Supersaturations homogeneity

Supersaturated homogeneous solutions are thus metastable, and the metastability decreases with increasing supersaturation. In other words, nucleation starts after the solute concentration has exceeded a definite value, and then solute molecules form aggregates or clusters. If, however, the crystals are placed in a supersaturated solution, the solution eventually attains equilibrium after the growth of the crystals upon crystallization. 

PRIMARY NUCLEATION. In scientific usage, nucleation refers to the birth of very small bodies of a new phase within a supersaturated homogenous existing phase. Basically, the phenomenon of nucleation is the same for crystallization from solution, crystallization from a melt, condensation of fog drops in a supercooled vapor, and generation of bubbles in a superheated liquid. In all instances, nucleation is a consequence of rapid local fluctuations on a molecular scale in a homogenous phase that is in a state of metastable equilibrium. The basic phenomenon is called homogeneous nucleation, which is further restricted to the formation of new particles within a phase iminfluenced in any way by solids of... 

Zeohte Y with an average crystal size of 80 run was synthesized by optimizing the synthetic composition and the addition of NaCl [42]. Van Grieken et al. [43] synthesized nanocrystalline ZSM-5 with crystal sizes ranging from 10 to 100 nm through hydrothermal crystallization of supersaturated homogeneous mixtures... 

Assume that a supersaturated homogeneous solution is flowing through a smooth duct containing no solid impurities either in the fluid or on the inner walls, precluding the possibility of heterogeneous nucleation. Whenever the equilibrium mole fraction of a solute, is lower than its mole fraction, the difference between the actual state of the solution (which is usually metastable) and the equilibrium state provides a driving force for the processes of precipitation. 

There are two process paths to precipitate nanopartides with the miniemulsion technique. The first requires the production of two water-in-oU emulsions where the dispersed phases are loaded with one predpitation precursor, respectivdy. Controlled coalescence of droplets containing the predpitation reactants results in a product of low solubility and - in case of supersaturation - homogeneous nudeation is induced. As high-pressure homogenization results in high coalescence rates (see Section 5.3.2), this is the process of choice. 

The central quantity of interest in homogeneous nucleation is the nucleation rate J, which gives the number of droplets nucleated per unit volume per unit time for a given supersaturation. The free energy barrier is the dommant factor in detenuining J J depends on it exponentially. Thus, a small difference in the different model predictions for the barrier can lead to orders of magnitude differences in J. Similarly, experimental measurements of J are sensitive to the purity of the sample and to experimental conditions such as temperature. In modem field theories, J has a general fonu... 

Both homogeneous and heterogeneous mechanisms requite relatively high supersaturation, and they exhibit a high order dependence on supersaturation. These factors often lead to production of excessive fines ia systems where primary aucleatioa mechanisms are important. The classical theoretical treatment of primary nucleation results ia the expressioa (5) ... 

Since the critical supersaturation ratio for homogeneous nucleation is typically greater than 3, it is not often reached in process equipment. 

It is imphcit that increasing the value of Ly will raise the supersaturation and growth rate to levels at which mass homogeneous nucleation can occur, thereby leading to periodic upsets of the system or cycling [Randolph, Beer, and Keener, Am. In.st. Chem. Eng. J., 19, 1140 (1973)]. That this could actually happen was demonstrated experimentally by Randolph, Beckman, and Kraljevich [Am. In.st. Chem. Eng. J., 23, 500 (1977)], and that it could be controlled dynamically by regulating the fines-destruction system was shown by Beckman and Randolph [ibid., (1977)]. Dynamic control of a ciystaUizer with a fines-destruction baffle and fine-particle-detection equipment... 

Control of a batch ciystaUizer is almost always the most difficult part and veiy often is not practiced except to permit homogeneous nucleation to take place when the system becomes supersaturated. If control is practiced, it is necessary to have some means for determining when the initial solution is supersaturated so that seed of the appropriate size, quantity, and habit may be introduced into the batch. Following seeding, it is necessaiy to limit the coohng or evaporation in... 

Solution enters the vessel (Figure 3.4) and is well-mixed throughout i.e. all eonditions - temperature, eoneentration, veloeity, turbulenee ete. are uniform (homogeneous). Supersaturation is generated (by evaporation, eooling, ete.) and nuelei form and grow into erystals. Sinee erystals have varying probabilities of residenee time in the vessel, however, the slurry exhibits a erystal size distribution (CSD). Produet slurry is eontinuously withdrawn and has exaetly the same eomposition as the vessel. 

Primary nucleation is the classical form of nucleation. It occurs mainly at high levels of supersaturation and is thus most prevalent during unseeded crystallization or precipitation. This mode of nucleation may be subdivided into either homogeneous viz. spontaneously from clear solution, or heterogeneous viz. in the presence of dust particles in suspension, or solid surfaces. 

The process of homogeneous nucleation is determined by the formation of stable nuclei in a supersaturated solution. 

State nucleation is negligible, i.e. when the steady-state nueleation rate is reaehed very quiekly. Indeed, Sohnel and Mullin (1988) have shown that non-steady state nueleation is not an important faetor during the formation of erystal eleetrolytes from aqueous solutions, at least at moderate supersaturation and viseosity, irrespeetive of whether there is heterogeneous or homogeneous nueleation oeeurring. 

The shape of the two part plot in Figure 5.8 ean be attributed to homogeneous nueleation at high levels of supersaturation (/(v) = 1) for the steeper, linear eurve, while the seeond part of the eurve is eonsistent with heterogeneous nueleation at low supersaturation (/(v) < 1). The inferred meehanism... 

Potassium sulfate has a solubility of 15 g/100 g water at 40°C. A solution is prepared by adding 39.0 g of potassium sulfate to 225 g of water, carefully heating the solution, and cooling it to 40°C. A homogeneous solution is obtained. Is this solution saturated, unsaturated, or supersaturated The beaker is shaken, and precipitation occurs. How many grams of potassium sulfate would you expect to crystallize out ... 

A procedure which is commonly employed to prevent supersaturation from occurring is that of precipitation from homogeneous solution. This is achieved by generating the precipitating agent within the solution by means of a homogeneous reaction at a similar rate to that required for precipitation of the species. 

Generally speaking, homogeneous nucleation needs the supersaturation level higher than heterogeneous one. In the system consisting of support solid and metal salt solution, the nucleation occurs on the surfaces of the solid. The selective reductive deposition is performed by the adsorption of metal ion or complexes on the surfaces and hereby the reduction. Namely, the initial adsorption of metal ions or complexes is the key point of this technique. Hence, key points of this method are... 

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