Phase inversion point

By maintaining the first-stage reactor just beyond the phase inversion point, the dispersed rubber phase is relatively rich in dissolved styrene. As polymerization subsequently proceeds in the LFR s, the dissolved styrene will react to form either a graft copolymer with the rubber or a homopolymer. The latter will remain within the rubber droplet as a separate occluded phase. Achieving the first-stage reactor conversion and temperature by recycling a portion of the hot second reactor effluent may permit simplification of the first reactor temperature control system. 

Figure 3. Morphology changes induced by stirring during the synthesis of a 10/90 COPE/PSN SIN. Sample poured into the mold at the phase inversion point...

Figure 2 illustrates the following sequence of steps. During the reactions, forty ml samples were removed from the reactor by pipeting the solution into bottles, followed by quenching in an ice bath. Samples were removed every 10 minutes early in the reaction and every 5 minutes close to the phase inversion point. 

The interfacial tension is a key property for describing the formation of emulsions and microemulsions (Aveyard et al., 1990), including those in supercritical fluids (da Rocha et al., 1999), as shown in Figure 8.3, where the v-axis represents a variety of formulation variables. A minimum in y is observed at the phase inversion point where the system is balanced with respect to the partitioning of the surfactant between the phases. Here, a middle-phase emulsion is present in equilibrium with excess C02-rich (top) and aqueous-rich (bottom) phases. Upon changing any of the formulation variables away from this point—for example, the hydrophilie/C02-philic balance (HCB) in the surfactant structure—the surfactant will migrate toward one of the phases. This phase usually becomes the external phase, according to the Bancroft rule. For example, a surfactant with a low HCB, such as PFPE COO NH4+ (2500 g/mol), favors the upper C02 phase and forms w/c microemulsions with an excess water phase. Likewise, a shift in formulation variable to the left would drive the surfactant toward water to form a c/w emulsion. Studies of y versus HCB for block copolymers of propylene oxide, and ethylene oxide, and polydimethylsiloxane (PDMS) and ethylene oxide, have been used to understand microemulsion and emulsion formation, curvature, and stability (da Rocha et al., 1999). 

For a constant amount of nonionic surfactant, the interfacial tension at the planar oil-water interface, for the same amounts of oil and water, passes through a minimum when plotted against the hydrophilic-lipophilic balance (HLB). The emulsion stability passes through maxima in the W/O and O/W ranges and through a minimum between the two at the phase inversion point. The minima in the two cases coincide. These observations are explained on the basis of thermodynamics. The stability of macroemulsions can be correlated with the surface excess of surfactant, which also passes through two maxima and a minimum between them [2.11]. 

The volume fraction of the dispersed phase changes. It increases up to the phase inversion point when mesophase is the dispersed phase and decreases above this point when isotropic liquid is the dispersed phase. 

The phase relationships of two-phase polymer systems also have been of considerable interest in recent years. In an important series of papers, Molau and co-workers (19-24) studied systems, which were denoted POO emulsions (polymeric oil-in-oil), prepared by dissolving a given polymer in monomer and then polymerizing the monomer. During polymerizations of this type the composition of the respective phases reverses, and a phase inversion process was proposed to explain this. A similar process has been suggested as the mechanism by which poly-butadiene forms the dispersed phase in the manufacture of high-impact polystyrenes (22,25). Recently, Kruse has pointed out that this phase-inversion point may correspond to that point on a ternary phase diagram at which the reaction line bisects a tie line (26), and we have advanced a similar point of view in our earlier reports (17,18, 27). 

To a stirred 0.3 mM dispersion of PS-fi e rfr-(NH2) in a 0.01 M KCl solution, a 0.3 mM amphiphile solution in toluene was added dropwise. By measuring the conductivity of the system as a function of the ratio toluene-water, it could be estimated whether toluene or water was the continuous phase. At the point where the conductivity dropped to zero, the phase inversion point was reached and toluene became dispersing phase. The effect of dendrimer generation on the position of this inversion point was investigated with PS-c enrfr-(NH2) with n — 2-16. VS-dendr-(NH2)32 could not be measured in the same manner, because this product proved to be insoluble in toluene. The conductivity measurements show a distinct difference between PS-denc r-(NH2)i6 and the lower generations. For PS-cfendr-(NH2) with n — 2-8 there is a strong tendency to stabilize toluene as a continuous phase. PS-dendr-(NE.2)2 even showed a remarkable phase inversion at 2 vol% of toluene. This can be explained by the fact that polystyrene is the dominant part in the amphiphilic... 

Related to particle sizing, Molau and Kesskula described the concept of type I and II occlusion [5]. The prepolymer is viscous and has a retarding effect on the phase inversion. In most cases multiple emulsions are formed after the phase inversion point. If the agitation is not extremely high these multiple emulsions survive the further copolymerization and give SAN occlusions in the rubber particles. These occlusions are called type I. Type II occlusions are formed when monomer dissolved in the rubber phase is copolymerized. Because SAN is not compatible with the rubber, separation occurs within the rubber particle, giving type II occlusions. 

