Avrami theory

The crystallisation kinetics of polymeric materials xmder isothermal conditions for various modes of nucleation and growth can be well approximated by the Avrami equation[9,10]. 

Where 0 is the volume fraction not transformed at time t, k is the kinetic rate constant and n is the Avrami exponent. The Avrami exponent is 

Avrami theory is derived by presuming random nucleation, a constant rate of nucleation (or a constant nucleation density). However these assumptions may not always hold true. The linear growth rate, for example, is not always constant with time. In addition, the number of nuclei may not increase continuously but may instead reach a limiting level after exhaustion of heterogeneous nuclei. Ihe use of the Avrami equation is further complicated [12] by additional factors such as  

The end results is an over simplification of crystallisation process. In general however, the Avrami equation is usually found to represent a good fit with the data. This has shown to be a consequence of the inherent strong correlation between tp the induction time of nucleation, and k and n, from Equation (2.4) [12,13]. 

Thus a plot of Log (- Ln (1-x)) versus Log(t -1.) should yield a straight line of slope n and intercept Log k if Avrami theory is applicable. 

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In this case the effect of overlapping of the individual nuclei can be simply expressed in terms of the statistical Kolmogorov-Avrami theory, where the right-hand side of Eq. (5.8.6) is multiplied by the factor exp(— N X2t2/z2F2Tll) and that of Eq. (5.8.7) by the factor (—jZKh2t3/3z2F2rll). 

The isothermal crystallization study on binary blends was performed with P(HB80-ET20)/PET (weight ratio, 4 3) and P(HB80-ET20)/PEN (weight ratio, 4 3). The Avrami theory was applied, as shown in the following equation [23, 46] ... 

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]. 

General Aspects of the Avrami Theory Under Isothermal Conditions... 

Transformation kinetics according to Nakamura and Ziabicki Nakamura (3) extended Avrami theory to non-isothermal transformations and proposed the following equation ... 

The kinetics of crumb firming have been described by an equation derived from the Avrami theory (Avrami 1939). This theory describes the rate of change of a supercooled amorphous material to an ordered crystalline structure when the process is governed by random production of stable nuclei ... 

Starch acts as the nucleating agent for poly(e-caprolactone) ciystallization. According to the Avrami theory, starch functioned as a nucleating agent to improve the ciystallinity rate of PCL. However, the XRD analysis revealed that the ciystallinity decreased Because mobility constraints existed in the PCL chains with the increasing starch concentration, the ciystallization ability of PCL decreased ... 

The Isothermal dilatometric growth rate data were fitted to the equation predicted by the Avrami theory (25,26,27) ... 

Non-isothermal crystallization kinetics can be analyzed by using the extension of the Avrami theory [68-70] and proposed by Ozawa [71, 72], This analysis accounts for the effect of cooling rate on crystallization from the melt by replacirtg the time variable in the Avrami equation with a variable cooling rate term, that is, by replacing f in the equation (3) with TIa as shown in the equation (4) ... 

In this chapter, we take a practical approach to briefly explain how to experimentally determine both spherulitic growth rates by polarized light optical Microscopy (PLOM) and overall isothermal crystallization kinetics by differential scanning calorimetry (DSC). We give examples on how to fit the data using both the Avrami theory and the Lauritzen and Hoffman theory. Both theories provide useful analytical equations that when properly handled represent valuable tools to understand crystallization kinetics and its relationship with morphology. They also have several shortcomings that are pointed out. 

The Avrami theory usually provides a good fit of the experimental data at least in the conversion range up to the end of the primary crystallization, that is, up to the impingement of spherulites at approximately 50% conversion to the solid... 

Crystallization kinetics have been studied in bulk and in dilute solution by a number of investigators (51-57). In general, these investigations were based on either the Avrami theory (58) or the Hoffman-Lauritzen theory of polymer crystallization (59-61). 

The Avrami theory was developed for bulk phases that are not interrupted. Therefore, the assumption of free growth in a bulk phase does not strictly apply to the cases where the crystallizing phase has been divided up into many isolated MDs. Nevertheless, as the results discussed previously have shown, several researchers have found a clear correlation between the Avrami... 

Computer Simulations On this topic, there have been a number of developments that have a kinetics basis, apparent connected with assumptions used in die Avrami theory fliat cmfy provides analytic solutions. In simulations, the approach has been used to model bulk transformations for ... 

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