Avrami equation/exponent

Table 4.3 Summary of Exponents in the Avrami Equation for Different Crystallization Mechanisms...

Wu and Woo [26] compared the isothermal kinetics of sPS/aPS or sPS/PPE melt crystallized blends (T x = 320°C, tmax = 5 min, Tcj = 238-252°C) with those of neat sPS. Crystallization enthalpies, measured by DSC and fitted to the Avrami equation, provided the kinetic rate constant k and the exponent n. The n value found in pure sPS (2.8) points to a homogeneous nucleation and a three-dimensional pattern of the spherulite growth. In sPS/aPS (75 25 wt%) n is similar (2.7), but it decreases with increase in sPS content, whereas in sPS/PPE n is much lower (2.2) and independent of composition. As the shape of spherul-ites does not change with composition, the decrease in n suggests that the addition of aPS or PPE to sPS makes the nucleation mechanism of the latter more heterogeneous. 

The Avrami equation (1), originally developed for the crystallization of metals from melt, has been applied by many researchers to the crystallization of oils and fats in order to elucidate information on their crystallization mechanism. The Avrami equation is based on the model of a growing sphere crystallizing from a melt of uniform density without impingement. The usual Avrami exponent, used to draw conclusions with respect to the crystallization mechanism of the system, is observed to be about three or four for oils and fats after rounding off to whole integers. 

In applying the Avrami equation to the crystallization of metals, for which the equation was originally developed, experimental data would give exponents which are whole numbers. When applied to polymers, it was observed that although... 

The exponent of the Avrami equation, n, has a theoretical value of 3 when crystallization takes the form of spherulitic growth of nuclei which came into being at the same instant in time. Integral values of n ranging from 1 to 4 can be attributed to other forms of nucleation and growth [22]. 

The isothermal crystallization kinetics is studied mainly with the Avrami equation (logarithmic form in equation 8.2), where < )(f) is the relative crystallinity, n and are the Avrami exponent and crystallization rate constant respectively. 

During the isothermal crystallization of PEN, a relatively high crystallinity is achieved. The rate can be described by the Avrami equation with the exponent n = 2.5. The activation energy for isothermal crystallization is determined to be 250 kJmol ... 

For the case of heterogeneous nucleation, the exponent n of the Avrami equation is equal to the dimensionality of growth. 

From the slope on the right graph of Fig. 99 an Avrami exponent of 3.2 results, close to the value expected for athermal nucleation followed by sphemlitic growth, but because of the many assumptions that went into the derivation of the Avrami equation still not proven without a detailed structural analysis. 

X 10 , 3.1 X 10 and 6.8 x 10 sec " for angular velocity of a supporting disc 240, 270, 300 and 330 rpm, respectively. However, although Johnson-Mehl-Avrami equation satisfactorily describes overall kinetics, it is hard to give any unambiguous physical interpretations of the derived values of Avrami exponent, n which varies from 2.14 to 3.57. 

Kinetic data from scattering experiments could be analysed in terms of the Avrami equation (Eq. 26). This equation describes the development of crystallinity (or other separate phase) with time, at a constant temperature, in terms of a rate coefficient k and an exponent n is the fraction of crystalHsable material which has crystallised at time t. The value of n reflects a combination of the kinetics of nucleation of the second phase and the number of dimensions in which crystallinity (or second phase) develops. A value of n=3 is consistent with a constant niunber of growing nuclei and growth in three dimensions, i.e. the kinetics of a constant number of expanding spheres. The Avrami equation allows for impinging growing phases and departures from the Avrami equation, at long times, are often explained in terms of secondary crystallisation within the already-formed spheruHtes ... 

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