Molecular relaxation mechanism

Fig. 3.9 Diagrams of molecular relaxation mechanisms (a) conformational flip of chlorohexane, (b) crankshaft rotation in polyethylene.

The stress-strain relations for viscoelastic materials are reviewed. The simplest case of intrinsic absorption in polymers is a molecular relaxation mechanism with a single relaxation time. However, the relaxation mechanisms which lead to absorption of sound are usually more complicated, and are characterized by a distribution of relaxation times. Under causal linear response conditions the attenuation and dispersion of sound in a... 

Infrared dichroism has been successfully applied to characterize the orientational relaxation of linear and branched polyst3rrene chains as well as binary blends of long and short chains. By deuterating some chains or parts of chains, infrared spectroscopy provides a method of analyzing the orientational behaviour of the different species and consequently probe the molecular relaxation mechanisms. 

Schwartz conducted ODP experiments using giga-dalton sized molecules (derived from yeast chromosomes) and obtained similar results (2) to those of Jamil and Lerman. However, the resolution mechanisms operating in the large and small molecular size ranges could be quite different. This could be partially due to size dependence of molecular relaxation mechanisms in a gel. 

In the studies of very high purity polymer films (which do not contain mobile additives), there appears to be a molecular relaxation mechanism, that is probably driven by entropy, that can cause a decrease in surface ener with time after plasma processing [40]. TTie rate of this decrease depends on the mobility of the polar moieties aroimd the polymer chain. The tendency is for the polar group to rotate and bury itself to reduce the surface energy. 

Besides the detailed characterization of molecular relaxation mechanisms and space charge effects, several research groups focused on the information extracted from dielectric and other thermal techniques on phase separation that develops in polyurethanes during the stochastic polyaddition reaction [e.g., Pissis et al. (1998), Roussos et al. 2004 Tsonos et al. 2004 ... 

Consider a nucleus that can partition between two magnetically nonequivalent sites. Examples would be protons or carbon atoms involved in cis-trans isomerization, rotation about the carbon—nitrogen atom in amides, proton exchange between solute and solvent or between two conjugate acid-base pairs, or molecular complex formation. In the NMR context the nucleus is said to undergo chemical exchange between the sites. Chemical exchange is a relaxation mechanism, because it is a means by which the nucleus in one site (state) is enabled to leave that state. 

Nuclear dipole-dipole interaction is a veiy important relaxation mechanism, and this is reflected in the relationship between 7, and the number of protons bonded to a carbon. The motional effect is nicely shown by tbe 7 values for n-decanol, which suggest that the polar end of the molecule is less mobile than the hydrocarbon tail. Comparison of iso-octane with n-decanol shows that the entire iso-octane molecule is subject to more rapid molecular motion than is n-decanol—compare the methyl group T values in these molecules. 

Goldflam R., Kouri D. J. On accurate quantum mechanical approximations for molecular relaxation phenomena. Averaged... 

For liquids, the dominant relaxation mechanism is the nuclear-nuclear dipole interaction, in which simple motion of one nucleus with respect to the other is the most common source of relaxation [12, 27]. In the gas phase, however, the physical mechanism of relaxation is often quite different. For gases such as the ones listed above, the dominant mechanism is the spin-rotation interaction, in which molecular collisions alter the rotational state of the molecule, leading to rotation-induced magnetic fluctuations that cause relaxation [27]. The equation governing spin-rotation relaxation is given by... 

Spin relaxation in NMR is known to provide information about the dynamics of molecular entities and possibly about molecular geometry or electron distribution. Generally, dynamical information is obtained if the tensor of the relevant relaxation mechanism is known from independent determinations. Conversely, if parameters describing the dynamics of the considered molecule have been deduced beforehand, geometrical parameters may be derived. Only in particular situations, one can hope to access both types of parameters (dynamical and geometrical). For... 

In the general case, when the shielding tensor is not of axial symmetry, in place of its diagonal elements axx, ayy and kyyl > axx i the following parameters are generally used asymmetry parameter V = <3xx — ayy)/Gzz = (3/2)(cTj.j. — oyy)/h.o. The second form of rj arises from the fact that, as far as relaxation is concerned, the shielding tensor can be defined with respect to any time-independent reference (which therefore will not act as a relaxation mechanism). [Pg.96]

There is greatly renewed interest in electron solvation, due to improved laser technology. However it is apparent that a simple theoretical description such as implied by Eq. (9.15) would be inadequate. That equation assumes a continuum dielectric with a unique relaxation mechanism, such as molecular dipole rotation. There is evidence that structural effects are important, and there could be different mechanisms of relaxation operating simultaneously (Bagchi, 1989). Despite a great deal of theoretical work, there is as yet no good understanding of the evolution of free-ion yield in polar media. 

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. 

For spin-f nuclei, dipolar interactions may be modulated by intramolecular (DF, reorientation etc.) and/or intermolecular (TD) processes. In general, the intra- and inter-molecular processes can produce quite different Tj frequency dispersion curves. In practice, NMR field cycling experiments are often needed to extend the frequency domain from those employed in conventional spectrometers to a lower frequency range (i.e., the kHz regime) for unambiguous separation (and identification) of different relaxation mechanisms. The proton spin relaxation by anisotropic TD in various mesophases has been considered by Zumer and Vilfan.131 133,159 In the nematic phase, Zumer and Vilfan found the following expression for T ... 

Since different molecular processes may simultaneously contribute to the spin relaxation in LC, the relaxation rates due to various relaxation mechanisms are additive if the motions can be decoupled on the basis of sufficiently different correlation times 30... 

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