Nucleation supersaturation

Over 50 acidic, basic, and neutral aluminum sulfate hydrates have been reported. Only a few of these are well characterized because the exact compositions depend on conditions of precipitation from solution. Variables such as supersaturation, nucleation and crystal growth rates, occlusion, nonequilihrium conditions, and hydrolysis can each play a role ia the final composition. Commercial dry alum is likely not a single crystalline hydrate, but rather it contains significant amounts of amorphous material. 

Crystallization from solution can occur only in supersaturated solution. Under lower supersaturation nucleation cannot occur spontaneously spontaneous nucleation... 

Typically, the precursor solutions (usually aqueous salt solutions) are mixed, and the desired salt is precipitated as a gel by adding an add/base or another reagent. Precipitation has three stages supersaturation, nucleation, and growth. The... 

The process of crystallization from solution is generally understood in terms of three interdependent conditions supersaturation, nucleation and growth. For crystallization from the melt or the gas phase, supersaturation is simply interpreted as undercooling. Of the essence is a metastable phase, at chemical potential higher than that of the crystalline phase under the same conditions. The transition from the metastable state to the state of equilibrium between phases corresponds to nucleation. 

There are several common processes involved in mechanisms of carbonate and sulfate mineralization in unicellular organisms. In both E. huxleyi and acantharia, membrane-bound vesicles are used to direct the shape, structure, and crystallographic orientation of the bioinorganic solids. Three key processes are controlled ionic concentrations (supersaturation), nucleation, and growth. 

Lespoaux D, Langlais F, Naslain R (1995) Correlations between gas phase supersaturation, nucleation process and physico-chemical characteristics of silicon carbide deposited from Si-C-H-Cl system on silica substrate. J Mater Sci 30 1500-1510... 

The complex interactions between supersaturation, nucleation, and growth are critical to all crystallization operations. The critical properties of organic compounds that affect these three characteristics include the nucleation rate, growth rate, and width of the metastable zone. These properties vary over large ranges because of the complexity and variety of molecular structures. Crystallization conditions for a particular compound are therefore species dependent and difficult to predict without experimentation. 

Also because of high supersaturation, nucleation may be primarily homogeneous rather than secondary, although this is also system dependent and may be reversed for organic molecules. Nucleation rate is a key issue because of its impact on the number of crystals formed. 

Precipitation occurs in three phases supersaturation, nucleation, and growth. Pertinent parameters producing supersaturation are shown in Fig. 

Figure 14.11 also mentions spinodal decomposition. This occurs especially in polymer solutions. Beyond a certain supersaturation, any small fluctuation in composition leads to a local decrease in free energy and will spontaneously grow to form a large region. This means that nucleation is not needed. For a smaller supersaturation, nucleation is needed for phase separation to occur. 

We have seen that in homogeneous-homomolecular nucleation, nucleation does not occur unless the vapor phase is supersaturated with respect to the species. When two or more vapor species are present, neither of which is supersaturated, nucleation can still take place... 

As stated above, control of the crystallization or precipitation process is essential to obtain crystals of biochemical compounds having appropriate properties. The phenomena, techniques, and analysis discussed in many of the previous chapters solubility and supersaturation, nucleation and growth kinetics, population balance methods, batch and continuous crystallizers, and factors governing crystal purity, habit and morphology are all relevant to the discussion of the crystallization of pharmaceuticals. We shall analyze the crystallization/precipitation of biomolecules in terms of these concepts. 

We have seen that in homogeneous-homomolecular nucleation, nucleation does not occur unless the vapor phase is supersaturated with respect to the species. When two or more vapor species are present, neither of which is supersaturated, nucleation can still take place as long as the participating vapor species are supersaturated with respect to a liquid solution droplet. Thus heteromolecular nucleation can occur when a mixture of vapors is subsaturated with respect to the pure substances as long as there is supersaturation with respect to a solution of these substances. The theory of homogeneous-heteromolecular nucleation parallels that of homogeneous-homomolecular nucleation extended to include two or more... 

The probability for nucleation to occur depends strongly on the degree of supersaturation of the solution. In the case of a very slight supersaturation, precipitation can take weeks or month to initiate, and at a certain degree of supersaturation nucleation and precipitation will happen immediately. This is called the critical supersaturation ratio. In the case of barium sulfate, a relatively high critical supersaturation ratio of about 32 has been determined. The supersaturation ratio is defined by the formula ... 

An over-simplified but graphic example of the interactive effects of supersaturation, nucleation and growth in the development of precipitated particles is given by Fiiredi-Milhofer and Walton (1969), who considered the homogeneous nucleation of three different systems at an arbitrary value of... 

The particular attraction of a continuous crystallizer is its built-in flexibility for control of temperature, supersaturation, nucleation, crystal growth, and all the other parameters that influence crystal size distribution. A continuous crystallizer, however, does not discharge its product under near equilibrium conditions... 

Crystal slurry is classified (crystal size classification) by the circulation amount of the outer cycle which is controlled by the suction nozzles. Small crystals from the solution are entrained from the crystal bed and recycled to the inner circulation driven by the propeller pump 3, where supersaturation is reduced due to degradation of crystal fines. Different crystal concentrations and sizes in inner and outer suspension cycles are caused by different circulation amounts in each cycle. With known crystallization behavior the cycle may be controlled in a way, that in the inner cycle at a low suspension concentration and a relatively high supersaturation nucleation occurs. Otherwise, in the outer cycle at a longer residence time and smaller supersaturation crystal growth is favored. Crystal sizes 0.8-4 mm No crystal fines below 0.3 mm... 

The difference in overpotential between the curves for a given supersaturation (nucleation on an inert substrate) and the curve for a supersaturation equal to unity (deposition on a native substrate) gives the value of the crystallization overpotential, ijcr [48]. It is equal to the difference in the overpotential at point c and at point e in Fig. 2.16. If the current is switched off at point e, the electrode potential will approach to the reversible potential of the deposited metal (point g) after switching on the current again at point g, the overpotential returns to the same value as at point e, i.e., the deposition overpotential, r/, meaning that a new phase is formed. On the contrary, if current is switched off before point c, the electrode potential will approach the initial stationary potential of the inert electrode, meaning that new phase has not been formed [47]. 

If a progressively increases from low supersaturations to high supersaturations, nucleation will be governed by a sequence of progressive heterogeneous processes associated with increasing/(m). 

Satode AL, Wang P, Obara S, Worthen DR (2013) Supersaturation, nucleation, and crystal growth during single- and biphasic dissolution of amorphous solid dispersions Polymer effects and implications for oral bioavailabihty enhancement of poorly water soluble drugs. Eur J Pharm Biopharm 86(3) 351-360... 

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