sensitivity of NMR instrumentation, making relaxation rate experiments of cadmium-metalloprotein systems feasible if not commonplace. Bailey et al. (41) have measured a 1.2 sec ( 20%) relaxation time for cadmium occupying the zinc binding sites in bovine superoxide dismu-tase. Theoretical considerations indicate nearly equal contributions to the relaxation rate from proton-cadmium dipolar and from chemical shielding anisotropy mechanisms. 

Chemical shielding anisotropy see Relaxation, chemical shielding anisotropy Chemical shift anisotropy see Relaxation, chemical shielding anisotropy Chemical shifts... 

Shielding anisotropies can be obtained from measured relaxation times when the chemical shift anisotropy relaxation mechanism or the spin-rotation mechanism is dominant. The correlation time has to be estimated or otherwise derived. There are large uncertainties associated with this method. 

Champmartin D and Rubini P 1996 Determination of the 0-17 quadrupolar coupling constant and of the C-13 chemical shielding tensor anisotropy of the CO groups of pentane-2,4-dione and beta-diketonate complexes in solution. NMR relaxation study/norg. Chem. 35 179-83... 

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