Avrami 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. 

Avrami indexes of the order of 1 or lower) unless the crystallization occurs at temperatures very close to the Tg of the crystallizing phase. 

Floudas et al. [135] also studied the isothermal crystallization of PEO and PCL blocks within PS-b-PEO-h-PCL star triblock copolymers. In these systems the crystallization occurs from a homogeneous melt Avrami indexes higher than 1 are always observed since the crystallization drives structure formation and does not occur under confined conditions. A reduction in the equilibrium melting temperature in the star block copolymers was also observed. 

Fig. 19 Avrami index as a function of crystallization temperature for PS-b-PE-fr-PCL and PE-fc-PS-fc-PCL triblock copolymers. (Reprinted from [94] with permission from Elsevier)...

Adamski, P. and Klimczyk, S. The crystallization rate constant and Avrami index for cholesterol pelargonate. Sov. Phys. Crystallogr. 23, 82 (1978)... 

Takebe et al. [28] studied the effect of temperature and molecular weight on the crystallization rate of SPS by DSC. When SPS was melted at 300 °C, then rapidly cooled to the crystallization temperature, T, the evolution of crystallization showed a sigmoidal curve with reference to crystallization time (Figure 18.6). The crystallization rate becomes slower as T approaches close to melting point. When the crystallization rate of SPS is analyzed based on Avrami theory, the Avrami index, n, is equal to 3, which suggests that crystallization of SPS proceeds via three-dimensional heterogeneous growth [28,29]. 

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... 

Table 3.7. Overall kinetic rate constant, k, Avrami index, n, and half time of crystallization, temperature and blend composition for some crystallizable miscible blends as function of the crystallization...

Avrami index n have been calculated at each - ---------- ---- -i-... 

Fig. 16. a. Kinetics constant versus temperature for a and mesomorphic phase b. Crystallinity volume fraction as a function of cooling rate for various values of n (Avrami index) and K0 D (crystallizability). 

Other kinetics parameters of the monoclinic phase are more difficult to be related to molecular parameters. Additionally, their physical meaning is not straightforward with the exception of Avrami index n. This last, in principle, represents the dimensionality of the growth and the kind of nucleation. Experiments, however, rarely well correlate with a value of n in line with the dimensionality of the crystallization process under observation. 

Table 5.3. Avrami index n for various nucleation processes...

Jeziomy directly applied Avrami equation to treat the non-isothermal crystallization peak in DSC scanning measurement (Jeziomy 1971). He obtained the Avrami index n and made a correction to K with the cooling rate a, as... 

Accordingly, on a series of crystallinity versus time curves (see Fig. 10.31b), one can take the data points along the horizontal equal-crystallinity line, and then obtain the ratios of the Avrami indexes and the rate constants separately from the slope and the intercept of log(fl) versus log(f)- The experiments have verified that a better linear relationship can be obtained in comparing this approach to the conventional Ozawa method. 

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