Anisotropic rotational reorientation

Problems that may be encountered due to external birefringence effects in the anisotropic absorption method of Shank and Ippen have been discussed. In the event of these interferences being unavoidable, methods have been described to allow the rotational reorientation times of the dye molecules in fluid solution to be determined. ... 

Carbon-13 NMR has been used to study anisotropic rotational motion in liquids, as have combinations of techniques. Gillen and Griffiths (1972) have obtained the two reorientational relaxation times for benzene (a symmetric top) by combining reorientation relaxation times obtained from Raman band shapes and deuterium spin-lattice NMR relaxation times. The most extensive series of measurements probing anisotropic molecular reorientations have been made by Pecora and co-workers (Alms et al., (1973a, b)), who combined Carbon-13 spin lattice relaxation times with those obtained from depolarized Rayleigh spectra. 

Proton, deuteron and carbon spin relaxation measurements of liquid crystals have provided detailed information about the molecular motions of such anisotropic liquids (anisotropic rotation and translation diffusion of individual molecules), and about a peculiar feature of liquid crystalline phases, namely collective molecular reorientations or order fluctuations. Spin relaxation in liquid crystalline mesophases has challenged NMR groups since the early 1970s, shortly after the publication of theoretical predictions that order fluctuations of the director (OFD, OF), i.e. thermal excitations of the long-range orientational molecular alignment (director), may play an important unusual role in nuclear spin relaxation of ordered liquids. Unique to these materials, which are composed of rod-like or disc-like (i.e. strongly anisotropic molecules), it was predicted that such thermal fluctuations of the director should, at the frequencies of these fluctuation modes, produce rather peculiar Ti(p) dispersion profiles. For example in the case of uniaxial nematic... 

Waldeck, D.H. and Fleming, G.R., Influence of viscosity and temperature on rotational reorientation. Anisotropic absorption studies of 3,3 -diethyloxadicarbocyanine iodide, /. Phys. Chem., 85, 2614, 1981. 

In the previous discussion, the electron-nucleus spin system was assumed to be rigidly held within a molecule isotropically rotating in solution. If the molecule cannot be treated as a rigid sphere, its motion is in general anisotropic, and three or five different reorientational correlation times have to be considered 79). Furthermore, it was calculated that free rotation of water protons about the metal ion-oxygen bond decreases the proton relaxation time in aqua ions of about 20% 79). A general treatment for considering the presence of internal motions faster than the reorientational correlation time of the whole molecule is the Lipari Szabo model free treatment 80). Relaxation is calculated as the sum of two terms 8J), of the type... 

Molecular motions in low molecular weight molecules are rather complex, involving different types of motion such as rotational diffusion (isotropic or anisotropic torsional oscillations or reorientations), translational diffusion and random Brownian motion. The basic NMR theory concerning relaxation phenomena (spin-spin and spin-lattice relaxation times) and molecular dynamics, was derived assuming Brownian motion by Bloembergen, Purcell and Pound (BPP theory) 46). This theory was later modified by Solomon 46) and Kubo and Tomita48 an additional theory for spin-lattice relaxation times in the rotating frame was also developed 49>. 

When the overall motion is not isotropic, the diagonal elements of the rotational diffusion tensor are no longer equivalent and rotation about the three principal axes of the diffusion tensor may be described by different diffusion coefficients or correlation times. For anisotropic motion, the correlation time in Eqs. 16 and 25 is an effective correlation time, r ff, containing contributions from the various modes of reorientation. Partitioning of the various components of rff can be achieved through appropriate dynamic models. The simplest case of anisotropic motion is that for a symmetric-top molecule. The r ff of a rigid ellipsoid is expressed in terms of two parameters, Dn and DL these two parameters respectively describe the rotational diffusion about the C3 symmetry axis (major axis) and the two perpendicular axes (minor axes), which are assumed to be equivalent25-44 (Fig. 4) ... 

Woessner47 has also treated the case of a methyl group attached to an axially symmetric ellipsoid, whereas Levy et al.66 derived equations for the methyl internal rotation superposed on a fully anisotropic motion. The effect of anisotropic reorientation can dramatically alter the relationship between rigidly held methine, methylene, and methyl C—H vectors. Deviation from the ratio T,(CH)/ T,(CH3) = 3 can be considerable, depending on the relative orientation of C—H vectors with respect to the principal diffusion axes. 

Anisotropy in the molecular reorientation of a disaccharide molecule is to be expected when a C—H bond vector of the molecule lies on or near a preferred axis of rotation. This results in a shorter 7, value for carbons whose C—H bonds lie along the anisotropic axis than for those having other orientations. 

Unfortunately, the usefulness of NMR for the investigation of chemical problems was strictly limited to liquid samples, so solid samples first had to be dissolved or melted. This is because of the anisotropic nuclear interactions which strongly depend on molecular orientation, and are therefore averaged by molecular motion. In liquids, the molecules reorient randomly very quickly a water molecule requires ca. 10 s for complete reorientation. Although certain solids have sufficient molecular motion for their NMR spectra to be obtainable without resorting to special techniques, in the general case of a true solid, there is no such motion, and conventional NMR, instead of sharp spectral lines, yields a broad hump which conceals most information of interest to chemists. For example, the width of the H NMR resonance in the spectrum of water is ca. 0.1 Hz, while the line from a static sample of ice is ca. 100 kHz wide, i.e., a million times broader. Andrew et al. [ 12], and independently Lowe [ 13], had the idea of substituting the insufficient molecular motion in solids for the macroscopic rotation of the sample. 

Levy and coworkers97 have measured 13C spin-lattice relaxation times, 7), for 3- and 4-aminobiphenyls in a number of solvent systems, and of the corresponding ammonium ions in acidic and nonacidic media. The observed 7) values indicated that the molecular tumbling is anisotropic for these species. In addition, the known biphenyl geometry allowed indentification and semiquantitative evaluation of internal rotation-libration motion. The protonated amine function is motionally more restricted by solvent-solute and ion-pair interactions than the corresponding neutral amine. Thus, in the 3-biphenylammonium ion, the principal axis for molecular reorientation is aligned close to the C3—NHj-bond, whereas in the amine the principal axis lies closer to the biphenyl C2-symmetry axis. In both 3- and 4-aminobiphenyls, the unsubstituted phenyl rings are less restricted due to rapid phenyl rotation or libration. Table 14 presents 13C Tj-data for 4-aminobiphenyl 37 (NH2 on C4) and 4-biphenylammonium acetate 38 and trifluoroacetate 39. 

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