A-relaxation curve

Figure 46. Separation of the overall oxidation curve into its two components a relaxation curve, responsible for the initial slope and the position of the chronoamperometric maximum, and a diffusion curve that controls the overall shape of the chronoampero-gram. (Reprinted from T. F. Otero, H.-J. Grande, and J. Rodriguez, J. Phys. Chem. 101, 3688, 1997, Figs. 1, 3, 6, 7, 13. Copyright 1997. Reprinted with permission from the American Chemical Society.)...

For partially miscible and immiscible blends, various domain/phase structures can be invoked. Unfortunately, the resonance position of a particular spin in each domain is not appreciably affected by its respective domain structure (see Section 10.2.2.1). Therefore, we cannot expect to observe highly resolved NMR resonances for different domains. Since relaxation times are different for each domain, a relaxation curve is observed to be a featureless multiexponential one and, in most of the cases, is too monotonous to include interdomain spin diffusion. Therefore, most of the experimental results have been explained by using the simplified picture of no interdomain spin diffusion and the observed multiexponential decay is fitted to a sum of exponential functions. Practically three exponentials are enough to realize the observed decay. Each relaxation time represents one domain, thus, only a few domains can be distinguished by one resonance line. Inevitably, the heterogeneous structures deduced from NMR relaxation experiments become simple. 

The temperature dependence of the photon-echo intensity for several excitation pulse separations was also reported and as an example we show in Fig. 33 a relaxation curve. In Ref. 69 it was reported that between... 

Actually, the two terms of equation (8.7) have to be modified in order to account for a relaxation time distribution on both polarisation and conduction phenomena. As x is the time constant describing the electric field delay to 0, only a molecular relaxation process having Tj dielectric measurements using the electric modulus, the lower frequency relaxation will always be associated with the relaxation of long-range transport phenomena. Nevertheless, due to the similarity of equation (8.3) and (8.7), the first sight of a relaxation curve doesn t allow us to distinguish a relaxation caused by a conduction mechanism coupled with a polarisation mechanism from a relaxation of the conduction mechanism characterised by a broad distribution of relaxation times. A more precise study on several samples has then to be done. 

Fig. 3.13. A certain arc height is imposed on the clamped-in-place HDPE geomembrane specimen by the inflow of a specified amount of water, which rapidly enters the burst test device. Because of the incompressibility of the water body the imposed centrepoint deflection does not change with time. However, water pressure will drop as a function of time and a relaxation curve for the plane state of stress can be determined, which typically occurs in the case of subsidence of the geomembrane foundation layer (BCreiter and Hutten 1990)...

The curves available for creep are the time extension curves. The complementary relaxation curves are rarely available and would involve a large mass of data since the curves would vary depending on the time that the load was on. Although this is an approximation, the inverse curve is used as a relaxation curve. This assumes that the strain recovery follows the same mechanisms as the straining process which cannot be exactly true as the previous discussion on molecular reaction... 

The isothermal curves of mechanical properties in Chap. 3 are actually master curves constructed on the basis of the principles described here. Note that the manipulations are formally similar to the superpositioning of isotherms for crystallization in Fig. 4.8b, except that the objective here is to connect rather than superimpose the segments. Figure 4.17 shows a set of stress relaxation moduli measured on polystyrene of molecular weight 1.83 X 10 . These moduli were measured over a relatively narrow range of readily accessible times and over the range of temperatures shown in Fig. 4.17. We shall leave as an assignment the construction of a master curve from these data (Problem 10). 

Fig. 38. Stress—relaxation curve for a lightly vulcanized rubber (242). To convert Pa to dyn/cm, multiply by 10.

Fig. 8.90 Load relaxation curves for a maraging steel stress corroded in 0.6 m NaCl at pH 2...

Data of Figs 8-10 give a simple pattern of yield stress being independent of the viscosity of monodisperse polymers, indicating that yield stress is determined only by the structure of a filler. However, it turned out that if we go over from mono- to poly-disperse polymers of one row, yield stress estimated by a flow curve, changes by tens of times [7]. This result is quite unexpected and can be explained only presumably by some qualitative considerations. Since in case of both mono- and polydisperse polymers yield stress is independent of viscosity, probably, the decisive role is played by more fine effects. Here, possibly, the same qualitative differences of relaxation properties of mono- and polydisperse polymers, which are known as regards their viscosity properties [1]. 

