Relative relaxation times

Data comparing the relative relaxation times of naturally occurring carbohydrate polymers with the transitions in helical conformations observed in some fermentation carbohydrate polymers have not been reported under comparable conditions. Considering the difference in segmental flexibility between synthetic and carbohydrate polymers it might be expected that a multistranded helix would provide a lower... 

Of particular importance to structural recovery models is the idea that the apparent mobility may depend on the temperature/pressure/stress path rather than on the instantaneous state of the material. This differs from all of the phenomenological equations for the characteristic relaxation time, including equation (19), which are presently used in other models of structural recovery. The dependence of the relaxation on the imique state has been investigated by Strvik (146), and although it was claimed that the relaxation time only appeared to depend on the instantaneous volume, there is considerable scatter in the data and the relationship appears to depend not only on the final aging temperature but also on the sample history (ie, the magnitude of down- and double-temperature jumps). The scatter may be due to the measurements of volume and relative relaxation time being made in separate instruments such that the thermal history of the samples were not identical. Alternatively, it may be an indication of a more complicated... 

THE POLARIZATION TYPES AND THEIR RELATIVE RELAXATION TIME... 

The polarizations discussed above have different relaxation times, as they are governed by the different physical origins. Figure 7 schematically shows the wide frequency spectrum of the dielectric properties of a heterogeneous system. All polarizations are depicted in Figure 7 on the basis of their relative relaxation times. The dielectric dispersion of the electronic polarization appears at the highest frequency, more than lO FIz. With the polarization entity size increase, the dielectric dispersion peak gradually appears at low frequencies in the sequence of the atomic, Debye, interfacial polarization, and the electrode polarization. The Debye polarization usually appears at 10 Hz, the interfacial polarizations appears around 1000 Hz, and the electrode polarization appears below 100 Hz. The Debye, interfacial, and electrode polarizations arc rather slow processes as compared with the electronic and the atomic polarizations. Usually, the former three... 

These expressions show that the important dimensionless parameters in the problem are the relative modulae, G = Gb/Ga, and the relative relaxation times, x = xb/xA. If, on the other hand, Eq. 77 is used then there is no shift in the stability condition in the vorticity direction i.e., Axdqz) = 0 whilst in the flow-gradient direction. 

This equation takes into account the dependence of the relaxation of the load. If we assume that Ug-aa U and to determine the relative relaxation time as t/t, (the ratio of the current value of the relaxation time of the initial value of you during the load application), then, on the basis of Eq. (18), we can represent this value as an expression ... 

Using the representation of the relative relaxation time of the duration of the periodic effects in the corresponding coordinates for the frequency of 0.17 Hz (Fig. 3) makes it possible to calculate the activation energy and the parameter b for the relaxation process of solid LDPE under these... 

Figure IV-10 illustrates how F may vary with film pressure in a very complicated way although the v-a plots are relatively unstructured. The results correlated more with variations in film elasticity than with its viscosity and were explained qualitatively in terms of successive film structures with varying degrees of hydrogen bonding to the water substrate and varying degrees of structural regularity. Note the sensitivity of k to frequency a detailed study of the dispersion of k should give information about the characteristic relaxation times of various film structures.

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. 

Now the relaxation times for all higher modes of vibration can be expressed relative to n ... 

The relative number of equivalent nuclei associated with each chemical shift is obtained from the integrated spectmm by normalizing the areas so that the area corresponding to the smallest peak in the spectmm is defined as 1. This relation may not be exactly correct in ft experiments where signals may be affected by significant differences in relaxation times for nuclei in different environments. 

Dicarbocyanine and trie arbo cyanine laser dyes such as stmcture (1) (n = 2 and n = 3, X = oxygen) and stmcture (34) (n = 3) are photoexcited in ethanol solution to produce relatively long-Hved photoisomers (lO " -10 s), and the absorption spectra are shifted to longer wavelength by several tens of nanometers (41,42). In polar media like ethanol, the excited state relaxation times for trie arbo cyanine (34) (n = 3) are independent of the anion, but in less polar solvent (dichloroethane) significant dependence on the anion occurs (43). The carbocyanine from stmcture (34) (n = 1) exists as a tight ion pair with borate anions, represented RB(CgH5 )g, in benzene solution photoexcitation of this dye—anion pair yields a new, transient species, presumably due to intra-ion pair electron transfer from the borate to yield the neutral dye radical (ie, the reduced state of the dye) (44). 

Quantum well interface roughness Carrier or doping density Electron temperature Rotational relaxation times Viscosity Relative quantity Molecular weight Polymer conformation Radiative efficiency Surface damage Excited state lifetime Impurity or defect concentration... 

This treatment illustrates several important aspects of relaxation kinetics. One of these is that the method is applicable to equilibrium systems. Another is that we can always generate a first-order relaxation process by adopting the linearization approximation. This condition usually requires that the perturbation be small (in the sense that higher-order terms be negligible relative to the first-order term). The relaxation time is a function of rate constants and, often, concentrations. 

If the timestep is short relative to the velocity relaxation time, the solvent does not play much part in the motion. Indeed, if y = 0, there are no solvent effects at all. A simple algorithm for advancing the position vector r and velocity v has been given by van Gunsteren (van Gunsteren, Berendsen and Rullmaim, 1981) ... 

If the velocity relaxation time is short relative to the integration timestep, the following result is obtained ... 

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