The phase behavior of surfactant formulations for enhanced oil recovery is also affected by the oil solubilization capacity of the mixed micelles of surfactant and alcohol. For low-surfactant systems, the surfactant concentration in oil phase changes considerably near the phase inversion point. The experimental value of partition coefficient is near unity at the phase inversion point (28). The phase inversion also occurs at the partition coefficient near unity in the high-surfactant concentration systems (31). Similar results were also reported by previous investigators (43) for pure alkyl benzene sulfonate systems. 

The effect of surfactants on the interfacial tension between water and supercritical fluids is a key property for describing emulsions and microemulsions (8), as shown in Figure 2. The v axis may be any formulation variable that influences surfactant partitioning between the phases such as the pressure or temperature. A minimum in y is observed at the phase inversion point, where the system is balanced with respect to the partitioning of the surfactant... 

The phase behavior of surfactant formulations for enhanced oil recovery is also affected by the oil solubilization capacity of the mixed micelles of surfactant and alcohol. For low concentration surfactant systems, the surfactant concentration in the oil phase changes considerably near the phase inversion point. 

The adempts to rationalize GrifHn s HLB scale from a physicochemical point of view were made in a number of studies. Various correlations were shown to exist between the HLB numbers and the chemical structure or molecular composition of the siufactants. Correlations were also fotmd between the HLB number and physicochemical properties of surfactants and their solutions, for example, stffface and interfacial tension, solubility, and heat of solution, spreading and distribution coefficient, dielectric permittivity of the surfactant, cloud point and phase inversion point, critical micelle concenlration, foaminess, etc. These studies are reviewed in Ref. 262. However, the correlations found are not generally applicable moreover, the concept of the additivity of HLB numbers as such for mixtures of surfactants or oils cannot be proven expermentally when the surfactant characteristics are varied over a wider range (265). 

Figure 3.4. Illustration of phase inversion during polymerization (Molau, 1965). Electron micrographs (transmission) of thin sections of a graft copolymer of p-t-butylstyrene with polystyrene (90/10). (a) Polymerized to 5.3 % conversion before the inversion point. The poly(p-t-butylstyrene) phase is white, and the polystyrene phase is black, (b) Polymerized to 7.8% conversion phase inversion is just beginning to occur, (c) The same system polymerized to 13.3% conversion after the phase inversion point.

On a perforated plate the liquid side mass transfer coefficient kLa and gas side mass transfer coefficient k( a, based on the column volume, vary linearly with the dispersion height. The true liquid- and gas-side mass transfer coefficients and first increase with the dispersion height and then go through a maximum and decrease slightly (123). Sharma and Gupta (124) attribute this to different behavior of the density of dispersion and the average bubble size with increase in gas flowrate, which leads to a phase inversion point. These authors correlate their experimental data for 10 cm i.d. perforated plates without downcomers by the following expressions... 

The significance of the function Q(A, X) will be discussed in the Sect. 7.3.1.2, dedicated to emulsion microrheology. Steinmann et al. suggested that, at the phase inversion point, the shape relaxation times of domains of the components meet at a maximum (Steinmann et al. 2002). 

This simple approach was found to be more accurate than models that used the shear viscosity ratio for blends with a viscosity ratio not far from unity [55], as the torque reflects to some extent also the effects of melt elasticity and elongational flow component. Lyngaae-Jorgensen and Utracki developed a model which predicts the range of cocontinuity, and not only the phase inversion point [56,57]. This model, which is based on the percolation theory, relates the degree of cocontinuity 0A. which can be determined experimentally from extraction experiments, to the volume fraction of the given blend component (pp (Eq. (3.27)). 

Several relations have been proposed in literature by giving the volume fraction at which co-continuity can be formed as a fimction of the viscosity ratio. These include the relations proposed by Paul and Barlow [65], Jordhamo et al. [66], Metelkin and Blekht [67], and Utracki [68]. All these relations describe the phase inversion as a function of the viscosity ratio. It has been shown by Willemse et al. that the viscosity ratio alone is not sufficient to predict the phase inversion point in all cases [69]. Parameters such as the interfacial tension, the absolute values of the viscosities rather than their ratio, the phase dimensions, and the mixing conditions can have an important effect on the formation of continuous phase structures. Therefore, Willemse et al. proposed a new empirical model by introducing the dependence of the formation of the continuous morphology on material properties (matrix viscosity, interfacial tension) and processing conditions via the consideration of the shape of the dispersed phase required for achieving phase cocontinuity [69]. 

The phase inversion in such systems can be predicted based on the hold up of dispersed phase and the changes in system properties [13], The authors [12] estimated the phase inversion point, Sauter mean diameter of the droplets in the dispersed phase and mass transfer coefficients for the toluene-HNOj mixtures at various concentrations to characterize the toluene-HNOj dispersion. Their subsequent studies [14] have established the improved catalyst stability in the HNO3 dispersed in toluene medium as compared to toluene dispersed in HNO3 medium. Batch nitration experiments were made under reflux conditions covering a wide range of toluene volume fractions (0.1 to 0.95) to generate the conversion and para selectivity profiles for this volume fraction range (Fig. 2.3). 

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