Supercooled or supersaturated

A primary concern is polymorphic crystallization in which the Ostwald step rule is very useful (9). This rule predicts that phase changes occur step by step by way of successively more stable phases. For the relative rate of nucleation of polymorphic crystals shown in Figure 2, it follows that nucleation of the metastable forms such as a and p occurs first before the most stable p form, when nucleation occurs under a large supercooling or high supersaturation. When the amount of supercooling or supersaturation is decreased, the law is broken and the most stable form tends to nucleate at a relatively slow rate. 

The key factors influencing the purity drop phenomena are considered at first. They must be the factors which enh ce primary nucleation or growth of attached tiny crystalline particles on the seed crystals therefore a list of factors would include solution supercooling (or supersaturation), agitation speed, suspension density, mass of seed crystals, pretreatment of seed crystals, cooling rate and phase equilibria of given systems. Effects of these factors investigated in literature are examined separately. 

Curvature further plays an important role in phase transitions. The formation of a new phase starts with nuclei, very small particles, droplets, or bubbles. The strong curvature retards the growth of the nuclei so that formation of the new phase therefore occurs only after superheating, supercooling, or supersaturation. 

In bulk media without impurities or template thin films, no crystallization occurs over a long time when supercooling or supersaturation is minimized. However, when template thin films are added, the induction time is dramatically minimized, as experimentally evidenced for n-alcohol crystallization in solution [51,52]. In such studies, the template effect was varied according to the type of host templates and the relationship between the chain lengths of the host and guest molecules (numbers of carbon atoms). 

It is a well-known fact that substances like water and acetic acid can be cooled below the freezing point in this condition they are said to be supercooled (compare supersaturated solution). Such supercooled substances have vapour pressures which change in a normal manner with temperature the vapour pressure curve is represented by the dotted line ML —a continuation of ML. The curve ML lies above the vapour pressure curve of the solid and it is apparent that the vapour pressure of the supersaturated liquid is greater than that of the solid. The supercooled liquid is in a condition of metastabUity. As soon as crystallisation sets in, the temperature rises to the true freezing or melting point. It will be observed that no dotted continuation of the vapour pressure curve of the solid is shown this would mean a suspended transformation in the change from the solid to the liquid state. Such a change has not been observed nor is it theoretically possible. 

Still another situation is that of a supersaturated or supercooled solution, and straightforward modifications can be made in the preceding equations. Thus in Eq. IX-2, x now denotes the ratio of the actual solute activity to that of the saturated solution. In the case of a nonelectrolyte, x - S/Sq, where S denotes the concentration. Equation IX-13 now contains AH, the molar heat of solution. 

Crystallization. Acidified aluminum sulfate solutions can be supercooled 10 °C or more below the saturation point. However, once nucleation begins, the crystallization rate is rapid and the supersaturated solution sets up. The onset of nucleation in a gentiy stirred supersaturated solution is marked by the appearance of silky, curling streamers of microscopic nuclei resulting from orientation effects of hydraulic currents on the thin, platelike crystals. Without agitation, nucleation in an acidified solution, in glass tubes, can yield extended crystalline membranes of such thinness to exhibit colors resulting from optical interference. 

DL-threonine and L-threonine crystals were supplied from Ajinomoto Co. Inc. and were used without further purification. Excess amounts of DL-threonine crystalline particles were dissolved in water kept at 55, 57, 58 or 60 C. After decantation and filtration each saturated solution was placed in the crystallizer maintained at 50 C. The difference between the saturation temperature and the crystallization temperature was defined as the initial supersaturation in terms of supercooling of the solution and was the driving force for the crystallization. 

A driving force is applied, which causes the process to proceed by the formation of a supersaturated or supercooled state. 

A fluid under a pressure lower than its vapor pressure, and especially under a negative pressure, is unstable thermodynamically with respect to formation of a bubble filled with vapors of the substance and even (in the case of negative pressure) of an empty one. A fluid subjected to negative pressure is completely analogous in this respect to a supersaturated vapor, unstable with respect to formation of a condensate, or to a supercooled liquid, unstable with respect to crystal formation. 

If particles (or ions) are already present in a supersaturated vapor, nucleation will take place preferentially on these particles at supersaturations far smaller than for the homogeneous vapor. In this case, nucleation takes place heterogeneously on the existing nuclei at a rate dependent on the free energy of a condensate cap forming on or around the nucleus. Heterogeneous nuclei always occur in the earth s atmosphere. They are crucial to the formation of water clouds and to the formation of ice particles in supercooled clouds. 

---