Avrami rate parameters

In polymer melt processing, the crystallization half-time, 0/2, is often a more useful parameter than the Avrami rate constant. An experienced individual can often estimate the processing conditions of a new polymer by comparing its 0/2 value with those of known polymers. Figure 11.6 compares the ty2 parameters of PET, PTT and PBT, with PTT falling in between the other two polyesters. 

When the molecular system is a solid or cross-linked fluid subject to constant deformation, the orientation of the molecule is independent of time and the rate parameters are constants dependent only on the deformation. However, if the orientation changes with time, then the rate constants, and possibly the mechanism, will also change and this time dependence will alter the basic form of the Avrami equation, i.e. to... 

Crystallization rate coefficient Crystallization rate parameter Dibenzylidene sorbitol Total volume of growing crystals Radial crystallization rate Preexponential factor in growth rate High density polyethylene Rate of nucleation Avrami constant... 

The Avrami—Erofe ev equation, eqn. (6), has been successfully used in kinetic analyses of many solid phase decomposition reactions examples are given in Chaps. 4 and 5. For no substance, however, has this expression been more comprehensively applied than in the decomposition of ammonium perchlorate. The value of n for the low temperature reaction of large crystals [268] is reduced at a 0.2 from 4 to 3, corresponding to the completion of nucleation. More recently, the same rate process has been the subject of a particularly detailed and rigorous re-analysis by Jacobs and Ng [452] who used a computer to optimize curve fitting. The main reaction (0.01 < a < 1.0) was well described by the exact Avrami equation, eqn. (4), and kinetic interpretation also included an examination of the rates of development and of multiplication of nuclei during the induction period (a < 0.01). The complete kinetic expressions required to describe quantitatively the overall reaction required a total of ten parameters. 

The primary crystallization process is characterized by three parameters. These are the rate of radial growth of the spherulite, G, the time constant for nucleation, t , and the time constant for the primary crystallization process, Tc, which is determined from the Avrami equation. All three parameters seem to depend on the stereoregularity of the polymer, but the nucleation rate seems to depend most strongly. 

Table 4 Parameters of the a-Time Curves Fitted by Avrami Erofe ev Rate Equation with n Fixed at 2 for...

We observe that quasi-isotherms shift downwards when the temperature T increases, it occurs as a consequence of slowing down of rate of ciystalhzation. One may state, isotherms and quasi-isotherms show deviations from Avrami at high conversions whereas, non-isotherms with s = const display deviations from Equation (34) at low conversions. The comparison of relevant parameters for isotherms and quasi-isotherms reveal that rates are lower and Avrami exponents are higher for isotherms as compared to quasi-isotherms. An example is given in Table 4. 

Isothermal crystallization of polymers is normally performed by cooling the sample at the fastest cooling rate possible from an (assumed) isotropic melt to a predetermined temperature where the crystallization process is monitored as a function of time. Coefficients similar to the reaction rate kinetic parameters have been developed to describe the isothermal crystallization of polymers based on Avrami s equation ... 

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