Phase diagram For a one-component

Figure 3.11 Phase diagram for a one-component system (unary phase diagram).

A typical temperature-pressure phase diagram for a one-component system is shown in Figure 2.10. The sublimation curve AX indicates the increase of the vapour pressure of the solid with an increase in temperature. This is expressed quantitatively by the Clapeyron equation written as... 

We cannot conclude this section without presenting some SCIETs predictions for the phase diagrams. As summarized, the accuracy of the chemical potential is cmcial for phase equilibria. For a one-component system, the conditions of coexistence of the gaseous (g) and the liquid (/) phases in contact with each other at a given temperature T are... 

The relationship between temperature and pressure for which two phases co-exist at equilibrium is called the vapor pressure curve. This diagram summarizes all the vapor-liquid phase behavior for a one-component system. 

Fig. 2.1. Schematic free energy diagram for a one-component system at constant pressure. G refers to the glassy phase, L to the liquid, a and fi to allotropic crystalline phases...

We begin by looking at the phase diagram for a pure component. Pure fluids may be present in any one of three phases sohd, hquid, or gas. The phase boundaries occur along well-defined equilibrium curves, which determine where two phases can exist simultaneously. Figure 7.7 is a typical phase diagram (PVT diagram), which describes the phase behavior of some arbitrary fluid. 

The basis for the separation is that when two polymers, or a polymer and certain salts, are mixed together in water, they are incompatible, leading to the formation of two immiscible but predominantly aqueous phases, each rich in only one of the two components [Albertsson, op. cit. Kula, in Cooney and Humphrey (eds.), op. cit., pp. 451 71]. A phase diagram for a polyethylene glycol (PEG)-Dextran, two-phase system is shown in Fig. 22-85. Proteins are known to distribute unevenly between these phases. This uneven distribution can be used for the selective concentration and partial purification of the products. Partitioning between the two phases is controlled by the polymer molecular weight and concentration, protein net charge and... 

In the case of a unary or one-component system, only temperature and pressure may be varied, so the coordinates of unary phase diagrams are pressure and temperature. In a typical unary diagram, as shown in Figure 3.11, the temperature is chosen as the horizontal axis by convention, although in binary diagrams temperature is chosen as the vertical axis. However, for a one-component system, the phase rule becomes F=l-P+2 = 3-P. This means that the maximum number of phases in equilibrium is three when F equals zero. This is illustrated in Figure 3.11 which has three areas, i.e., solid, liquid, and vapour In any... 

Fig. 10.6. Schematic diagram of the energy, E, versus the number of particles, N, for a one-component fluid with a phase transition. Squares linked by dashed lines are coexisting phases joined by tie lines and the filled square indicates the critical point of the transition. Ellipses represent the range of particle numbers and energies sampled during different GCMC runs. Reprinted by permission from [6]. 2000 IOP Publishing Ltd...

Temperature and pressure are the two variables that affect phase equilibria in a one-component system. The phase diagram in Figure 15.1 shows the equilibria between the solid, liquid, and vapour states of water where all three phases are in equilibrium at the triple point, 0.06 N/m2 and 273.3 K. The sublimation curve indicates the vapour pressure of ice, the vaporisation curve the vapour pressure of liquid water, and the fusion curve the effect of pressure on the melting point of ice. The fusion curve for ice is unusual in that, in most one component systems, increased pressure increases the melting point, whilst the opposite occurs here. 

F is at most two because the minimum value for p is one. Thus, the temperature and pressure can be varied independently for a one-component, one-phase system and the system can be represented as an area on a temperature versus pressure diagram. 

Figure 4. Phase diagram from a two component system with one intermediate compound, 7, which exhibits peritectic melting and displaying limited solid solubility for a and ft.

A totally different way of looking at microemulsions —and one that connects this topic with previous sections of the chapter —is to view them as complicated examples of micellar solubilization. From this perspective, there is no problem with spontaneous formation or stability with respect to separation. Furthermore, ordinary and reverse micelles provide the basis for both O/W and W/O microemulsions. From the micellar point of view, it is the phase diagram for the four-component system rather than y that holds the key to understanding microemulsions. 

The projection of the three-dimensional surface on the pressure-temperature plane gives the familiar pressure-temperature diagram of a one component system. The projection for only the solid, liquid, and vapor phases... 

The simplest type of phase diagram involves a single component that can exist in more than one crystalline form, that is, a mineral having two or more polymorphs. For example, CaC03 can exist either in the form of calcite or aragonite. Using the equations we have derived, we can calculate either p or A Gp p for both... 

The phase diagram for a typical one-component system is illustrated in Fig. 9-1. The solid, liquid, and vapor regions are one-phase systems for which / = 2. The curves, whose slopes are given by Eq. (9-14), represent states of coexistence of pairs of phases and are univariant. At the triple point, three phases coexist, and the system then is invariant. 

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