Crystallization kinetics rate maximum

Samples can be concentrated beyond tire glass transition. If tliis is done quickly enough to prevent crystallization, tliis ultimately leads to a random close-packed stmcture, witli a volume fraction (j) 0.64. Close-packed stmctures, such as fee, have a maximum packing density of (]) p = 0.74. The crystallization kinetics are strongly concentration dependent. The nucleation rate is fastest near tire melting concentration. On increasing concentration, tire nucleation process is arrested. This has been found to occur at tire glass transition [82]. 

One consequence of the negative-order kinetics is auto catalysis of the crystallization process. If the initial concentration is higher than that of the rate maximum, crystal growth will accelerate initially as the concentration decreases. This is illustrated in Fig. 13. Once past the concentration of the growth-rate maximum, the rate drops off. Interestingly, the positions of steepest slope in the time dependencies of crystal length and width do not coincide (Fig. 13), as the positions of the maxima in Guo and Gioo differ (Fig. 12). 

Stein, Gray and Guillet 82, 83) demonstrated the suitability of the GC method to study crystallization kinetics, through the variation of the retention volume with time. When the pcdymer stationary phase is cooled from the melt to a temperature below Tj, the retention volume decreases with time at the rate at which crystdline domains are being formed. The maximum possible crystallinity at a given temperature is obtained from the relation... 

Since some crystals are dissolved, crystallization must be performed at a higher rate to maintain a desired production rate. The correspondingly higher supersaturation results in a higher nucleation rate. Depending on several factors, such as the cut size and the crystallization kinetics, the net nuclei density may or may not be decreased by operation at the maximum dissolution rate. 

Figure 3.55 shows the plots of the times to reach maximum crystallization rate and the maximum crystallization rate, d /dr, as a function of the melting temperature. Both plots show that, at higher melting temperatures, the resulting rate of crystallization is diminished, with the implication that crystal nuclei are destroyed. As seen, under none of the conditions utilized did the overall rate of crystallization of the samples under high stress reduce to those observed for the samples under low stress. Jaffe also found that the time spent in the melt had an effect similar to the melt-temperature level. As the melt time increases, crystallization kinetics slow down. 

Above, a theory known today as the surface nucleation theory was described in Sections 6.6.2.3 to 6.6.3. The surface nucleation theory assumes an ensemble of crystals, each of which grows with constant thickness. This thickness is close to the thickness for which the crystals have the maximum growth rate. While the theory correctly describes a wide range of crystallization kinetics, it has a major shortcoming in being based primarily on enthalpic concepts. 

Figure 11.17 shows a schematic representation of the concentration versus time profiles during kinetic studies. The maximum concentration achieved during these experiments is determined by the co-crystal dissolution rate and crystallization rate of a less soluble form. This maximum concentration is therefore not correlated with solubility under conditions of rapid conversion and highly soluble co-crystals may even elude detection. 

The above thermodynamic information gives an idea about the maximum amount of material that will crystallize as a solid however, to get an insight into the rate of the prodnction of crystals we need information about its kinetics. The crystallization kinetics provide design information like crystal production rate, size distribution, and its shape. 

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