The resulting data can then be presented as a series of curves much like the isometric stress curves in Fig. 2-27. A relaxation modulus similar to the creep modulus can also be derived from the relaxation data. It has been shown that using the creep modulus calculated from creep curves can approximate the decrease in load from stress relaxation. 

All relaxation curves exhibited more than one phase at various degrees of conversion and at different temperatures. This clearly rules out the all-or-none mechanism (AON) although the AON model is able to fit easily to the measured equilibrium transition curve. However, a mechanism has been proposed which allows the existence of side... 

R.L. Bohon, AnalChem 35 (12), 1845-52 (1963) CA 60,1527 (1964) Approx heats of expin, Qv were detd on mg amounts of propints and expls by differential thermal analysis (DTA). Small-screw-cap metal cupsi sealed with a Cu washer served as constant vol sample containers the initial cup pressure could be controlled from 0 to approximately lOOOpsia. The calibration constant was calcd for each run from the total heat capacity of the cup and the relaxation curve, thereby compensating for equipment variations. 

Fig. 1.13. Kinetics of rotational relaxation in differential (curve a), integral (curve b) and impact (curve c) theories at k = 10 (+ + + + asymptotic result of Eq. (1.118)).

It should be stressed that below a critical (Blocking) temperature (Tg) S.P. clusters will have a slow relaxation time (t) at which their net moment will align so-to-speak "parallel" to H, and thus appear to behave as if they had an apparent "bulk-like" ferromagnetic behavior. This aspect will result in a hysteresis or an "apparent" ferromagnetic behavior. Conversely, above the Tg, the hysteresis will disappear and the clusters will show a unique curve with no hysteresis (Fig. 2). 

A linear regression of A (ul, x) for < 0.8 was performed for each value of x, the slope giving A °(x) which is found to be linear in x. From the linear dependence of A °(x) on x, the original relaxation curves can be retraced. Inserting Eq. (86) into the modified Arrhenius equation ... 

Fig. 17. High-spin low-spin relaxation of [Fe(ptz)j](BF4)2 a normalized relaxation curves at temperatures between 57.5 and 66.5 K b activation energy AE as a function of n. The solid line represents a simultaneous fit of the five experimental curves displayed under a. The broken line is the result of a linear regression determined by AE° = — 164 cm" = — 0.47 kcal mol" as slope and AE = 797 cm" = 2.28 kcal mol" as intercept. Notation in the figure uses yi, A instead of Hl,...

A more complex but faster and more sensitive approach is polarization modulation (PM) IRLD. For such experiments, a photoelastic modulator is used to modulate the polarization state of the incident radiation at about 100 kHz. The detected signal is the sum of the low-frequency intensity modulation with a high-frequency modulation that depends on the orientation of the sample. After appropriate signal filtering, demodulation, and calibration [41], a dichroic difference spectrum can be directly obtained in a single scan. This improves the time resolution to 400 ms, prevents artifacts due to relaxation between measurements, and improves sensitivity for weakly oriented samples. However, structural information can be lost since individual polarized spectra are not recorded. Pezolet and coworkers have used this approach to study the deformation and relaxation in various homopolymers, copolymers, and polymer blends [15,42,43]. For instance, Figure 7 shows the relaxation curves determined in situ for miscible blends of PS and PVME [42]. The (P2) values were determined... 

Equation (3) is plotted with two different time scales in Figures 1 and 2 for values somewhat typical of an elastomer. All the initial deformation takes place in the spring at a later time the dashpot starts to relax and allows the spring to contract. Most of the relaxation takes place within one decade of time on both sides of the relaxation time, but this is shown clearly only in Figure 2. On the logarithmic time scale, the stress-relaxation curve has a maximum slope at the time / = T and the stress ratio cr/cr is 0.3679 ore. The stress relaxation may also be given in terms of a stress-relaxation modulus Er(t) ... 

The longest relaxation time. t,. corresponds to p = 1. The important characteristics of the polymer are its steady-state viscosity > at zero rate of shear, molecular weight A/, and its density p at temperature 7" R is the gas constant, and N is the number of statistical segments in the polymer chain. For vinyl polymers N contains about 10 to 20 monomer units. This equation holds only for the longer relaxation times (i.e., in the terminal zone). In this region the stress-relaxation curve is now given by a sum of exponential terms just as in equation (10), but the number of terms in the sum and the relationship between the T S of each term is specified completely. Thus... 

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