Relation with phase diagrams

It is evident that the study of crystalline copolymers presents some very difficult as well as intriguing problems. The theoretical development of equilibrium relations and phase diagrams can be accomplished in principle when it is recognized that one must be concerned with the sequence propagation probability and not the composition. One major difficulty is that although the liquidus of the phase diagram can be determined quite easily, the solidus is extremely difficult to establish in most cases. In addition, it is virtually impossible to establish equilibrium on an experimental basis. As we have enumerated above there is a large number of important contributions to the deviations from equilibrium. The major ones are the finite crystallite size (relative to the equilibrium requirement), possible defected structures within the lattice and most importantly the structure of the interphase. 

The relations between the compositions of Pordand cements and some other common hydrauhc cements are shown in the CaO—Si02—AI2O2 phase diagram of Figure 2 (5). In this diagram, Fe202 has been combined with AI2O2 to yield the Al O content used. This is a commonly appHed approximation that permits a two-dimensional representation of the real systems. 

The curious phase relations between phosphorus, sulfur and their binai compounds are worth noting. Because both P4 and Sg are stable molecules the phase diagram, if studied below 100°, shows only solid solutions with a simple eutectic at 10° (75 atom % P). By contrast, when the mixtures are heated above 200° the elements react and an entirely different phase diagram is obtained however, as only the most stable compounds P4S3, P4S7 and P4S10... 

This work raises some interesting issues. The first is that the stoichiometry of a complex is not necessarily the most obvious. For example, it was reported initially that phthalic acid formed a 2 1 complex with alkoxystil-bazole [34], when in fact a careful study carried out by constructing a binary phase diagram (Fig. 11) revealed the complex to have a 1 1 ratio of the two components [35]. The reluctance of the system to form the more obvious 2 1 complex may relate to the presence of intramolecular hydrogen bonding or could even relate to the change in the pfCa of the second acid proton on com-plexation. 

When a reversible transition from one monolayer phase to another can be observed in the 11/A isotherm (usually evidenced by a sharp discontinuity or plateau in the phase diagram), a two-dimensional version of the Gibbs phase rule (Gibbs, 1948) may be applied. The transition pressure for a phase change in one or both of the film components can be monitored as a function of film composition, with an ideally miscible system following the relation (12). A completely immiscible system will not follow this ideal law, but will... 

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