Crystallization kinetics overall rate

It has been reported that the overall rate of crystallization of pure PHB is relatively low compared to that of common synthetic polymers, showing a maximum in the temperature range of 55-60°C [23]. The spherulite growth rate kinetics have been evaluated [59] in terms of the theory by Hoffmann et al. [63], At about 90 °C, the spherulite growth rate displayed a maximum, which is not excessively low compared to that of common synthetic polymers. Therefore it was stated that the low overall crystallization rate of PHB centers on the nuclea-tion process rather than the subsequent crystal growth. Indeed, it has been shown that PHB has an exceptionally low level of heterogeneous nuclei [18]. 

Nucleation and Growth (Round 1). Phase transformations, such as the solidification of a solid from a liquid phase, or the transformation of one solid crystal form to another (remember allotropy ), are important for many industrial processes. We have investigated the thermodynamics that lead to phase stability and the establishment of equilibrium between phases in Chapter 2, but we now turn our attention toward determining what factors influence the rate at which transformations occur. In this section, we will simply look at the phase transformation kinetics from an overall rate standpoint. In Section 3.2.1, we will look at the fundamental principles involved in creating ordered, solid particles from a disordered, solid phase, termed crystallization or devitrification. 

Now, knowing the strong influence of particles (nuclei-I) on the overall crystallization kinetics, the increase of the crystallization rate with the gel ageing at ambient temperature (6,12,13,44,45) can be explained by the increase in the number of nuclei-I and/or the number of nuclei-II, respectively, during the gel ageing (11,12). 

Measurements of the specific surface area, SSA, of the products grown at various times indicate that the initial formation of a microcrystalline or amorphous precursor leads to a rapid increase in SSA. The development of these phases is also observed by scanning electron microscopy, and dissolution kinetic studies of the grown material have indicated the formation of OCP as a precursor phase ( , 7). The overall precipitation reaction appears to involve, therefore, not only the formation of different calcium phosphate phases, but also the concomitant dissolution of the thermodynamically unstable OCP formed rapidly in the initial stages of the reaction. In the presence of magnesium ion the overall rate of crystallization is reduced and lower Ca P ratios are observed for the first formed phases (51). 

The kinetics of chemical reactions on surfaces is described using a microscopic approach based on a master equation. This approach is essential to correctly include the effects of surface reconstruction and island formation on the overall rate of surface reactions. The solution of the master equation using Monte Carlo methods is discussed. The methods are applied to the oxidation of CO on a platinum single crystal surface. This system shows oscillatory behavior and spatio-temporal pattern formation in various forms. 

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. 

Quite clearly information about the number of nuclei, their moment of appearance, and the subsequent crystal growth rate can be gained from such a microscopic picture. If the produced crystals are of larger than micrometer size, a microscopic inspection of the completed crystallization, or even better a video taping of the overall process, should be part of the thermal analysis of the crystallization process. More about the detailed crystallization kinetics will be discussed in Sect. 3.6. 

The details of the polymer crystallization process can be quite complicated. Practically, one may not care about the details of crystal nucleation and the linear crystal growth rates, but just want to characterize the overall crystallization kinetics. The degree of crystallization process can be roughly defined as crystallinity, regardless of their detailed crystal morphologies. The conventional methods to characterize the crystallinity include DSC, X-ray diffraction and dilatometer. Depending on the measured quantity, crystallinity is also separated into the weight crystallinity... 

Ozawa proposed to study the overall crystallization kinetics from several simple DSC scanning experiments (Ozawa 1971). Assuming that when the polymer sample is cooled from To with a fixed cooling rate a = dT/dt, both the radial growth rate v T) of the spherulites and the nucleation rate 1(T) will change with temperature. For a sphemlite nucleated at time t, its radius at time t will be... 

---