Supersaturation and Metastability

Figure 1 Supersaturation and Metastable Zone Width in a Cooling Crystallization...

Figure 4 Phase diagram for a protein solution. In the undersaturation (soluble) zone crystals do not grow but dissolve the first line marks the saturation limit. Above that, the solution is supersaturated and metastable with respect to the crystals existing crystals will grow, but no spontaneous nucleation occurs. In the nucleation zone, new crystals form on their own, and in the precipitation zone nonspecific aggregation dominates.

In our discussions of supersaturation and metastability, we have always focused on situations where supersaturation is created by temperature change (cooling). While this is a very common method to generate supersaturation and induce crystallization, it is not the only method available. 

Posner clusters i.e., Cag(P04)6), with sizes close to 0.8 nm, are present in supersaturated and metastable CaP solutions claimed to simulate the electrolyte portion of blood plasma, as experimentally proved by Oyane etal. using dynamic light scattering [49]. Directly quoting from the work of Posner [50, 51], in the process of AGP formation in solution, Ca9(P04)6 clusters form first (with the experimental support to this provided by the later work of Oyane et al. [49]) and then are aggregated randomly to produce the larger spherical particles with the inter-duster space filled with water. The solution of Table 1 shall have the similar Posner dusters prior to its in sfru precipitation of AGP when it is warmed up. 

The time elapsed from the ereation of the initial supersaturation to the detee-tion of the first erystals formed in the system is known as the induetion period. The level of supersaturation attained is then akin to the metastable limit . Neither quantity (viz. the induetion time and metastable limit) is therefore a fundamental quantity. Both are useful measures, however, of the propensity of a solution to nueleate. Measurement of the induetion time as a funetion of supersaturation ean be used to help determine erystallization kineties and meehanism. Thus, the induetion time may be expressed by (Walton, 1967)... 

The most frequent site for erystal enerustation is on a eompatible solid surfaee within a zone of high supersaturation and low agitation. Seleetion of a less eompatible material having a smooth surfaee ean avoid the major exeesses of enerustation. Dunean and Phillips (1979) and Shoek (1983), respeetively, reveal a eonneetion between the metastable zone width of erystallizing solutions and their propensity to enerust. It is well known that judieious erystal seeding ean also help minimize enerustation. Simple laboratory tests are reeommended to determine all these issues before the plant is built. 

If fluids initially in equilibrium with quartz ascend rapidly, some metastable minerals (amorphous silica, cristobalite, wairakite) may precipitate because of supersaturation with respect to Si02 (e.g., Wolery, 1978 Bird and Norton, 1981). Important processes for the supersaturation and deviation from the equilibrium between fluids and rocks are adiabatic boiling, mixing of fluids and conductive cooling of fluids (Giggenbach, 1984). 

Precipitation can occur if a water is supersaturated with respect to a solid phase however, if the growth of a thermodynamically stable phase is slow, a metastable phase may form. Disordered, amorphous phases such as ferric hydroxide, aluminum hydroxide, and allophane are thermodynamically unstable with respect to crystalline phases nonetheless, these disordered phases are frequently found in nature. The rates of crystallization of these phases are strongly controlled by the presence of adsorbed ions on the surfaces of precipitates (99). Zawacki et al. (Chapter 32) present evidence that adsorption of alkaline earth ions greatly influences the formation and growth of calcium phosphates. While hydroxyapatite was the thermodynamically stable phase under the conditions studied by these authors, it is shown that several different metastable phases may form, depending upon the degree of supersaturation and the initiating surface phase. 

In considering the state of supersaturation, Ostwald(20) introduced the terms labile and metastable supersaturation to describe conditions under which spontaneous (primary) nucle-ation would or would not occur, and Miers and Isaac(21) have represented the metastable zone by means of a solubility-supersolubility diagram, as shown in Figure 15.8. 

In the absence of nuclei and agitation, solutions of lactose are capable of being highly supersaturated before spontaneous crystallization occurs. Even in such solutions, crystallization occurs with difficulty. Solubility curves for lactose are shown in Figure 2.6 and are divided into unsaturated, metastable and labile zones. Cooling a saturated solution or continued concentration beyond the saturation point, leads to supersaturation and produces a metastable area where crystallization does not occur readily. At higher levels of supersaturation, a labile area is observed where crystallization occurs readily. The pertinent points regarding supersaturation and crystallization are ... 

Ostwald in 1897 is credited with introducing the concept of supersaturation and extending it to metastable and labile areas (Mullin 1961). The metastable area occurs in the first stages of supersaturation produced by cooling a saturated solution or by continued evaporation beyond the saturation point. Crystallization does not occur readily in this supersaturation range. The labile area is found at higher levels of supersaturation, where crystallization occurs readily. 

Figure 16.5. Supersaturation behavior, (a) Schematic plot of the Gibbs energy of a solid solute and solvent mixture at a fixed temperature. The true equilibrium compositions are given by points b and e, the limits of metastability by the inflection points c and d. For a salt-water system, point d virtually coincides with the 100% salt point e, with water contents of the order of 10-6 mol fraction with common salts, (b) Effects of supersaturation and temperature on the linear growth rate of sucrose crystals [data of Smythe (1967) analyzed by Ohara and Reid, 1973],...

