Polymers chemical shielding tensor

Many solid-state NMR studies of oriented polymer fibers or film other than silk have been described. Orientation-dependent chemical shielding tensors especially serve as probes with which the relative orientations of specific bond vectors can be determined [10]. This analytical method can be applied to obtain structural information from oriented polyamide fibers such as poly (p-phenylene terephthalamide) (PPTA) [11], poly(m-phenylene isophthalamide) (PMIA) and poly(4-methyl-m-phenylene terephthalamide) (P4M-MPTA) fibers without isotope labeling of the samples [12] (Chapter 12). Oriented carbonyl carbon labeled poly (ethylene terephthalate) (PET) films have also been analyzed with this method [13] (Chapter 14). Especially, more quantitative structural information will be obtained for a locally ordered domain which has been recognized as an amorphous domain in X-ray diffraction analysis in heterogeneous polymer samples. 

The determination of polymer structure at the atomic level is possible by analyzing orientation-dependent NMR interactions such as dipole-dipole, quadrupole and chemical shielding anisotropy as mentioned above. The outline of the atomic coordinate determination for oriented protein fibers used here is described more fully in Ref. [30]. The chemical shielding anisotropy (CSA) interaction for N nucleus in an amide (peptide) plane can be interpreted with the chemical shielding tensor transformation as shown in Fig. 8.3. [31, 32]. 

For the NMR chemical shieldings of four polymers, the chemical shielding tensors were calculated in the coupled perturbed Hartree-Fock (CPHF) method with the gauge-invariant atomic orbital (GIAO) [10], The calculated chemical shift for is defined by... 

Of particular interest to polymer scientists is the CSA of methylene carbons. For the methylene carbon, the values of the chemical-shift tensors are as follows cti i, which bisects the H—H bond, has a value of 50.5 15 ppm <722, which bisects the H—C—H angle, has a value of 37 10 ppm and <733, which is perpendicular to the H—C—H plane, has a value of 16 17 ppm. The three elements of the chemical-shielding tensor and their assignments in an all-trans methylene chain [50] are shown in Fig. 8.10. 

Line broadening in solid-state NMR arises from spin interactions which can be described in first order by coupling tensors of rank two (cf. Section 3.1) [Hael, Mehl, Schl], The spin interactions are either linear or bilinear in the spin operator. Linear interactions are the Zeeman interaction, the chemical shielding, and the interaction with the rf field. Bilinear interactions are the J coupling, the dipole-dipole coupling, and the quadrupolar interaction. In isotropic materials like powders, glasses, and undrawn polymers, wide lines are observed as a result of an isotropic orientational distribution of coupling tensors. 

Nuclear magnetic resonance (NMR) is a technique of considerable versatility in polymer science. It is used universally as a probe of chemical configurations, it provides information on the dynamics and relaxation times of a polymer system and it offers a route to the determination of orientation parameters, the exact route depending on the particular nuclei employed. In principle quadrupolar, dipolar, shielding tensor and indirect spin coupling interactions can all be employed " however, in practice only the first two have any universal appeal. Dipolar coupling using proton NMR offers the simplest approach in terms of material preparation and will be considered first. 

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. 

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