Isothermal crystallization conversion rate

K " and n can be extracted from the intercept and the slope of Avrami plot, lg[-ln(l-.A0] versus lg(f-f ), respectively. The prime requirement of Avrami model is the ability of spherulites of a polymer to grow in a free space. Besides, Avrami equation is usually only valid at low degree of conversion, where impingement of polymer spherulites is yet to take place. The rate of crystallization of polymer can also be characterized by reciprocal half-time (/ 5). The use of Avrami model permits the understanding on the kinetics of isothermal crystallization as well as non-isothermal crystallizatioa However, in this chapter the discussion of the kinetics of crystallization is limited to isothermal conditions. 

The results of Muller et al. [103] on PPDX-fo-PCL diblock copolymers differ from those obtained previously by Bogdanov et al. [105] when they studied by DSC the crystallization kinetics of 80/20 PCL-fo-PEO diblock copolymers. In their case, the PCL block crystallized first from a homogeneous melt and the Avrami parameters K and n were found to be similar to the kinetics parameters of the isothermal crystallization of a corresponding PCL homopolymer. Significant crystallization retardation was found for the PEG block that crystallized second. The retardation was attributed to the mutual influence between the PEG constituent and the PCL crystal phase which fixes (hardened) the total copolymer structure [ 105]. In the PPDX-fo-PCL diblock copolymer case, conversely, when the PPDX block crystallizes it does so at a slower rate than a comparable PPDX homopolymer. The crystallization of the PCL block, on the other hand, strongly depends on the composition of the diblock copolymer as shown in Fig. 9. However, for D77 C23 , the overall kinetics is retarded, which could be regarded as similar to the retardation experienced by the PEG block in the 80/20 PCL-fi-PEG diblock copolymer studied by Bogdanov et al. [105] the Avrami index in both cases was also of the order of 2. 

In a similar fashion, DSC isothermal scans were recorded in order to study the crystallization kinetics of the PPDX homopolymer after melting the samples for 3 min at 150 °C and quenching them (at 80 °C/min) to the desired crystallization temperature (7(.). After the crystallization was complete, the inverse of the half -crystallization time, (i.e., the time needed for 50% relative conversion to the crystalline state [31,60]), was taken as a measure of the overall crystallization (nucleation and crystal growth) rate and its dependence on the crystallization temperature was analyzed. 

It has been concluded that, for most cases, catalysis over zeolites occurs within the intracrystalline voids. Strong supporting evidence for this was provided by Weisz (71), who compared the rates of dehydration of 2-butanol over Linde lOX and 5A zeolites at relatively high temperatures and low conversion. The rate constant per unit volume of 5A was 1/lOO-l/lOOOth that for lOX, a magnitude consistent with the ratio of available surface areas for the external area of 1-5/x-sized 5A crystals and for lOX, where the internal surface area was available to the alcohol. The strong driving force for occlusion within the intracrystalline zeolite voids is exemplified by the rapid adsorption kinetics and rectangular adsorption isotherms observed for molecules whose dimensions are not close to those of the entry pores. 

Isothermal dehydrations of single crystals (about 1 mm ) of the hexahydrate [111] in vacuum between 213 and 243 K gave or-time curves for conversion to the trihydrate with no induction period and a constant rate of water loss during a large fraction of reaction. The rate of dehydration decreased linearly with the prevailing pressure of water (contrasting with the behaviour of many other hydrates) attributed to the occurrence of the reverse reaction. The activation energy for conversion of... 

Recently the statistical approach was developed [5] for the description of the kinetics of conversion of melt to spherulites and the kinetics of formation of spherulitic pattern during both isothermal and nonisothermal crystallizations. The final spherulitic pattern can also be described. The rates of formation of spherulitic interiors and boundaries (boundary lines, surfaces and points) as well as the their final amounts could be predicted if spherulite growth and nucleation rates are known. Applied to iPP crystallized during cooling with various rates, the approach allowed for the predictions of tendencies in the kinetics of formation of spherulitic structure and its final form. 

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