Reorientational relaxation process

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,. 

In our description of spin reorientational relaxation processes, tensorial quantities are used for which it is necessary to know the transformation properties concerning rotation. A clear and compact formulation is obtained by replacing the cartesian components with a representation in terms of irreducible spherical components. It is known that any representation of the group of rotations can be developed into a sum of irreducible rqpre-sentations D of dimension 2/ +1. If for the description of general rotation R(U) we use the Euler angles Q = (a, p, y), this rotation will be defined by... 

Woessner D E 1962 Spin relaxation processes in a two-proton system undergoing anisotropic reorientation J. Chem. Rhys. 36 1-4... 

The stress—relaxation process is governed by a number of different molecular motions. To resolve them, the thermally stimulated creep (TSCr) method was developed, which consists of the following steps. (/) The specimen is subjected to a given stress at a temperature T for a time /, both chosen to allow complete orientation of the mobile units that one wishes to consider. (2) The temperature is then lowered to Tq T, where any molecular motion is completely hindered then the stress is removed. (3) The specimen is subsequendy heated at a controlled rate. The mobile units reorient according to the available relaxation modes. The strain, its time derivative, and the temperature are recorded versus time. By mnning a series of experiments at different orientation temperatures and plotting the time derivative of the strain rate observed on heating versus the temperature, various relaxational processes are revealed as peaks (243). 

Reorientations produce characteristic maxima in the relaxation rate, which may be different for the various symmetry species of CD4. The measured relaxation rates exhibit dependence on two time constants at low temperatures, but also double maxima for both relaxation rates. We assume that molecules may move over some places (adsorption sites) on the cage walls and experience different local potentials. Under the assumption of large tunnelling splittings the T and (A+E) sub-systems relax at different rates. In the first step of calculation the effect of exchange between the different places was considered. Comparison with experimental data led to the conclusion that we have to include also a new relaxation process, namely the contribution from an external electric field gradient. It is finally quite understandable to expect that such effect appears when CD4 moves in the vicinity of a Na+ ion. 

The description of the chain dynamics in terms of the Rouse model is not only limited by local stiffness effects but also by local dissipative relaxation processes like jumps over the barrier in the rotational potential. Thus, in order to extend the range of description, a combination of the modified Rouse model with a simple description of the rotational jump processes is asked for. Allegra et al. [213,214] introduced an internal viscosity as a force which arises due to a transient departure from configurational equilibrium, that relaxes by reorientational jumps. Thereby, the rotational relaxation processes are described by one single relaxation rate Tj. From an expression for the difference in free energy due to small excursions from equilibrium an explicit expression for the internal viscosity force in terms of a memory function is derived. The internal viscosity force acting on the k-th backbone atom becomes ... 

A surprising aspect of SD is how rapidly C i) in highly polar solvents decays relative to other relaxation processes such as reorientation of solvent dipoles. This very rapid time scale cannot be ascribed to dynamical solvent-solvent correlations, which, as illustrated in Fig. 6, are modest even for the longest ranged A . Thus the key to imderstanding the reasons for the rapid decay of C i) is in examining how solvent-solvent correlations contribute to it and to what extent their contributions can be accounted for in terms of static correlations measured by ((5A ) ), Eq. (32). The initial cmvature of C(t), which characterizes its short-time Gaussian-like behavior is often characterized in terms of the solvation frequency co o/v... 

A detailed comparative study of dielectric behaviour of smectic and nematic polymers was carried out for polymers of acrylic and methacrylic series, containing identical cyanbiphenyl groups (polymers XI and XII) 137 138>. The difference in structural organization of these polymers consists in a more perfect layer packing of smectic polymer XI (see Chaps. 4.1 and 4.2) with antiparallel orientation of CN-dipoles. This shifts the relaxation process of CN-dipole reorientation to a low frequency region compared to nematic polymer XII. Identification of Arrhenius plots for dielectric relaxation frequencies fR shows that for a smectic polymer the value of fR is a couple of orders lower than for a nematic polymer (Fig. 21). Though the values... 

The interpretation of carbon T p data is complicated by the fact that spin-spin (cross-relaxation) processes as well as rotating frame spin-lattice processes may contribute to the relaxation (40). Only the latter process provides direct information on molecular motion. For the CH and CH2 carbons of PP, the Tip s do not change greatly over the temperature interval -110°C to ambient and, as opposed to the T behavior, the CH2 carbon has a shorter T p than the CH carbon. These results suggest that spin-spin processes dominate the Tip (46). However, below ca. -115°C, the Tip s for both carbons shorten and tend toward equality. McBrierty et al. (45) report a proton Ti minimum (which reflects methyl group reorientation at KHz frequencies) at -180°C. No clear minimum is observed in the data, perhaps due to an interplay of spin-spin and spin-lattice processes. Nonetheless, it is apparent that the methyl protons are responsible for the spin-lattice portion of the Tip relaxation for CH and CH2 carbons. 

In triethylenediamine, the relaxation processes are somewhat different because the reorientation of the molecules around their C3 axis does not influence the electric field gradient acting on the nitrogen nuclei indeed the variation of the dipolar coupling between the nitrogen nuclei and the neighboring protons is the cause of the relaxation 291, which is maximum when the molecule rotation frequency is precisely equal to the pure quadrupole resonance frequency. At the corresponding temperature, the relaxation time vs. temperature curve shows a minimum. 

The first relaxation process, which is observed in the low-temperature region from — 100°C to +10° C is due to the reorientation of the water molecules in ice-like water cluster structures. It was shown that the hindered dynamics of the water molecules located within the pores reflects the interaction of the absorptive layer with the inner surfaces of the porous matrix [153,155]. 

The second relaxation process has a specific saddle-like shape and manifests itself in the temperature range of —50°C to +150°C. This relaxation process is thought to be a kinetic transition due to water molecule reorientation in the vicinity of a defect [155]. 

We propose that following the onset of the phase transition the small Cu+ ions residing in the large K+ sites are shifted to an off-center position and produce a distortion in the neighboring unit cells. This imparts to each of these unit cells the ability to behave as a relaxing dipole. In a pure (copper-free) crystal these dipoles are closely interlaced with the complementary part of their respective unit cells and, hence, are unable to reorient. Thus the relaxation process that is linked with these dipoles is not observed in the pure KTN crystal. 

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