Critical miscibility temperature

It is clear that the Flory-temperature is the critical miscibility temperature in the limit of infinite molar weight. Fox (1962) succeeded in correlating 0F-temperatures of polymer-solvent systems with the solubility parameter 5S of the solvent. Plots of 8S as a function of 0F are shown in Fig. 7.8. 

The precipitation behavior of the polymer is intapreted by a photostimulated change of the critical miscibility temperature T. For polystyrene dissolved in cyclohexane, the polymer precipitates at temperature below T. According Fox and Flory [65], T depends on the molecular weight M as... 

Fig. 32. Molecutar weight (M) depmdence of critical miscible temperature, T. T Q and Te(T) indicate the values of T, for polystyrene with cis and trans azobenzene groups at M = oo, respectively. See text for M, t, t Tm, and T ...

Theory thus predicts that the reciprocal of the critical temperature (in °K ) for the onset of opalescence should vary linearly with the reciprocal of the square root of the molecular weight in a given polymer-solvent system. Furthermore, 9 may now be identified as the critical miscibility temperature in the limit of infinite molecular weight. 

The theta temperature may also be phenomenologically defined as the critical miscibility temperature at the limit of infinite molar mass (110). Since a solution may exhibit two... 

Partially miscible liquids. Critical solution temperature. 

The third type of system gives a closed solubility curve and therefore possesses both an upper and lower critical solution temperature. The first case of this type to be established was that of nicotine and water the solubility curve is illustrated in Fig. I, 8, 3. The lower and upper consolute temperatures are 60 8° and 208° respectively below the former and above the latter the two liquids are completely miscible. 

It should be noted that the modern view is that all partially miscible liquids should have both a lower and upper critical solution temperature so that all such systems really belong to one class. A closed solubility curve is not obtain in all cases because the physical conditions under normal pressure prevent this. Thus with liquids possessing a lower C.S.T., the critical temperature (the critical point for the liquid vapour system for each component, the maximum temperature at which liquefaction is possible) may be reached before the consolute temperature. Similarly for liquids with an upper C.S.T., one or both of the liquids may freeze before the lower C.S.T. is attained. 

Influence of added substances upon the critical solution temperature. For a given pressure the C.S.T. is a perfectly defined point. It is, however, affected to a very marked extent by the addition of quite a small quantity of a foreign substance (impurity), which dissolves either in one or both of the partially miscible liquids. The determination of the consolute temperature may therefore be used for testing the purity of liquids. The upper consolute temperature is generally employed for this purpose. 

If the temperature is changed the miscibility of the liquids alters, and at a particular temperature the miscibility may become total this is called the critical solution temperature. With rise of temperature the surface of separation between the liquid and vapour phases also vanishes at a definite temperature, and we have the phenomenon of a critical point in the ordinary sense. According to Pawlewski (1883) the critical temperature of the... 

We consider a binary liquid mixture of components 1 and 3 to be consistent with our previous notation, we reserve the subscript 2 for the gaseous component. Components 1 and 3 are completely miscible at room temperature the (upper) critical solution temperature Tc is far below room temperature, as indicated by the lower curve in Fig. 27. Suppose now that we dissolve a small amount of component 2 in the binary mixture what happens to the critical solution temperature This question was considered by Prigogine (P14), who assumed that for any binary pair which can be formed from the three components 1, 2 and 3, the excess Gibbs energy (symmetric convention) is given by... 

Equations (115)—(117), indicate that under the conditions just described, 8Tc/8x2 is both large and positive, as desired i.e., dissolution of a small amount of component 2 in the 1-3 mixture raises the critical solution temperature, as shown in the upper curve of Fig. 27. From Prigogine s analysis, we conclude that if component 2 is properly chosen, it can induce binary miscible mixtures of components 1 and 3 to split at room temperature into two liquid phases having different compositions. 

Most hydrophobic substances have low solubilities in water, and in the case of liquids, water is also sparingly soluble in the pure substance. Some substances such as butanols and chlorophenols display relatively high mutual solubilities. As temperature increases, these mutual solubilities increase until a point of total miscibility is reached at a critical solution temperature. Above this temperature, no mutual solubilities exist. A simple plot of solubility versus temperature thus ends at this critical point. At low temperatures near freezing, the phase diagram also become complex. Example of such systems have been reported for sec-butyl alcohol (2-butanol) by Ochi et al. (1996) and for chlorophenols by Jaoui et al. (1999). 

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