Phase inversion rule

The notion of twin-states of the VBSCD and the phase inversion rule of Longuet-Higgins were utilized by Zilberg and Haas to delineate unified selection rules for conical intersections, and rationalize the outcome of a variety of photochemical reactions. 

Electi ocyclic reactions are examples of cases where ic-electiDn bonds transform to sigma ones [32,49,55]. A prototype is the cyclization of butadiene to cyclobutene (Fig. 8, lower panel). In this four electron system, phase inversion occurs if no new nodes are fomred along the reaction coordinate. Therefore, when the ring closure is disrotatory, the system is Hiickel type, and the reaction a phase-inverting one. If, however, the motion is conrotatory, a new node is formed along the reaction coordinate just as in the HCl + H system. The reaction is now Mdbius type, and phase preserving. This result, which is in line with the Woodward-Hoffmann rules and with Zimmerman s Mdbius-Huckel model [20], was obtained without consideration of nuclear symmetry. This conclusion was previously reached by Goddard [22,39]. 

Ehase Inversion Temperatures It was possible to determine the Phase Inversion Temperature (PIT) for the system under study by reference to the conductivity/temperature profile obtained (Figure 2). Rapid declines were indicative of phase preference changes and mid-points were conveniently identified as the inversion point. The alkane series tended to yield PIT values within several degrees of each other but the estimation of the PIT for toluene occasionally proved difficult. Mole fraction mixing rules were employed to assist in the prediction of such PIT values. Toluene/decane blends were evaluated routinely for convenience, as shown in Figure 3. The construction of PIT/EACN profiles has yielded linear relationships, as did the mole fraction oil blends (Figures 4 and 5). The compilation and assessment of all experimental data enabled the significant parameters, attributable to such surfactant formulations, to be tabulated as in Table II. 

A few empirical and theoretical studies to postulate a general set of rules for the fabrication of asymmetric membranes by phase inversion mechanism (in which the polymer solution is coagulated within a nonsolvent bath) have been attempted. Thus, for example, from the literature which described the formation of asymmetric membranes, Klein and Smith (5) compiled working rules in the early 1970s regarding the requirements of a casting solution ... 

In the aromatic transition state approach, the basic criterion was that a reaction is allowed in the ground state if and only if there occurs in the transition state aromatic stabilization. This criterion led to the Dewar-Zimmerman selection rule (Equation 11.36), where p. i. = 0 signifies an even number of phase inversions, p. i. = 1 signifies an odd number of phase inversions, and N is the total number of electrons. 

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). 

Keywords Macroemulsion stability Hydrophilic-hydrophobic balance (HLB) Interfacial tension vs. HLB Surface excess vs. HLB Surface excess vs. temperature Phase inversion temperature Bancroft rule... 

A cyclic array of orbitals is a Mobius system if it has an odd number of phase inversions. For a Mobius system, a transition state with An electrons will be aromatic and thermally allowed, while that with An+ 2 electrons will be antiaromatic and thermally forbidden. For a concerted photochemical reaction, the rules are exactly the opposite to those for the corresponding thermal process. 

Phase inversion in dead-end membrane emuisification When one prepares an oil-in-water emulsion and presses this through a hydrophilic membrane, die resulting fine emulsion will be an oil-in-water emulsion as well. However, if you would use a hydrophobic membrane, the resulting emulsion will be a water-in-oil emulsion (assuming that the surfactant system would support the formation of a water-in-oil emulsion—see the Bancroft Rule). In this case, the emulsion is inverted from an 0/W towards a W/0 emulsion (see Figure 15.21). The same can be done with a water-in-oil emulsion pressed through a hydrophilic membrane, which leads to an oil-in-water emulsion. 

This work ably illustrates the importance of the surface selection rule. Unfortunately, the phase inversion technique described in this paper has not been further developed by Pons and co-workers and there are some difficulties associated with it it is evident, for example, that exact balancing of the positive and negative phases will lead to complete cancellation of the cen-treburst. This is of significance as the spectrometer software may well rely on the location of this centreburst to allow the Fourier transform to take place. It is, therefore, essential to build in mis-match into the phase-inversion amplifiers, though this in turn makes the technique very difficult to use quantitatively. Suffice to say that the authors of this report have not found it easy to use in practice and have relied on the subtraction of spectra already transformed as described above. 

