Relaxation temperatures, dependence

Resin system Type of relaxation Temperature dependence of dielectric relaxation time References... 

D.E. Woessner B.S. Snowden, Jr. (1967). J. Chem. Phys., 47, 378-381. Proton spin-lattice relaxation temperature dependence in ammonium bromide. 

Figure 6.5. Schematic of an Arrhenius plot for mechanisms commonly observed in polymers. The lines correspond to Arrhenius [Eq. (6.8) for y, p, and Maxwell-Wagner-Sillars (MWS) relaxations] and Vogel-Tammann-Fulcher-Hesse [VTFH Eq. (6.10)], for a and normal-mode (n-) relaxation] temperature dependences for the relaxation time t(T). Relaxations ascribed to small, highly mobile, dipolar units appear in the upper right side of the plot, while those originating from bulky dipolar segments, slowly moving ions, and MWS mechanisms are located in the lower-left part of the plot.

For constant temperature dynamics where the constant temperature check box in the Molecular Dynamics Options dialog box is checked, the energy will not remain constant but will fluctuate as energy is exchanged with the bath. The temperature, depending on the value set for the relaxation constant, will approach con-stan cy. 

The occurrence of nonradiative losses is classically illustrated in Figure 3. At sufficiently high temperature the emitting state relaxes to the ground state by the crossover at B of the two curves. In fact, for many broad-band emitting phosphors the temperature dependence of the nonradiative decay rate P is given bv equation 1 ... 

If the amount of the sample is sufficient, then the carbon skeleton is best traced out from the two-dimensional INADEQUATE experiment. If the absolute configuration of particular C atoms is needed, the empirical applications of diastereotopism and chiral shift reagents are useful (Section 2.4). Anisotropic and ring current effects supply information about conformation and aromaticity (Section 2.5), and pH effects can indicate the site of protonation (problem 24). Temperature-dependent NMR spectra and C spin-lattice relaxation times (Section 2.6) provide insight into molecular dynamics (problems 13 and 14). 

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. 

Shown in Fig. 4a is the temperature dependence of the relaxation time obtained from the isothermal electrical resistivity measurement for Ni Pt performed by Dahmani et al [31. A prominent feature is the appearance of slowing down phenomenon near transition temperature. As is shown in Fig. 4b [32], our PPM calculation is able to reproduce similar phenomenon, although the present study is attempted to LIq ordered phase for which the transition temperature, T]., is 1.89. One can confirm that the relaxation time, r, increases as approaching to l/T). 0.52. This has been explained as the insufficiency of the thermodynamic driving force near the transition temperature in the following manner. 

Figure 5. Temperature dependence of percentage relaxation of Au adatom on the low-index faces of Cu with respect to the bulk interlayer spacing.

We have studied the vibrational properties of Au adatoms on the low-index faces of copper. From the position of new phonon modes, which are due to the presence of the adatom, it comes out that the gold adatom is weakly coupled with the atoms of Cu(l 11) for the directions parallel to the surface and tightly bound with those of Cu(lOO). These modes are found in lower frequencies than those of the Cu adatom. The temperature dependence of MSD s and relaxed positions of the Au adatom along the normal to the surface direction, reveal that this atom is more tightly bound with the (111) face and less with the (110) face. 

In molecular doped polymers the variance of the disorder potential that follows from a plot of In p versus T 2 is typically 0.1 eV, comprising contributions from the interaction of a charge carrier with induced as well as with permanent dipoles [64-66]. In molecules that suffer a major structural relaxation after removal or addition of an electron, the polaron contribution to the activation energy has to be taken into account in addition to the (temperature-dependent) disorder effect. In the weak-field limit it gives rise to an extra Boltzmann factor in the expression for p(T). More generally, Marcus-type rates may have to be invoked for the elementary jump process [67]. 

The WLF approach is a general extension of the VTF treatment to characterize relaxation processes in amorphous systems. Any temperature-dependent mechanical relaxation process, R, can be expressed in terms of a universal scaling law ... 

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. 

Fig. 1.17. The temperature-dependence of angular momentum relaxation time (+) in nitrogen [71] and accompanying density change due to cooling (0).

Fig. 1.25. Temperature-dependence of rotational relaxation cross-section from [81], For the lowest temperature point the experimental uncertainty is indicated, the latter being the biggest one over the whole set of measurements.

The important fact is that the number of collisions Zr increases with temperature. It may be attributed to the effect of attraction forces. They accelerate the molecule motion along the classical trajectories favouring more effective R-T relaxation. This effect becomes relatively weaker with increase of temperature. As a result the effective cross-section decreases monotonically [199], as was predicted for the quantum J-diffusion model in [186] (solid line) but by classical trajectory calculations (dotted and broken lines) as well. At temperatures above 300 K both theoretical approaches are in satisfactory mutual agreement whereas some other approaches used in [224, 225] as well as SCS with attraction forces neglected [191] were shown to have the opposite temperature dependence for Zr [191]. Thus SCS results with a... 

Winter T. G., Hill G. L., Raff L. M. The temperature dependence of the rotational relaxation time in gases, 6th Intern. Congr. on Acoustics (Tokyo), J-4-2 (1968). 

Strekalov M. L., Burshtein A. I. Temperature dependence of dephasing relaxation in dense media, Chem. Phys. Lett. 86, 295-8 (1982). 

An extensive study by Blackman (3) and a recent study by Millikan and White (21) on the vibrational relaxation of 02 are shown in Figure 2. The impurity of Blackman s sample varied from 1-5%, but the bulk impurity was nitrogen. Blackman s data at lower temperatures are significantly different from Millikan and White s values. The latters data have the same temperature dependence as Equation 5 over the... 

The accessibility of chitin, mono-O-acetylchitin, and di-O-acetylchitin to lysozyme, as determined by the weight loss as a function of time, has been found to increase in the order chitin < mono-O-acetylchitin < di-O-acetylchitin [120]. The molecular motion and dielectric relaxation behavior of chitin and 0-acetyl-, 0-butyryl-, 0-hexanoyl and 0-decanoylchitin have been studied [121,122]. Chitin and 0-acetylchitin showed only one peak in the plot of the temperature dependence of the loss permittivity, whereas those derivatives having longer 0-acyl groups showed two peaks. 

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