One-Component Phase Diagrams

While the Gibbs phase rule provides for a qualitative explanation, we can apply the Clapeyron equation, derived earlier [equation (5.71)], in conjunction with studying the temperature and pressure dependences of the chemical potential, to explain quantitatively some of the features of the one-component phase diagram. 

For all one-component phase diagrams, choose the correct statement from the following list. 

Shown below is a one-component phase diagram. There exist 4 different phases, namely, a, P, y and 5. 

There are a number of applications of one-component phase diagrams in ceramics. One such application is the development of commercial production of synthefic diamonds from graphite. For this, high temperatures and high pressures are necessary. This is evident from the phase diagram of carbon shown in Figure 4.1 [1]. 

Perhaps the simplest and easiest type of phase diagram to understand is that for a one-component system, in which composition is held constant (i.e., the phase diagram is for a pure substance) this means that pressure and temperature are the variables. This one-component phase diagram (or unary phase diagram, sometimes also called a pressure-temperature [or P-T diagram) is represented as a two-dimensional plot of... 

For one-component phase diagrams, the logarithm of the pressure is plotted versus the temperature solid-, liquid-, and vapor-phase regions are found on this type of diagram. 

Prototypical pure substances occur in at least one solid phase, a liquid phase, and a vapour (gas) phase and can be defined/identified in terms of their one-component-phase diagram, triple point(s) connecting the phases. Intermediate substances can be identified by their location in phase diagrams. Substances that seem to occur in only one phase or which cannot be put into bottles for one reason or another can be situated relative to protot3q>ical substances. Different research contexts may lead to different classifications of non-standard cases, but often a distinction of component, substance, and species will resolve some ambiguities. 

A common use of three-component phase diagrams is in analysis of miscible displacement. For instance, Figure 2-30 gives the phase envelope of an oil mixed with carbon dioxide.6 The oil is plotted as an artificial two-component mixture, with methane as one component and all other constituents added together as the other component. 

In situ polymerisation does not however guarantee homogeneous blends as two phase regions can exist within the polymer/polymer/monomer three component phase diagram. In the case of vinyl chloride polymerisation with solution chlorinated polyethylene, the vinyl chloride has limited solubility in both poly(vinyl chloride) and chlorinated polyethylene. The phase diagram has the form shown in Fig. 3 The limit of swelling of vinyl chloride in the chlorinated polyethylene is A and the highest concentration of PVC prepared by a one-shot polymerisation is B. 

Fig. 3. The three component phase diagram for vinyl chloride, PVC and a chlorinated polyethylene is A and the highest concentration of PVC in a homogeneous blend prepared by a one-shot polymerisation is B...

For systems of more than one chemical component, the concentrations of each are additional variables. A typical two-component phase diagram displays the variation of vapor pressure or melting point with composition at a fixed pressure, for example. 

A phase diagram is a graphic representation of the phase behavior of a system under study. The behavior of a single component as a function of temperature and pressure can be represented on a phase diagram, which will show the conditions under which a material is a solid, liquid, or gas. More complex phase diagrams may involve several components. Phase diagrams are very useful tools for formulation, as they allow one to define not only the acceptable composition range of a product but also enable one to optimize the order of addition of the different raw materials. 

Such a phase diagram is valid at one temperature. The effect of temperature on a three-component phase diagram can be visualized in three dimensions, with temperature on the elevation axis. The phase diagram looks like a triangular prism, with every horizontal slice corresponding to one temperature. 

Similar treatment can also be applied to three-component systems, in which two of the three components are immiscible with each other, but each of these components is infinitely miscible with the third one. The phase diagrams in such three-component systems contain a so-called line of the critical states, which shows the critical composition as a function of temperature. In such systems the critical state can be approached from the side of a two-phase system by both changing the temperature and altering the composition. 

Clarke and Vincent presented their results in the form of what they termed triangular, three component phase diagrams, one of which is reproduced as Fig. 16.3. 

It is interesting to note that this Scandinavian contribution was in agreement with Schulman s original concept of microemulsions as micellar solutions [3] the name microemulsions was coined much later [27]. Following Gillberg et al.. Ranee and Friberg [28] demonstrated that the O/W microemulsion is a direct continuation of the well-known Ekwall et al. aqueous micellar solutions [17] (Fig. 3). It should be noted that the common presentation of these four-component phase diagrams as phase maps in one plane... 

The simple crystallization of a binary eutectic system only produces one of the components in pure form, while the residual mother hquor composition progresses towards that of the eutectic (section 4.3.1). There is often a need, however, to produce both components in pure form, and one way in which this may be achieved is to add a third component to the system which forms a compound with one of the binary components. Phase diagrams for systems with compound formation are discussed in section 4.3.2. 

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