Temperature dependence relaxation time

All the examples described above show that confinement in different cases may be responsible for nonmonotonic relaxation kinetics and can lead to a saddle-like dependence of relaxation time versus temperature. However, this is not the only possible reason for nonmonotonic kinetics. For instance, work [258] devoted to the dielectric study of an antiferromagnetic crystal discusses a model based on the idea of screening particles. Starting from the Arrhenius equation and implying that the Arrhenius activation energy has a linear dependence on the concentration of screening charge carriers, the authors of Ref. 258 also obtained an expression that can lead to nonmonotonic relaxation kinetics under certain conditions. However, the experimental data discussed in that work does not show clear saddle-like behavior of relaxation time temperature dependence. The authors of Ref. 258 do not even discuss such a possibility. 

Abstract Contribution of the Jahn-Teller system to the elastic moduli and ultrasonic wave attenuation of the diluted crystals is discussed in the frames of phenomenological approach and on the basis of quantum-mechanical theory. Both, resonant and relaxation processes are considered. The procedure of distinguishing the nature of the anomalies (either resonant or relaxation) in the elastic moduli and attenuation of ultrasound as well as generalized method for reconstruction of the relaxation time temperature dependence are described in detail. Particular attention is paid to the physical parameters of the Jahn-Teller complex that could be determined using the ultrasonic technique, namely, the potential barrier, the type of the vibronic modes and their frequency, the tunnelling splitting, the deformation potential and the energy of inevitable strain. The experimental results obtained in some zinc-blende crystals doped with 3d ions are presented. 

The next step is simulation of the relaxation time temperature dependence, the procedure similar to what was considered by Sturge [2], As a result, one will obtain the magnitudes of the potential barrier, Vq, the mnnelling splitting, rF, the vibrational frequency, vq, the deformation potential, b), and the energy of inevitable... 

Now we will overview some experiments that reveal the specificities of the Jahn-Teller effect in diluted crystals. First of all, we will discuss a justification of their relaxation origin. We have mentioned before that the first experiments were done on the crystals of aluminum oxide (corundum), yttrium aluminum garnet, yttrium iron garnet, and lithium gallium spinel doped with a number of 3d ions [10,11]. The main result was the discovery of attenuation maximum which was considered to be observed at cot 1 and reconstruction of the relaxation time temperature dependence. In some experiments reported later both the velocity and attenuation of ultrasound were measured as functions of the temperature. They were done on ZnSe and ZnTe crystals doped with transition metals. These crystals have the zinc-blende structure with the Jahn-Teller ion in tetrahedral coordination. The following... 

Woessner DE, Zimmerman J (1963) Nuclear transfer and anisotropic motional spin phenomena relaxation-time temperature-dependence studies of water adsorbed on silica gel. IV J Chem Phys 67 1590-600... 

Generally, the effect of the filler on the relaxation-time temperature dependence can be described as the increase of the values Fg (124,126,127,129). 

The time/temperature-dependent change in mechanical properties results from stress relaxation and other viscoelastic phenomena that are typical of these plastics. When the change is an unwanted limitation it is called creep. When the change is skillfully adapted to use in the overall design, it is referred to as plastic memory. 

One further point needs to be mentioned when probing the feasibility of a particular experiment. Apart from its dependence on temperature and concentration (for instance of ions, solutes, impurities, isotopes), relaxation times - in particular the longitudinal relaxation time Tj - depend on the field strength. This can be understood from the concept that energy exchange is most efficient if the timescale of molecular motion is equal to the Larmor frequency. Often, molecular motion takes place over a wide range of frequencies, so that the func-... 

The T, relaxation time is dependent on molecular motion. T, can exhibit more than one minimum when measured as a function of temperature. This happens when several distinct motions occur simultaneously. The T1 relaxation time is dependent upon molecular motion and has more than one minimum as well. The T2 relaxation time is related to the inverse of the NMR linewidth. 

It may be noted that all the above formulae for heavier molecules, which take into account only the repulsive part of the intermolecular potential, give rot as independent of temperature. This is in striking contrast to vibrational relaxation rotational relaxation times, which depend also on the gas-kinetic collision frequency, would thus be expected to show weak temperature dependence varying... 

While the network density v is more or less given by the concentration of the surfactant, the relaxation time can depend on many parameters such as surfactant concentration, temperature, type of counterions or ionic strength. 

To understand properly the relationship between the glass transition phenomenon observed in computer-simulated systems and that observed in laboratory systems, it is necessary to be familiar with the temperature dependence of the relaxation time. The point to be made is that the transition, which is the thermodynamic manifestation of a failure to maintain equilibrium during cooling, occurs sharply in laboratory systems but diffusely in simulated systems, primarily because of a great difference in relaxation time temperature (or volume) dependence in the time-scale regimes in which the processes are observed in the two cases. 

When q Rg > 1, concentration fluctuations within single macromolecules dominate the correlation tunction. The calculation ot the light-scattering correlation tunction S q,x) tor a single macromolecule in solution is described in detail in Berne and Pecora. The chain is modeled as shown in Equation 5.10. Intramolecular concentration fluctuations resolve into a set ot modes with characteristic relaxation times that depend on the subchain friction coefficient, the overall radius ot gyration, and the temperature. The correlation txmction can be expressed as ... 

The transverse relaxation time strongly depends on temperature (cf Fig. 37a), so that the temperature can be mapped by parameter imaging of T2. Axial parameter projections have been acquired in dynamic equilibrium at a shear rate of 10 Hz and for carbon-black contents ranging from 10 to 70 phr. Onedimensional cross sections through those projections are depicted in Figure 37b. An increase of the temperature in the center of the sample is observed with increasing carbon-black contents which scales with the increasing loss modulus of... 

Summary. Both temperature and scan frequency affect the patterns created by movement of a nanoscopic tip in contact with a polymer surface. At experimental time scales which are faster than the relaxation time associated with the elongation of a polymer coil, the polymer s response to the tip-induced shearing forces is elastic. Experimental time scales slower than the characteristic relaxation time results in alignment of the polymer with the tip trajectory and net translational movement of polymer towards the center of the scan area. The time-temperature dependence of the patterns are well-described by the WLF equation which is typically used to describe viscoelastic behavior. Analysis of our data further suggests that the Tg of the polymer is elevated in the region confined between the tip and the substrate. 

An alternative physical probe of solvent motion is oscillatory electrical birefringence (OEB), as applied to Aroclor 1248 solutions of polystyrene and polybutadiene by Morris, et a/. (43). In these systems, OEB gives a solvent relaxation time that depends on temperature and polymer concentration. Measurements of r at the... 

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