Weak reorientation

Weak reorientation of permanent dipoles occiurs by 32a) if the electric field E is weak or the temperature of the system T is high, leading to Xi < 1. Equation (237) now yields ... 

In the case of weak reorientation, Xt < I, the reorientation function (238) is expressed in sufiBcient approximation by the series ... 

Weak reorientation. In this case, the reorientation function (233) is, in a first approximation. 

For the case of weak reorientation Xi < 1 (weak field E, or small value of the dipole p, or high temp ture T), the Langevin functions assume the form ... 

Figure 3 Illustration of the evolution of mixing efficiency for (a) simple shear flow (h) simple shear flow with weak reorientation and (c) shear flow with strong reorientation (after Ottino, 1989).

AH distortions of the nematic phase may be decomposed into three basic curvatures of the director, as depicted in Figure 6. Liquid crystals are unusual fluids in that such elastic curvatures may be sustained. Molecules of a tme Hquid would immediately reorient to flow out of an imposed mechanical shear. The force constants characterizing these distortions are very weak, making the material exceedingly sensitive and easy to perturb. 

Data for the pc-Au/DMF + LiC104 interface have been collected by Borkowska and Jarzabek.109 The value of ffa0was found to be 0.27 V (SCE in H20) and the roughness factor / = 1.3 (Table 8). Unlike Hg, Bi, In(Ga), and Tl(Ga) electrodes and similarly to the Ga/DMF interface, the inner-layer capacity for pc-Au in DMF depends weakly on a, and thus the effect of solvent dipole reorientation at pc-Au is less pronounced than at In(Ga), Bi, and other interfaces. 

Relations (2.46) and (2.47) are equivalent formulations of the fact that, in a dense medium, increase in frequency of collisions retards molecular reorientation. As this fact was established by Hubbard within Langevin phenomenology [30] it is compatible with any sort of molecule-neighbourhood interaction (binary or collective) that results in diffusion of angular momentum. In the gas phase it is related to weak collisions only. On the other hand, the perturbation theory derivation of the Hubbard relation shows that it is valid for dense media but only for collisions of arbitrary strength. Hence the Hubbard relation has a more general and universal character than that originally accredited to it. 

The solvents themselves are adsorbed on the electrode surface, as is shown by the capacitance-potential graphs illustrated in Fig. 9 (Payne, 1967, 1970) potassium hexafluorophosphate, the electrolyte in each of the solvents, is thought to be adsorbed only very weakly. The solvents show somewhat differing curves and the peaks have been interpreted both in terms of competition between the solvent and anions for sites at the surface and also in terms of solvent reorientation. Ethers are adsorbed from the amide solvents most strongly at the potentials around the peaks and this has been postulated to be due to an increase in freedom for the solvent to rotate at these potentials (Dutkiewicz and Parsons, 1966). 

Qualitatively, xc can be viewed as the time necessary for a reorientation by one radian. xc is very weak (10 11-10 12 s) for small size molecules in non-viscous solvents. Conversely, for large molecules (such as proteins in aqueous solution), it can reach much more important values (10 9 s or higher). All (normalized) auto-correlation spectral densities have the same expressions since, in the molecule, all directions are equivalent... 

Obviously, the model is crude and does not take into account many of the factors operating in a real molecular stack. Lack of symmetry with respect to the polar axis and the fact that dipoles may not necessarily be situated in one plane represent additional complications. The angle a could also be field dependent which is ignored in the model. The model also requires that interactions between molecules in adjacent stacks be very weak in order for fields of 10 to 20KV/cm to overcome barriers for field induced reorientation. The cores are then presumably composed of a more or less ordered assembly of stacks with a structure similar to smectic liquid crystals. 

The NMRD profiles of V0(H20)5 at different temperatures are shown in Fig. 35 (58). As already seen in Section I.C.6, the first dispersion is ascribed to the contact relaxation, and is in accordance with an electron relaxation time of about 5 x 10 ° s, and the second to the dipolar relaxation, in accordance with a reorientational correlation time of about 5 x 10 s. A significant contribution for contact relaxation is actually expected because the unpaired electron occupies a orbital, which has the correct symmetry for directly overlapping the fully occupied water molecular orbitals of a type (87). The analysis was performed considering that the four water molecules in the equatorial plane are strongly coordinated, whereas the fifth axial water is weakly coordinated and exchanges much faster than the former. The fit indicates a distance of 2.6 A from the paramagnetic center for the protons in the equatorial plane, and of 2.9 A for those of the axial water, and a constant of contact interaction for the equatorial water molecules equal to 2.1 MHz. With increasing temperature, the measurements indicate that the electron relaxation time increases, whereas the reorientational time decreases. 

Existence of a high degree of orientational freedom is the most characteristic feature of the plastic crystalline state. We can visualize three types of rotational motions in crystals free rotation, rotational diffusion and jump reorientation. Free rotation is possible when interactions are weak, and this situation would not be applicable to plastic crystals. In classical rotational diffusion (proposed by Debye to explain dielectric relaxation in liquids), orientational motion of molecules is expected to follow a diffusion equation described by an Einstein-type relation. This type of diffusion is not known to be applicable to plastic crystals. What would be more appropriate to consider in the case of plastic crystals is collision-interrupted molecular rotation. 

Therefore, data of Fig. 6 show the change of the reorientational-vibrational relaxation time of acetonitrile molecules confined in mesopores upon adsorption and desorption. Before the capillary condensation, the relaxation time is smaller than that of bulk liquid, whereas it is greater than that of the bulk liquid after condensation. The difference of molecular motion between precondensation and postcondensation states is not significant, but this work can show clearly the presence of such a difference. If vibrational and reorientational relaxation processes are dominated by molecular collisions, the molecular reorientation is more rapid before condensation and it becomes slower than that of the bulk liquid with the progress of the capillary condensation, which indicates the formation of a weakly organized molecular assembly structure in mesopores. Even the mesopore can affect the state of the condensates through a weak molecular potential. The organized state should be stable in mesopores, because the relaxation time is almost constant above the condensation PIP,. 

SDS micelles [188-190]. These results may be a consequence of a lack of template-induced orientation or of the orientational forces being too weak to overcome the orientational preferences between an excited and a ground state molecule. It is certainly the case in all of the micellar examples cited that the solvent relaxation times should allow molecules to reorient themselves at the interface (should they so choose) on timescales which are comparable to those necessary for an excited molecule to form its photoproducts. 

Here td is the so-called Debye dielectric relaxation time. One could view td as a phenomenological time constant which applies to dielectric relaxation measurements, or alternatively for simple causes, involving dielectric relaxation of weakly interacting dipoles, tD is related to the reorientation time constant of the solvent dipole in the laboratory frame. 

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