Relaxation and molecular motion

As it have been demonstrated above, dielectric spectroscopy yields a wealth of information on the different molecular motions and relaxations processes, which are... 

Nitrogen quadrupole resonance studies have so far followed two major directions of investigation on the one hand, quadrupole coupling constants are interpreted in terms of the distribution of the bonding electrons, with many attempts to use the available molecular orbitals computed from models of various degrees of sophistication on the other hand, the effect of temperature on resonances yields information on the molecular motions and relaxation processes. 

MOLECULAR MOTION AND RELAXATION IN FREE-RADICAL SOLUTIONS OF BENZENE, TOLUENE, AND SOME ETHERS AS STUDIED BY DYNAMIC NUCLEAR POLARIZATION. 

Monomer B5A can be photopolymerized at room temperature in its Sg phase to near completion with little volume change. The smectic liquid crystalline structure is retained and locked into the resulting polymeric network upon polymerization. This can be attributed to the topochemical control exerted by the LC monomer matrix on the as-formed polymer a quasi-topochemical polymerization reaction is involved (B5A-RT and PB5A-RT has almost the same unit cell parameters). Fixation of the LC structure is realized through cross-linking, which severely restricts molecular motion and relaxation. The LC structure is maintained up to very high temperatures. This could extend the application temperature of... 

The accurate determination of time correlation (relaxation) functions for a variety of molecular motions and relaxation processes is of crucial importance for detailed study of the liquid state. Such response functions [1,5] are currently used for a wide variety of purposes. 

We begm tliis section by looking at the Solomon equations, which are the simplest fomuilation of the essential aspects of relaxation as studied by NMR spectroscopy of today. A more general Redfield theory is introduced in the next section, followed by the discussion of the coimections between the relaxation and molecular motions and of physical mechanisms behind the nuclear relaxation. 

Both spin-lattice and spin-spin relaxation depend on rates of molecular motion, for relaxation results from the interaction of fluctuating magnetic fields set up by nuclei in the spin system and in the lattice. A quantitative theory of this dependence was given by Bloembergen et al., who obtained... 

The accessibility of chitin, mono-O-acetylchitin, and di-O-acetylchitin to lysozyme, as determined by the weight loss as a function of time, has been found to increase in the order chitin < mono-O-acetylchitin < di-O-acetylchitin [120]. The molecular motion and dielectric relaxation behavior of chitin and 0-acetyl-, 0-butyryl-, 0-hexanoyl and 0-decanoylchitin have been studied [121,122]. Chitin and 0-acetylchitin showed only one peak in the plot of the temperature dependence of the loss permittivity, whereas those derivatives having longer 0-acyl groups showed two peaks. 

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. ... 

FIG. 23 A schematic illustration of the molecular motions and associated T2 relaxation curve behavior for the three major domains in foods—liquid, viscous liquid, and solid (crystalline and glassy). Typical H T2 NMR relaxation time values observed in these domains, and values specific for water in liquid and crystalline domains, are listed. 

An interesting feature of the relaxation is that it is not a spontaneous incident, but governed by molecular motion and interactions between nuclei. Consequently, it provides valuable information about the physical and chemical environments in which the nuclei are embedded. As mentioned above, meat contains approximately 75% water, organised within different structures, which is of fundamental significance for the quality of... 

Table II highlights the 3C NMR relaxation times that reflect molecular motions and help define the physical properties of the cutin polymer. For those solid-like carbons that cross polarized, considerable motional freedom was evidenced for (CH2)n and CH2OCOR groups, on both MHz and kHz timescales, by the short values of Tj(C) and Tip(C), respectively. By contrast, the CHOCOR moiety was more restricted dynamically as judged from its long value of TX(C) low-frequency motions in particular were implicated by the strong dependence of Tip(C) on Bi. These latter groups...

The T, relaxation time is dependent on molecular motion. T, can exhibit more than one minimum when measured as a function of temperature. This happens when several distinct motions occur simultaneously. The T1 relaxation time is dependent upon molecular motion and has more than one minimum as well. The T2 relaxation time is related to the inverse of the NMR linewidth. 

At 55 kHz field, where relaxation times should indicate molecular motion, the relaxation times of the methyl groups showed a temperature dependence between —30 °C and 50 °C. An unresolved peak containing methylene and methine resonances showed a very weak temperature variation. Garroway et al. 62) concluded that the observed C-13 Tle values for fields above 40 kHz were not dominated by spin-spin effects for the DGEBA-PIP system. 

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 ... 

Polymethacrylates and polyacrylates have extensively been studied from the viewpoint of relaxations occurring in the glassy state. Though a vast amount of information has been collected to date, even a qualitative interpretation of the relaxation phenomena on a molecular level often remains questionable. This situation exists despite some favorable circumstances, i.e. polymethacrylates are amorphous polymers with comparatively simple molecular motions and it is possible to alter systematically their constitution and prepare various model polymers. 

The influence of temperature and strain rate can be well represented by Eyring s law physical aging leads to an increase of the yield stress and a decrease of ductility the yield stress increases with hydrostatic pressure, and decreases with plasticization effect. Furthermore, it has been demonstrated that constant strain rate. Structure-property relationships display similar trends e.g., chain stiffness through a Tg increase and yielding is favored by the existence of mechanically active relaxations due to local molecular motions (fi relaxation). 

The questions to be considered here are, how overall and segmental motion are correlated to each other, whether certain segments of a chain behave like rigid subparts or whether each carbon atom undergoes individual reorientation, the behaviour of the end groups, the determination of temperature and thereby the influence of macroviscosity on the various parts of the molecular motion, and how branching of the chains or of some attached substituents influences the relaxation. For this reason chain-like molecules were very early objects of relaxation measurements. After some earlier theoretical papers (Levine et al., 1974) many experimental studies have been published recently. The general... 

The persistence of the fluctuating local fields before being averaged out by molecular motion, and hence their effectiveness in causing relaxation, is described by a time-correlation function (TCF). Because the TCF embodies all the information about mechanisms and rates of motion, obtaining this function is the crucial point for a quantitative interpretation of relaxation data. As will be seen later, the spectral-density and time-correlation functions are Fourier-transform pairs, interrelating motional frequencies (spectral density, frequency domain) and motional rates (TCF, time domain). 

The results of the T2 relaxation studies prove that this method is a very useful technique for the quantitative characterisation of network structures, while the more sophisticated NMR techniques, which also determine the residual dipole-dipole interactions [31, 53-60], provide specific information for the chemical structure and molecular mobility, which may be useful in determining mechanisms of molecular motions and refining interpretations of the non-selective T2 relaxation method, especially for composite materials. 

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