Reorientation mechanism dependence

We present here some very general exact results, which hold for arbitrary reorientation mechanisms of any molecule in an equilibrium isotropic fluid (but not a liquid crystal). A coordinate frame (R) is rigidly attached to the molecule of interest. Its orientation in the laboratory frame (L) is defined by the Euler rotation = (affy) that carries a coordinate frame from coincidence with the laboratory frame L to coincidence with the molecular frame R/ The conditional probability per unit Euler volume [( (0r at time t must depend only on the Euler rotation A = 1 (i.e., rotate first by < 0 then... 

In Section V the reorientation mechanism (A) was investigated in terms of the only (hat curved) potential well. Correspondingly, the only stochastic process characterized by the Debye relaxation time rD was discussed there. This restriction has led to a poor description of the submillimeter (10-100 cm-1) spectrum of water, since it is the second stochastic process which determines the frequency dependence (v) in this frequency range. The specific vibration mechanism (B) is applied for investigation of the submillimetre and the far-infrared spectrum in water. Here we shall demonstrate that if the harmonic oscillator model is applied, the small isotope shift of the R-band could be interpreted as a result of a small difference of the masses of the water isotopes. 

Some consequences which result from the proposed models of equilibrium surface layers are of special practical importance for rheological and dynamic surface phenomena. For example, the rate of surface tension decrease for the diffusion-controlled adsorption mechanism depends on whether the molecules imdergo reorientation or aggregation processes in the surface layer. This will be explained in detail in Chapter 4. It is shown that the elasticity modulus of surfactant layers is very sensitive to the reorientation of adsorbed molecules. For protein surface layers there are restructuring processes at the surface that determine adsorption/desorption rates and a number of other dynamic and mechanical properties of interfacial layers. 

The frequencies that allow microwave dielectric heating to take place are 918 MHz and 2.45 GHz, the latter being the most used. This mechanism depends on the ability of the dipole to reorientate under the applied electric field. The capability of a substance to convert the electromagnetic energy into heat is given by the dielectric loss tan 8 that is equal to the ratio of the dielectric loss e" to the relative permittivity e. The relative permittivity represents the measure of the ability of a molecule to be polarized, while the dielectric loss is the ability of a medium to convert dielectric energy into heat. 

The measurement of correlation times in molten salts and ionic liquids has recently been reviewed [11] (for more recent references refer to Carper et al. [12]). We have measured the spin-lattice relaxation rates l/Tj and nuclear Overhauser factors p in temperature ranges in and outside the extreme narrowing region for the neat ionic liquid [BMIM][PFg], in order to observe the temperature dependence of the spectral density. Subsequently, the models for the description of the reorientation-al dynamics introduced in the theoretical section (Section 4.5.3) were fitted to the experimental relaxation data. The nuclei of the aliphatic chains can be assumed to relax only through the dipolar mechanism. This is in contrast to the aromatic nuclei, which can also relax to some extent through the chemical-shift anisotropy mechanism. The latter mechanism has to be taken into account to fit the models to the experimental relaxation data (cf [1] or [3] for more details). Preliminary results are shown in Figures 4.5-1 and 4.5-2, together with the curves for the fitted functions. 

The chemically realistic simulations we are discussing have been performed using a united atom representation of PB, which leads to the question How does one actually measure a CH vector reorientation for such a model The answer to this question is to use the trick we discussed in the analysis of the pressure dependence of the melt structure factor of PB. Hydrogen atoms are placed on the backbone carbons at their mechanical equilibrium positions for each structure that has been sampled along the MD trajectory. The CH vector dynamics we are showing in Figure 16 is solely from the backbone reorientations of the chain. 

In general, fluctuations in any electron Hamiltonian terms, due to Brownian motions, can induce relaxation. Fluctuations of anisotropic g, ZFS, or anisotropic A tensors may provide relaxation mechanisms. The g tensor is in fact introduced to describe the interaction energy between the magnetic field and the electron spin, in the presence of spin orbit coupling, which also causes static ZFS in S > 1/2 systems. The A tensor describes the hyperfine coupling of the unpaired electron(s) with the metal nuclear-spin. Stochastic fluctuations can arise from molecular reorientation (with correlation time Tji) and/or from molecular distortions, e.g., due to collisions (with correlation time t ) (18), the latter mechanism being usually dominant. The electron relaxation time is obtained (15) as a function of the squared anisotropies of the tensors and of the correlation time, with a field dependence due to the term x /(l + x ). 

No field dependence in the electron relaxation time was ever found in the investigated region between 0.01 and 100 MHz of proton Larmor frequency, or at 800 MHz when high resolution is achieved (28). It was shown that Tie is essentially independent of the reorientational time of the macromolecule and the viscosity of the solution. Therefore, rotation independent mechanisms have to be operative. We also find that Tie decreases with increasing temperature, as also shown in Fig. 5. 

Two polarization mechanisms are possible. If the molecules possess a permanent electric dipole moment pbp rm, each molecule can align its moment with the field direction by reorientation, producing a macroscopic dipole moment. Even if perm = 0 in the field-free limit, each molecule can achieve a field-dependent dipole moment pind by induction. The induced dipole moment is proportional to field strength, pind = a , where a is the electric polarizability of the molecule. In both cases, work must be performed on the system to achieve the macroscopic polarization. Molecules with large permanent dipole moments correspond to high k. 

The molecular motions underlying the dynamic mechanical and dielectric f3 transition in PMMA have been studied in detail [77] by using the 2D exchange NMR experiment. This detects slow reorientations that occur during a mixing time, fm, by measuring the angular-dependent NMR frequencies (expressed in ppm) before and after tm. The 2D frequency spectrum S( >i,... 

It is interesting to compare the results obtained for ordinary and heavy water. To interpret the difference, we show in Fig. 33 by solid curves the total absorption attained in the R-band (i.e., near the frequency 200 cm-1). Dashed curves and dots show the components of this absorption determined, respectively, by a constant (in time) and by a time-varying parts of a dipole moment. In the case of D20, the R-absorption peak vR is stipulated mainly by nonrigidity of the H-bonded molecules, while in the case of H20 both contributions (due to vibration and reorientation) are commensurable. Therefore one may ignore, in a first approximation, the vibration processes in ordinary water as far as it concerns the wideband absorption frequency dependences (actually this assumption was accepted in Section V, as well is in many other publications (VIG), [7, 12b, 33, 34]. However, in the case of D20, where the mean free-rotation-frequency is substantially less than in the case of H20, neglecting of the vibrating mechanism due to nonrigid dipoles appears to be nonproductive. 

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