Reorientation mechanism model

The Debye phenomenology is consistent with both gas-like and solidlike model representations of the reorientation mechanism. Reorientation may result either from free rotation paths or from jumps over libration barriers [86]. Primary importance is attached to the resulting angle of reorientation, which should be small in an elementary step. If it is... 

The Hubbard relation is indifferent not only to the model of collision but to molecular reorientation mechanism as well. In particular, it holds for a jump mechanism of reorientation as shown in Fig. 1.22, provided that rotation over the barrier proceeds within a finite time t°. To be convinced of this, let us take the rate of jump reorientation as it was given in [11], namely... 

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. 

Examination of the reorientation angle distribution W(6,t) obtained at Tg exhibits a secondary peak at around 6 = W that does not change its angular position with time. This is interpreted to indicate the presence of a second reorientation mechanism by which the bond undergoes a large angle jump. Such a revelation of the presence of the second mechanism would not have been possible if only the time-correlation functions, and not the full distributions, had been evaluated. This provides an example in which the molecular modeling offers information that cannot easily be obtained from experiment. 

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. 

As the density of a gas increases, free rotation of the molecules is gradually transformed into rotational diffusion of the molecular orientation. After unfreezing , rotational motion in molecular crystals also transforms into rotational diffusion. Although a phenomenological description of rotational diffusion with the Debye theory [1] is universal, the gas-like and solid-like mechanisms are different in essence. In a dense gas the change of molecular orientation results from a sequence of short free rotations interrupted by collisions [2], In contrast, reorientation in solids results from jumps between various directions defined by a crystal structure, and in these orientational sites libration occurs during intervals between jumps. We consider these mechanisms to be competing models of molecular rotation in liquids. The only way to discriminate between them is to compare the theory with experiment, which is mainly spectroscopic. 

In conclusion, the steady-state kinetics of mannitol phosphorylation catalyzed by II can be explained within the model shown in Fig. 8 which was based upon different types of experiments. Does this mean that the mechanisms of the R. sphaeroides II " and the E. coli II are different Probably not. First of all, kinetically the two models are only different in that the 11 " model is an extreme case of the II model. The reorientation of the binding site upon phosphorylation of the enzyme is infinitely fast and complete in the former model, whereas competition between the rate of reorientation of the site and the rate of substrate binding to the site gives rise to the two pathways in the latter model. The experimental set-up may not have been adequate to detect the second pathway in case of II " . The important differences between the two models are at the level of the molecular mechanisms. In the II " model, the orientation of the binding site is directly linked to the state of phosphorylation of the enzyme, whereas in the II" model, the state of phosphorylation of the enzyme modulates the activation energy of the isomerization of the binding site between the two sides of the membrane. Steady-state kinetics by itself can never exclusively discriminate between these different models at the molecular level since a condition may be proposed where these different models show similar kinetics. The II model is based upon many different types of data discussed in this chapter and the steady-state kinetics is shown to be merely consistent with the model. Therefore, the II model is more likely to be representative for the mechanisms of E-IIs. 

Loutfy and coworkers [29, 30] assumed a different mechanism of interaction between the molecular rotor molecule and the surrounding solvent. The basic assumption was a proportionality of the diffusion constant D of the rotor in a solvent and the rotational reorientation rate kOI. Deviations from the Debye-Stokes-Einstein hydrodynamic model were observed, and Loutfy and Arnold [29] found that the reorientation rate followed a behavior analogous to the Gierer-Wirtz model [31]. The Gierer-Wirtz model considers molecular free volume and leads to a power-law relationship between the reorientation rate and viscosity. The molecular free volume can be envisioned as the void space between the packed solvent molecules, and Doolittle found an empirical relationship between free volume and viscosity [32] (6),... 

The non-collective motions include the rotational and translational self-diffusion of molecules as in normal liquids. Molecular reorientations under the influence of a potential of mean torque set up by the neighbours have been described by the small step rotational diffusion model.118 124 The roto-translational diffusion of molecules in uniaxial smectic phases has also been theoretically treated.125,126 This theory has only been tested by a spin relaxation study of a solute in a smectic phase.127 Translational self-diffusion (TD)29 is an intermolecular relaxation mechanism, and is important when proton is used to probe spin relaxation in LC. TD also enters indirectly in the treatment of spin relaxation by DF. Theories for TD in isotropic liquids and cubic solids128 130 have been extended to LC in the nematic (N),131 smectic A (SmA),132 and smectic B (SmB)133 phases. In addition to the overall motion of the molecule, internal bond rotations within the flexible chain(s) of a meso-genic molecule can also cause spin relaxation. The conformational transitions in the side chain are usually much faster than the rotational diffusive motion of the molecular core. 

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 this article and its precursor (4) we have presented the mathematical and physical consequences of a model of polymer dynamics which consider the reorientation of monomer level damped torsional oscillators (DTO model). This mechanism was compared and contrasted with the Rouse-Bueche (RB) model which is concerned with motions of large scale segments of the macromolecular chain. The discussion accounts for certain viscoelastic and dielectric properties of polymers. 

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