Plateau zone

This model, whilst not entirely satisfactory, can give a reasonable prediction of the elasticity in the plateau zone. The approach does not readily lend itself to a prediction of the dynamic behaviour. There have been numerous attempts to predict the low shear viscosity using entanglement models. For example Graessley obtained... 

The variation of the yield as a function of r does not therefore give a linear response except in the plateau zone. It is therefore impossible to refer to a standard curve, plotted independently. This makes it necessary to use an internal standard allowing correction of the effects of non linearity, since this standard s behavior is a satisfactory reflection of the behavior of A9-THC in the test sample. 

Frontal analysis gives the retention times of all the fronts that can be identified. These retention times can be used to calculate the velocities of the associated shocks and, therefore, the normalized velocities of the corresponding fronts. These velocities can be used to determine using Eq. 4.79. In the first plateau zone, the least retained component (i.e. component n) is pure. In this zone, the concentrations of all the components, except that of the less retained one, are equal to zero. The concentration, C , of the least retained component n is given by Eq. 4.76 which simplifies to... 

At lamella intersections the liquid is more bulky . Tree film pairs come together at an angle of 120°. These zones are called Plateau Boarders (J.J. Plateau, French Chemist 1861). Because of the pressure difference by diameter as well as symmetrical considerations, the vapour pressure is lower than in a lamella which results in a sucking effect towards Plateau zones, helping the drainage of liquid. 

The second definition of efficiency used here is based on the surface tension reduction at a specific concentration, chosen to give maximum differentiation between homologous series. Taking all three surfactant classes into account, the obvious concentration to select for this purpose is 10 M. It adroitly avoids the region of limiting surface tension, the so-called plateau zone, where differentiation... 

The sensor yam signal is divided into pseudo-periodic patterns. There arc some plateau zones that last a period of 2.4 s, and areas including peaks, also included in a period of 2.4 s of the binding warp yams. 

On Table 1, values of Ca and of adsorbed P concentration (CaP) from representative samples of both zones of the isotherm, are presented. For the first two samples conesponding to the first plateau zone, CaP values are similar (0.4-0.5 %P). The same situation lakes place with the other two samples corresponding to the second plateau, though in this case, the CaP value is significantly higher (2.7 %P). This shows the adrorbed phosphorus also presents two different zones which are coincident with those of the molybdenum adsorption isotherm. 

On the other hand, even when the CaP/Ca molar ratio in the solid of the second plateau zone (0.25) is greater than that of the first plateau (0.12), it is still less than the value used in the original solution (0.4) which in mm corresponds to die stoichiometric ratio of the... 

In the case of samples prepared firom FK solutions, the Mo(o)/Mo(t) ratio increases as Cf increases but, as in the corresponding isotherms, no two plateau zone but a continuous increment is observed (Figures 4b, 4c, 4d). This is basically related to the fact that the adsorbed species is the same, regardless of the solution concentration under use. 

The question as to whether the same ot reduction factors can be applicable in both the transition and terminal zones depends on whether parameters such as Qe or Me vary with temperature. On the basis of the entanglement concept or the tube model, such temperature dependence would be expected to be very slight. In a number of cases, the same reduction factors have been found to be applicable in both zones to a close approximation. However, in polyisobutylene anc especially in very precise investigations of polystyrene >2 and poly(vinyl acetate) the absolute values of log aj in the transition zone were found to be somewhat greater than those calculated from equation 13. On the other hand, for certain methacrylate polymers and their concentrated solutions, the absolute values of log ar are found to be smaller in the transition zone than in the terminal zone. This behavior, formally attributable to a temperature-dependent Qe or Me, does not prevent successful use of the method of reduced variables within a single zone of the time scale, but in the plateau zone a complicated transition takes place (Section F below). 

FIG. 11-16. Loss compliance of four solutions of poly(/i-butyl methacrylate) in the plateau zone, reduced to a reference temperature of 0°C by ar factors derived from data in the transition zone and fitted to equation 21. Numbers denote concentrations in weight percent. 

FIG. 13-3. Logarithmic plots of G and G against frequency reduced to I OO C encompassing the plateau zone, from curves IV of Figs. 2-3 and 2-4 (cf. also Fig. 12-9), for poly(n-octyl methacrylate). 

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