Anisotropy of molecular motion

21) discussed in Section 3.3.2 is only valid if the motion of the molecules under study has no preferential orientation, i.e. is not anisotropic. Strictly speaking, this applies only for approximately spherical bodies such as adamantane. Even an ellipsoidal molecule like trans-decalin performs anisotropic motion in solution it will preferentially undergo rotation and translation such that it displaces as few as possible of the other molecules present. This anisotropic rotation during translation is described by the three diagonal components Rlt R2, and R3 of the rotational diffusion tensor. If the principal axes of this tensor coincide with those of the moment of inertia - as can frequently be assumed in practice - then Rl, R2, and R3 indicate the speed at which the molecule rotates about its three principal axes. 

The connection between anisotropic molecular motion and nuclear relaxation was derived by Woessner as early as 1962 [161]. Accordingly, the dipole-dipole relaxation time of a carbon nucleus is a function of the diagonal components R, R2, and R3 of the rotational diffusion tensor and the cosines X, p, and v of the angles assumed by the C —H bonds relative to the principal axes of this tensor  

If the position of the principal axes of the rotational diffusion tensor were known with respect to the molecular coordinates, then the motion of the molecule could be calculated from the measured relaxation times. With simple molecules, however, it is possible to interpret the Tt values qualitatively in terms of an anisotropic motion. 

the C —H nuclei in the para position of monosubstituted benzene derivatives relax faster than those in the ortho or meta positions (Table 3.16 [151]). The reason for this behavior lies in a preferred rotation about the molecular axis passing through the substituent X and the p-carbon. During this motion, the para C —H bond does not change its direction relative to the field B0 fluctuating local fields can only arise at the p-C nucleus by rotations of the molecule perpendicular to the preferred axis. However, 

Preferred rotation is also conceivable in 3-methyl-5,6,7,8-tetrahydroquinoline, i.e. about the axis passing through C-7, C-3, and the methyl group [162]. Accordingly, the C-7 methylene group exhibits a smaller 7, value than all the other CH2 groups of this molecule. 

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Anisotropy of molecular motion monosubstituted benzene rings, e.g. phenyl benzoate (44), show a very typical characteristic in the para position to the substituents the CH nuclei relax considerably more rapidly than in the ortho and meta positions. The reason for this is the anisotropy... 

Some properties of polydimethylsiloxane (PDMS) polymer networks, which have been put into evidence by use of Deuterium Nuclear Magnetic Resonance ( H NMR), will be described in this paper. The anisotropy of molecular motions (in the time range 10 to 10" s) may be investigated with this technique, It has been already shown that deuteriated probes(solvent or free PDMS chains)dissolved in uniaxially deformed networks, acquire a uniaxial orientational order, which means that their motions, in the range 10" s, become uniaxial around the applied force direction This property and... 

Structural Elucidation of IsoX Phase. Spectral analysis by C NMR and X-ray diffraction measurements suggests that upon the SmC IsoX transition, an interlayer correlation may be broken, whereas dimerization or tetramerization via a stereospecific intermolecular interaction through fluorines at chiral centers within each layer is assumed to be operating. The dimerization or tetramerization reduces the anisotropy of molecular motion to increase rotation around the short axis. This change in molecular dynamics may release entropy of the system to induce the endothermic transition. The IsoX phase is not a result of the competition between helical structure and mesophase ordering but a result of the chirality-dependent stereospecific interaction or chiral molecular recognition (7. 

The previous approach is valid as long as the molecular reorientation can be described by a single correlation time. This excludes molecules involving internal motions and/or molecular shapes which cannot, to a first approximation, be assimilated to a sphere. Due to its shape, the molecule shown in Figure 15 cannot evidently fulfil the latter approximation and is illustrative of the potentiality of HOESY experiments as far as carbon-proton distances and the anisotropy of molecular reorientation are concerned.45 58... 

In the review period there have been many studies of molecular motion using analysis of chemical shift anisotropy lineshapes. One that nicely illustrates what is currently possible concerns the motion of 13CO intercalated in C o.9 This is a particularly interesting example as both the CO and C6o molecules undergo reorientation, with the onset of motion occurring at different temperatures for the two species. Furthermore, the work uses a prior calculation of the potential... 

It has recently become more widely appreciated that the presence of rotational diffusional anisotropy in proteins and other macromolecules can have a significant affect on the interpretation of NMR relaxation data in terms of molecular motion. Andrec et al. showed how commonly used NMR relaxation data (Ti, T2 and NOE) obtained at two spectrometer frequencies can be analyzed using a Bayesian statistical approach to reliably detect and... 

