Quaternary diagrams

Figure 3.4 Bidimensional cuts (b, d) through a tridimensional quaternary diagram (a, c). Seen is a cut at constant surfactant-to-alcohol ratio (b) and at constant water-to-oil ratio (d), respectively...

Quaternary systems, such as surfactant-alcohol-oil-water (SAOW), are analyzed in a quaternary diagram made in a regular tetrahedron as indicated in Fig. 16. The brute force method that consists of selecting hundred.s of composition points in the diagram (located at some grid pattern) and in analyzing the phase behavior in all the.se points is of course too tedious to be carried out. 

Figure 17, upper left is a tetrahedron representation of a quaternary diagram containing a hydrophilic surfactant and a quite lipophilic alcohol (109). The other diagrams in Fig. 17 are different cuts at constant S/A ranging from a very hydro-... 

Figure 17 Quaternary diagram and dirfcreni pseudotimi cuts ai S/A constant. (Adapted from Ref. I09.)...

The methods of experimental determination and the calculation of different values associated with chemical reactions (enthalpies, entropies, calorific capacities, free and constant equilibrium enthalpies) lead to complex equilibrium calculations and their graphical representations in various forms pole figures, generalized Ellingham diagrams, binary, tertiary and quaternary diagrams. 

Chapter 3 discusses the different aspects of the law of mass action and the equilibrium constants associated therewith. A number of graphical representations used in the study of chemical equilibria are presented. In turn, we examine pole diagrams and equilibrium representations with temperature, with the generalization of Ellingham diagrams. The ehapter ends with a presentation of binary, ternary and quaternary diagrams of chemical equilibria. 

It is often recommended to use a pair of emulsifiers (one of high HLB, another of low HLB) rather than only one emulsifier. In this case, a quaternary diagram is used instead of the ternary one. 

First, it is obvious that none of the Winsor diagrams will match this behavior because the amphiphile mixture has a varying affinity that depends on the relative amounts of, for instance, a hydrophilic surfactant (S) and a lipophilic alcohol (A). A quaternary diagram is required to handle this four-component system (e.g., a regular tetreihedron with equal sides). At each vertex, one of the components is represented. 

The physico-chemical formulation deals with the nature of the components, which are at least three, and will be referred to as surfactant (S), oil.(0), and water (W). For the sake of simplicity, the alcohol effect is going to be taken into accoimt as another formulation variable, which is an elegant way of avoiding entering the maze of quaternary diagram phase behavior. 

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