Phase diagram condensed phases

Without phase diagrams, condensed phosphate chemistry would be almost impossible to understand. Properly prepared, a phase diagram is an equilibrium diagram, but in industrial processes equilibrium is seldom, if ever, achieved. Often, systems are very slow to reach demonstrable equilibrium. Industrial processes frequently require the production of hundreds of tons of materials in a short period and equilibrium must be compromised. However, if quality crystals are to be grown, even from industrial melts, equilibrium must be approached. This means that melts must be of uniform homogeneity and cooled at a rate that will allow diffusion to crystal surfaces to be orderly rather than forced. For most phosphate systems much reorganization is required for molecules to acquire dimensions and orientations to fit within a crystal lattice. 

Fig. IV-17. A schematic phase diagram illustrating the condensed mesophases found in monolayers of fatty acids and lipids.

It was estabhshed ia 1945 that monolayers of saturated fatty acids have quite compHcated phase diagrams (13). However, the observation of the different phases has become possible only much more recendy owiag to improvements ia experimental optical techniques such as duorescence, polarized duorescence, and Brewster angle microscopies, and x-ray methods usiag synchrotron radiation, etc. Thus, it has become well accepted that Hpid monolayer stmctures are not merely soHd, Hquid expanded, Hquid condensed, etc, but that a faidy large number of phases and mesophases exist, as a variety of phase transitions between them (14,15). 

The density functional approach has also been used to study capillary condensation in slit-like pores [148,149]. As in the previous section, a simple model of the Lennard-Jones associating fluid with a single associative site is considered. All the parameters of the interparticle potentials are chosen the same as in the previous section. Our attention has been focused on the influence of association on capillary condensation and the evaluation of the phase diagram [42]. 

FiG. 16 Phase diagrams for nonassociating and associating systems. The dashed lines denote the bulk coexistence while the solid lines denote the location of the capillary condensation. The sohd and dashed lines are, from the bottom, for = 0, 7, and 10. (From Ref. 42.)... 

Another interesting class of phase transitions is that of internal transitions within amphiphilic monolayers or bilayers. In particular, monolayers of amphiphiles at the air/water interface (Langmuir monolayers) have been intensively studied in the past as experimentally fairly accessible model systems [16,17]. A schematic phase diagram for long chain fatty acids, alcohols, or lipids is shown in Fig. 4. On increasing the area per molecule, one observes two distinct coexistence regions between fluid phases a transition from a highly diluted, gas -like phase into a more condensed liquid expanded phase, and a second transition into an even denser... 

FIG. 4 Phase diagram of Langmuir monolayers at low and intermediate surface coverage (schematic). Not shown are the various phases on the condensed side at high surface coverage. 

FIG. 8 Phase diagram of a Langmuir monolayer in a model of grafted stiff Lennard-Jones chains. LE denotes a disordered expanded phase, LC-U a condensed phase with untilted chains, LC-NN and LC-NNN condensed phases with collective tilt towards nearest neighbors and next-nearest neighbors, respectively, and LC-mod a phase which has a superstructure and an intermediate direction of tilt. (From Stadler and Schmid [151].)... 

The method of construction of this type of diagram will be illustrated using the general case of the three component system metal-sulphur-oxygen (M-S-O) whose values of AG for the reactions between the various condensed phases are given in Talile 7.37 on page 7 191. 

These isothermal diagrams can be used to consider the phase stability areas for more than one metal in contact with a common atmosphere and thus to assess the condensed phases which can be stable under the prevailing conditions. Figure 7.75 shows a stability diagram having phase areas for Co-S-O solid lines) and for Cu-S-O system broken lines). From this diagram it can be seen clearly that at 950 K at certain gas mixtures, pure metals Co and... 

SOLUTION Although the phase diagram in Fig. 8.6 is not to scale, we can find the approximate locations of the points. Point A is at 5 Torr and 70°C so it lies in the vapor region. Increasing the pressure takes the vapor to the liquid-vapor phase boundary, at which point liquid begins to form. At this pressure, liquid and vapor are in equilibrium and the pressure remains constant until all the vapor has condensed. The pressure is increased further to 800 Torr, which takes it to point B, in the liquid region. 

As discussed in Chapter 6, water forms strong hydrogen bonds and these lead to a number of important features of its atmospheric behavior. All three phases of water exist in the atmosphere, and the condensed phases can exist in equilibrium with the gas phase. The equilibria between these phases is summarized by the phase diagram for water. Fig. 7-9. 

We see from this diagram that partial pressures of H2O at ordinary conditions range from very small values to perhaps 30 or 40 mbar. This corresponds to a mass concentration range up to about 25 g H20/m. In typical clouds, relatively little of this is in the condensed phase. Liquid water contents in the wettest of cumulus clouds are around a few grams per cubic meter ordinary mid-latitude stratus clouds have 0.3-1 g/m. ... 

When two metals A and B are melted together and the liquid mixture is then slowly cooled, different equilibrium phases appear as a function of composition and temperature. These equilibrium phases are summarized in a condensed phase diagram. The solid region of a binary phase diagram usually contains one or more intermediate phases, in addition to terminal solid solutions. In solid solutions, the solute atoms may occupy random substitution positions in the host lattice, preserving the crystal structure of the host. Interstitial soHd solutions also exist wherein the significantly smaller atoms occupy interstitial sites... 

N2 and CO2 have triple points that are well below room temperature. Although both are gases at room temperature and pressure, they behave differently when cooled at P = 1 atm. Molecular nitrogen liquefies at 77.4 K and then solidifies at 63.3 K, whereas carbon dioxide condenses directly to the solid phase at 195 K. This difference in behavior arises because the triple point of CO2, unlike the triple points of H2 O and N2, occurs at a pressure greater than one atmosphere. The phase diagram of CO2 shows that at a pressure of one atmosphere, there is no temperature at which the liquid phase is stable. 

Allen, M.P., Simulation and phase diagrams. In Proceedings of the Euroconference on Computer simulation in Condensed Matter Physics and Chemistry, Binder, K., Ciccotti, G., Eds. European Union, 1996, pp. 255-284... 

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