Anisotropy of molecular movement monosubstituted benzene rings, e.g. phenyl benzoate (44), show a very typical characteristic in the para position to the substituents the CH nuclei relax considerably more rapidly than in the ortho and meta positions. The reason for this is the anisotropy of the molecular motion the benzene rings rotate more easily around an axis which passes through the substituents and the para position, because this requires them to push aside the least number of neighbouring molecules. This rotation, which affects only the o-and m-CH units, is too rapid for an effective spin-lattice relaxation of the o- and m-C atoms. More efficient with respect to relaxation are the frequencies of ijiolecular rotations perpendicular to the preferred axis, and these affect the p-CH bond. If the phenyl rotation is impeded by bulky substituents, e.g. in 2,2, 6,6 -tetramethylbiphenyl (45), then the T, values of the CH atoms can be even less easily distinguished in the meta and para positions (3.0 and 2.7 s, respectively). 

There is no straightforward and completely rigorous procedure for determining the relative combinations of the various relaxation mechanisms, except where one mechanism clearly dominates (e.g., if the maximum possible nuclear Overhauser effect (NOE) for a resonance is obtained, dipolar relaxation must dominate its relaxation or an increase in relaxation rate in proportion to the square of the applied field must be due to chemical shift anisotropy). Hence, the study of molecular motion in proteins from relaxation data is performed most readily on nuclei directly bonded to H, and so principally relaxed via dipole-dipole interactions (see Section 4(e)(iii)). 

The chemical shift anisotropies for the carbonyl and aromatic carbons of Hytrel were reconstructed from a Herzfeld-Beiger analysis (24) of the intensities of the sidebands from NMR magic angle spinning experiments. The results in Table III indicate that the carbonyl carbon chemical shift anisotropy is axially symmetric for each terephthalate ester. We attribute this axial symmetry to a general property of terephthalate esters, rather than as a consequence of molecular motion, as the highly crystalline dimethyl terephthalate also has an axially symmetric carbonyl carbon chemical shift tensor. 

Anisotropy of the rigid lattice response (such that the frequency of molecular motion is much less than the NMR line width in Hz, which often occurs at low temperature), usually determined from line width or second moment measurements. 

These earlier papers did not take into account the fact that the oriented polymers were partially oriented. It is therefore now necessary to extend the previous discussion of the aggregate model to the situation where molecular motion occurs. This has been done independently by Olf and Peterlin, McBrierty and Douglass, and Folkes and Ward. McBrierty and Douglass paper gives a formal theoretical treatment, as part of a general discussion of the influence of molecular motions on Tj, Tz and the other papers are particularly concerned with an analysis of the effects of molecular motion on the second moment anisotropy but nevertheless provide explicit results for special types of motion. The results are then applied to oriented mats of polyethylene single crystals and to... 

The current application of NMR methods to the study of polymeric materials falls essentially into two categories. Of initial interest is its potential for characterising molecular orientation rather more precisely than has hitherto been possible in the past, using other methods. At present, experimental inaccuracies and mathematical complexities pose a limitation to its application to those polymer systems involving low symmetries. Set against this, is its well established success in characterising orientation in uniaxially drawn semi-crystalline polymers and perhaps even more impressively its application to non-crystalline polymers. Secondly, we have seen that the anisotropy of the second moment can also be quantitatively analysed in the case of various forms of molecular motion. Providing the firequency of molecular motion is comparable to the NMR line width it will have a predictable effect on the second moment anisotropy and this has already been studied in a number of oriented polymer systems. The implications for a molecular interpretation of mechanical relaxations are clear. 

Lineshape analysis of or NMR signals arising from the quadrupolar interaction or chemical shifts anisotropy, respectively, can yield invaluable information about amplitude and motions in the solid [3,150-156]. The quadrupolar interaction, in particular, dominates the spectral pattern in NMR. The frequency of a deuterium resonance in the absence of molecular motion is given by... 

There are also multidimensional solid-state NMR experiments, even though, because of the more stringent instrumental requirements, they are more difficult to perform than solution experiments [49-51]. Correlations can be established between the isotropic chemical shift and chemical-shift anisotropy, and between isotropic shift and dipolar coupling. Solid-state exchange NMR provides information about the geometry of molecular motion in the sample, and spin-diffusion measurements are useful for probing domain size [52,53]. 

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