Phase Equilibria in Poor Solvents

The conditions for equilibrium between two phases in a binary system are given by the equality of the chemical potentials in the two phases that is. 

Equations (3.48) and (3.49), derived previously, express the ehemical potentials and p2 as functions of the volume fraction 4 i of the polymer (note that = 1-02) and a single parameter X (note thatx and are equal) occms in these fractions. Ful llment of the conditions represented by Eqs. (3.94) and (3.95) requires that there be two concentrations at which the chemical potential yUi or AyUi has the same value, and so also the chemical potential p2 or A//2. Since and fi2 are derived by differentiating the same free energy function, Eq. (3.45), it suf ces to consider only one of them. 

Problem 3.13 A polymer solution was cooled slowly until phase separation took place. The volume fractions of polymer in the two phases at equilibrium were found to be 0.01 and 0.89, respectively. Using the Hory-Huggins equation for Ayui [cf. Eq. (3.48)] and the equilibrium condition A j = Ap[, obtain a value of the polymer-solvent interaction parameterfor the conditions of phase separation. 

In order to use the Flory-Huggins equation for Ayui, the number-average value of cr (the number of segments per polymer molecule) should be known. However, for most polymers, cr is suf ciently large for (1 - 1/cr) 1.0. Making this assumption and applying the c ndition AyUj = Ap leads to 

It is readily seen from Fig. 3.6 that for each value of if abovethere are two different values of p2 at which the chemical potential of the solvent in the two phases is the same. This means that solutions with concentrations represented by these two values of f 2 can be in thermodynamic equihbrium for x Xc- It also implies that a solution which has an intermediate value of 2 will spontaneously separate into two stable liquid phases with these two concentrations and a concomitant decrease in the free energy. Thus, if is increased by decreasing the temperature, a fully miscible system at higher temperamres is transformed to one of limited miscibiUty at the lower temperature. At some critical temperature Tc, during this process, incipient phase separation (as indicated by the onset of an opalescence) is encountered, followed by separation into distinct liquid phases at still lower temperatures. 

Application of the critical conditions to the chemical potential as given by Eq. (3.53) yields 

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Several methods can be used to determine theta solvents. These include phase equilibria studies (see Phase Equilibria in Poor Solvents), determination of second virial coeflJicient (see Problem 3.8), viscosity-molecular weight relationship, and cloud point titration. 

In the cloud point titration method, polymer solutions of different concentrations are titrated with a nonsolvent until the first sign of cloudiness (see Phase Equilibria in Poor Solvents). The logarithm of the nonsolvent concentration at the cloud point is then plotted against the logarithm of the polymer concentration at the cloud point and extrapolated to 100% polymer. The solvent/non-solvent mixture corresponding to the 100% polymer is a theta-mixture. 

Macrosyneresis, in which the network polymer is contained only in one phase is not the only possibility for phase equilibria in networks. Under favorable conditions two polymer phases can coexist in a network with a diluent phase (50). The two polymer phases in equilibrium differ in the conformations of the network chains. The transition resembles the condensation of a real gas or, in macromolecules, an intramolecular transition due to long-range net attraction between segments in a poor solvent (coil-globule type transition [139)). 

Quaternary ammonium or phosphonium salts. In the above-mentioned case of NaCN, the uncatalyzed reaction does not take place because the CN" ions cannot cross the interface between the two phases, except in very low concentration. The reason is that the Na ions are solvated by the water, and this solvation energy would not be present in the organic phase. The CN ions cannot cross without the Na ions because that would destroy the electrical neutrality of each phase. In contrast to Na+ ions, quaternary ammonium (R4N )4116 and phosphonium (R4P ) ions with sufficiently large R groups are poorly solvated in water and prefer organic solvents. If a small amount of such a salt is added, three equilibria are set up ... 

Extraction and phase equilibria measurements have shown, that in the temperature range with good extraction rates the solubility is rather poor. Nevertheless it was possible to extract 70 vol.% of the binder within one hour without damaging the parts. This is a good improvement compared to usual pyrolysis or extraction processes with organic solvents or water, which last 1-2 days for parts of the described geometry. 

In general, an extraction process involves an extractor and a solvent-recovery operation. The recovered solvent is recycled back to the extractor, making an extraction loop necessary. The feasibility of the loop must be demonstrated. This is especially important for chemical systems with complex and poorly understood phase equilibria. For example, a systems where the slope of the equilibrium line changes significantly with solute concentration may be prone to pinching. 

Eq. (28) thus obtained can be used to represent the solubility of poorly soluble drugs in aqueous mixed solvents if information about the properties of the binary solvent (composition, phase equilibria and molar volume), the nonideality parameters and the constant A is available. These parameters can be considered as adjustable, and determined by fitting the experimental solubilities in the binary solvent. We applied such a procedure to the solubilities of caffeine in water/AW-dimethylformamide (Herrador and Gonzalez, 1997) and water/1,4-dioxane (Adjei et al., 1980), of sulfamethizole in water/1,4-dioxane (Reillo et al., 1995) as well as of five solutes in water/ propylene glycol (Rubino and Obeng, 1991). It was shown that Eq. (28) provides accurate correlations of the experimental data. 

Phase Equilibria. From recent research (Schneider and Peters) it became apparent that in the near-critical region of certain ternary carbon dioxide mixtures, due to co-solvency effects of the two solutes relative to each other, the fluid multiphase behavior can be quite complex. Phenomena like immiscibility windows and holes are not unusual, which have their consequences for separations in near-critical processing. Peters stressed that for many applications in supercritical technology carbon dioxide is not an appropriate choice since for many solutes it is a poor solvent that would require the use of a cosolvents. If safety and environmental constraints permit, it is certainly worthwhile to consider alternatives for carbon dioxide. Gulari, Schneider and Peters emphasized the importance of studying representative model systems in order to obtain insight into the systematic variations of the complex phase behavior that may occur in near-critical multicomponent mixtures. Debenedetti stressed the importance of focusing on complex fluids like emulsions. 

Studies on ternary liquid-liquid equilibria have centred on specific challenges facing the chemical, petrochemical, pharmaceutical and biochemical industries. A summary of the ternary liquid-liquid equilibria data (selectivities, capacities) for aliphatic-aromatic separations with ionic hquids is presented in Table 1. The aromatic content (expressed as a percentage) is included to provide an indication of the region in which the selectivity and capacity values are determined (since these are a function of the overall composition). Selectivity and capacity values of traditionally or commercially employed solvents have been included for comparative purposes. The favourable characteristics required for solvents suitable for aromatic-aliphatic separations are the following large selectivity and capacity values, high solubihty of the aromatic components in the ionic hquid, poor solubihty of the ahphatic components in the ionic liquid and the availability of fairly simple and inexpensive means to recover the ionic hquid from the extract and raffinate phases. 

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