Reorientation, molecular

NMR can provide detailed information about type and timescale of slow molecular motion. Slow molecular reorientational processes can be probed by making use of the angular dependence (3.1.23) of the resonance frequency. Slow molecular translation can be investigated with NMR by measuring the particle diffusion and flow in magnetic field gradients (cf. Section 7.2.6) [Call, Cal2, Karl, Kiml, Stil]. 

Molecular motions generally appear incoherent and are described by a normalized stochastic process f(t). One important quantity to characterize stationary stochastic processes is the auto-correlation function a a) (cf. Section 4.3), 

In many cases the auto-correlation function is an exponential function with a time constant Tc, which is called the correlation time of the process. Following the definition of the correlation time for an exponential correlation function (3.2.10) the correlation time for a nonexponential correlation function is defined as 

In polymeric materials distributions of correlation times are observed for molecular motions. Such a distribution can be interpreted in two ways. Either different molecules exhibit different correlation times during the time of observation (heterogeneous distribution) or a single molecule exhibits different correlation times in different observation intervals (homogeneous distribution). 

For reorientations with correlation times in the range of the inverse spectral width of the powder spectrum, temperature-dependent changes of the lineshape are observed which are characteristic of the motional process [Jell, Miill, Spil, Spi2]. As an example. Fig. 3.2.5 shows NMR spectra for different motional mechanisms and different correlation times [Miill]. However, such wideline spectra cannot be readily measured with single-pulse excitation, because the beginning of the FID will decay within the 

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Reverse saturable absorption is an increase in the absorption coefficient of a material that is proportional to pump intensity. This phenomenon typically involves the population of a strongly absorbing excited state and is the basis of optical limiters or sensor protection elements. A variety of electronic and molecular reorientation processes can give rise to reverse saturable absorption many materials exhibit this phenomenon, including fuUerenes, phthalocyanine compounds (qv), and organometaUic complexes. 

Fig. 1. Examples of temperature dependence of the rate constant for the reactions in which the low-temperature rate-constant limit has been observed 1. hydrogen transfer in the excited singlet state of the molecule represented by (6.16) 2. molecular reorientation in methane crystal 3. internal rotation of CHj group in radical (6.25) 4. inversion of radical (6.40) 5. hydrogen transfer in halved molecule (6.16) 6. isomerization of molecule (6.17) in excited triplet state 7. tautomerization in the ground state of 7-azoindole dimer (6.1) 8. polymerization of formaldehyde in reaction (6.44) 9. limiting stage (6.45) of (a) chain hydrobromination, (b) chlorination and (c) bromination of ethylene 10. isomerization of radical (6.18) 11. abstraction of H atom by methyl radical from methanol matrix [reaction (6.19)] 12. radical pair isomerization in dimethylglyoxime crystals [Toriyama et al. 1977].

FIG. 4 Dependence of molecular reorientation times of benzene on the concentration of polystyrene denotes the parallel ( frisbee ) mode, the perpendicular ( tumbling ) mode [26]. 

The dielectric medium is normally taken to have a constant value of e, but may for some purposes also be taken to depend for example on the distance from M. For dynamical phenomena it can also be allowed to be frequency dependent i.e. the response of the solvent is different for a fast reaction, such as an electronic transition, and a slow reaction, such as a molecular reorientation. 

Although long-time Debye relaxation proceeds exponentially, short-time deviations are detectable which represent inertial effects (free rotation between collisions) as well as interparticle interaction during collisions. In Debye s limit the spectra have already collapsed and their Lorentzian centre has a width proportional to the rotational diffusion coefficient. In fact this result is model-independent. Only shape analysis of the far wings can discriminate between different models of molecular reorientation and explain the high-frequency pecularities of IR and FIR spectra (like Poley absorption). In the conclusion of Chapter 2 we attract the readers attention to the solution of the inverse problem which is the extraction of the angular momentum correlation function from optical spectra of liquids. 

Relations (2.46) and (2.47) are equivalent formulations of the fact that, in a dense medium, increase in frequency of collisions retards molecular reorientation. As this fact was established by Hubbard within Langevin phenomenology [30] it is compatible with any sort of molecule-neighbourhood interaction (binary or collective) that results in diffusion of angular momentum. In the gas phase it is related to weak collisions only. On the other hand, the perturbation theory derivation of the Hubbard relation shows that it is valid for dense media but only for collisions of arbitrary strength. Hence the Hubbard relation has a more general and universal character than that originally accredited to it. 

The Hubbard relation is indifferent not only to the model of collision but to molecular reorientation mechanism as well. In particular, it holds for a jump mechanism of reorientation as shown in Fig. 1.22, provided that rotation over the barrier proceeds within a finite time t°. To be convinced of this, let us take the rate of jump reorientation as it was given in [11], namely... 

In the general case of collisions, changing the molecular reorientation, (A7.23) contains a fully averaged (T) = f T(g)ip(g) dg, where the integral operator should satisfy the only obvious condition... 

Lynden-Bell R. M. The effect of molecular reorientation on the line-shapes of degenerate vibrations in infra-red and Raman spectra of liquids, Mol. Phys. 31, 1653-62 (1976). 

Jameson C. J., Jameson A. K., Smith N. C. 15N spin-relaxation studies of N2 in buffer gases. Cross-sections for molecular reorientation and rotational energy transfer, J. Chem. Phys. 86, 6833-8 (1987). 

