Temperature dependence, of correlation times

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...

A molecular transition model involving the -relaxation in PMMA has been first put forward by Johnson and Radon They explained the transition in crack speed behavior based on a correlation between the temperature dependence of a time to failure inferred from fracture experiments and the temperature variation of the reciprocal frequency of the P-relaxation peak. They thus assumed that the crack transition is caused when the P-process is fully active. Also the fracture mechanics parameter K, governing the transition from slow to fast crack growth, shows a time and temperature dependence equal to that of the p-transition... 

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. 

TEMPERATURE DEPENDENCE OF WATER AND SUCROSE CORRELATION TIMES IN A 90.1% (WAV) SUCROSE-WATER SYSTEM (Te = 261.5 K)... 

Figure 18 Temperature dependence of the C-H vector (selected, filled symbols) and torsional correlation (open symbols) times for PB from simulation. Also shown is the mean waiting time between transitions for the cis-allyl, trans-allyl, and (3 torsions in PB. The solid lines are VF fits, whereas the dashed lines assume an Arrhenius temperature dependence.

In the discussion on the dynamics in the bead-spring model, we have observed that the position of the amorphous halo marks the relevant local length scale in the melt structure, and it is also central to the MCT treatment of the dynamics. The structural relaxation time in the super-cooled melt is best defined as the time it takes density correlations of this wave number (i.e., the coherent intermediate scattering function) to decay. In simulations one typically uses the time it takes S(q, t) to decay to a value of 0.3 (or 0.1 for larger (/-values). The temperature dependence of this relaxation time scale, which is shown in Figure 20, provides us with a first assessment of the glass transition... 

The increase of the lateral diffusion rate with increasing temperature was used to estimate the activation energy for diffusion in the LC and GI phases. The temperature dependence of the correlation-time for molecular diffusion, Xd, can be formulated in terms of the activation energy E ) for the motion affecting Xd in an Arrhenius expression (t > = exp( a/R7 ))- Since D = a ldx ... 

Fig. 4.36 Scaling representation of NSE data (density correlation function) corresponding to PI at Q=1.92 A [second maximum of S(Q)]. Times have been divided by the KWW time Tpair to obtain a master curve. T=230 (cross), 240 (empty circle), 250 (plus), 264 (empty square), 280 (empty triangle), 320 K (empty diamond). The solid line indicates the fit with the KWW law for 250 K

We analyzed the temperature dependence of 1/Ti using the semi-classical BPP model for the effect of molecular motion on 1/Ti [32]. In this model, 1/Ti can be related to the values of correlation time, Tc, which is the characteristic time between significant fluctuations in the local magnetic field experienced by a spin due to moleciflar motions or reorientations of a molecule. As usual, it is assumed that Tc follows Arrhenius-hke behavior ... 

For the complete expressions for T] and T2 the reader is referred to the original literature (5). Let it suffice here to note that the temperature dependent term resides in the correlation times rc (dipolar interaction) and t6 (exchange interaction). The temperature dependences of the individual correlation times are ... 

Substitution of Eqs. (39) into Eq. (40) gives the temperature dependence of the net correlation time... 

Figure 6. Temperature dependence of the average correlation time of water in the water-NaLS system.

The first observation of Zn NMR in zinc metal was by Abart and coworkers in a measurement at 4.2 K, using a field sweeping technique, which yielded a value of = 12 73(4) MHz. No subsequent NMR observation has been reported. A measure of the temperature dependence of the Zn nuclear quadrupole coupling in zinc metal has been obtained from time differential perturbed angular correlation (TDPAC) measurements using an excited state of Zn (/ = 9/2 605 keV). However, the use of liquid helium temperatures and exotic short-lived isotopes precludes the adoption of these techniques for general material characterization. 

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