Relaxation time ratio

Figure 13 plots the relaxation times ratio x, / x j and the amplitude A corresponding to the macroscopic relaxation time of the decay function determined by (25). Near the percolation threshold, x, /xi exhibits a maximum and exhibits the well-known critical slowing down effect [152], The description of the mechanism of the cooperative relaxation in the percolation region will be presented in Section V.B. 

Fig. 1. (a) Variations with temperature (relative to fusion temperature, 7)) of the relaxation times within the amorphous phase, T , and out of the amorphous phase into the crystalline phase (nucleation time), t ,. (h) Variations with temperature of the relaxation time ratio... 

Fig. 2. Conjectured relation between the relaxation time ratio and temper-...

The fact that these two relaxation-time ratios are a universal function of M/Mg indicates that the universality of the G t) line shape extends to the PA t) process region, pxit) is situated between pA t) and the processes PB t) and pc t)- Thus, although we do not have the theoretical form for Px t), its characteristic time tx normalized with respect to should also be a function of the normalized molecular weight M/Mg- From the G t) line shape analysis in terms of Eq. (9.19) as discussed in detail in Chapter 10, it has been found that tx is best described by... 

If the frictional factor if in a blend solution were the same as that in its pure component-two melt, the terminal-relaxation-time ratio of the two systems could be obtained from Eq. (9.12) as... 

The melt elasticity ratio is said to be important for the texture of the mixture and the shape of the immiscible domains. Furthermore, it is to be noted that the relaxation is time-dependent. A stable deformed droplet can only be obtained if the ratio of the characteristic relaxation time ratio of the dispersed and continuous phase is larger than one ... 

The low-frequency limiting viscoelastic behavior is thus governed by the sums S1 and 82- Values of these, together with 1S2/5 and the first two relaxation time ratios, are given in Table 9-II for several choices of h and other parameters. The greatest differences are seen in the ratio 82/8 to which the steady-state compliance Je is proportional. The table also includes some data for branched polymers which will be discussed in Section 8. 

Fig. 13. Longest and segmental relaxation time ratio as a function of the molecular weight at 250 K. The vertical axis is scaled by to emphasize the transition from the Rouse to the intermediate regime. The solid line corresponds to the description of the data with a sharp crossover between two power law regimes with different exponents. Reprinted with permsision from Riedel et al, Rheologica Acta 49,507-512 Copyright 2010 Springer...

A parameter indicating whether viscoelastic effects are important is the Deborah number, which is the ratio of the characteristic relaxation time of the fluid to the characteristic time scale of the flow. For small Deborah numbers, the relaxation is fast compared to the characteristic time of the flow, and the fluid behavior is purely viscous. For veiy large Deborah numbers, the behavior closely resembles that of an elastic solid. 

The number of bonded H atoms if all parts within a molecule move at the same rate (the same Tc for all C atoms), the relaxation times Tj decrease from C//via C// to C//j in the ratio given by ... 

The rheological parameter variations with blend compositions are shown in Figs. 4,5 and 6. The variation of relaxation time (Fig. 4) seems to show an increasing pattern up to 40% of NBR, then there is a sharp decrease until 60% of NBR, and finally there is a further increase of relaxation time in the preblends. Preheating of blends, however, results in a longer relaxation time than in the preblends and a maximum at 50 50 ratio at all shear rates. 

Shear modulus also changes with the blending ratio (Fig. 5), such as the relaxation time. Preblends show an... 

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. 

A representative measure of rubbery elasticity of a material may be two quantities dimensionless ratio (ct/t) and characteristic relaxation time 9 = ct/2ty. According to the data of works [37, 38] when fibers are introduced into a melt, ct/t increases (i.e. normal stresses grow faster than stresses) and 0 also increases on a large scale, by 102-103 times. However, discussing in this relation the papers published earlier, we noted in the paper cited that the data were published according to which if fibers were used as a filler (as in work [37]), 9 indeed increased [39], but if a filler represented disperse particles of the type Ti02 or CaC03, the value of 0 decreased [40],... 

This ratio of orientational relaxation times is sometimes used to identify the situation corresponding to perturbation theory [85]. 

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