Avrami parameters

Table 17.3. Avrami parameters for ehemically interesterified and non-interesterified 20%SSS/ 80%OOO blends crystallized at 30°C, 40°C and 50°C. (NA) the data is not available because the system did not crystallize.

Plotting the left part of this equation against logt should result in a straight line, from which both Avrami parameters, n (slope) and k (intercept), can be obtained. In Table 3.7 some literature data on the Avrami constants and the half time of crystallization are presented. 

Eq 3.21 is valid for a < and Eq 3.22 for a > Instead of two Avrami parameters, five parameters are required to describe the process. They have the following physical meaning k and n (the primary crystallization parameters) depend on crystallization temperature, nature of primary nucleation and the fast growth the secondary... 

Under nonisothermal conditions, the ultimate Avrami parameters will be averages of the parameters of the subsequent steps. 

The Avrami parameter, n, can also be determined from a single exotherm using the expression from Augis and Bennett ... 

Figure 3.54 shows actual DSC curves for samples A and B melted at 170°C. The fit of the calculated Avrami parameters to the experimental data is also shown. As seen, the sample spun under high stress crystallized much more rapidly than the sample produced under low stress. Moreover, it was observed that the starting spherulitic and row-nucleated structures were retained in the recrystallized samples. 

Figure 8.20. Log-log plot of Xa against time showing technique for estimating values of Avrami parameters n and k,.

For mai polymers, reliable values for the two Avrami parameters could be determined by applying the indicated procedures. 

TABLE 9 The values of Avrami parameters, and M, forcrystaUizedPTT as presented... 

The crystallization exothermic trace is directly measurable by DSC method when the crystallization temperature chosen is between 250°C and 258°C, which is several degrees higher than the onset temperature. By following Avrami treatment, the relative crystallinity versus time is calculated. Then, the Avrami parameter n is obtained from log (—In (1 — 0)) versus logC curves as shown in Figure 3.13. The average n value is around 2.6, which is much higher than the n value for the crystallization process observed at 260 and 262°C. 

The Avrami parameter, n, is computed as a function of temperature, and their values are summarized in Table 3.8. All the n values are in the low range of 0.2 to 0.5, which may be due to the fact that each crystal does not grow with a constant radial growth rate. 

TABLE 3.8. Avrami Parameters of the Transition Kinetics of Vectra A-950. 

Equation 3.21 is valid for a < [, and Eq. 3.22 for a > C- InstEad of two Avrami parameters, five parameters are required to describe the process. They have the following physical meaning k and n (the primary crystallization parameters) depend on crystallization temperature, nature of primary nucleation, and the fast growth the secondary crystallization parameters, k and n, depend on the conditions under which the slow crystallization of the remaining amorphous regions takes place and a fifth parameter, i, indicates the weight fractiOTi of material crystallized up to the moment the primary crystallization ends, t is the moment at which the third region starts (e.g., pure secondary crystallization). 

Table 9.1 Avrami parameters and crystallization half times of PLA-based nanocomposites containing 1 wt% of the nucleating agent.

Crystallinity and Avrami parameters for the samples crystallized isothermically at 392 K. 

When the filler is pressent at polypropylene crystallization, can be expected that this affects its crystalline order, being the Avrami parameter n the key to these changes. In our study, whereas in the isothermal crystallization of unfilled polypropylene the value of n is near three, i.e. similar to the values reported in the literature (4) corresponding to a tridimensional athermal nucleation, in the composites containing the block copolymer, sepiolite or talc, apart from deviating notably from the value found for unfilled polypropylene, it does not remain constant with filler concentration. The dif ferent behaviour observed between the composites containing the different fillers points toward the qualitative fact that different fillers promote different structures in the polypropylene composites containing them, which undoubtlessly has an impact on their physical properties. 

As an example, of pure PEEK with different relative molecular mass measured by means of DSC is shown in Figure 4.19. The values of U ranged from 19.3 to 117.3 kj mol These results were measured by means of DSC. The relationship among Avrami parameters, k, n... 

Table 4.3 The Avrami parameters, n and k of polypropylene crystallized isothermally at various temperatures...

Usually, the measurement of the relative values of G is sufficient to evaluate the overall crystallization behavior and free energies under isothermal conditions. According to nucleation theories, a simple relationship between the linear growth rate of the spherulite, G, and the Avrami parameters n and k is... 

G can be detected by using a polarizing optical microscope. If the experiments were carried out by means of DSC, the Avrami parameters, k and n, can be measured. Accordingly, equation (4.50) is modified to... 

The results shown were analyzed with the Avrami empirical equation, av=l-exp(-kf"), where k is the rate constant, and w is a constant. The data on Uv obtained at the initial and intermediate stages gave a linear relationship between ln(ln(l-av) i) and ln(f) with a correlation coefficient of more than 0.99. The Avrami parameter and rate constants obtained are summarized in Table 1. Based on the Arrhenius relationship (Fig. 9), k=Aexp(-Ev/RT) with v as the activation energy and constants A and R, on those k values which increased with increasing temperature, we obtained an activation energy of kj/mol,... 

In the non-isothermal method, the values of the Avrami parameter, n, are determined from the Ozawa equation (Qelikbilek et al., 2011 Ozawa, 1971 Prasad Varma, 2005) ... 

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