Relaxation time parameter

Polymer chain dynamics in the solid state Several relaxation time parameters can be distinguished in solid state NMR. For the study of polymer dynamics T2, Tlp and TCP are mostly used. 

The identification of material heterogeneities based on differences in molecular motion is an important feature of NMR imaging. The importance of slow molecular motion for image contrast is demonstrated in Figure 31 with relaxation time parameter images through a partially aged sheet of carbon-black-filled styrene-co-butadiene rubber (SBR) (147). 

Loss pe of some secondary processes can obscure with the stronger inter-component H-bonding in blend Physical meaning of relaxation times parameters obtained by fitting DRS data by existing molecular mobility models still unclear... 

Plate 7.5 Response spectra for floor 1 and 2 for different relaxation time parameter values containment 1, vessel 2, building... 

Depending on the resolution of the numerical grid, the relaxation time parameter can limit the maximum Reynolds number. A more detailed description of the basic principles of Ihe LBM can be found in previous publications [11-13, 21] as well as in Crouse [8], which also gives details on the implemented tree data structure. 

Values of the dipole moments and relaxation time parameters of trifluoromethylsulphur pentafluoride (and of sulphur chloride pentafluoride) have been obtained through a study of dielectric relaxation spectra the n.m.r. spectra of a number of pol)d1uoroalkylsulphur pentafluorides have been... 

Pulsed ENDOR offers several distinct advantages over conventional CW ENDOR spectroscopy. Since there is no MW power during the observation of the ESE, klystron noise is largely eliminated. Furthemiore, there is an additional advantage in that, unlike the case in conventional CW ENDOR spectroscopy, the detection of ENDOR spin echoes does not depend on a critical balance of the RE and MW powers and the various relaxation times. Consequently, the temperature is not such a critical parameter in pulsed ENDOR spectroscopy. Additionally the pulsed teclmique pemiits a study of transient radicals. 

Stress relaxation time, obtained from rheograms based on viscometric flows, is used to define a dimensionless parameter called the Deborah number , which quantifies the elastic character of a fluid... 

Of the adjustable parameters in the Eyring viscosity equation, kj is the most important. In Sec. 2.4 we discussed the desirability of having some sort of natural rate compared to which rates of shear could be described as large or small. This natural standard is provided by kj. The parameter kj entered our theory as the factor which described the frequency with which molecules passed from one equilibrium position to another in a flowing liquid. At this point we will find it more convenient to talk in terms of the period of this vibration rather than its frequency. We shall use r to symbolize this period and define it as the reciprocal of kj. In addition, we shall refer to this characteristic period as the relaxation time for the polymer. As its name implies, r measures the time over which the system relieves the applied stress by the relative slippage of the molecules past one another. In summary. 

Of the various parameters introduced in the Eyring theory, only r—or j3, which is directly proportional to it-will be further considered. We shall see that the concept of relaxation time plays a central role in discussing all the deformation properties of bulk polymers and thus warrants further examination, even though we have introduced this quantity through a specific model. 

Direct determination of relaxation time through viscoelastic studies (all mechanical properties involve this important parameter). 

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. 

Various theoretical and empirical models have been derived expressing either charge density or charging current in terms of flow characteristics such as pipe diameter d (m) and flow velocity v (m/s). Liquid dielectric and physical properties appear in more complex models. The application of theoretical models is often limited by the nonavailability or inaccuracy of parameters needed to solve the equations. Empirical models are adequate in most cases. For turbulent flow of nonconductive liquid through a given pipe under conditions where the residence time is long compared with the relaxation time, it is found that the volumetric charge density Qy attains a steady-state value which is directly proportional to flow velocity... 

FIG. 28 Log-normal plot of relaxation time t2 vs bias for three different chain lengths (given as a parameter) and a series of medium densities [21]. 

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. 

The rheological parameters with blend compositions are shown in Figs. 10-12. The relaxation time increases with the increase in NBR content up to a 50% level for both the preblends and preheated blends. Comparing the preblends and preheated blends, we see that... 

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. 

Plotting U as a function of L (or equivalently, to the end-to-end distance r of the modeled coil) permits us to predict the coil stretching behavior at different values of the parameter et, where t is the relaxation time of the dumbbell (Fig. 10). When et < 0.15, the only minimum in the potential curve is at r = 0 and all the dumbbell configurations are in the coil state. As et increases (to 0.20 in the Fig. 10), a second minimum appears which corresponds to a stretched state. Since the potential barrier (AU) between the two minima can be large compared to kBT, coiled molecules require a very long time, to the order of t exp (AU/kBT), to diffuse by Brownian motion over the barrier to the stretched state at any stage, there will be a distribution of long-lived metastable states with different chain conformations. With further increases in et, the second minimum deepens. The barrier decreases then disappears at et = 0.5. At this critical strain rate denoted by ecs, the transition from the coiled to the stretched state should occur instantaneously. 

In these circumstances the relaxation follows first-order kinetics, and a rate constant k = k a = k] + 4k i [P]e characterizes the system. A plot of k versus [P]t provides k] and k from the intercept and slope. The time parameter value called the relaxation time is given by r = l/k. 

Fig. 2. The pulse sequence for the CP/MAS experiment. The values of the different time parameters depend on the relaxation behaviours and on the mobilities of the nuclei in the compounds investigated. (Reproduced with permission of Ref. I0))...

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