Homogeneous nucleation INDEX

Fig. 5 Schematic plot showing reported crystallization temperatures for PEO in the bulk and as a component of block copolymers of varying compositions. The morphology of the PEO block is indicated on the x-axis. The filled bars are for data where isothermal crystallization measurements were performed and Avrami indexes of 1 or less were reported. The horizontal lines indicate the maximum temperature range that can be associated with PEO homogeneous nucleation, see text...

We have represented schematically in Fig. 5, the maximum temperature range that can be associated with homogeneous nucleation temperatures for PEO. Some data, where Avrami indexes of 1 or lower have been reported, have crystallization temperatures that fall above this range, so they should not be associated with homogeneous nucleation. Another origin for the low Avrami indexes may be involved in these cases. 

At some distance close to the mineral surface, the saturation index (SI, IAP/Xsp) of pyromorphite must be greater than zero to allow local super saturation and precipitation. The question is whether this is a heterogeneous nucleation/ surface precipitation reaction or a dissolution homogeneous nucleation reaction. 

The exponent values in expressions (5.2)—(5.5) depend on the particular parameters in the exponent index, but they are usually much larger than the unit at r < 10-50 nm (see Table 5.1). In a homogeneous mother sys tern (free of seeds for the solid phase condensation), the process rate depends on the rate of homogeneous nucleation of the new phase from nonequilibrium (oversaturated) systems. The high partial pressure of the equilibrium vapor or solute over small particles allows the first condensed particles nuclei of the new phase) to form at a considerable oversaturation of the vapor in the initially homogeneous system. 

From theoretical considerations, an Avrami exponent of four would imply three-dimensional growth with sporadic nucleation. For an Avrami index of three, the implication can either be spontaneous or instantaneous homogeneous nucleation with three-dimensional growth or a sporadic heterogeneous nucleation followed by two-dimensional growth (Table 1). From theoretical considerations (9-11), it was stated that spontaneous or homogeneous nucleation should rarely occur in fats. Hence from theoretical considerations, oils and fats should crystallize with Avrami exponent of four. However, from literature it can be seen that most oils and fats tend to have an Avrami index of three, including the work on palm oil... 

An interesting result obtained by the simulations is that the hard confined nanospheres nucleate homogeneously and crystallize with a first-order kinetics at high temperatures with an Avrami index close to one. As the crystallization temperature was decreased, the Avrami index dropped to 0.5. Several experimental results on diblock copolymers have reported qualitatively similar trends (see Table 12.3). In more complex systems such as triblock terpolymers with two crystallizing blocks, Avrami indices of 0.5 and lower have also been experimentally determined [316]. 

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