Solubility multicomponent liquid system

This chapter summarizes the thermodynamics of multicomponent polymer systems, with special emphasis on polymer blends and mixtures. After a brief introduction of the relevant thermodynamic principles - laws of thermodynamics, definitions, and interrelations of thermodynamic variables and potentials - selected theories of liquid and polymer mixtures are provided Specifically, both lattice theories (such as the Hory-Huggins model. Equation of State theories, and the gas-lattice models) and ojf-lattice theories (such as the strong interaction model, heat of mixing approaches, and solubility parameter models) are discussed and compared. Model parameters are also tabulated for the each theory for common or representative polymer blends. In the second half of this chapter, the thermodynamics of phase separation are discussed, and experimental methods - for determining phase diagrams or for quantifying the theoretical model parameters - are mentioned. 

Chemical Description. The constituents of the system include atoms, ions, molecules as well as molecular and nonmolecular solids. The homogeneous catalytic reaction of interest occurs in the multicomponent liquid phase Pl- By definition, all the molecular and ionic species S involved directly in the catalysis are soluble in this liquid phase. In particular, one or more organic reagents must be present in Pl- The liquid phase must contain numerous soluble transition-metal... 

Whilst it is obviously valuable to measure the solubility of reagents in the SCF, it is important to be aware that the solubility in a multicomponent system can be very different from that in the fluid alone. It is also important to note that the addition of reagents and catalysts can have a profound effect on the critical parameters of the mixture. Indeed, at high concentrations of reactants, the mole fraction of C02 is necessarily lower and it may not be possible to achieve a supercritical phase at the temperature of interest. Increases in pressure (i.e. further additions of C02) could yield a single liquid phase (which would have a much lower compressibility than scC02). For example, the Diels-Alder reaction (see Chapter 7) between 2-methyl-1,3-butadiene and maleic anydride has been carried out a pressure of 74.5 bar and a temperature of 50 °C, assuming that this would be under supercritical conditions as it would if it were pure C02. However, the critical parameters calculated for this system are a pressure of 77.4bar and a temperature of 123.2 °C, far in excess of those used [41]. 

Very few generalized computer-based techniques for calculating chemical equilibria in electrolyte systems have been reported. Crerar (47) describes a method for calculating multicomponent equilibria based on equilibrium constants and activity coefficients estimated from the Debye Huckel equation. It is not clear, however, if this technique has beep applied in general to the solubility of minerals and solids. A second generalized approach has been developed by OIL Systems, Inc. (48). It also operates on specified equilibrium constants and incorporates activity coefficient corrections for ions, non-electrolytes and water. This technique has been applied to a variety of electrolyte equilibrium problems including vapor-liquid equilibria and solubility of solids. 

The Wilson parameters Ay and NRTL parameters Qy inherit a Boltzmann-type T dependence from the origins of the expressions for G, but it is only approximate. Computations of properties sensitive to this dependence (e.g., heats of mixing and liquid/liquid solubility) are in general only qualitatively correct. However, all parameters are found from data for binary (in contrast to multicomponent) systems, and this makes parameter determination for the local composition models a task of manageable proportions. 

These three approaches have found widespread application to a large variety of systems and equilibria types ranging from vapor-liquid equilibria for binary and multicomponent polymer solutions, blends, and copolymers, liquid-liquid equilibria for polymer solutions and blends, solid-liquid-liquid equilibria, and solubility of gases in polymers, to mention only a few. In some cases, the results are purely predictive in others interaction parameters are required and the models are capable of correlating (describing) the experimental information. In Section 16.7, we attempt to summarize and comparatively discuss the performance of these three approaches. We attempt there, for reasons of completion, to discuss the performance of a few other (mostly) predictive models such as the group-contribution lattice fluid and the group-contribution Flory equations of state, which are not extensively discussed separately. 

As will be evident from the examples cited below, the S-S theory for multicomponent systems has been successful in describing thermodynamics (e.g., phase equilibria, CED, solubility) and PVT behavior of polymer mixtures with gases, liquids, or solids. For binary systems, Eqs. (6.49) and (6.51) might be written as... 

As could be expected, challenges facing the pharmaceutical industry contribute to the advancement of the computational soUd-state chemistry. For example, some of the virtual screening and other CPSSC methods were developed specifically to help address issues of the pharmaceutical industry. Significant progress has been made recently in many traditional applications (e.g., solubility prediction [55], CSP [56], and morphology prediction [25, 57, 58]) in order to accommodate predictions for complex pharmaceutical systems (solid and liquid multicomponent phases of relatively large and flexible molecules). 

It is more complicated to calculate LLE in multicomponent systems accurately than to describe vapor-liquid or solid-hquid equilibria. The reason is that in the case of LLE the activity coefficients have to describe not only the concentration dependence but also the temperature dependence correctly, whereas in the case of the other phase equilibria (VLE, SLE) the activity coefficients primarily have to describe the deviation from ideal behavior (Raoult s law resp. ideal solid solubility), and the temperature dependence is mainly described by the standard fugacities (vapor pressure resp. melting temperature and heat of fusion). 

In closing, we would like to mention some applications of the GEMC/CBMC approach and very much related combination of CBMC and the grand canonical Monte Carlo technique to other complex systems prediction of structure and transfer free energies into dry and water-saturated 1-octanol [72], prediction of the solubility of polymers in supercritical carbon dioxide [73], prediction of the upper critical solution pressure for gas-expanded liquids [74], investigation of the formation of multiple hydrates for a pharmaceutical compound [75], exploration of multicomponent vapor-to-particle nucleation pathways [76], and investigations of the adsorption of articulated molecules in zeolites and metal organic frameworks [77, 78]. 

Except for the consideration of solvent vaporization in the above discussion of adiabatic packed towers, it has thus far been assumed that only one component of the gas stream has an appreciable solubility. When the gas contains several soluble components or the liquid several volatile ones for stripping, some modifications are needed. The almost complete lack of solubility data for multicomponent systems, except where ideal solutions are formed in the liquid phase and the solubilities of the various components are therefore mutually independent, unfortunately makes estimates of even the ordinary cases very difficult. However, some of the more important industrial applications fall in the ideal-solution category, e.g., the absorption of hydrocarbons from gas mixtures in nonvolatile hydrocarbon oils as in the recovery of natural gasoline. 

Properties of multicomponent systems includes solubility, activity coefficients, diffusion coefficients, phase diagrams, vapor-liquid equilibrium data on mixtures, etc. These are generally functions of temperature, pressure, and composition. 

---