Sublimation pressure relationship

Along the line AB, solid is in equilibrium with vapor. If the pressure is decreased below the line AB, the solid will sublime. This relationship is the basis of freeze-drying foods, such as those shown in Figure 25. The food is frozen, and then a vacuum is applied. Water sublimes, which dehydrates the food very quickly. The food breaks down less when water is removed at the low temperature than when water evaporates at normal temperatures. 

Two substances frequently occur in process calculations as solids water and carbon dioxide. It is useful to know the relationships of their sublimation pressures. They are... 

Enthalpy of Vaporization (or Sublimation) When the pressure of the vapor in equilibrium with a liquid reaches 1 atm, the liquid boils and is completely converted to vapor on absorption of the enthalpy of vaporization ISHv at the normal boiling point T. A rough empirical relationship between the normal boiling point and the enthalpy of vaporization (Trouton s rule) is ... 

Properties.— The salt separating from its vapour is orange-red, as are thin films, but in mass the sublimed material appears black. It sublimes readily at pressures below 10" mm. at above 90°. Attempts to determine the vapour pressure-temperature relationship failed because pressures developed below 130° are small in comparison with the probable error, and the compound reacts with the glass container above that temperature. When heated in a sealed tube it melts to a viscous liquid at 219° and evolves a little gas. But decomposition is incomplete at this temperature since A -ray photographs still show the characteristic cubic phase. 

Makatun and Pechkovskii [70MAK/PEC] measured the vapour pressure of Se02(g) over supercooled Se02(l) (Se02(cr) sublimes) and Se02(cr) in the temperature interval 530 to 660 K. No primary data are available and the results were represented by the relationships ... 

A number of studies have explored ways in which partial vapor pressures may be obtained using TGA data, thereby allowing both prediction of vapor pressure under a range of circumstances and calculation of the constants associated with the approaches described previously. In particular, Price and Hawkins (12) have argued that the rate of mass loss for vaporization and sublimation within a TGA should be a zero-order process, and hence should be constant for any given temperature, subject to the important condition that the available surface area also remains constant. This means that the value of v from Equation 6.4 should be easily calculated from the TGA data. If one performs this experiment for materials with known vapor pressure and temperature relationships (the authors used discs of acetamide, benzoic acid, benzophenone, and phenanthrene), then the constant k for the given set of TGA experimental conditions may be found. Once this parameter is known, the vapor pressure may be assessed for an unknown material in the same manner. 

The volume of a material is a function of both the temperature T and the pressure p, as described by its pressure-volume-temperature (PVT) relationships. These relationships incorporate a description of the complete phase behavior of a material, such as the significant changes which take place when the material undergoes a phase transition (for example when a solid melts or sublimes, or when a liquid boils). The preceding discussion focused on the dependence of the volumetric properties on the temperature only, at atmospheric pressure, since there are no simple and general quantitative stmcture-property relationships to describe the full PVT behavior. This topic is of great importance, however, and will now be reviewed. 

The complex relationship between chamber pressure and temperatures of shelf and product, and its impact on the sublimation rate, is illustrated in Figure 6 for a recombinant protein preparation. " Let us assume that Tg for such a composition is -20°, so that the drying conditions must be set to ensure that the product temperature does not exceed this value at any time during the primary drying cycle. The sublimation rate corresponding to point A, at a chamber pressure of 40... 

The 8,-82-V triple point is one at which the reversible transformation of the crystalline polymorphs can take place. If both 8, and 82 are capable of existing in stable equilibrium with their vapor phase, then the relation is termed enantiotropy, and the two polymorphs are said to bear an enantiotropic relationship to each other. For such systems, the 8,-82-V triple point will be a stable and attainable value on the pressure-temperature phase diagram. A phase diagram of a hypothetical enantiotropic system is shown in Fig. 7. Each of the two polymorphs exhibits a 8-V sublimation curve, and they cross at the same temperature at which they meet the 8,-82 transition curve. The 82-V curve... 

Phase Transitions The states of matter can be interconverted by heating or cooling. Two phases are in equilibrium at the transition temperature such as boiling or freezing. Solids can also be directly converted to vapor by sublimation. Above a certain temperature, called the critical temperature, the gas of a substance cannot be made to liquefy. The pressure-temperature relationships of solid, liquid, and vapor phases are best represented by a phase diae... 

This relationship for the Knudsen regime (low total gas pressure, low sublimation temperature) has been validated by Hottot et al. (2005) who compared with freezedrying experiments conducted with a model BSA formulation with annealing treatment (cf. Fig. 3.19). In the case ofa standard freeze-drying cyde, this successful validation represents a positive result due to numerous assumptions involved in the model and to quite large uncertainties in the corresponding modd parameter values. 

---