Relaxation Typical behavior

FIG. 23 A schematic illustration of the molecular motions and associated T2 relaxation curve behavior for the three major domains in foods—liquid, viscous liquid, and solid (crystalline and glassy). Typical H T2 NMR relaxation time values observed in these domains, and values specific for water in liquid and crystalline domains, are listed. 

This time t a actually is the maximum time for which Eq. [48] is valid, to structural relaxation. Typical a time scales diverge as... 

The temperature dependence of the NMR relaxation rate Tf1 for the Au compound (Fig. 9) exhibits a typical behavior of one-dimensional conductors with deviations to the Korringa law (Tf1 T) shown by the upward curvature at high temperatures similarly to (TMTTF)2PF6 [41] and TTF[Ni(dmit)2] [42]. Since there are no localized spins on the dithiolate chain, the relaxation comes from the hyperfine contact and dipolar interactions, 7 1 + r j, produced by the spins of the itinerant electrons along the perylene stacks. The enhancement of the relaxation is, however, less important than that shown by the Bechgaard salts [45]. 

At least two points should be especially emphasized, (i) From the solvent part, the parent radical cations exist in a non polar surrounding. Hence, the cations have practically no solvation shell which makes the electron jump easier in respect to more polar solvents. In a rough approximation the kinetic conditions of FET stand between those of gas phase and liquid state reactions, exhibiting critical properties such as collision kinetics, no solvation shell, relaxed species, etc. (ii) The primary species derived from the donor molecules are two types of radical cations with very different spin and charge distribution. One of the donor radical cations is dissociative, i.e. it dissociates within some femtoseconds, before relaxing to a stable species. The other one is metastable and overcomes to the nanosecond time range. This is the typical behavior needed for (macroscopic) identification of FET ... 

Fig. 4. Schematic of the variation of spin-relaxation time, (a) Typical behavior with no phase transition (b) continuous-phase transition (c) discontinuous-phase transition with a jump upward or downward depending on the jump of the magnitude of the fluctuations. In (b) and (c), it was assumed that cdlt T)> in both phases.

Most studies have focused on ternary and quaternary systems (with an electrolyte as the fourth component or an alcohol as cosurfactant in the latter) of both ionic [6,37-41] and nonionic [28,42] surfactants. The shape of the transient birefringence signal and the number, amplitude, and rate of the relaxations typically depend on composition, temperature, and field strength. Since the thermodynamic conditions affect the aggregation number ( , size, and stability of the particles as well as the phase behavior of the system, the distance (Tc — T) from a critical temperature and the distance from a critical composition Cc also have a major influence. 

The interpretation of these data becomes clearer when introducing an entropy relaxation by slow cooling before an analysis with a faster heating rate (see Sect. 6.1.3). Figure 7.79 documents that the enthalpy relaxation centers at the glass transitions of the homopolymers with a reduction in peak amplitude on copolymerization that is larger than expected from the reduction in concentration. This is the typical behavior of phase-separated polymers. Even more conclusive is that electron microscopy on the same samples reveals that all these high-molar-mass S/MS block copolymers are microphase-separated. 

Dielectric spectroscopy and scattering studies on the structural relaxation in many different materials have assumed that the normal T-dependence of the relaxation time of a liquid will closely resemble that of propylene glycol (PG), that is, both bulk water and confined PG relax in the same manner, and with an apparent continuity. The main relaxation time of PG exhibits a thermal behavior that differs from that proposed for bulk and confined water. Confined water relaxation times seem substantiaiiy altered when compared to bulk water (which evidently is not the case in confined EG). It also shows an apparent FSC. In addition, an even more dramatic change in the T-dependence of water confined in nanoporous MCM-41 is clearly evident. These results are not unique in that they simply exhibit the typical behavior of supercooled water in biological materials and in other confined environments. Thus, we consider both bulk and confined ethylene glycol (EG, OHCH2CH2OH). Figure 17 shows the EG dielectric relaxation times studied. 

FIGURE 57.13 Typical behavior of solder in response to a constant applied displacement (for example, due to thermal expansion).The initial stress is relaxed over time as the solder elongates. 

Figure 6 24 DEA results for thermoplastic polyurethane films with various metals in the chain extender (a) comparison between c(f) and M"(f) spectra recorded at 25 ""C (b) M (f) plot for a polyurethane sample PU(Cu ) placed in a brass electrode capacitor. Isothermal scans were performed between -55 °C and 40 °C, in 5 ° increments. The progressive upshift of various relaxations with increasing temperature of the scan is a typical behavior. [Adapted from Kalogeras, I. M., Roussos, M., Vassilikou-Dova, A., Spanoudaki, A., Pissis, P, Savelyev, Yu. V., Shtompel, V. L, and Robota, L. P. (2005), Eur. Phys. J. E 18,467. Copyright 2005. With kind permission of Springer Science and Business Media.l...

Polymer properties exhibit time-dependent behavior, which is dependent on the test conditions and polymer type. Figure 1.7 shows a typical viscoelastic response of a polymer to changes in testing rate or temperature. Increases in testing rate or decreases in temperature cause the material to appear more rigid, while an increase in temperature or decrease in rate will cause the material to appear softer. This time-dependent behavior can also result in long-term effects such as stress relaxation or creep. These two time-dependent behaviors are shown in Fig. 1.8. Under a fixed displacement, the stress on the material will decrease over time, and this is called stress relaxation. This behavior can be modeled nsing a... 

Fig. 7. Sketch of the typical behavior of physical properties at The symbols indicated at each curve are V, sound velocity Gruneisen parameter c/ , elastic modulus 8, density n, refractive index ct, thermal expansion coefficient Cp, specific heat t], dynamic viscosity and Tj, longitudinal relaxation time.

Wave profiles in the elastic-plastic region are often idealized as two distinct shock fronts separated by a region of constant elastic strain. Such an idealized behavior is seldom, if ever, observed. Near the leading elastic wave, relaxations are typical and the profile in front of the inelastic wave typically shows significant changes in stress with time. 

The typical viscoelastic response, as shown in Fig. 2.18, is the propagation of a shock due to the compression, followed by a relaxation to an equilibrium state. The relaxation response is a significant part of the total response. Relaxation times are typically in the 0.1 /is regime. At pressures over about 2 GPa, PMMA shows a change in relaxation time which may be indicative of mechanical failure. Anderson has recently extended this work to other polymers and found similar strong viscoelastic behavior [92A01]. 

Typical dynamic properties like the scaling of relaxation times, e.g., ri, or diffusion coefficient with N are found in the simulation to change systematically from typical Rouse-like behavior Dj< ocN, t oc to... 

One could assume that this characteristic behavior of the mobility of the polymers is also reflected by the typical relaxation times r of the driven chains. Indeed, in Fig. 28 we show the relaxation time T2, determined from the condition g2( Z2) = - g/3 in dependence on the field B evidently, while for B < B t2 is nearly constant (or rises very slowly), for B > Be it grows dramatically. This result, as well as the characteristic variation of with B (cf. Figs. 27(a-c)), may be explained, at least phenomenologically, if the motion of a polymer chain through the host matrix is considered as consisting of (i) nearly free drift from one obstacle to another, and (ii) a period of trapping, r, of the molecule at the next obstacle. If the mean distance between obstacles is denoted by ( and the time needed by the chain to travel this distance is /, then - (/ t + /), whereby from Eq. (57) / = /Vq — k T/ DqBN). This gives a somewhat better approximation for the drift velocity... 

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