Nucleation causing metastability

Experiments in laboratoiy and industrial ciystallizers have shown that nuclei ate bom at supersaturations Ac Ac gj hom in presence of crystals (either product crystals or added seed ciystals). Such nuclei are called secondary nuclei. This secondary nucleation caused by the removal of preordered species on a crystal sm-face and attrition fragments can take place at very small supersaturations however, < c gj hetsecondary nuclei. In Fig. 8.4-1 the solubility c and the three metastable zone widths ACmet,hom, Ac gj het, a d Ac gj, gg Valid for homogeneous, heterogeneous, and secondary nucleation, respectively, are shown as a function of temperature T. 

As mentioned above, crystallization is possible when the concentration of the solute is larger than the equilibrium saturation, i.e. when the solution is supersaturated with the solute. The state of supersaturation can be easily achieved if the solution is cooled very slowly without agitation. Above a certain supersaturation (this state is also called supersolubility) spontaneous formation of crystals often, but not always, occurs. Spontaneous nucleation is less probable in the state between equilibrium saturation and supersolubility, although the presence of fine solid impurities, rough surfaces, or ultrashort radiation can cause this phenomenon to occur. The three regions (1) unsaturation (stable zone), where crystallization is impossible and only dissolution occurs, (2) metastable zone, extending between equilibrium saturation and supersolubility, and (3) labile zone, are shown in Fig. 5.3-20. 

Crystallization can occur only from supersaturated solutions. Growth occurs first by formation of nuclei and then by their gradual growth. At concentrations above supersaturation, as at point d on Figure 16.1(d), nucleation is conceived to be spontaneous and rapid. In the metastable region, nucleation is caused by mechanical shock or friction and secondary nucleation can result from the breakup of already formed crystals. It has been observed that the rate depends on the extent of supersaturation thus... 

Discontinuous transformations In this type of transformation, there is a free-energy barrier to infinitesimal variations and the system is initially metastable. However, a sufficiently large variation can cause the free energy to decrease. The transformation therefore can be initiated at a finite rate only by a variation that is large in degree but small in extent (i.e., nucleation is required). Examples include the formation of B-rich precipitates from a supersaturated A-B solution. 

Actually, the PV behavior predicted in this region by proper cubic equations of state is not wholly fictitious. When the pressure is decreased on saturated liquid devoid of vapor-nucleation sites in a carefully controlled experiment, vaporization does not occur, and the liquid phase persists alone to pressures well below its vapor pressure. Similarly, raising the pressure on a saturated vapor in a suitable experiment does not cause condensation, and the vapor persists alone to pressures well above the vapor pressure. These nonequilibrium or metastable states of superheated liquid and subcooled vapor are approximated by those portions of the PV isotherm which lie in the two-phase region adjacent to the saturated-liquid and saturated-vapor states. 

The influence of methanol proportions in solvents, and temperature, on the solubility and the transformation behavior of 2-(3-cyano-4-isobutyloxyphenyl) -methylthiazole-5-carboxylic acid (BPT) was investigated. The transformation behavior was explained by the chemical potential difference between the stable and metastable forms. It was shown that a specific solute-solvent interaction contributes to the preferential nucleation and growth of the stable or metastable forms and influences the transformation behaviors, and the solubility of the solvated crystals is much more influenced by the solvent compositions than the true polymorphs. The solubility ratio of the solvated crystals depends on the solvent composition, whereas the solubility ratio of the true polymorphs is considered to be independent of the solvents. The crystallization behavior was also investigated. The transformation rate after crystallization appeared to depend on the initial concentration of BPT and the addition rate of the antisolvent. The cause of this phenomenon was presumed to be a slight inclusion of the stable form in the metastable form <2005PAC581>. 

Another popular concept has been the idea that the hysteresis is caused at the single pore level by the existence of metastable states analogous to the supercooled liquid and superheated vapor states which can be encoimtered in bulk systems when nucleation of condensation or evaporation is delayed. Hysteresis loops of this type will emerge from any theory of the van der Waals or mean field t3q)e. This idea dates back to... 

The high supersaturation at filtration temperature, S = 5 at 15 C, is acceptable because of the increased width of the metastable zone in aqueous solution combined with a longer induction period—also in aqueous solution. During this time, sterile filtration to the crystallizer without nucleation can be completed—a gift of nature to the development team. Note, however, that premature nucleation from aqueous solution in the feed line to the sterile filter will cause slow sterile filtration and jeopardize successful completion of the run. 

The existence of metastable states is caused by the activation character of the initial stage of a first-order phase transition. Homogeneous nucleation determines the upper boundary of the liquid superheat and supercooling. The appearance of a viable new-phase nucleus in a metastable liquid is connected with the performance of the work IT. determined by the height of the thermod5mamic potential barrier, which is to be overcome for the subsequent irreversible growth of a new phase. The dimensionless complex W, k T, where kg is the Boltzmann constant and T is the temperature, is the stability measure of the metastable phase. ... 

Our findings can be interpreted as follows Due to the release of aggressive species by metastable pits the oxide layer in their vicinity is weakened. Here, the probability for nucleation of pits is dramatically enhanced. Each new pit releases additional aggressive ions, leading to further weakening of the oxide layer and hence an expansion of the weakened area. This causes chain-reaction-like development of pits and a spreading of the active surface area. 

Problems caused by polymorphism appear in many fields such as fine chemicals in industries (pharmaceuticals(7,2), foods, etc.), optical electronic materials(i), clathrate compounds(4) and biominerals(5). In crystallizations of these materials the crystallization behavior of the polymorphs is controlled first by basic operational conditions such as temperature, supersaturation degree, stirring rates. In addition to these basic factors, solvents, additives and guest molecules (in clathrate compounds) should be also considered as the important factors((5,7). The crystallization process of the polymorphs is composed of comp)etitive nucleation, competitive growth of polymorphs and transformation from metastable to stable form. Accordingly individual step should be investigated to clarify the crystallization mechanism of polymorphs. 

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