Supersaturation phenomena

Supersaturation phenomena in solutions are, of course, very important, but, unfortu-... 

Experimental Advances Resulting from Studies of Nucleation and Supersaturation Phenomena... 

The Kelvin equation helps explain an assortment of supersaturation phenomena. All of these —supercooled vapors, supersaturated solutions, supercooled melts —involve the onset of phase separation. In each case the difficulty is the nucleation of the new phase Chemists are familiar with the use of seed crystals and the effectiveness of foreign nuclei to initiate the formation of the second phase. 

Fig. 77 in this figure the dotted lines can be observed only on account of supersaturation phenomena. 

The Si—0—Si-Hndgres Hydrolysis of Si—O—Si-bridges on the silica gel surface is possible. The socalled solubility of silica gel is attributed to such processes. A limiting concentration of about 0.01 % SiOg is attained at 20° C in the system silica gel-water. It rises with increase in temperature and rises especially markedly above pH 9. It can be concluded from the solution properties that equilibrium states are reached and that supersaturation phenomena are possible [700]. 

Here, r is positive and there is thus an increased vapor pressure. In the case of water, P/ is about 1.001 if r is 10" cm, 1.011 if r is 10" cm, and 1.114 if r is 10 cm or 100 A. The effect has been verified experimentally for several liquids [20], down to radii of the order of 0.1 m, and indirect measurements have verified the Kelvin equation for R values down to about 30 A [19]. The phenomenon provides a ready explanation for the ability of vapors to supersaturate. The formation of a new liquid phase begins with small clusters that may grow or aggregate into droplets. In the absence of dust or other foreign surfaces, there will be an activation energy for the formation of these small clusters corresponding to the increased free energy due to the curvature of the surface (see Section IX-2). 

StiU another possible role of supersaturation is that it affects the solution stmcture and causes the formation of clusters of solute molecules. These clusters may participate in nucleation, although the mechanism by which this would occur is not clear. Evidence of the existence of cluster formation in supersaturated solutions has been presented for citric acid (21) while others have examined the phenomenon in greater detail (22,23). 

The real atmosphere is more than a dry mixture of permanent gases. It has other constituents—vapor of both water and organic liquids, and particulate matter held in suspension. Above their temperature of condensation, vapor molecules act just like permanent gas molecules in the air. The predominant vapor in the air is water vapor. Below its condensation temperature, if the air is saturated, water changes from vapor to liquid. We are all familiar with this phenomenon because it appears as fog or mist in the air and as condensed liquid water on windows and other cold surfaces exposed to air. The quantity of water vapor in the air varies greatly from almost complete dryness to supersaturation, i.e., between 0% and 4% by weight. If Table 2-1 is compiled on a wet air basis at a time when the water vapor concentration is 31,200 parts by volume per million parts by volume of wet air (Table 2-2), the concentration of condensable organic vapors is seen to be so low compared to that of water vapor that for all practical purposes the difference between wet air and dry air is its water vapor content. 

Growth rate fluetuations appear to inerease with an inerease in temperature and supersaturation leading to erystals of the same substanee, in the same solution at identieal supersaturation, exhibiting different growth rates this is thought to be a manifestation of the phenomenon of either size-dependent crystal growth or alternatively, growth rate dispersion. 

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. 

For any fixed batch crystallization temperature, the effective nucleation rate passes through a maximum even at high seed densities. It is suggested that the induction period r uired to activate the seed surfaces may be responsible for the lower initial nucleation rate observed when the supersaturation was higher. It is also suggested that agglomeration may have caused the observed phenomenon. 

Crystallization is a phase transition phenomenon. Crystals grow from an aqueous protein solution when the solution is brought into supersaturation (Ataka, 1993). Supersaturation is achieved by varying the concentrations of precipitant, protein and additives, pH, temperature, and other parameters (McPherson, 1999 Ducruix and Giege, 1992 Ducruix and Giege, 1999). 

Despite many advantages fluoridation may also have some drawbacks. One of the most important is increased formation of dental calculi. As fluoridation considerably reduces the solubility of apatites, the supersaturation of saliva with respect to apatite is appreciably increased and may favour the spontaneous precipitation of fluoridated apatites and the formation of dental calculi. This phenomenon would occur especially in the case of fluoridated toothpaste, and most of them... 

According to simple solubility considerations, a precipitate will be formed when the product of the concentrations of anions and cations exceeds the solubility product. From another viewpoint, phase transformation occurs when the free energy of the new phase is lower than that of the initial (metastable) phase. However, there are many examples where the ion product exceeds K p, yet no precipitation occurs—the phenomenon of supersaturation. The solubility product also does not provide information on how the particles of the precipitate form—nucleation. Nucleation involves various physical processes, and both thermodynamic and kinetic aspects must be considered. 

Throughout this review of biomineralization, one outstanding phenomenon has been consistently evaded. This is the problem of apparent solubility products and supersaturation. It is obvious, however, that almost by definition this is the one phenomenon that directly relates to the whole problem, but it is consistently evaded because there is no simple theory to account for the observations. In order to highlight the importance of this phenomenon, therefore, an attempt will be made to relate extracellular theories to this concept. 

Periodic reactions of this kind have been mentioned before, for example, the Liese-gang type phenomena during internal oxidation. They take place in a solvent crystal by the interplay between transport in combination with supersaturation and nuclea-tion. The transport of two components, A and B, from different surfaces into the crystal eventually leads to the nucleation of a stable compound in the bulk after sufficient supersaturation. The collapse of this supersaturation subsequent to nucleation and the repeated build-up of a new supersaturation at the advancing reaction front is the characteristic feature of the Liesegang phenomenon. Its formal treatment is quite complicated, even under rather simplifying assumptions [C. Wagner (1950)]. Other non-monotonous reactions occur in driven systems, and some were mentioned in Section 10.4.2, where we discussed interface motion during phase transformations. 

Vacancy quenching experiments where the destruction rate at climbing dislocations of supersaturated vacancies obtained by quenching the metal from an elevated temperature is measured (see the analysis of this phenomenon in the following section)... 

The above studies support the notion that nucleation is a very stochastic phenomenon when the sample is held at constant temperature, compared to when the sample was cooled at a constant cooling rate. As suggested previously, the magnitude of the driving force can affect the degree of stochastic or random behavior of nucleation. For example, on the basis of extensive induction time measurements of gas hydrates, Natarajan (1993) reported that hydrate induction times are far more reproducible at high pressures (>3.5 MPa) than at lower pressures. Natarajan formulated empirical expressions showing that the induction time was a function of the supersaturation ratio. 

This phenomenon is not fully understood however, it may be described as the formation of minute particles of the solute, which act as nuclei for further deposition of the solute from a supersaturated solution. The probable mechanism is bimolecular addition of drug molecules, X, and may be represented as follows ... 

Sometimes very low Tafel slopes are claimed (<15mV) [99,253]. It seems difficult to interpret such an observation in terms of a specific mechanism. It is more probable that anomalously low Tafel slopes are the result of a combined thermal activation of the reaction and of the electrode surface state, resulting in a reaction rate limited by the diffusion of molecular hydrogen away from the electrode. Supersaturation of the electrode ad-layer by the evolved gas can also play a decisive role [254,255]. This phenomenon has been amply discussed in the case of Cl2 evolution on oxide electrodes [256], but the same idea can be applied to the case of H2 evolution [257,258],... 

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