Nucleation spontaneous

In terms of spontaneous crystallization, the assumption that N nuclei commence to grow simultaneously at t = 0 is the most unrealistic. We can modify the model to allow for sporadic, spontaneous nucleation by the following... 

Under equiUbrium vapor pressure of water, the crystalline tfihydroxides, Al(OH)2 convert to oxide—hydroxides at above 100°C (9,10). Below 280°—300°C, boehmite is the prevailing phase, unless diaspore seed is present. Although spontaneous nucleation of diaspore requires temperatures in excess of 300 °C and 20 MPa (200 bar) pressure, growth on seed crystals occurs at temperatures as low as 180 °C. For this reason it has been suggested that boehmite is the metastable phase although its formation is kinetically favored at lower temperatures and pressures. The ultimate conversion of the hydroxides to comndum [1302-74-5] AI2O2, the final oxide form, occurs above 360°C and 20 MPa. 

Two conditions must be fulfilled for spontaneous nucleation (1) the chemical potential of the primary product should be no less than and (2) conditions enabling the encounter of particles of the primary product should exist. 

TBP and injected into a hot ( 350 °C) solution of TOPO (12 g). The injection of CdSe precursors into the hot solution ofTOPO resulted in spontaneous nucleation of CdSe nanocrystals and a decrease in temperature. Once the temperature was stabilized, an additional amount (0.4 mL) of the precursor solution was added for the growth of the nucleated nanocrystals. Here, Ostwald ripening was avoided by separating the nucleation and growth processes. All the reagents and the reaction were kept under an Ar atmosphere to avoid fire hazard and surface oxidation of the nanocrystals. 

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. 

Board, S. J., Hall,R. W., and Brown, G. E. (1974). The Role of Spontaneous Nucleation in Thermal Explosions Freon/Water Experiments, RD/BIN 3007. Central Electricity Generating Board, Berkeley Nuclear Laboratories, Great Britain. 

Consider the case where the protein consists of o /3 dimers exclusively at the very beginning of an assembly experiment. Suppose further that spontaneous nucleation is sufficiently infrequent as the polymerization reaction reaches 5-10% of its maximal amplitude achieved over the remaining course of elongation. In this case, a reduction of the protomer concentration from about 20 to 18 JU.M would reduce the apparent extent of nucleation by a factor of about 10-20, such that the polymer number concentration remains fixed throughout the ensuing elongation phase. If nucleation were viewed as a one-step cooperative event, then the rate of nucleation would be proportional to the ith power of the protomer concentration if /protomers cooperatively form the polymerization nucleus ... 

Another experiments were also carried out to see whether spontaneous nucleation would occur or not at the similar supersaturation levels as those in the resolution experiments. 

The development of the freeze concentration process for fruit juices has been hampered by the fact that solute concentrate is entrained by the ice crystals. This incomplete separation of the entrained concentrate from the ice results in a considerable increase of the cost of the process. In this investigation sucrose solutions were concentrated by the formation of an ice layer on the externally cooled walls of the crystallizer. The formation of the layer was initiated by secondary nuclei induced by rotating ice seeds, at subcoolings smaller than the critical subcooling needed for spontaneous nucleation. A minimum in the amount of sucrose entrapped in the ice layer was observed at a subcooling smaller than the critical subcooling for spontaneous nucleation. The effect of soluble pectins on the minimum was also studied. 

A minimum is observed at a subcooling value smaller than foe subcooling required for spontaneous nucleation. For instance in figure 4 spontaneous nucleation in foe absence of foe seeds occurred at AT>1.7 K. The minimum at AT = 1.2 K is observed in foe region in which only secondary nucleation takes place. This result points out that in processes in which foe ice is formed by spontaneous nucleation, as in most of foe industrial processes involving scraped ice m cooled surfaces, the entrapment will be always higher than in processes that involve secondary nucleation. 

The area of conditions called the metastable zone is situated between the solubility and supersolubility curves on the crystallization phase diagram (Fig. 3.1). The supersolubility curve is defined as the line that separates the conditions where spontaneous nucleation (or phase separation or precipitation) occurs, from those where the crystallization solution remains clear if left undisturbed (Ducruix and Giege, 1992 Ducruix and Giege, 1999). 

However, care must be taken to ensure that seed nuclei are present on which condensation can occur. If a very clean system is used in which nuclei are not present, spontaneous nucleation may occur this process is such that nuclei do not appear uniformly either in space or in time, and the initial particle growth rate depends on the degree of supersaturation. As a result, a polydisperse aerosol is produced under these conditions. 

Polymer-protected, monodisperse, nanoscale silver particles (Fig. 9.2.1c and d) have been obtained through spontaneous nucleation by the polyol process as follows (23). PVP (1-25 g) and AgNOj (50-3200 mg) were dissolved in EG (75 mL) at room temperature. Then the solution was heated up to 120°C at a constant... 

Fig. 9.23 SEM images of monodisperse silver powders obtained by reduction of AgNOj in ethylene glycol in the presence of PVP (a) quasi-spherical particles obtained by spontaneous nucleation (dm = 0.64 pun, cr = 0.13 p.m) (b) rodlike particles obtained by heterogeneous nucleation using H2PtCl6 as nucleating agent (particle dimensions 3 xm long and 0.3 xm thick). (From Ref. 13.)...

Spontaneous nucleation. Monodisperse micrometer-size Co or Ni particles have been obtained as follows (16,18) cobalt or nickel hydroxide was suspended in EG (250 mL) the molar ratio hydroxide/polyol was varied from 0.01 to 0.15. The suspension was stirred and brought to boil (195°C). The metal precipitation does not occur immediately when the boiling point is reached but only after an induction time. The water and the volatile products resulting from the oxidation of ethylene glycol were distilled off, while the main part of the polyol was refluxed. For Co the reduction was completed in a few hours. For nickel hydroxide it was difficult to achieve a complete reaction due to an incomplete dissolution of this hydroxide. This could be overcome by adding a small amount (a few milliliters) of... 

Fig. 9.2.8 SEM images of different powders in the CoNi system synthesized by reduction in polyols (A) Co obtained by spontaneous nucleaiion. = 1.75p.m,cr = 0.14dm ( B) Co20N igo obtained by spontaneous nucleation, dnl = 1.4 p.111,

---