Relaxation processes isotropic

Nuclear spins can be considered as dipoles that interact with each other via dipolar couplings. While this interaction leads to strongly broadened lines in soUd-state NMR spectroscopy, it is averaged out in isotropic solution due to the fast tumbUng of the solute molecules. In Uquid-state NMR spectroscopy, the dipolar interaction can only be observed indirectly by relaxation processes, where they represent the main source of longitudinal and transverse relaxation. 

In a subsequent communication, Elliott and coworkers found that uniaxially oriented membranes swollen with ethanol/water mixtures could relax back to an almost isotropic state. In contrast, morphological relaxation was not observed for membranes swollen in water alone. While this relaxation behavior was attributed to the plasticization effect of ethanol on the fluorocarbon matrix of Nafion, no evidence of interaction between ethanol and the fluorocarbon backbone is presented. In light of the previous thermal relaxation studies of Moore and co-workers, an alternative explanation for this solvent induced relaxation may be that ethanol is more effective than water in weakening the electrostatic interactions and mobilizing the side chain elements. Clearly, a more detailed analysis of this phenomenon involving a dynamic mechanical and/ or spectroscopic analysis is needed to gain a detailed molecular level understanding of this relaxation process. 

We will discuss some preliminary results, which have been performed recently l01). In Fig. 39a the results for polymer No. 2d of Table 10 are shown, which were obtained by torsional vibration experiments. At low temperatures the step in the G (T) curve and the maximum in the G"(T) curve indicate a p-relaxation process at about 120-130 K. Accordingly the glass transition is detected at about 260 K. At 277 K the nematic elastomer becomes isotropic. This phase transformation can be seen only by a very small step in G and G" in the tail of glass transition region, which is shown in more detail in Fig. 39 b. From these measurements we can conclude, that the visco-elastic properties are largely dominated by the properties of the polymer backbone the change of the mesogenic side chains from isotropic to liquid crystalline acts only as a small disturbance and in principle the visco-elastic behavior of the elastomer... 

Unpaired electronic density can be delocalized onto the various nuclei of the complex via through-bond scalar hyperfine interactions involving occupied orbitals containing s-character (direct interaction or polarization according to the Fermi mechanism, Wertz and Bolton (1986)). Random electron relaxation thus produces a flip-flop mechanism which affects the nuclear spin and increases nuclear relaxation processes (Bertini and Luchinat, 1996). Since these interactions are isotropic, they do not depend on molecular tumbling and re is the only relevant correlation time for non-exchanging semi-rigid complexes. Moreover, only electronic spin can be delocalized via hyperfine interactions (no orbital contribution) and the contact re-... 

In relaxation processes of the macromolecular coil to equilibrium, the competing mechanisms of mobility of particles are present simultaneously. However, in the region of weakly entangled macromolecules, relaxation occurs due to isotropic mobility of particles of the chain - the diffusive mechanism -... 

Another advantage of the polarization moments is the possibility of describing relaxation processes in the most rational way. Thus, if the relaxation process is isotropic, then the various moments and their components relax independently for details see Section 5.8. All multipole components of certain rank K relax at one and the same rate constant... 

Finally, the last term in Eq. (5.92) describes isotropic relaxation processes in the ground state. 

We will now dwell on relaxation processes. Since we intend to discuss only relaxation which is isotropic with respect to orientations of J, its probability depends only on the angle 0 between the initial 0, p and the final 0,

bipolar harmonics [379] in the form... 

As can be seen, for any isotropic relaxation process different rank polarization moments change independently. The question arises can the relaxation constants 7 and Tk be arbitrary The following simple example [135] shows that this is not the case. Let us assume that the angular momentum J = 1 and the initial state are such that only level M = 1... 

Isotropic scattering In addition to the dephasing time T2, the correlation time rc of the purely vibrational relaxation process can be measured, providing quantitative information on the question of homogeneous/inhomogeneous line broadening. 

In order to compare primary dynamics with secondary relaxation steps, we depict on the left-hand side of Fig. 15 the anisotropic spectra (a-c), which consist mainly of spectral components with the same linear polarization as directly induced by the pump pulse. On the right-hand side of the figure the corresponding isotropic spectra (d-f) are shown. In the latter spectral components can notably contribute that result from a relaxation process, where the initially orientation of the OH transition dipole is (partially) lost. 

In that final relaxation process the molecule recovers its final isotropic configuration by a reptation motion. The characteristic time for the reptation process is (see so chapters 1.1 and L3) ... 

These results point out the value of the weak cooperative interaction between the dopant molecules and the anisotropic liquid crystalline environment. The reason for the sharp drop in with increasing temperature in the nematic region is unclear at this point. Competing equilibria involving molecular association combined with temperature-dependent relaxation processes may have something to do with it. These effects were not observed in the isotropic system discussed earlier. 

We also draw attention to a funnel techniqu in which a hydrophobic funnel is moved across a LG surface in order to compress or expand its area isotropically. A counter-body compensates for the displaced liquid by moving in the opposite direction. In this way the meniscus level remains constant. Relaxation processes, induced by the funnel movement are monitored through a Wilhelmy plate. In this... 

Hence we see that there is a great deal of the overall behavior that is common to all four of the specific examples that we have considered. Each is isotropic in the equilibrium state, maintained by a relaxation process (or more than one in some cases) that is characterized by a finite relaxation time, In the presence of flow each becomes anisotropic in structure,... 

The results obtained for the two relaxation processes presented in Figs. 9 through 12 belong to one and the same initial value of the isotropic distribution. Let us now briefly consider the impact of different initial values on the relaxation time. For the same two field strengths considered so far, but for two center... 

Figure 13 makes it obvious that different initial values for the isotropic distribution and thus different initial phases in the temporal relaxation process are of less importance for the entire duration of the relaxation process. 

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