Relaxation times for various

Thermal Conductivity and Relaxation Times for Various Densities" at Zb = 2... 

Table 2. Relaxation times for various processes in the low pressure plasma ...

Figure 5.14 Calculated ratio of the relaxation time for various counter ions to that of proton (H ) Tretax/Tretax,ht (Reprinted with permission from Yamaue, T., Mukai, H., Asaka, K. andDoi, M., Electrostress Diffusion Coupling Model for Polyelectrolyte Gels, Macromolecules, 38 (4), 1349-56. Copyright (2005) American Chemical Society).

TABLE II Proton Relaxation Times for Various Substances... 

We measured the temperature-dependance of the spin-lattice relaxation time, for various alumino-silicate aerogels, corresponding porous glasses and crystalline counterparts. The purpose of these experiments is threefold (i) to compare the relaxation response of these very porous amorphous materials to the general one of more classical glasses, (ii) to see whether fractons, whose vibrationnal amplitudes are large, contribute to relaxation mechanisms, (iii) to follow - through variations of the density - the dependance of this dynamical property on the structural parameters, (iv) to test the theoretical predictions about relaxation in disordered systems proposed by R. Orbach and S. Alexander. 

This approach has been applied extensively in recent years to polymers [16,27-31]. From comparisons of segmental relaxation times for various polymers made on the basis of 7g-scaled Arrhenius plots, correlations between the shape of the relaxation function and chemical structure have been demonstrated [3,16,32,33]. Fragility plots are also useful in interpreting the relaxation behavior of polymer blends, since the relaxation function itself is complicated due to inhomogeneous broadening [34-37]. 

From the various autocorrelation times which characterized macromolecular fluctuations, those associated with the fluctuation of the electrostatic field from the protein on its reacting fragments are probably the most important (see Ref. 8). These autocorrelation times define the dielectric relaxation times for different protein sites and can be used to estimate dynamical effects on biological reactions (see Chapter 9 for more details). 

If we assume that the same discrepancy between theory and experiment in M-M enters in M +-M, we can estimate the vibrational relaxation times for the molecular ions. Table II shows the estimated vibrational relaxation times r+ at various temperatures. The values are shorter than those for the neutrals by factors given in Figure 4. 

A fully realistic picture of solvation would recognize that there is a distribution of solvent relaxation times (for several reasons, in particular because a second dispersion is often observable in the macroscopic dielectric loss spectra [353-355], because the friction constant for various types or modes of solute motion may be quite different, and because there is a fast electronic component to the solvent response along with the slower components due to vibration and reorientation of solvent molecules) and a distribution of solute electronic relaxation times (in the orbital picture, we recognize different lowest excitation energies for different orbitals). Nevertheless we can elucidate the essential physical issues by considering the three time scales Xp, xs, and Xelec-... 

Since l is proportional to and q is proportional to 1/L, i is proportional to. Substitution of Eq. (67) into Eq.(62) gives the Langevin equation for the Rouse modes of the chain within the approximations of preaveraging for hydrodynamic interactions and mode-mode decoupling for intersegment potential interactions. Equation (62) yields the following results for relaxation times and various dynamical correlation functions. 

A NMR study of water adsorbed on silica gel has been made by Zimmerman el al. 18). Transverse (Ta) and longitudinal (Ti) relaxation times of various amounts of water adsorbed at 25° have been obtained with the use of the spin-echo technique and a two-phase behavior of both Ta and T relaxation times has been observed as illustrated in Figs. 10a and b. Generally only one T value is obtained, as for a single phase, except for x/m g HaO/g solid) values in the vicinity ol x/m = 0.126. Two values of Ta... 

Under equilibrium conditions in a stressed b.c.c. Fe crystal, interstitial C atoms are generally unequally distributed among the three types of sites identified in Fig. 8.86. This occurs because the C atoms in sites 1, 2, and 3 in Fig. 8.86 expand the crystal preferentially along the x, y, and 2 directions, respectively. These directions are oriented differently in the stress field, and the C atoms in the various types of sites therefore have different interaction energies with the stress field. In the absence of applied stress, this effect does not exist and all sites are populated equally. In Exercise 8.22 it was shown that when the stress on an equilibrated specimen is suddenly released, the relaxation time for the nonuniformly distributed C atoms to achieve a random distribution, t, is t = 2/(3r), where T is the total jump frequency of a C atom in the unstressed crystal. 

