Sublimation curve

Figure 8 An example of the decreasing heat requirement during primary drying at a chamber pressure of 0.15 torr. 5% mannitol maintained at -20°C during primary drying. Results obtained by computer simulation of freeze drying (see Ref. 3). Heavy curve Shelf Fluid. Light curve Shelf surface. Lightweight dashed curve Product Bottom. Heavy dashed curve Sublimation.

At a given temperature and pressure, a pure compound can exist in one, two or three states. The compound exists at three different states at the triple point and at two different states along the curves of vaporization, freezing and sublimation. Refer to Figure 4.6. 

To understand the conditions which control sublimation, it is necessary to study the solid - liquid - vapour equilibria. In Fig. 1,19, 1 (compare Fig. 1,10, 1) the curve T IF is the vapour pressure curve of the liquid (i.e., it represents the conditions of equilibrium, temperature and pressure, for a system of liquid and vapour), and TS is the vapour pressure curve of the solid (i.e., the conditions under which the vapour and solid are in equili-hrium). The two curves intersect at T at this point, known as the triple point, solid, liquid and vapour coexist. The curve TV represents the... 

The sublimation and evaporation curves of solid and liquid phosphonium chloride (PH4C1), however, meet at a very decided angle at the triple point (Tammann, Kryst. und Schmelz., p. 291). The curves are represented in Fig. 48. 

Kirchhoffs investigation does not show that the sublimation and evaporation curves meet each other at the temperature at which solid and liquid are in equilibrium with vapour it proves that they are inclined at an angle, but the further fact that they intersect requires separate proof, which was inferred by James Thomson, and experimentally demonstrated by Ferche (1891) in the case of benzene the point of intersection, calculated from the vapour-pressure curves, was 5 405° C, whereas the melting-point was 5 42° C. 

With the help of these data Ktot and b/p can be calculated, if the water pressure at the sublimation front (pj and the partial vapor pressure in the chamber, measured by a hygrometer, is taken from the respective curves. 

Wagner, W., Saul, A., and Pruss, A. 1994. International equations for the pressure along the melting and along the sublimation curve of ordinary water substance. J. Phys. Chem. Ref. Data 23, 515-527. 

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. 

A sublimation process is controlled primarily by the conditions under which phase equilibria occur in a single-component system, and the phase diagram of a simple one-component system is shown in Figure 15.30 where the sublimation curve is dependent on the vapour pressure of the solid, the vaporisation curve on the vapour pressure of the liquid, and the fusion curve on the effect of pressure on the melting point. The slopes of these three curves can be expressed quantitatively by the Clapeyron equation ... 

Curve AB It is sublimation or vapour pressure curve of solid a. Along this curve, two phases a and vapour are in equilibrium. 

Curve BC It is vapour pressure or sublimation curve for b. On this curve two phases b and vapour are in equilibrium. 

The vap. press, curve of solid iodine is indicated by PO, Fig. 16 that of liquid iodine by 00 and the effect of press, on the m.p. of iodine by ON. At the triple point 0 these curves meet. Fig. 18 shows a similar curve for water. The curve PO thus represents the sublimation curve or hoar-frost line OC. the boiling or vaporization curve, i.e. the effect of press, on the b.p. of the liquid. The same phenomenon occurs with water, iodine, etc., and the principle involved is the same as indicated in the law represented by Clapeyron-Clausius equations with respect to the lowering of the m.p. by an increase of press. Consequently, if the vap. press, of iodine be less than that of th,e triple point, the solid does not melt, but rather sublimes directly without melting at the triple point at 114-15° (89 8 mm.) and A. von Richter at 116 1° (90 mm.). According to R. W. Wood, if the condensation of iodine vapour occurs above —60°, a black granular deposit is formed, but below that temp, a deep red film is produced. 

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