Liquid-phase precipitation homogeneous nucleation

Nucleation plays a fundamental role whenever condensation, precipitation, crystallization, sublimation, boiling, or freezing occur. A transformation of a phase a, say, a vapor, to a phase p, say, a liquid, does not occur the instant the free energy of p is lower than that of a. Rather, small nuclei of p must form initially in the a phase. This first step in the phase transformation, the nucleation of clusters of the new phase, can actually be very slow. For example, at a relative humidity of 200% at 20°C (293 K), far above any relative humidity achieved in the ambient atmosphere, the rate at which water droplets nucleate homogeneously is about 10 54 droplets per cm3 per second. Stated differently, it would take about 1054 s (1 year is 3 x 107 s) for one droplet to appear in 1 cm3 of air. Yet, we know that droplets are readily formed in air at relative humidities only slightly over 100%. This is a result of the fact that water nucleates on foreign particles much more readily than it does on its own. Once the initial nucleation step has occurred, the nuclei of the new phase tend to grow rather rapidly. Nucleation theory attempts to describe the rate at which the first step in the phase transformation process occurs—the rate at which the initial very small nuclei appear. Whereas nucleation can occur from a liquid phase to a solid phase (crystallization) or from a liquid phase to a vapor phase (bubble formation), our interest will be in nucleation of trace substances and water from the vapor phase (air) to the liquid (droplet) or solid phase. 

Colloidal dispersions can be formed either by nucleation with subsequent growth or by subdivision processes [1-6]. The nucleation/condensation process requires a phase change, such as condensation of vapour to yield liquid or solid, or precipitation from solution. The colloidal species are built up by deposition on nuclei that may be of the same or different chemical species. If the nuclei are of the same chemical species, the process is referred to as homogeneous nucleation if the nuclei are of different chemical species, the process is referred to as heterogeneous nucleation. Tadros reviews nucleation/condensation processes and their control [7]. Some mechanisms of such colloid formation are listed in Table 7.1. 

The most serious difficulty encountered when the precipitation of an inorganic solid in an LLC phase is attempted is the fact that two reactive components have to be mixed intimately within LLC phase before precipitation occurs. The mixing process is usually associated with difficulties, as both reactants should be dissolved in the LLC phase, which is of more or less viscous consistency, making homogenization difficult. One way around this problem is to let the reactant that causes precipitation diffuse into the LLC phase either via the gas or the solution phase. In this way nucleation can be slowed down considerably so that larger particles form instead of small ones that would be dispersed in the hydrophilic domains of the liquid crystalline phase. 

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