Avrami analysis

The Avrami analysis was performed on the crystallization data. The DLI measurements provided high Avrami exponents in the blends, but the analysis on the DLI data is extremely inaccurate because of all the difficulties inherent to the method. The IR measurements show Avrami exponents that range from 2.5 to 1.5 for PET and PBT. These studies were made on the diffusion-controlled region. It is our belief that the Avrami analysis strongly depends on the method used to follow the crystallization and always has to be accompanied with direct observations on the morphology. 

Avrami Analysis The Avrami equation, a general approach for description of isothermal phase transformation kinetics originally developed for polymers (46), is often used for describing nucleation and crystal growth in fats. The Avrami equation is given as... 

Data on the development of crystallinity, obtained by adiabatic calorimetry are depicted in Fig. 3.99. Note, that for the Avrami analysis the crystallinity must be calculated in volume fraction, v, while the heat of fusion is usually expressed in weight-fraction, w, as displayed in Figs. 3.84 and derived in Fig. 5.80, respectively. The correlation between the two crystallinities is given by ... 

Why do we say that the Avrami analysis is also a kind of scaling analysis ... 

The average values n are indicative of thermal and/or athermal nucleation followed by a three-dimensional crystal growth. Indeed, for spherulitic growth and athermal nucleation, n is expected to be 3. In the case of thermal nucleation, it is expected to be 4 [2], However, complications in the Avrami analysis often arise because several assumptions, not completely applicable to polymer crystallization, are involved in the derivation. A comparison of some crystallization kinetics parameters is summarized in Table 3.5 [70-80]. 

The Avrami exponent (n) increases with increasing dimensionality of the crystal growth (Table 6.2). Diffusion-controlled growth reduees the value of the exponent by a factor of 1/2 compared with the corresponding free growth case. There are certain limitations and special considerations for polymers with regard to the Avrami analysis ... 

Differential scanning calorimetry (DSC) can be used to study the onset of crystallization on cooling from the melt where nudeated polymers have higher onset temperatures (Figures 2 and 3). Isothermal studies provide kinetic data where Avrami analysis (equation 2, where x = reduced... 

The crystallization kinetics of iPP has been extensively examined via the Avrami analysis, as reported by Janimak [111] and Hieber [160]. 

Another approach used in the literature is the use of the mere Avrami analysis also on data obtained from nonisothermal measurements [179, 180]. By plotting log —ln[l — X t)] against logt for each cooling rate, one single line can be obtained. It must be taken into account that, in this treatment, the values of n and K do not have the same physical meaning as in isothermal processes, because under nonisothermal conditions the temperature changes continuously. In this case, K and n are two adjustable parameters to be fitted to the data. 

The Avrami exponent, w, can be determined from the slope of a plot of log n[ ht - hoo)l ho - hoo)] against log t. Fig. 4.26 shows an Avrami plot for polypropylene crystallizing at different temperatures. It is often difficult to estimate n from such plots because its value can vary with time. Also, non-integral values can be obtained and care must be exercised in using the Avrami analysis, as interpretation of the value of n in terms of specific nucleation and growth mechanisms can sometimes be ambiguous. 

Although the Avrami analysis is fairly successful in explaining the phenomenology of crystallization it does not give any insight into the molecular process involved in the nucleation and growth of polymer crystals. There have been many attempts to develop theories to explain the important aspects of crystallization. Some of the theories are highly... 

Avrami analysis of DSC measurements) frequently deviates from the theoretically predicted integer numbers. It appears that the Avrami analysis yields ... 

DSC experiments may be also a source of errors in the calculations of conversion degree. Indications concerning the proper protocol for DSC measurements are given in recently published works [30,60] and in Chapter 1. The recommended procedure is to heat up a sample above the equilibrium melting temperature to erase history, and then to cool it as fast as possible to the desired temperature of crystallization. The apparatus response should be subtracted from the signal and the baseline correctly determined. The beginning of crystallization may be delayed with respect to time at which the selected temperature was reached by a time called induction time. In this case, it is necessary to resolve the onset of crystallization, which is difficult because of negligibly small thermal effects produced by the nucleation. If the assumed onset time of crystallization differs from the true value by U, the Avrami analysis yields n instead of n ... 

It was also demonstrated that in polymer composites, volume inhabited by embedded fibers inaccessible for crystallization and additional nucleation on internal interfaces [53,62,63], can markedly influence the overall crystallization kinetics, as described in Chapter 13. Similar problems might be encountered during crystallization in other polymer systems such as composites with particulate fillers and immiscible polymer blends. Under such conditions, the simplified Avrami equation (Eq. 7.10) does not apply and, as a consequence, the classic Avrami analysis may yield nonlinear plots and/ or noninteger n values. It must be emphasized that the problem cannot be solved by application of other, incorrect models, like that of Tobin, which are essentially based on the same assumptions as the Avrami-Evans theory but yield different equations due to incorrect reasoning. 

Similarly, as in the case of the Avrami analysis of isothermal crystallization, the discrepancies between experimentally determined curves and predictions of the Ozawa equation originate mainly from oversimplified assumptions concerning the polymer crystallization. Those discrepancies inspired some authors to search for other equations enabling a better description and analysis of nonisothermal crystallization. For instance, the classic isothermal Avrami analysis based on Equation (7.5) with E expressed by Equation (7.10) was applied to nonisothermal crystallization [65, 66]. Such an approach has no theoretical justification. Even if a straight line Avrami plot is obtained, the parameters k and n are, at best, two adjustable parameters without a clear physical meaning. The Jeziomy method [67] deserves similar criticism. Jeziomy proposed using Equation (7.5) and Equation (7.10) and characterizing the process with the parameter kc defined as ... 

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