Zero retardation decrease

At the analyzer these vectors Ez and Ey are combined to form a beam of light polarized 90° to the incident beam. It should be clear that the intensity of this final light will depend on the phase angle 8 which in turn depends on the retardation. As 8 increases from zero (retardation increases) the light transmitted will periodically vary from zero to a maximum and decrease to zero again. Theoretically one can show that this dependence of transmitted intensity, It, depends on the retardation as follows... 

A number of authors (Bl, B2, H3, HIO, M8) have solved Eq. (11-44) numerically, often neglecting the history term and using empirical approximations for Cd- Typical predictions are shown in Fig. 11.16. Qualitatively, the trends are the same as predicted by Eq. (11-58), but the numerical approach predicts less retardation since decreases as Re increases (T4). Here is predicted to become zero only for oc at finite. Thus assumption of constant leads to significant error. A rather different approach was initiated by Bailey... 

At yet larger separations, all frequencies over which A(Z )2 decreases on its own have been screened out for the remaining terms, A(Z )2 is essentially constant. It has its zero-frequency value A(f = 0)2, but the screening factor continues to act. The result is to make the coefficient A(l) decrease as the first power in Z and to make the total interaction energy vary as the inverse-third power of separation. Sometimes referred to as the purely retarded limit, this peculiar behavior is more rigorously examined in Level 2. 

In equation (6) the quantities A, E, n, m, D, and F are semiempirical parameters. It can be seen that this rate equation predicts that the methanol yield would decrease as the C02 partial pressure is increased and would drop to zero for synthesis gas that contains carbon dioxide only. Hence Eq. (6) describes a process in which carbon dioxide is a retardant but not at all a reactant or a promoter. 

Without any electrolyte (i.e., vacuum), ss(/i) a h in both the nonre-tarded limit as - 0 and in the retarded limit as - oo. In between these limits the retardation varies with position h according to a different relationship. With electrol5d e, decreases to zero as /i —>... 

The rate is of order between zero and plus one with respect to the activator. The additional denominator term reflects the fact that some catalyst material is present as the not yet activated species, cat. This retarding term is infinitely large if no activator is present, and decreases with increasing activator concentration. 

If the new radicals T- or MpQ- do not react readily with more monomer, there will be a decrease in the concentration of reactive radicals and a concurrent reduction in the rate of polymerization. When the rate of reaction (6-91 b) or (6-9 Ic) is very much greater than that of reaction (6-9la) and the new radicals T- or M Q- do not add monomer then high-molecular-weight polymer will not be formed and will beefl ectively zero. This is a case of inhibition. In retardation the polymerization is slowed but not entirely suppressed. This occurs if (I) the rate of either alternative process is close to that of the monomer addition reaction (6-91 a) and the new radicals from steps (6-9lb) or (6-9Ic) do not reinitiate, or (2) if the alternative processes are fast compared to ordinary monomer addition but the new radicals formed reinitiate slowly. 

Viscosity is the property of a fluid which characterizes its resistance to flow. It is often measured by timing the flow of a liquid through a cylindrical tube under the influence of gravity. In order to understand the definition of the viscosity, consider a fluid flowing between two large plane parallel plates (fig. 6.1). The velocity of the fluid in the direction of the flow, varies with position. It is at its maximum midway between the plates and decreases to zero between each plate on the basis of experimental observation. Now imagine that the fluid is made up of horizontal layers which are parallel to the plates. The movement of one layer with respect to another is retarded by a frictional force which is related to the fluid s viscosity. The origin of this friction is clearly intermolecular forces. 

Figure 3 shows the CL - time profile for samples of PP containing different concentrations of the profluorescent nitroxide TMDBIO. The CL curve for unstabilized PP shows that after a very short time, there is an exponential increase in CL corresponding to rapid oxidation and embrittlement of the polymer. The effect of the added nitroxide is not to decrease totally the CL from the PP, but rather to retard the emission so that there is a slower development of the CL emission intensity. There is thus an increase in the time taken to see the exponential increase in emission intensity, but the emission is not reduced to zero in this retardation period. In contrast, if a peroxy-radical scavenging, hindered phenol such as Irganox 1010 were to be added to the PP then the increase with time of the CL intensity would be totally suppressed and there would be an apparent induction period 8), This result may be interpreted within the framework of the free-radical reactions in Figures 1 and 2 above. 

As the three angles u, a and y increase the current waveform moves to the right of the phase voltage waveform. The centre of the current waveform is approximately the position of the peak value of the fundamental current component. Consequently as the current increases the power factor of the fundamental current decreases. Table 15.1 shows values of the harmonic components of current and the power factor as the retardation angle u is increased from zero to 60°. The fundamental component is taken as unity reference at each value of u. 

For a Hookean solid, say a metal, the load will produce a deformation that stays constant over time. On the other hand, for a polymeric material the same load will produce an initial deformation, followed by a slow and constant deformation up to a certain value (creep). This is an illustration of a retardation process, where the final response of the material to the load is retarded. On the other hand, one can also visualize an experiment where a constant strain is imposed to both, a Hookean solid and a viscoelastic solid. Under these experimental conditions, a constant stress is developed in the first case, whereas in the second case, the stress is nonconstant it starts at an initial value and then decreases up to a zero value. This experimental behavior constitutes a relaxation process. 

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