Relaxation times energy ratio

Associated with couplings is a spectrum of intrinsic characteristic times, Xi, and extrinsic characteristic times, Xe, also called the operational "drive time. With intrinsic characteristic times, it is referred to structural relaxation, energy distribution and dissipation times, and with extrinsic characteristic times it is pointed to operational dependent times that are connected to the rate of the applied external forces. The relationship between the two relaxation times (the ratio is called the... 

Earlier studies [14,15] clearly reveal that there is a reaction between two polymers and that the extent of reaction depends on the blend ratio. As 50 50 ratio has been found to the optimum (from rheological and infrared studies) ratio for interchain crosslinking, the higher heat of reaction for the NBR-rich blend may be attributed to the cyclization of NBR at higher temperatures. There is an inflection point at 50 50 ratio where maximum interchain crosslinking is expected. Higher viscosity, relaxation time, and stored elastic energy are observed in the preheated blends. A maximum 50-60% of Hypalon in NBR is supposed to be an optimum ratio so far as processibility is concerned. 

Rheological parameters, such as relaxation time, shear modulus, and stored elastic energy, are determined from the extrudate swell and stress-strain data as previously described. Representative examples of the variation of these parameters with blend ratios for both blends are shown in Figs. 16-18. Figure 16 shows that relaxation time for both preblends without heating and... 

The plot of the rheological parameters (relaxation time, shear modulus, and stored elastic energy) are shown in Figs. 22-24. The relaxation time increases as the ACM content is increased to attain a maximum at 60 40 = ACM XNBR blend ratio for the preblends. For lower shear rate the rise is sharp and after 60 40 blend ratio, // remains almost constant, whereas for the higher shear rate region the rise is not sharp and after 60 40 blend ratio ty decreases as ACM percent increased in the blend. In the case of the preheated blends the /y increases up to 50 50 blend ratio and then decreases with the addition of ACM in the blend. The preheating increases the ty in both shear rate regions. 

The plot of the rheological parameters (relaxation time, /r shear modulus, G and stored elastic energy, W ) are given in Figs. 28-30. The relaxation time of both preblends and preheated blends remains almost constant up to 50 50 blend ratio and then shoots up drastically at both shear rates. Up to 50 50 blend ratio it is observed that the relaxation time is more at lower shear rate. Preheating of blends lowers the values. 

Carlo-simulations for LI2 superlattice including saddle-point energies for atomic jumps in fact yielded two-process kinetics with the ratio of the two relaxation times being correlated with the difference between the activation barriers of the two sorts of atom. 

In Eqs. (4)-(7) S is the electron spin quantum number, jh the proton nuclear magnetogyric ratio, g and p the electronic g factor and Bohr magneton, respectively. r//is the distance between the metal ion and the protons of the coordinated water molecules, (Oh and cos the proton and electron Larmor frequencies, respectively, and Xr is the reorientational correlation time. The longitudinal and transverse electron spin relaxation times, Tig and T2g, are frequency dependent according to Eqs. (6) and (7), and characterized by the correlation time of the modulation of the zero-field splitting (x ) and the mean-square zero-field-splitting energy (A. The limits and the approximations inherent to the equations above are discussed in detail in the previous two chapters. 

Work in groups of three. The shift factor, or, in the WLF Equation [Eq. (5.76)], is actually a ratio of stress relaxation times, f , in the polymer at an elevated temperature, T, relative to some reference temperature. To, and can be related via an Arrhenius-type expression to the activation energy for relaxation, Erei as... 

As described in the section on nonlinear absorption, the transmission of a pulse which is short compared to the various molecular relaxation times is determined by its energy content. A measurement of the energy transmission ratio will then give the peak intensity of the pulse when its pulse shape is known 44>. In fact, the temporal and spatial pulse shape is of relatively little importance. Fig. 11 gives the energy transmission as a function of the peak intensity I [W/cm2] for the saturable dye Kodak 9860 with the pulse halfwidth as a parameter. It is seen that this method is useful in the intensity region between 10 and 1010 MW/cm2 for pulses with halfwidths greater than 5 to 10 psec. Since one can easily manipulate the cross-section and hence the intensity of a laser beam with a telescope, this method is almost universally applicable. 

Sect. 6 a Aa T Do Fsh T X A M R De final radius of cylindrical gel after swelling displacement relaxation time for swelling collective diffusion constant shear energy trace of the strain tensor u,k swelling rate ratio total change of the radius of the gel longitudinal modulus ratio of the shear modulus to the longitudinal modulus effective collective diffusion constant... 

The Mossbauer spectra do, however, indicate that the anisotropy energy barrier for the particle magnetization flipping is quite large, 10-20 J (215), for the 1.5-nm iron particles. As discussed in Section III, A, 3, this barrier was estimated from Mossbauer spectra at various temperatures by measuring the fraction of the spectral area that appears paramagnetic. At the temperature for which this ratio is 0.5, the relaxation time can be estimated... 

Figure 1.3 Dielectric spectra for range of alcohols in the frequency range of 107-10n Hz. The absolute permittivities at low frequencies fall as the size of the alcohol increases and they began to respond to the microwave fields at lower frequencies because their relaxation times become longer. The loss factors that control the efficiency of conversion of microwave into thermal energies also reach their maxima at lower frequencies. The loss tangent is the ratio of the loss factor and permittivity at that frequency. (Idealised from the raw data illustrated in Ref. 10.)...

The absorption of ultrasonic energy is also influenced by relaxation effects. At the frequencies of near 100 MHz that are employed, the relaxation times are of the order of ns, rather than the ps for dielectric relaxation. The relevant quantity is the absorption coefficient, a, divided by the square of the frequency, f2. Values of a//2 in 10-15 s2 nr1 have been measured for many solvents near 25 °C at the frequency of 104 to 107 MHz (Heasall and Lamb 1956 Krebs and Lamb 1958) and are shown in Table 3.10, being considered accurate within 2%. For a few solvents the ratio a//2 depends strongly on the frequency as it decreases somewhat for all solvents, e g., for carbon disulfide a//2/ (10-15 s2 nr1) = 2068 at 104 MHz and 776 at 189 MHz and for dichloromethane it decreases from 779 at 107 MHz to 550 at 193 MHz... 

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