Segmental diffusion rotation axis

Fig. 6.2.2. Left Simulated NMR lineshapes that are averaged by various characteristic segmental motions. In the case of fast rotation, y represents the angle between the rotation axis and the C—bond. For a two-site jump, j3 denotes the angle between the C—bond in the two configurations, and the effective asymmetry parameter becomes 17 7 0. Right Calculated 2D exchange spectra for a two-site jump with /3 = 120° (top), and for continuous diffusion (bottom). The distribution functions P(/3) of the reorientation angle are shown, together with the contour maps of the corresponding spectra. All data are displayed on the reduced frequency scale in units of Cq, and mixing times are set equal to the motional correlation time r,..

Figure 5. Main features of the device for formation of radial gradient of process duration in the centrifugal field (chemical reaction/exchange diffusion) on the lens surface (diametrical cross-section) 1 cylinder reactor, 2 lid 3 gasket 4 immovable pipe/air eliminator for injection/ehmination of active/inert hquids 5 reactor rotation axis 6 immovable pipe for injection/ehmination of active/inert liquids 7 lens sample (A convex, B concave) a cylinder pipe thickness of active liquid b radius of the active liquid cylinder, h height of the internal space of the reactor (1) cylinder on periphery K height of the spherical base layer of the cylinder pipe (x = a) of the active hquick K height of the spherical layer base of the cylinder pipe (x = a) of the inert liquid H height of the spherical segment R radius of the lens sample r radius of the sphere, to which the lens sample surface corresponds.

An increase in the concentration of the permeant in the polymer swells it and promotes the free rotation of the polymer segments about the chain axis resulting in lower activation energy for diffusion. 

The higher diffusivities of p-xylene compared to those of benzene in silicahte-1 can be ascribed to the combination of enthalpy and entropy effects [60-62]. The sorbed benzene molecules have to lose their rotational freedom around their hexagonal axis, Ce, when they move from an intersection to a channel segment, i.e., there is a large decrease in entropy in this jump step. For p-xylene, the molecules are, however, orientated with their long molecular axis along either channel direction when they are located at an intersection. The diffusion jump step involves, therefore, only a very small... 

Fenchenko studied free induction decays and transverse relaxation in entangled polymer melts. He considered both the effects of the dipolar interactions between spins in different polymer chains and within an isolated segment along s single chain. Sebastiao and co-workers presented a unifying model for molecular dynamics and NMR relaxation for chiral and non-chiral nematic liquid crystals. The model included molecular rotations/ reorientations, translational self-diffusion as well as collective motions. For the chiral nematic phase, an additional relaxation mechanism was proposed, associated with rotations induced by translational diffusion along the helical axis. The model was applied to interpret experimental data, to which we return below. 

The ESR studies of local segmental dynamics of polymers benefited from the progress achieved in theoretical description of the effects of dynamics on line shape of nitroxide ESR spectra and in resulting software. The Schneider-Freed set of programs made possible the analysis of slow-motional spectra of nitroxides subjected to anisotropic rotational diffusion with rotation symmetry axis oriented quite arbitrarily with respect to the nitroxide axis system. The simulation of one such ESR spectrum with computers available in the 1980s required 20 min of computer time and the best fits to experimental spectra were found by visual comparison simulated spectra with experimental ones. 

A successful MOMD model for analyzing ESR line shapes for spin-labeled polymers was introduced by Meirovitch et al. This model, mentioned in Section 3.3, allows for constraints in the rotational diffusion. More precisely, the polymer chain segmental motion sensed by the tethered nitroxide, that is, the wobbling motion of the effective axis of internal rotation, was considered as constrained by an orienting potential, typically given by Eq. 3,... 

---