Correlated motion relaxation behaviour

Current theoretical work on relaxation apparently centres on two issues, the problems of cross relaxation and cross correlation in multispin systems and the effect of anisotropic motion on nuclear relaxation. Both lines of effort come together in very recent theoretical and experimental work on the relaxation behaviour of the methyl group to which in the past three years alone more than 10 papers have been devoted. 

If several protons affect the carbon atom in question, and also undergo mutually correlated motions, as in a rotating methyl group, then they become even less independent of each other. Their resulting relaxation behaviour is complex, and is now non-exponential even when all the protons are simultaneously irradiated [2]. For this reason, particular care must be taken in treating methyl group relaxation in polymers. 

Natural rubber (NR) is a well studied elastomer. Of particular interest is the ability of NR to crystallize, specifically the strain-induced crystallization that takes place whilst the material is stretched. Moreover, in many elastomer applications, network chain dynamics under external stress/strain are critical for determining ultimate performance. Thus, a study on how the strain-induced crystallization affects the dynamics of a rubbery material is of outmost importance. Lee et al [1] reported their initial findings on the role of uniaxial extension on the relaxation behavior of cross-linked polyisoprene by means of dielectric spectroscopy. Nonetheless, to our best knowledge no in-depth study of the effects of strain induced crystallization on the molecular dynamics of NR has been undertaken, analyzing the relaxation spectra and correlating the molecular motion of chains with its structure. Broadband dielectric spectroscopy (BDS) has been chosen in order to study the dynamic features of segmental dynamics, because it is a comparatively simple technique for the analysis of the relaxation behaviour over a suitable frequency interval. This study is important from a basic and practical point of view, since an elongated crosslinked polymer at equilibrium may be considered as a new anisotropic material whose distribution of relaxation times could be affected by the orientation of the chains. 

A more complete study of the factors influencing relaxation behaviour has been made on arsonium salts by altering the alkyl group, the temperature, the solvent, the concentration and the counterion. It has been shown that the line width of the resonances increases with increasing size of the alkyl group, i.e. with increasing molecular mass of the species under investigation in fact, the isotropic motion of a solute in a mobile liquid can be correlated to the correlation time by... 

The dynamic RIS model developed for investigating local chain dynamics is further improved and applied to POE. A set of eigenvalues characterizes the dynamic behaviour of a given segment of N motional bonds, with v isomeric states available to each bond. The rates of transitions between isomeric states are assumed to be inversely proportional to solvent viscosity. Predictions are in satisfactory agreement with the isotropic correlation times and spin-lattice relaxation times from 13C and 1H NMR experiments for POE. 

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... 

When the H- H dipole-dipole interaction can be measured for a specific pair of H nuclei, studies of the temperature dependence of both the H NMR line-shape and the H NMR relaxation provide a powerful way of probing the molecular dynamics, even in very low temperature regimes at which the dynamics often exhibit quantum tunnelling behaviour. In such cases, H NMR can be superior to quasielastic neutron scattering experiments in terms of both practicality and resolution. The experimental analysis can be made even more informative by carrying out H NMR measurements on single crystal samples. In principle, studies of both the H NMR lineshape and relaxation properties can be used to derive correlation times (rc) for the motion in practice, however, spin-lattice relaxation time (T measurements are more often used to measure rc as they are sensitive to the effects of motion over considerably wider temperature ranges. 

The 2-site 120° jump motion for the basal molecules switches between these two hydrogen bonding arrangements and clearly requires correlated jumps of the hydroxyl groups of all three basal molecules. On the assumption of Arrhenius behaviour for the temperature dependence of the jump frequencies, the activation energies for the jump motions of the apical and basal deuterons were estimated to be 10 and 21 kj mol-1, respectively. This dynamic model was further supported by analysis of the dependence of the quadrupole echo 2H NMR lineshape on the echo delay and consideration of 2H NMR spin-lattice relaxation time data. 

Relaxation rates of nuclear spins can also be related to aspects of molecular structure and behaviour in favourable circumstances, in particular internal molecular motions. It is true to say, however, that the relationship between relaxation rates and structural features are not as well defined as those of the chemical shift and spin-spin coupling constants, and are not used on a routine basis. The problem of reliable interpretation of relaxation data arises largely from the numerous extraneous effects that influence experimental results, meaning empirical correlations for using such data are not generally available and this aspect of NMR will not be pursued further in this book. 

The plot below compares the behaviour of the longitudinal and transverse relaxation rate constants. As the correlation time increases the longitudinal rate constant goes through a maximum. However, the transverse rate constant carries on increasing and shows no such maximum. We can attribute this to the secular part of transverse relaxation which depends on 7(0) and which simply goes on increasing as the correlation time increases. Detailed calculations show that in the fast motion limit the two relaxation rate constants are equal. 

It is of interest to note that, as shown by results reported in [11], the relaxation data obtained from poly(vinylmethyl ether) in CDCI3 solution are described by exactly the same values of the ratios of the correlation times Ti/tq and T2/T1 and the angle of the libration cone 0 as those listed in Table 6.3 for the bulk local dynamics. Only the temperature dependence of the correlation times is different. Such a similarity in behaviour shows that the very nature of the motions involved in the magnetic relaxation at a given frequency... 

The hydration dependence studies of the internal protein dynamics of hen egg white lysozyme by and H NMR relaxation have been presented. The relaxation times were quantitatively analysed by the well-established correlation function formalism and model-free approach. The obtained data was described by a model based on three types of motion having correlation times around 10 , 10 and 10 s. The slowest process was shown to originate from correlated conformational transitions between different energy minima. The intermediate process was attributed to librations within one energy minimum, and the fastest one was identified as a fast rotation of methyl protons around the symmetry axis of methyl groups. A comparison of the dynamic behaviour of lysozyme and polylysine obtained from a previous study revealed that in the dry state both biopolymers are rigid on both fast and slow time scales. Upon hydration, lysozyme and polylysine showed a considerable enhancement of the internal mobility. The side chain fragments of polylysine were more mobile than those of lysozyme, whereas the backbone of lysozyme was found to be more mobile than that of polylysine. 

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