LLE

There are two different situations for the liquid-liquid equilibrium in polymer-solvent systems  

Case (i) is considered now, case (ii) is specially considered below as swelling equilibrium. 

LLE-measurements do not provide a direct result with respect to solvent activities. Equation (4.4.8) says that solvent activities at given temperature and pressure must be equal in both coexisting phases. Since the solvent activity of such a coexisting phase is a priori not known, one has to apply thermodynamic models to fit LLE-data as functions of temperature and concentration. Solvent activities can be obtained from the model in a subsequent step only. 

As this subchapter is devoted to solvent activities, only the monodisperse case will be taken into account here. However, the user has to be aware of the fact that most LLE-data were measured with polydisperse polymers. How to handle LLE-results of polydisperse polymers is the task of continuous thermodynamics, Refs. Nevertheless, also solutions of monodisperse polymers or copolymers show a strong dependence of LLE on molar mass of the polymer, or on chemical composition of a copolymer. The strong dependence on molar mass can be explained in principle within the simple Flory-Huggins %-function approach, please see Equation [4.4.61]. 

Experimental methods can be divided into measurements of cloud-point curves, of real coexistence data, of critical points and of spinodal curves  

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In the next three sections we discuss calculation of liquid-liquid equilibria (LLE) for ternary systems and then conclude the chapter with a discussion of LLE for systems containing more than three components. 

For systems of type II, if the mutual binary solubility (LLE) data are known for the two partially miscible pairs, and if reasonable vapor-liquid equilibrium (VLE) data are known for the miscible pair, it is relatively simple to predict the ternary equilibria. For systems of type I, which has a plait point, reliable calculations are much more difficult. However, sometimes useful quantitative predictions can be obtained for type I systems with binary data alone provided that... 

Figure 16 shows observed and calculated VLE and LLE for the system benzene-water-ethanol. In this unusually fortunate case, predictions based on the binary data alone (dashed line) are in good agreement with the experimental ternary data. Several factors contribute to this good agreement VLE data for the mis-... 

For systems containing four components, most previous attempts for calculating LLE use geometrical correlations of ternary data (Branckner, 1940), interpolation of ternary data (Chang and Moulton, 1953), or empirical correlations of ternary data (Prince, 1954 Henty, 1964). These methods all have two... 

Guffey and Wehe (1972) used excess Gibbs energy equations proposed by Renon (1968a, 1968b) and Blac)c (1959) to calculate multicomponent LLE. They concluded that prediction of ternary data from binary data is not reliable, but that quarternary LLE can be predicted from accurate ternary representations. Here, we carry these results a step further we outline a systematic procedure for determining binary parameters which are suitable for multicomponent LLE. 

Type B. Components 1 and 2 are only partly miscible with each other. Both 1 and 2 are completely miscible with all other components in the system (3 through m). Components 3 through m are also miscible in all proportions. Both binary and ternary data are needed for a reliable description of the multicomponent LLE ... 

LLE provided that care is taken in obtaining optimum binary para-... 

Many well-known models can predict ternary LLE for type-II systems, using parameters estimated from binary data alone. Unfortunately, similar predictions for type-I LLE systems are not nearly as good. In most cases, representation of type-I systems requires that some ternary information be used in determining optimum binary parameter. 

I lle HIO+force field option in HyperChem hasno hydrogen bond-in g term, Th is is con sisten I with evolution andcommon useofthe CH.ARMM force field (even the 1983 paper did n ot usc a liydrogen boruiin g term in its exam pic calculation s an d men lion ed that the functional form used then was u n satisfactory and under review). 

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