Translational diffusion induced rotation

Translational self-diffusion. Whereas in bulk nematics, translational self-diffusion modulates only the dipolar interactions between protons on different molecules (i.e. intermolecular interactions), in microdroplets it also modulates intra-molecular dipolar interactions because the director field in a confined geometry is non-uniform. This new relaxation mechanism is called translational diffusion induced rotation (TDIR). Since intramolecular dipolar interactions are generally stronger than intermolecular interactions, translational selfdiffusion represents a much more effective relaxation mechanism in micro-droplets than in bulk nematics. TDIR is also effective at much lower frequencies than diffusion induced modulation of inter-molecular... 

The first term is the result of translational diffusion induced rotation in the limit 0), T 1 whereas the second term, which is frequency independent includes the contributions of both (7 j p)buik, and of the crossrelaxation to the polymer. The time during which a liquid crystal molecule remains attached to the surface has been estimated as Tg 8 10" s [207]. Deuteron NMR studies... 

The colloid particle or polyelectrolyte molecule may possess a permanent dipole moment. Considerable influence of this moment on the magnitude and the sign of the electro-optical effect is expected in the range of particle rotation. Discrimination between the induced and the rotational relaxation of the particles can be reached, however, since the electro-optical response to a sinusoidal electric field is the sum of a time-independent term adc and a term a2rjJ that is sensitive to the particle rotation [24,45]. The critical frequency of the alrjJ relaxation depends on the rotational diffusion coefficient Dr of the particle, while the critical frequency of relaxation of the time-independent term adc depends on the translational diffusion coefficient of the ions moving on the particle surface. 

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. 

NMR, and particularly deuterium NMR, are the best experimental techniques for the determination of the director field and the molecular dynamics in submicron nematic droplets. The theoretical static proton NMR spectra of the nematic micro-droplets for a bipolar and a radial configuration are shown in Fig. 17 a. The corresponding motionally averaged spectra are shown in Fig. 17 b. Here the motional averaging is produced by translational diffusion which induces slow molecular rotations due to the non-uniform orientational ordering in the droplet [206]. 

In the nematic phase the spin-lattice relaxation rate at high Larmor frequencies is determined by local reorientations of the molecule and internal molecular motions. The spin-spin relaxation rate, I/T2, on the other hand, is determined by nematic order director fluctuations and rotations induced by translational diffusion [216]. 

Measurements of enhancement spectra exist for several gases and mixtures. Figure 3.14 shows the collision-induced absorption spectra of H2-X pairs, with X = He, Ne, Ar, Kr, Xe [213]. The translational lines were omitted for technical reasons. Because the spectra are recorded at room temperature, the So(J) lines of H2 are quite diffuse. Most prominent is the So(l) line at 587 cm-1, but lines at other rotational transition frequencies of H2 are also discernible, for example So(0) at 354 cm-1, So(2) at 815 cm-1, and So(3) at 1035 cm-1, especially for the massive pairs. 

The principal concept was already described in the early 70 s by the first paper on this topic by Magde et al. (2J. A real renaissance arrived in 1993 with the introduction of the confocal illumination scheme for FCS by Rigler et al. fSJ, Since then FCS has been developed towards probably the most important technique for single molecule detection (SMD). FCS allows measuring rates of binding/unbinding reactions SJ, coefficients of translational and rotational diffusion (6, 7, 8, 9J, conformational states and a manifold of photophysical parameters (JO, II, 12) of the induced fluorescent process. 

Jamil and Russo studied translational and rotational diffusion of poly-tetrafluoroethylene latex in aqueous sodium polystyrenesulfonate (NaPSS)(75). Spectra were single exponentials Dp and Dr were extracted from the dependence of the spectral linewidths. Addition of NaCl causes the probes to aggregate further addition of NaPSS reverses the salt-induced probe aggregation, even though it appears that NaPSS does not bind to the latex particles. The Dr tracks the changes in viscosity of the solution attendant on addition of polymer, in the sense that rjDr is independent of polymer concentration, other parameters being fixed. However, at fixed c, qDr does decrease as the salt concentration is increased. 

It is also meaningful to discuss the phenomenon of polymer assembly in the disclination from the viewpoint of entropy. As mentioned above, the orientational order of liquid crystals is induced by the entropy of translation, while the random coUs of polymers are due to the entropy of rotation. The coexistence of a liquid crystal and a polymer causes a conflict between the different entropies. The polymers in the liquid crystal phase thus assemble in the discUnation region, where the orientational order is lowered and the polymers can maximize their conformational entropy. A satisfactory coexistence is then self-sufficiently achieved by cooperation between the blue phase (which must have disclinations) and the polymer (which tends to be excluded from the ordered region). The elastic energy of the liquid crystal orientational field that accumulates around the disclination also plays an important role in the diffusion of the polymer. The curvature of the director increases closer to the disclination core. The elastic energy, which is proportional... 

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