Inverse half-crystallization time

The experimentally determined inverse half-crystallization time (1/t5o%) is presented in Figure 11.13 as a function of the... 

From isothermal crystallization experiments performed by DSC, the inverse of the experimental half-crystallization time can be obtained, a quantity that is proportional to the overall crystallization rate since it includes contributions from primary nucleation and growth. Figure 3.10 shows the inverse of half-crystallization time (xsoo/J as a function of crystallization temperature for different PLA samples (different molecular weights and o-isomer concentration). Some of the curves presented in Figure 3.9 also contain the two maxima that have the same origin as in Figure 3.8. Di Lorenzo indicates that PLAs display discontinuity in crystallization rate at around 118 °C. 

Generally, the inverse of half-crystallization time decreases with the D-isomer content, as reported by Kolstad, who indicates that the reduction is approximately 45% with increasing 1% in meso-lactide content. On the other hand, the effect of the molecular weight and similar o-isomer concentration shows that the inverse of half-crystallization time decreased with molecular weight as a consequence of the low chain mobility. 

Figure 3.15 a) The inverse of the half-erystallization time versus isothermal ciystal-lization temperature for PLLA and the PLLA block of the indicated diblock copol nner. b) Inverse of the half-crystallization time versus isothermal crystallization temperature for the PE block within the indicated copol nners and for PE homopol aner (modified from Refs. 122 and 123). 

When the isothermal crystallization is determined by spherulitic growth experiments, the energy barrier determined by applying the LH model refers exclusively to secondary nucleation or crystal growth. Instead, when the inverse of half-crystallization time (1/t5q%) values obtained from DSC isothermal overall crystallization kinetic data is considered, both primary nucleation and crystal growth are considered. Therefore, the energetic parameters that we obtained after applying any classical kinetic crystallization theory to DSC data will include contributions from both processes. 

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. 

Figure 11.13 (a) Inverse of half-crystallization times lization temperature (r ) needed to obtain a value of =0.15 min Castillo et al. [66]. 

Isothermal Crystallization Polyamide Phase Figure 11.18 shows the inverse of the half-crystallization time as a function of crystallization temperature. The trend... 

Figure 11.18 Variation of the inverse of the half-crystallization time (1/ 50%) as a function of the crystallization temperature for the polyamide component within the studied blends and for the neat polyamide homopolymers as function of the crystallization temperature (r ) see Table 11.7. Adapted from Cdrdova et al. [[70], p. 16], Figure 18. Reproduced with permission of John Wiley and Sons.

Figure 12.14 presents the values of the inverse of the half-crystallization time, I/Tsoo/, as a function of reported by Muller et al. [133] for a PLLA-6-PE and a corresponding homopolymer. The results clearly indicate that the PLLA block within the copolymer crystallizes at much slower rates than homo-PLLA when similar crystallization temperatures are considered by extrapolation. Such a decrease in the overall crystallization rate of the PLLA block within the copolymer (and the higher supercooling needed for crystallization) is considered responsible for the coincident crystallization effect that can be observed when the PLLA-6-PE diblock copolymer is cooled down from the melt at rates larger than 2°C/min. A similar effect has also been reported by Muller et al. for weakly segregated poly (p-dioxanone) -6-polycaprolactone diblock copolymers [135,136]. 

Fig. 9 Inverse of the crystallization half-time as a function of isothermal crystallization temperature for PCL11 homopolymer and for the PCL block of the indicated copolymers. All experiments were performed after the PPDX block had been previously crystallized until saturation. Solid lines are fits to the Lauritzen and Hoffman theory. (From [103]. Reproduced with permission of the Royal Society of Chemistry)...

The half time is proportional to the square of the crystal size and inversely proportional to the diffusivity. We see that the half time is largest for the case of slab, and smallest for the spherical case. This is not surprising as the exterior surface area per unit volume is largest for the sphere and smallest for the slab hence mass transfer per unit volume of crystal is fastest in the case of spherical crystals. 

Figure 18.7 Plot of the inverse of the half-time of crystallization at 130 and 250°C for SPS/PPO blends against PPO contents.

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