Pressure-composition phase diagrams

Area within the coexistence curve of an isobaric phase diagram (temperature vs. composition) or an isothermal phase diagram (pressure vs. composition). 

Phase transitions in binary systems, nomially measured at constant pressure and composition, usually do not take place entirely at a single temperature, but rather extend over a finite but nonzero temperature range. Figure A2.5.3 shows a temperature-mole fraction T, x) phase diagram for one of the simplest of such examples, vaporization of an ideal liquid mixture to an ideal gas mixture, all at a fixed pressure, (e.g. 1 atm). Because there is an additional composition variable, the sample path shown in tlie figure is not only at constant pressure, but also at a constant total mole fraction, here chosen to be v = 1/2. 

The locations of the tietriangle and biaodal curves ia the phase diagram depead oa the molecular stmctures of the amphiphile and oil, on the concentration of cosurfactant and/or electrolyte if either of these components is added, and on the temperature (and, especially for compressible oils such as propane or carbon dioxide, on the pressure (29,30)). Unfortunately for the laboratory worker, only by measuriag (or correcdy estimatiag) the compositions of T, Af, and B can one be certain whether a certain pair of Hquid layers are a microemulsion and conjugate aqueous phase, a microemulsion and oleic phase, or simply a pair of aqueous and oleic phases. 

Fig. 12. Pressure-swing distillation of a minimum boiling binary azeotrope, (a) Temperature—composition phase diagram showing the effect of pressure on...

Figure 1.1 Phase diagram of the chromatograpliic mobile phase (after reference (21)), where the plane desaibes changing the composition and pressure at constant temperature.

The general thermodynamic treatment of binary systems which involve the incorporation of an electroactive species into a solid alloy electrode under the assumption of complete equilibrium was presented by Weppner and Huggins [19-21], Under these conditions the Gibbs Phase Rule specifies that the electrochemical potential varies with composition in the single-phase regions of a binary phase diagram, and is composition-independent in two-phase regions if the temperature and total pressure are kept constant. 

In phase diagrams for two-component systems the composition is plotted vs. one of the variables of state (pressure or temperature), the other one having a constant value. Most common are plots of the composition vs. temperature at ambient pressure. Such phase diagrams differ depending on whether the components form solid solutions with each other or not or whether they combine to form compounds. 

Experimental and theoretical studies, as well as computer simulators, all require knowledge of the number and compositions of the conjugate phases, and how these change with temperature, pressure, and/or overall (k ., system) composition. In short, all forms of enhanced oil recovery that use amphiphiles require a detailed knowledge of phase behavior and phase diagrams. 

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... 

At a given temperature and pressure eqs. (4.7) and (4.8) must be solved simultaneously to determine the compositions of the two phases a and P that correspond to coexistence. At isobaric conditions, a plot of the composition of the two phases in equilibrium versus temperature yields a part of the equilibrium T, x-phase diagram. 

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