Avrami exponent

Thus the slope of a plot of ln[ln(l - 6) ] versus In t will have a slope equal to the Avrami exponent. 

If this result is substituted into the previous expressions containing f, the effect is to replace f with (20) " and to multiply those t s which accompany f by t This rather complex array of possibilities is summarized in Table 4.3. Table 4.3 lists the predicted values for the Avrami exponent for the following cases ... 

Those exponents which we have discussed expUcitly are identified by equation number in Table 4.3. Other tabulated results are readily rationalized from these. For example, according to Eq. (4.24) for disk (two-dimensional) growth on contact from simultaneous nucleations, the Avrami exponent is 2. If the dimensionality of the growth is increased to spherical (three dimensional), the exponent becomes 3. If, on top of this, the mechanism is controlled by diffusion, the... 

Avrami exponent Crystal geometry Nucleation mode Rate determination Equation ... 

While there are several instances of redundancy among the Avrami exponents arising from different pictures of the crystallization process, there is also enough variety to make the experimental value of this exponent a valuable way of characterizing the crystallization process. In the next section we shall examine the experimental side of crystallization kinetics. 

These unpredicted Avrami exponents may be indications that multiple mechanisms are operative and/or that f and/or N is itself a function of d. 

Using density as the property measured to determine crystallinity, evaluate 0 as a function of time for these data. By an appropriate graphical analysis, determine the Avrami exponent (in doing this, ignore values of 6 < 0.15, since errors get out of hand in this region). Calculate (rather than graphically evaluate) the value of K consistent with your analysis. 

Balsamo et al. [94] in a recent contribution considered that the Avrami exponent is given by the addition of two terms ... 

Furthermore, an Avrami exponent of 1 could also be obtained from surface nucleation. So far, no measurements are available in the literature of the nu-cleation kinetics as a function of droplet or MD size, and therefore the scaling between the relevant time constant associated with the nucleation event and the MD dimensions is unknown. 

Composition (weight ratio) Temperature (°C) Avrami exponent, n Crystallization function, K(t)... 

Conclusively, the calculated Avrami exponents reveal a three-dimensional growth of the crystalline regions for each blend. The rate of crystallization of each blend increased with the decrease in crystallization temperature, and the rate of crystallization of the (PHB80-PET20)/PEN blend was faster than that of the (PHB 80-PET20)/PET blend. 

To confirm the shape of the spherulites described by the Avrami exponent, polarized optical micrographs of the isothermal crystallized melt blends were taken, and are shown in Figure 20.26 [44],... 

The morphology of the spherulites was in the form of a Maltese Cross , which was confirmed by the Avrami exponent value in the DSC study. The spherulite size of the binary blends was smaller than that of pure PET and PEN. 

Fig. 6. Avrami plots of the increase in volume fraction crystallinity as a function of time for Avrami exponents n from 1 to 6 (see Eq. (7)). For partial crystallization vc would be normalized to the ultimate crystallinity reached. K represents the geometry and time constants and nucleation terms19)...

Price and Wendorff31 > and Jabarin and Stein 32) analyzed the solidification of cholesteryl myristate. Under equilibrium conditions it changes at 357.2 K from the isotropic to the cholesteric mesophase and at 352.9 K to the smectic mesophase (see Sect. 5.1.1). At 346.8 K the smectic liquid crystal crystallized to the fully ordered crystal. Dilatometry resulted in Avrami exponents of 2, 2, and 4 for the respective transitions. The cholesteric liquid crystal has a second transition right after the relatively quick formation of a turbid homeotropic state from the isotropic melt. It aggregates without volume change to a spherulitic texture. This process was studied by microscopy32) between 343 and 355.2 K and revealed another nucleation controlled process with an Avrami exponent of 3. 

Fig. 7. Double logarithmic Avrami plots for the crystallization of liquid crystalline poly(oxy-2 -dimethylazoxybenzene-4,4 -diyloxydodecanedioyl) to the fully ordered state between 322 and 362 K. Average of the Avrami exponent 3.5 0.3. Diagram courtesy J. Wiley and Sons27 ...

Adamski and Klimczyk analyzed cholesteryl pelargonate36) and caproate 37) liquid crystal to fully-ordered-crystal transitions over a temperature range of about 25 K. Again, the appearance of the fully ordered crystals was that of a spherulitic superstructure. The nucleation was time dependent, and the linear growth rate of the spherulites decreased with decreasing temperature by a factor 1/2 to 1/3, in contrast to the nonanoate and acetate. The Avrami exponent was close to 4 as judged from the measurement of the crystallized volume in the field of view under the microscope. 

Little information is available for the crystallization of condis crystals from the isotropic melt, but even less difference from the crystallization of fully ordered crystals is expected. It will be shown in Sect. 5.3 that one possible special effect of crystallization of macromolecular condis crystals is the ability to chain extend after initial crystallization. This process has been analyzed to some degree and occasional low Avrami exponents have been reported39). No information is available for the kinetics of... 

There are several reasons why the Avrami exponent may be less than 4. The nucleation rate may decrease with time because most favorable nucleation sites are used up early. In the extreme, it is possible that all nucleation sites are used up at the very start so nucleation makes no contribution to the exponent. In some cases, the growth rate may decrease with time. This is true for precipitation from solid solution. For precipitation, the rate of growth is inversely proportional to the square root of time. Finally, if growth is in only one or two dimensions instead of three, the contribution of growth will contribute less to the exponent. Table 11.1 lists the contributions to the exponents. 

Figure 4.10. Change of volume with three different Avrami exponents.

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