Steele W. A. Molecular reorientation in liquids. II. Angular autocorrelation functions, J. Chem. Phys. 38, 2411-18 (1963). 

Snider S., McClung R. E. D. Raman studies of molecular reorientation in liquid sulfur hexafluoride, Can. J. Phys. 52, 1209-14 (1974). 

Normal vibrational spectroscopy generates information about the molecular frequency of vibration, the intensity of the spectral line and the shape of the associated band. The first of these is related to the strength of the molecular bonds and is the main concern of this section. The intensity of the band is related to the degree to which the polarisability is modulated during the vibration and the band shape provides information about molecular reorientational motion. 

Given the specific, internuclear dipole-dipole contribution terms, p,y, or the cross-relaxation terms, determined by the methods just described, internuclear distances, r , can be calculated according to Eq. 30, assuming isotropic motion in the extreme narrowing region. The values for T<.(y) can be readily estimated from carbon-13 or deuterium spin-lattice relaxation-times. For most organic molecules in solution, carbon-13 / , values conveniently provide the motional information necessary, and, hence, the type of relaxation model to be used, for a pertinent description of molecular reorientations. A prerequisite to this treatment is the assumption that interproton vectors and C- H vectors are characterized by the same rotational correlation-time. For rotational isotropic motion, internuclear distances can be compared according to... 

Another important linear parameter is the excitation anisotropy function, which is used to determine the spectral positions of the optical transitions and the relative orientation of the transition dipole moments. These measurements can be provided in most commercially available spectrofluorometers and require the use of viscous solvents and low concentrations (cM 1 pM) to avoid depolarization of the fluorescence due to molecular reorientations and reabsorption. The anisotropy value for a given excitation wavelength 1 can be calculated as... 

As seen from the above theoretical developments, accessing geometrical (and stereochemical) information implies at least an estimation of the dynamical part of the various relaxation parameters. The latter is represented by spectral densities which rest on the calculation of the Fourier transform of auto- or cross-correlation functions. These calculations require necessarily a model for describing molecular reorientation... 

Small-step rotational diffusion is the model universally used for characterizing the overall molecular reorientation. If the molecule is of spherical symmetry (or approximately this is generally the case for molecules of important size), a single rotational diffusion coefficient is needed and the molecular tumbling is said isotropic. According to this model, correlation functions obey a diffusion type equation and we can write... 

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... 

The characteristic material response times for molecular reorientation are 10-12 s. Then, in the microwave band, electromagnetic fields lead to rotation of polar molecules or charge redistribution. The corresponding polarization processes are denoted orientation polarization. 

Molecular Motions and Dynamic Structures. Molecular motions are of quite general occurrence in the solid state for molecules of high symmetry (22,23). If the motion does not introduce disorder into the crystal lattice (as, for example, the in-plane reorientation of benzene which occurs by 60° jumps between equivalent sites) it is not detected by diffraction measurements which will find a seemingly static lattice. Such molecular motions may be detected by wide-line proton NMR spectroscopy and quantified by relaxation-time measurements which yield activation barriers for the reorientation process. In addition, in some cases, the molecular reorientation may be coupled with a chemical exchange process as, for example, in the case of many fluxional organometallic molecules. ... 

For the rectifiers listed in Table 1, the current was found to decay with successive measurements of the same junction for 36a, 38, 39, 40, 42, and 44 between Au electrodes (where the monolayers were not sufficiently rigid, there probably was room in the Au I monolayer I Au sandwich for molecular reorientation under applied bias) (see Fig. 18d, g, and i for examples). In contrast, the current did not decay at all in subsequent cycles for 36b (Fig. 18b) or 36c, where the molecules were chemisorbed onto the Au electrode with an S anchor, or for 41 (Fig. 18f), 43, or 45 (where the monolayer was sufficiently rigid and closely packed to resist reorientation). 

Vittadini, E., Dickinson, L.C., and Chinachoti, P. 2002. NMR water mobility in xanthan and locust bean gum mixtures Possible explanation of microbial response. Carbohydr. Polym. 49, 261-269. Wachner, A.M. and Jeffrey, K.R. 1999. A two-dimensional deuterium nuclear magnetic resonance study of molecular reorientation in sugar/water glasses. J. Chem. Phys. Ill, 10611-10616. Wagner, W. and Pruss, A. 1993. International equations for the saturation properties of ordinary water substance Revised according to the international temperature scale of 1990. J. Phys. Chem. Ref. Data 22, 783-787. 

The non-collective motions include the rotational and translational self-diffusion of molecules as in normal liquids. Molecular reorientations under the influence of a potential of mean torque set up by the neighbours have been described by the small step rotational diffusion model.118 124 The roto-translational diffusion of molecules in uniaxial smectic phases has also been theoretically treated.125,126 This theory has only been tested by a spin relaxation study of a solute in a smectic phase.127 Translational self-diffusion (TD)29 is an intermolecular relaxation mechanism, and is important when proton is used to probe spin relaxation in LC. TD also enters indirectly in the treatment of spin relaxation by DF. Theories for TD in isotropic liquids and cubic solids128 130 have been extended to LC in the nematic (N),131 smectic A (SmA),132 and smectic B (SmB)133 phases. In addition to the overall motion of the molecule, internal bond rotations within the flexible chain(s) of a meso-genic molecule can also cause spin relaxation. The conformational transitions in the side chain are usually much faster than the rotational diffusive motion of the molecular core. 

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