The vapor pressure at equilibrium depends on the temperature and the solution, but it is independent of the relative or absolute amounts of liquid and vapor. When air adjacent to pure water is saturated with water vapor (100% relative humidity), the gas phase has the maximum water vapor pressure possible at that temperature — unless it is supersaturated, a metastable, nonequilibrium situation. This saturation vapor pressure in equilibrium with pure water (P ) increases markedly with temperature (Fig. 2-16) for example, it increases from 0.61 kPa at 0°C to 2.34 kPa at 20°C to 7.38 kPa at 40°C (see Appendix I). Thus, heating air at constant pressure and constant water content causes the relative humidity to drop dramatically, where... 

Both types of US effects (namely physical, which facilitate mixing-homogenization, and chemical, resulting from radical formation through cavitation) influence crystallization by altering the principal variables involved in this physical process (namely induction period, supersaturation concentration and metastable zone width). These effects vary in strength with the nature of the US source and its location also, their influence is a function of the particular medium to which this form of energy is applied. 

If a saturated solution is cooled, the solubility of the solute generally decreases in order for the cooled solution to return to equilibrium, some solute must come out of solution as solid crystals. The crystallization rate may be slow, however, so that a metastable condition can exist in which the concentration of the solute is higher than the equilibrium value at the solution temperature. Under such conditions, the solution is said to be supersaturated and the difference between actual and equilibrium concentrations is referred to as supersaturation. Ail problems involving solid-liquid separations in this text assume that equilibrium exists between the solid and liquid phases, so that supersaturation need not be considered. 

When submicrometer seed crystal is added to the CET solution, the CET solution must be saturated or supersaturated and the resulting suspension must maintain the metastable state. In order to prepare the supersaturated solution, special equipment has been invented. This includes a high-performance solvating machine used as a heat exchange perfusion method, in which CET is dissolved by... 

Nucleation kinetics are experimentally determined from measurements of the nucleation rates, induction times, and metastability zone widths (the supersaturation or undercooling necessary for spontaneous nucleation) as a function of initial supersaturation. The nucleation rate will increase by increasing the supersaturation, while all other variables are constant. However, at constant supersaturation the nucleation rate will increase with increasing solubility. Solubility affects the preexponential factor and the probability of intermolecular collisions. Furthermore, when changes in solvent or solution composition lead to increases in solubility, the interfacial energy decreases as the affinity between crystallizing medium and crystal increases. Consequently, the supersaturation required for spontaneous nucleation decreases with increasing solubility, ° as shown in Fig. 7. 

Accounts of nucleation inhibition in the pharmaceutical literature are sometimes confusing because the dependence of the nucleation event (nucleation rate, metastability zone width, or induction time) on supersaturation is not considered. In search of additives that inhibit nucleation, induction times are often measured as a function of additive concentration, while the dependence of the nucleation event on supersaturation is neglected. Results from such studies possibly lead to the erroneous conclusion that the additive inhibited nucleation when indeed the additive decreased the supersaturation and frequently led to an undersaturated state. Hence, the system is under thermodynamic control instead of kinetic control. 

The perplexing difficulties that arise in the crystallization of macromolecules, in comparison with conventional small molecules, stem from the greater complexity, lability, and dynamic properties of proteins and nucleic acids. The description offered above of labile and metastable regions of supersaturation are still applicable to macromolecules, but it must now be borne in mind that as conditions are adjusted to transport the solution away from equilibrium by alteration of its physical and chemical properties, the very nature of the solute molecules is changing as well. As temperature, pH, pressure, or solvation are changed, so may be the conformation, charge state, or size of the solute macromolecules. 

The width of the metastable zone is affected by the solvent as well as a number of other factors including the agitation rate, the cooling rate, the presence of soluble additives, and the thermal history of the solution (Birchall and Davey, 1981 Garti etal., 1981 Nakai etal., 1973). The solvent influences the metastable zone width primarily because the nucleation rate of a given compound will vary from solvent to solvent. This is because nucleation rate is directly affected by the supersaturation and solubility a compound may attain in a given solvent, as well as molecular recognition phenomena between solute and solvent, as discussed in the next sections. 

The driving force for crystallization, the supersaturation, is composed of two zones, the metastable and unstable zones (Figure 7.1). The solid line in Figure 7.1 represents a saturation or solubility curve (S), while the dashed line corresponds to the supersolubility or supersaturation curve (SS). Below S, crystallization is impossible. Above S, in the metastable zone, the system is supersaturated and crystallization is possible with the aid of agitation or seeding. On the other hand, in the unstable region, crystallization is spontaneous and crystals appear after nucleation... 

If the steam is superheated at the start of the expansion, then the value y = 1.3 is used, the reason being that condensation will not occur immediately the saturation temperature is reached. Instead, the steam stays wholly in dry vapour form, when it is known as supersaturated . This metastable state cannot be maintained indefinitely, however, and condensation will occur suddenly at some point after the steam has passed through the nozzle. 

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