Temperature dependence, of correlation

Fig. 8.3. (a) Temperature dependence of correlation lengths of 5 degrees of freedom of the nematic order in the isotropic and nematic phase. Continuations of the lines across the dotted vertical correspond to the correlation lengths in the appropriate metastable phase. Correlation lengths determine the relaxation rates of fluctuations as Pi = 1/Tj oc -t- where q is the corresponding wavevector. (b) Sketch of a typical relaxation spectra for a system with a Goldstone and soft mode, respectively. 

The temperature dependence of correlation times for Icx l motion in POE is displayed in Fig. 12. Points represent the experimental tesults by Lang et al. [101]. The solid line is obtained by the DRIS a -oach, using the same model and parameters as above. It is noted that perturbations arising from the temperature dependence of the viscosity are eliminated in this representation, inasmuch as the correlation times are normalized with respect to the solvent viscosity which is itself temperature dependent. The slope of the theoretical line... 

Fig. 12. Comparison of theory and ESR experiments for temperature dependence of correlation times associated with local motions of POE. An Arrhenius type temperature dependence with activation energy equal to 7.5 kj/mol is obtained...

FIGURE 4.21 The temperature dependences of correlation J (1), informational (2) and Hausdorff d (3) dimensions of PC multifractal structure [73]. 

A typical temperature dependence of is shown in fig. 53. Clough et al. [1981] have found a universal correlation between the temperature at which has a minimum, r in, and A, when the measurements are performed at the same Zeeman frequency. This correlation, demonstrated in fig. 54, holds for all molecular solids studied so far, with A covering a range of four orders... 

Recently, Okahara and his co-workers have investigated a variety of one-pot crown ether syntheses which are referred to in Sects. 3.4, 4.3, 5.4. During the course of these investigations, they examined the temperature dependence of the cyclization yield . Using either sodium hydroxide or potassium hydroxide and forming 15-crown-5, 18-crown-6 and 21-crown-7, an attempt was made to correlate yield and reaction temperature. For most of the reactions, yield was recorded over the range from 20 ° — 120 °C... 

In addition to the temperature dependence of Sq T) is that of the correlation functions, which also determine the coverage dependence. 

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 dependence of birefringence on the temperature seems to be correlated to the temperature dependence of the lattice parameters ratio c/a shown in Fig. 102. 

Equilibrium vapor pressures were measured in this study by means of a mass spectrometer/target collection apparatus. Analysis of the temperature dependence of the pressure of each intermetallic yielded heats and entropies of sublimation. Combination of these measured values with corresponding parameters for sublimation of elemental Pu enabled calculation of thermodynamic properties of formation of each condensed phase. Previ ly reported results on the subornation of the PuRu phase and the Pu-Pt and Pu-Ru systems are correlated with current research on the PuOs and Pulr compounds. Thermodynamic properties determined for these Pu-intermetallics are compared to analogous parameters of other actinide compounds in order to establish bonding trends and to test theoretical predictions. 

In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

Simulation programs for the ESR line shapes of peroxy radicals for specific models of dynamics have been developed for the study of oxidative degradation of polymers due to ionizing radiation [66]. The motional mechanism of the peroxy radicals, ROO, was deduced by simulation of the temperature dependence of the spectra, and a correlation between dynamics and reactivity has been established. In general, peroxy radicals at the chain ends are less stable and more reactive. This approach has been extended to protiated polymers, for instance polyethylene and polypropylene (PP) [67],... 

On the other hand, the low-conductance values (L) give a poor linear correlation of the molecular length with an approximate decay constant fiN 0.45 0.09, distinctively different from the H and M sequences. The estimated value of fiN(L) is rather close to results reported by Cui [28] and Haiss [243]. Haiss et al. [244] found a pronounced temperature dependence of these L values, which scales logarithmically with 7 1 in the temperature range 293-353 K, indicating a transport mechanism different from a simple tunneling model. 

We will first describe the results obtained for n-type GaAs doped with silicon and then those on p-type GaAs and InP, trying to show how the spectroscopic results correlate with the electrical measurements to provide a consistent picture of the neutralization of dopants by hydrogen in III-V semiconductors. After considerations on the temperature dependence of the widths and positions of the H-related lines, we will discuss the occurrence and origin of other vibration lines associated also with hydrogen in as grown bulk and epitaxial III-V compounds. 

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