Such a conclusion is supported by the fact that the Tg s of all the ERL-4221 systems are much higher than predicted by any of the rules of mixtures (Equations 1 to 3). Indeed even with 50% of diluent, the Tg of the resin was reduced relatively little in comparison with that of the neat resin. This certainly suggests the likelihood of a phase-separated oil-based component. One might well expect a sigmoidal curve of Tg vs concentration of epoxy prepolymer If the epoxy resin constitutes the continuous phase a phase Inversion would then be expected at some value of epoxy resin content. 

One limitation of the HLB concept is its failure to account for variations in system conditions from that at which the HLB is measured (e.g., temperature, electrolyte concentration). For example, increasing temperature decreases the water solubility of a nonionic surfactant, ultimately causing phase separation above the cloud point, an effect not captured in a temperature-independent HLB value. When both water and oil are present, the temperature at which a surfactant transitions from being water soluble to oil soluble is known as the phase inversion temperature (PIT). Below the PIT, nonionic surfactants are water soluble, while above the PIT. they are oil soluble. Thus, from Bancroft s rule, a nonionic surfactant will form an 0/W emulsion below its PIT and a W/0 emulsion above its PIT. Likewise, increasing salt concentrations reduces the water solubility of ionic surfactant systems. At elevated salt concentrations, ionic surfactants will eventually partition into the oil phase. This is illustrated in Fig. 13. which shows aqueous micelles at lower salt concentrations and oil-phase inverse micelles at higher salt concentrations. Increasing the system temperature will likewise cause this same transition for nonionic surfactant systems. 

Hence, the rate of film thinning in System II is much greater than that in System I. Therefore, the location of the siufactant has a dramatic effect on the thinning rate and, thereby, on the drop lifetime. Note also that the interfacial tension in both systems is the same. Henee, the mere phase inversion of an emulsion, from Liquid 1-in-Liquid 2 to Liquid 2-in-Liquid 1 (Fig. 15), could change the emulsion lifetime by orders of magnitude. As diseussed in Sec. V, the situation with interaction in the Taylor regime (between spherical, nondeformed drops) is similar. These facts are closely related to the explanation of the Bancroft rule for the stability of emulsions (see Sec. V) and the process of chemical demulsifrcation (1). 

Equation 4.26 corresponds to a series model or the inverse rule of mixture as introduced in Chapter 3. Considering that phase 1 is the undecomposed material and phase 2 is the decomposed material, Eq. (4.27) can be obtained ... 

The temperature-dependent thermal conductivity was estimated by the inverse rule of mixture with reference to the physical series model. Again the volume fraction of each phase (undecomposed and decomposed) was directly obtained from the decomposition model and mass transfer model. The rapid decrease of thermal conductivity during the decomposition process was also well described in this way in the modeling of effective thermal conductivity. The modeling approach was compared with previous models and validated by experiments using the hot disk method. 

Phase inversion (route 4 in Figure 8.2) is a process, where for a given stabilizer, the continuous phase becomes the dispersed one and vice versa. This is mainly observed in the case of polymeric surfactants with a stabilizing moiety possessing a critical solution temperature. Prominent examples of these are surfactants with poly(ethylene glycol) units. Increasing the temperature leads to a decrease in the HLB of the surfactant and it may subsequently, in accordance with Bancroft s rule, promote the stabilization of a water-in-oil instead of an oil-in-water emulsion. Furthermore, whether or not... 

From the discussion of phase inversion in Sect. 7.1.2, the emulsion model predicts that immiscible blends should show positive deviation, PDB, from the log-additivity rule In r] = X In T]i. However, while PDB has been found in about 60 % of such blends, the remaining four types (see Fig. 7.32) must also be accounted for. This means that at least one other mechanism must be considered when modeling the viscosity-concentration dependence of polymer blends. This second mechanism should lead to the opposite effect, which is to the negative deviation fi om the log-additivity rule, NDB. 

As a rule, the HLB number is sensitive to temperature variation. For most surfactants, HLB increases by raising the temperature, so that at a certain temperature a phase transition may take place. Thus, a w/o emulsion may invert into an o/w emulsion upon increasing the temperature. Around the phase inversion temperature, HLB == 7, which results in a rather unstable emulsion. 

The extrudate swell ratio, B, plotted as a function of composition, was found to go through a local maximum within the phase inversion region. As a rule, B in blends is large and shows PDB. The effect is not related to deformation of the macromolecular coil (as in homopol)nner melts), but rather to the form recovery of the dispersed phase. 

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