Incipient phase

CHECK FOR VALID FEED COMPOSITIONS AND FOR ESTIMATE OF INCIPIENT PHASE... 

A study by Bames and co-workers of the equilibrium spreading behavior of dimyristol phosphatidylcholine (DMPC) reconciles the differences between spreading of bulk solids and dispersions of liposomes [41]. This study shows the formation of multibilayers below the monolayer at the air-water interface. An incipient phase separation, undetectable by microscopy, in DMPC-cholesterol... 

PVA and TaM -for the 88%-hydrolyzed PVA. The same dependence was found for the adsorbed layer thickness measured by viscosity and photon correlation spectroscopy. Extension of the adsorption isotherms to higher concentrations gave a second rise in surface concentration, which was attributed to multilayer adsorption and incipient phase separation at the interface. The latex particle size had no effect on the adsorption density however, the thickness of the adsorbed layer increased with increasing particle size, which was attributed to changes in the configuration of the adsorbed polymer molecules. The electrolyte stability of the bare and PVA-covered particles showed that the bare particles coagulated in the primary minimum and the PVA-covered particles flocculated in the secondary minimum and the larger particles were less stable than the smaller particles. 

Both Qv(x) and Q°(x) decrease as the polymerization proceeds and, after a definite conversion Qv(x) may reach the value of Qx(x). Since the dilution of a gel cannot be greater than its equilibrium degree of swelling, the excess of solvent should separate from the gel phase resulting in the syneresis, i.e. in phase separation. The condition for incipient phase separation during copolymerization of divinyl/vinyl monomers is given by [107]... 

Compared to other risky activities, such as parachuting or motorcycling, risks related to food safety are unique. While some risks can be avoided, food safety-related risks can only be bypassed to a limited extent. Even when a person switches from one product to another, contaminated food still remains harder to avoid than parachuting, especially in the incipient phase where the risk is not yet known to the public and when consumers do not have full control over these risks. 

The parts of the CPC where the incipient phase has higher or lower density than the original phase are sometimes referred to as dew and bubble curve, respectively. 

Finally we should not overlook one—perhaps unexpected—feature of the critical distribution It shows that clear signatures of the two (incipient) phases persist along the coexistence curve and right through to the critical point in a finite system. Failure to appreciate this will lead (as it has in the past) to substantial overestimates of critical temperatures [100b]. 

In the range where bicontinuous morphologies are obtained, KIc may attain a maximum local value (but it then increases again for phase-inverted structures). The presence of this maximum seems to be related to the formation of an incipient phase-inverted structure that exhibits a lack of adhesion between both phases. In these cases, bicontinuous or double-phase morphologies lead to a better fracture resistance (Girard-Reydet et al., 1997). 

A fire occurs in four distinct phases. In the incipient phase, warming causes the emission of invisible but detectable gases. In the second phase, smoldering, smoke is formed so smoke detectors can be used. In the third phase, when the ignition temperature has been reached, flames and their emitted radiation (IR and UV) can be detected. In the fourth and last stage of the fire, heat is released the temperature of the space starts to rise, and the use of thermal sensors becomes feasible. 

It is quite remarkable how many firm deductions are based on a single hypothesis. Beginning with the Margules formulation (3.13.12) for r , thermodynamics leads directly to the specification of AGm, as shown in (3.13.13). All other mixing functions are then found from (3.13.3)—(3.13.7). When phase separation does occur the composition of the two phases in equilibrium is specified by Eq. (3.13.14). The critical value of B required for incipient phase separation and the critical composition of the mixture are specified by Eq. (3.13.15c). Finally, one may construct diagrams such as shown in Fig. 3.13.3 by which deviations from Raoult s Law are predicted. The foregoing is a beautiful illustration of the power of thermodynamic methodology. 

Fig. 13 is a TTT cure diagram of three systems a neat epoxy resin and the same epoxy modified with two reactive rubbers at the same concentration level. The times to the cloud point, gelation and vitrification are shown for each system. The cloud point is the point of incipient phase separation, as detected by light transmission. The modified system with the longer times to the cloud point and gelation, and the greater depression of Tg, contains the more compatible of the two rubbers. The difference in compatibility could then be used to account for differences in the volume fractions of the phase separated rubber-rich domains and in the mechanical properties of the neat and the two rubber-modified systems. 

The volume fraction at incipient separation of the nematic phase lies just beyond the volume fraction v at which exhibits critical behavior with respect to the disorder index y, according to the 1956 theory. The confusion of v calculated using Eq. (11) with Vp at incipience therefore has led to underestimation of the latter volume fraction according to that version of the theory. The improved theory leads to somewhat lower values of the volume fraction at incipient phase separation. Hence, the error attending misapplication of Eq. (11) is offset by inaccuracies of the original theory, with the fortuitous consequence that this equation offers a slightly better approximation for the threshold volume fraction than for vj, for which latter it was originally intended. The widespread misuse of Eq. (11) is therefore well justified. 

With established over the entire range of 0, conditions for phase separation can be formulated. When G < 0 the G° (0) curve is concave (it has a minimum like that of in fig. 3.16) but in the opposite case it may exhibit a maximum, separating two minima, (as in fig. 1.2.9 for the three-dimensional equivalent) leading to demixing. The critical G° for incipient phase separation follows from the criteria... 

In contrast to their general use, the isotherms describing phase separation are not indicative of the existence of a real equilibrium between the phases they only indicate incipient phase-separation at zero time. Although neither of the starch fractions separately studied was subfractionated (and, therefore, each represents in itself a polycomponent system), they will be treated as if they were pure, single components. Likewise, magnesium sulfate will be considered to be a pure single component. The system is, then, one con-... 

FIGURE 16.9 The cloud-point and shadow curves for poly(ethylene-octene)-hexane at450 K from experiment (points) and the SAFT equation of state (curves). The dotted curve shows the composition of the incipient phase at the cloud point. Results for monodisperse and polydisperse polymer are included. (From Jog, P.K. et al., Ind. Eng. Chem. Res., 41(5), 887, 2002. With permission.)... 

It is readily seen from Fig. 3.8 that for each value of x above Xc there are two different values of 2 at which the chemical potential of the solvent in the two phases is the same. This implies that solutions with concentrations defined by these two values of 2 can be in thermodynamic equilibrium for X > Xc- Moreover, it implies that a solution with an intermediate value of (j)2 will spontaneously separate into two stable liquid phases defined by these two concentrations this will occur with a concomitant decrease in the free energy. Such phenomena are in fact observed with solutions of flexible polymers for values of x above a critical value (Xc)- Thus, if X is increased by decreasing the temperature, an initially totally miscible system at higher temperatures is transformed to one of limited miscibility by lowering the temperature at some critical temperature Tc, incipient phase separation (as indicated by the onset of an opalescence) is encountered, followed by separation into distinct liquid phases at still lower temperatures. 

However, the critical solution temperature shifts to the left or right ascending branch of the spinodal curve depending on the value of a1/a2. For ai/a2 > 1 the critical point shifts to higher concentrations of component 1. For a1/a2 < 1 it shifts to higher concentrations of component 2. The binodal and cloud-point curves temperature of incipient phase separation for poly disperse sys-... 

From Equation 25.16 the conditions for incipient phase separation are [12, 45]... 

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