Force for crystals

Model calculations of the growth rate R are shown in Fig. 3. These are plotted as a function of the driving force for crystallization, A/x ln(p/pg), where p and Pg are the actual and equilibrium vapor pressures, respectively. At very low temperatures, the growth rate is essentially... 

Supersaturation is the driving force for crystallization and is a prerequisite before a solid phase will appear in a saturated solution. Figure 1. shows the situation for a cooling crystallization. At point 1 the system is under saturated and the concentration of dissolved solute is below the solubility curve defined by Eq 3. As the system cools it becomes saturated at point 2 but remains as a metastable liquid phase until the metastable zone is crossed at point 3, where... 

Hancock and Parks (2000) have critically evaluated the theoretical and practical aspects of utilizing the amorphous state. Theoretically, the gain in solubility though the use of an amorphous was predicted to be between 10- and 1600-fold. However, these elevated solubilities also represen very favorable driving forces for crystallization, and as a result, the realized gains are appreciably less. 

Mode of crystallization The means by which a thermodynamic driving force for crystallization is created. 

Solubility The equilibrium solute concentration. The dimensions in which solubility is expressed include, but are not limited to, mass or mole fraction, mass or mole ratio of solute to solvent, and mass or moles of solute per unit volume of solvent or solution. Supersaturation The difference between existing and equilibrium conditions the quantity represents the driving force for crystal nucleation and growth. 

The driving force, < >, for crystallization in a pure system can be given as... 

Often, the driving force for crystallization in melt systems is given simply by the temperature difference, AT, with the melting point temperature. In general, the lower the temperature of a system, the greater the rate of crystallization until reduced mass ttansfer limits nucleation at very low temperatures. 

In solution systems, the driving force for crystallization is the difference in chemical potential between molecules in the liquid state and those in the crystalline state. Therefore, the supersaturation driving force, (j>, for crystallization of a solute from solution is given by... 

In order to understand and control lipid crystallization, one should know the thermodynamic driving force for crystallization. In a pure system, like a single TAG, the melting point, T, defines the driving force and a temperature below is required to induce crystallization. That is, the subcooling or the melting temperature minus the actual temperature (Tm — T) defines the driving force for crystallization. 

Eutectic behavior is seen where the SFC of a mixture falls below the SFC for either of the two individual components, as seen between 30% and 70% milkfat in Figure 7. Isosolids diagrams allow phase compatibility to be studied (4), but they do not provide a thermodynamic measure of driving force for crystallization. Again, because the crystal phase composition may be different at different temperatures (and mixture ratios), isosolids diagrams do not represent true phase diagrams. 

Secondary nucleation is influenced by numerous parameters, including the driving force for crystallization, temperature, additives, impurities, agitator, agitation rate, the number and size of existing crystals, and roughness of the crystallizer surface. The parameters affecting nucleation and nucleation rate will be reviewed in a subsequent section. 

To truly control crystallization to give the desired crystalline microstructure requires an advanced knowledge of both the equilibrium phase behavior and the kinetics of nucleation and growth. The phase behavior of the particular mixture of TAG in a lipid system controls both the driving force for crystallization and the ultimate phase volume (solid fat content) of the solidified fat. The crystallization kinetics determines the number, size, polymorph, and shape of crystals that are formed as well as the network interactions among the various crystalline elements. There are numerous factors that influence both the phase behavior and the crystallization kinetics, and the effects of these parameters must be understood to control lipid crystallization. 

The driving force for crystallization (AG ) is thus a key thermodynamic variable associated with the transformation process, as is the surface energy. This latter factor has been explored in reasonable depth in other approaches to the problem, " and in some instances this property is believed to dictate the ability to prepare oriented films by CSD. Other investigators have discussed the impact of electrode reaction layers or decomposition pathways. " " ... 

FIGURE 27.5 Schematic diagram of the free energies of a CSD-derived amorphous film, a conventionally prepare amorphous material, and the crystaUine perovskite phase. AG, is the thermodynamic driving force for crystallization. Also shown is the influence of crystallization temperature on the magnitude of AG,. After Schwartz et al. and Roy. ... 

Knowledge of the driving force for crystallization is essential, not only to characterize the kinetics, but also... 

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