Phase fraction, rigid,

The discussion of the influence of the interphase need not be limited to just linear polyethylenes. Interphases of several nm have been reported in polyesters and poly-hydroxy alkanoates. One major difference between the interphase of a flexible polymer like polyethylene and semi-flexible polymers like PET, PEN and PBT is the absence of regular chain folding in the latter materials. The interphase in these semi-flexible polymers is often defined as the rigid amorphous phase (or rigid amorphous fraction, RAF) existing between the crystalline and amorphous phases. The presence of the interphase is more easily discerned in these semi-flexible polymers containing phenylene groups, such as polyesters. 

Figures 6.127 and 6.128 illustrate that for the two macromolecules the strain on the amorphous fraction is so large that a portion of the amorphous phase remains rigid up to the transition region and a lower increase in heat capacity at Tg results than is expected from the fraction of the amorphous sample, (1 - wj. This fraction is called the rigid-amorphous fraction, RAF. The method of its evaluation is described in Figs. 6.16-18 for the case of poly(oxymethylene). For PEEK, the RAF is illustrated in Fig. 6.127. It is calculated as the ratio to the total amorphous fraction and increases...

According to Mullins, carbon black-filled vulcanized rubbers consist of a rigid hard phase and an extensible soft phase. The rigid hard phase is associated with the carbon black and the soft extensible phase is the rubber. When carbon blacks are loaded into rubbers, the stiffness of the rubber increases markedly. The stiffness of the black-filled vulcanizate can be expressed quantitatively in terms of the volume fraction of the filler in the vulcanized rubber by the Guth and Gold equation ° ... 

Although difficult to apply in practice, models for coalescence rate provide an appreciation for the physical phenomena that govern coalescence. They also provide an appreciation for why it is difficult to interpret stirred tank data or even to define the appropriate experiment. For instance, it can be clearly seen from eq. (12-49) to (12-51) that the collision frequency increases with e, whereas the coalescence efficiency decreases with e. For constant phase fraction, the number of drops also increases with e. The models for coalescence of equal-sized drops are quite useful to guide the interpretation of data that elucidate the time evolution of both mean diameter and drop size distribution during coalescence. To this end, Calabrese et al. (1993) extended the work of Coulaloglou and Tavlarides (1977) to include turbulent stirred tank models for rigid spheres and deformable drops with immobile and partially mobile interfaces. The later model accounts for the role of drop viscosity. In practice, models for unequal-sized drops are even more difficult to apply, but they do suggest that rates are size dependent. They are useful in the application of the population balance models discussed in Section 12-4. 

When polymers are deformed and as the crystal axes tilt, the chains in the amorphous domains also become oriented. This orientation results in concentration of the intensity of the amorphous halo into an arc centered on the equator, as shown in Figure 2.lid from a drawn PET fiber [67]. The oriented chains in the amorphous domains become more densely packed than when they are not oriented. These domains are sometimes considered as intermediate phases or rigid amorphous phases [38,70]. The nature of the oriented amorphous phase influences numerous polymer properties such as diffusion, strength and modulus, and shrinkage and dimensional stability. XRD patterns can be used to determine the fraction of this phase, the degree of lateral and orientational order that is present in these ordered but noncrystalline domains [41]. 

Apart from chemical composition, an important variable in the description of emulsions is the volume fraction, outer phase. For spherical droplets, of radius a, the volume fraction is given by the number density, n, times the spherical volume, 0 = Ava nl2>. It is easy to show that the maximum packing fraction of spheres is 0 = 0.74 (see Problem XIV-2). Many physical properties of emulsions can be characterized by their volume fraction. The viscosity of a dilute suspension of rigid spheres is an example where the Einstein limiting law is [2]... 

As a good first approximation (187), the heat conduction of low density foams through the soHd and gas phases can be expressed as the product of the thermal conductivity of each phase times its volume fraction. Most rigid polymers have thermal conductivities of 0.07-0.28 W/(m-K) and the corresponding conduction through the soHd phase of a 32 kg/m (2 lbs/fT) foam (3 vol %) ranges 0.003-0.009 W/(m-K). In most cellular polymers this value is deterrnined primarily by the density of the foam and the polymer-phase composition. Smaller variations can result from changes in cell stmcture. 

Stainless steel flat six-blade turbine. Tank had four baffles. Correlation recommended for ( ) < 0.06 [Ref. 156] a = 6( )/<, where d p is Sauter mean diameter when 33% mass transfer has occurred. dp = particle or drop diameter <3 = iuterfacial tension, N/m ( )= volume fraction dispersed phase a = iuterfacial volume, 1/m and k OiDf implies rigid drops. Negligible drop coalescence. Average absolute deviation—19.71%. Graphical comparison given by Ref. 153. ... 

In a comparative study of the crystallinity of isomeric aliphatic polyamides by NMR, DSC and X-ray, the NMR-based crystallinity was obtained by a two component fit of the proton broad-line spectra and their associated mobilities by Tip determination. Compared to the crystallinity estimates from DSC and WAXS, the content of rigid material obtained from NMR is significantly higher, but comparable to the crystallinity determined by SAXS. The difference with the DSC value was associated with a fraction of intermediate order within the crystalline phase [193]. 

Pons et al. have studied the effects of temperature, volume fraction, oil-to-surfactant ratio and salt concentration of the aqueous phase of w/o HIPEs on a number of rheological properties. The yield stress [10] was found to increase with increasing NaCl concentration, at room temperature. This was attributed to an increase in rigidity of films between adjacent droplets. For salt-free emulsions, the yield stress increases with increasing temperature, due to the increase in interfacial tension. However, for emulsions containing salt, the yield stress more or less reaches a plateau at higher temperatures, after addition of only 1.5% NaCl. 

Ford and coworker [104] have studied HIPEs of water-in-xylenes, stabilised by a variety of surfactants, and postulated three properties which an emulsifier should possess in order to form stable w/o HIPEs of high volume fraction a) a lowering of the interfacial tension between water and oil phases, b) the formation of a rigid interfacial film and c) rapid adsorption at the interface. 

These examples involve partitioning of elements as liquids cooled and crystallized. Partial melting of a solid rock also results in partitioning of incompatible elements into the liquid phase, which contains no rigid crystalline sites. Separation of the melt then fractionates incompatible elements from the compatible elements left behind in the solid residue. 

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