Supersaturation definition

The resistance to nucleation is associated with the surface energy of forming small clusters. Once beyond a critical size, the growth proceeds with the considerable driving force due to the supersaturation or subcooling. It is the definition of this critical nucleus size that has consumed much theoretical and experimental research. We present a brief description of the classic nucleation theory along with some examples of crystal nucleation and growth studies. 

Any of these definitions of supersaturation can be used over a moderate range of system conditions. For example, a difference ia chemical potential A// = — fi is proportional to both c — c and T — T over a modest range of conditions. Of the five expressions given, however, the second is most... 

When a process is continuous, nucleation frequently occurs in the presence of a seeded solution by the combined effec ts of mechanical stimulus and nucleation caused by supersaturation (heterogeneous nucleation). If such a system is completely and uniformly mixed (i.e., the product stream represents the typical magma circulated within the system) and if the system is operating at steady state, the particle-size distribution has definite hmits which can be predic ted mathematically with a high degree of accuracy, as will be shown later in this section. 

Folding is defined in Background and Definitions and is a significant problem in most process applications, and somewhat of a problem in most water applications. RO membranes may be fouled by sparingly soluble sealants which supersaturate at the membrane. 

For ionie systems, however, the definition of the appropriate driving foree beeomes more eomplex sinee the ionie eoneentrations are not neeessarily in stoiehiometrie ratio and the solubility produet generally applies. Thus the supersaturation ratio of sparingly soluble systems ean be deseribed by... 

It ean be seen from these definitions of driving foree that sparingly soluble substanees ean easily exhibit high levels of relative supersaturation. Henee, the erystallization proeess ean be very fast and the preeipitation diffieult to eontrol, espeeially on the large seale (see Sohnel and Garside, 1992). 

This observation is in accordance with the phenomena of the crystallization in the resolution operation mentioned above in the following points. There are no clear, definite critical supersaturations above which nucleation of D-threonine occurs. Ohtsuki (2), however, reported supersolubility curve for this system, who gave the value of the supersaturation width At=7 C at 50 C. Their definition of the metastablllty was that no nucleation of the enantiomer other than seeded one was observed for two hours of resolution experiments. According to this definition, the supersolubility can be determined to lie somewhere between At=8 and 5 C from the present experimental data, this being in agreement with his result. If the crystallization proceeds further, however, D-threonine crystals may start to crystallize from the solution even if the initial supersaturation is 5 C. In this sense it is no longer the metastablllty limit. 

Precipitation of ferric hydroxide gel was also observed in the preparation of spindlelike hematite (a-Fe203) particles in a dilute ferric chloride solution in the presence of phosphate (9). In this case, however, the positive role of the gel was not definite since similar uniform hematite paricles were obtained as well in homogeneous systems in the presence of the same anions (9). Also, Hamada and Matijevic (10) prepared uniform particles of pseudocubic hematite by hydrolysis of ferric chloride in aqueous solutions of alcohol (10-50%) at I00°C for several days. In this reaction, it was observed that acicular crystals of (3-FeOOH precipitated first, and then they dissolved with formation of the pseudocubic particles of hematite. The intermediate P-FeOOH appears to work as a reservoir of the solute to maintain an ideal supersaturation for the nucleation and growth of the hematite. Since the (3-FeOOH as an intermediate and the pseudocubic shape tire not peculiar to the alcohol/water medium... 

Heat the test tube with its contents to obtain a transparent solution again, carefully cool it, and rub the inner wall of the test tube containing the solution with a glass rod. Explain the precipitation of crystals. Give definitions of saturated, unsaturated, and supersaturated solutions. 

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. 

The microscopic image shows a juxtaposition of differently orientated areas whose sizes, varying between a few microns and several tens of microns, are associated particularly with the elementary composition of the initial carbonaceous material (4, 18, 19). The formation of a texture of this type, often called a mosaic structure, can be compared (20) to the crystallization of a supersaturated solution areas, each characterized by a definite orientation, develop from nuclei up to the total consumption of the isotropic material surrounding them. 

Although most additives that have been studied retard growth on all faces of the crystal, there are some which definitely promote growth on certain faces. For example, repeated recrystallization of lactose removes growth-promoting trace substances, so that crystal growth is much slower in supersaturated solutions of this lactose than in less purified solutions. The tendency toward spontaneous nucleation is also lowered upon repeated recrystallization. 

Note that this definition requires a saturated solution to be at equilibrium with undissolved solid. Substances that are more soluble at high temperature than at low temperature can sometimes form what are called supersaturated solutions, which contain a greater-than-equilibrium amount of solute. For example, when a saturated solution of sodium acetate is prepared at high temperature and then cooled slowly, a supersaturated solution results, as shown in Figure 11.5. Such a solution is unstable, however, and precipitation occurs when a tiny seed crystal of sodium acetate is added to initiate crystallization. 

It should be kept in mind that, in spite of these major variations in the CO2-carbonic acid system, virtually all surface seawater is supersaturated with respect to calcite and aragonite. However, variations in the composition of surface waters can have a major influence on the depth at which deep seawater becomes undersaturated with respect to these minerals. The CO2 content of the water is the primary factor controlling its initial saturation state. The productivity and temperature of surface seawater also play major roles, in determining the types and amounts of biogenic carbonates that are produced. Later it will be shown that there is a definite relation between the saturation state of deep seawater, the rain rate of biogenic material and the accumulation of calcium carbonate in deep sea sediments. 

The definitions of supersaturation ratio and relative supersaturation can be extended to any of the other variables used in the definition of supersaturation. For example, defining Sai = a,- /af gives ... 

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