Polymer Physics

Substituting (10.42) and (10.43) into (10.36) in the above derivation process for
Avrami equation, one obtains

lnP¼

m

V

<Vi>¼

ðT

Tm

m

V

pr^2 dr

¼

ðT

Tm

pNðT 0 Þ½RðTÞRðT 0 ފ^2 vðT 0 ÞdT 0 a^4

¼K 0 ðTÞa^4 ð 10 : 44 Þ

K 0 (T)is called the cooling function. Accordingly, the Ozawa equation is derived
as given by

1 Xc¼exp½K 0 ðTÞaqŠ (10.45)

Here,qis called the Ozawa index. Corresponding to one-dimensional growth,
q¼2; two-dimensional growth,q¼3; and three-dimensional growth,q¼4. In
practical measurements, one may determine the values of crystallinityXc(a)at a
constant temperature from a series of DSC crystallization curve with various
cooling ratesa, and then plot lg[ln(1Xc)] versus lg(a), to obtain the Ozawa
index directly from the slope, as illustrated in Fig.10.31a–c.
With a change of cooling rate, the temperature region for polymer crystallization
shifts. The Ozawa method may not be easy to provide enough data points exhibiting
a good linear relationship. Liu and Mo proposed a combination of Ozawa equation

Fig. 10.31 Illustration of the Ozawa method to treat (a) several DSC curves with various cooling
ratesa.(b) A group of crystallinity dataXcare read at a constant temperature, then (c) the Ozawa
index can be obtained from the slope of lg[ln(1Xc)] versus lg(a)

218 10 Polymer Crystallization