We are in the process of examining time dependent properties such as the diffusion coefficient and the relaxation times of various correlation functions as a function of both chain length and density. Following the work of Kirkwood (24) and Rouse (24) we assume that the velocity of the polymer is proportional to the forces acting on it at any time this is the high-viscosity limit in which inertial terms are neglected. Neglecting also hydrodynamic forces, we then have for the velocity of the jth bead at time t... 

UC NMR Spin-Lattice Relaxation Times for Starch of Various Origins81... 

B. One is slip lnd the other is stick. In ethanol, the rotational relaxation time was to be shorter than those estimated for aprotic solvents with a similar viscosity. The viscosity dependence of the rotational relaxation time in various solvents will be discussed. 

Figure 3.30 (a) The nonlinear shear relaxation modulus G (r, y)// as a function of time for various... 

Table 2. Relaxation times for conjugated polystyrene with various luminescent markers in toluene at 25 °C and values of — and (Symbols for types of LM as in Table 1) 6 0... 

Fig. 9. Relaxation times for solutions of poIy(methyl methacrylate) (PMM) (LMs marker) of various molecular weights in toluene-octane mixtures as a function of the octane content at 25 °C, rjred 0.38 cP. M 1 6.6 x 10 , 2 3 x 10 , 3 6 x 10 the polymer concentration in solution is 0.003%...

Fig. 10. Relaxation times characterizing the IMM of POiMAA-l 1 (1), PCMAA-11 (5), copolymers P(ChMAA-lI-MA-4) containing 10(2), 25(3) and 60(4) mol%of MA-4-butyl methacrylate units in aliphatic hyrocarbons as a function of temperature. The LMi marker is the 9-anthryl methyloxycarbonyl group (one group per 300-600 monomer units) (al is the specific optical rotation for (1) in heptane. Values of relaxation times at various temperatures are reduced to one solvent viscosity 0.38 cP...

TaUe 17. Relaxation times for PMMA with covalent luminescent junctkms in various solvents at 25 °C (%ej = 0.38 cP) M = molecular weight of the linear fragment... 

Table 19. Relaxation times for PAA and PMAA in polymer complexes with insulin formed at various pH and for uncomplexed PMAA and PAA molecules in an ammonium buffer a is the degree of ionization 0.1% PMAA, pH = 9.1, 25 °C...

The dynamic characteristics of adsorbed molecules can be determined in terms of temperature dependences of relaxation times [14-16] and by measurements of self-diffusion coefficients applying the pulsed-gradient spin-echo method [ 17-20]. Both methods enable one to estimate the mobility of molecules in adsorbent pores and the rotational mobility of separate molecular groups. The methods are based on the fact that the nuclear spin relaxation time of a molecule depends on the feasibility for adsorbed molecules to move in adsorbent pores. The lower the molecule s mobility, the more effective is the interaction between nuclear magnetic dipoles of adsorbed molecules and the shorter is the nuclear spin relaxation time. The results of measuring relaxation times at various temperatures may form the basis for calculations of activation characteristics of molecular motions of adsorbed molecules in an adsorption layer. These characteristics are of utmost importance for application of adsorbents as catalyst carriers. They determine the diffusion of reagent molecules towards the active sites of a catalyst and the rate of removal of reaction products. Sometimes the data on the temperature dependence of a diffusion coefficient allow one to ascertain subtle mechanisms of filling of micropores in activated carbons [17]. 

Fig. 21. Stress relaxation curves (solid lines) and spectrum of relaxation times for phosphate sample in terminal region at various temperatures...

Figure 13. Dielectric loss data at various combinations of temperature and pressure as indicated to demonstrate the invariance of the dispersion of the a-relaxation at constant a-loss peak frequency va or equivalently at constant a-relaxation time for (a) poly(vinylacetate) (PVAc), (b) poly(methyltolylsiloxane) (PMTS), and (c) polyfphenyl glycidyl ether)-co-formaldehyde (PPGE) d)poly(oxy butylene) (POB). In all cases, spectra obtained at higher P are normalized to the value of the maximum of the loss peak obtained at the same frequency at atmospheric pressure.

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