Transverse translational diffusion

For wave numbers p < p the transverse translational diffusion of a chain is hindered by the entangling chains. In the framework of the Rouse theory the interactions with other chains are purely frictional, since there is no elastic restoring force associated with interchain interactions. We will represent the effect of hindered lateral diffusion by a modification of the friction coefficient... 

To explain the Green function method for the formulation of Dx, D and D, of the fuzzy cylinder [19], we first consider the transverse diffusion process of a test fuzzy cylinder in the solution. As in the case of rodlike polymers [107], we imagine two hypothetical planes which are perpendicular to the axis of the cylinder and touch the bases of the cylinder (see Fig. 15a). The two planes move and rotate as the cylinder moves longitudinally and rotationally. Thus, we can consider the motion of the cylinder to be restricted to transverse diffusion inside the laminar region between the two planes. When some other fuzzy cylinders enter this laminar region, they may hinder the transverse diffusion of the test cylinder. When the test fuzzy cylinder and the portions of such other cylinders are projected onto one of the hypothetical planes, the transverse diffusion process of the test cylinder appears as a two-dimensional translational diffusion of a circle (the projection of the test cylinder) hindered by ribbon-like obstacles (cf. Fig. 15a). 

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. 

An exception to this has been found in the smectic A phase of octyloxy-p -pentylphenyl thiolbenzoate [7.59]. Furthermore, the activation energy for Dy is much higher than both the activation energy for transverse diffusion and the corresponding value for nematics. Using a parametrized form of the momentum autocorrelation function, Chu and Moroi [7.60] calculated the anisotropy in the translational diffusion constants for nematics as... 

Figure 22 shows typical transverse relaxation curves. For Mwtranslational diffusion relative to the inhomogeneities of the magnet). The chain-end blocks reveal themselves only above the critical molecular weight Me as visualized in Fig. 22 by the transverse relaxation curve for Mw Mc. 

When the solution is dilute, the three diffusion coefficients in Eq. (40a, b) may be calculated only by taking the intramolecular hydrodynamic interaction into account. In what follows, the diffusion coefficients at infinite dilution are signified by the subscript 0 (i.e, D, 0, D10> and Dr0). As the polymer concentration increases, the intermolecular interaction starts to become important to polymer dynamics. The chain incrossability or topological interaction hinders the translational and rotational motions of chains, and slows down the three diffusion processes. These are usually called the entanglement effect on the rotational and transverse diffusions and the jamming effect on the longitudinal diffusion. In solving Eq. (39), these effects are taken into account by use of effective diffusion coefficients as will be discussed in Sect. 6.3. 

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