Polymer Physics

t 1 = 2 ¼ð

ln 2

K

Þ^1 =nþt 0 (10.40)

It should be noted that the time evolution of crystallinity includes not only
crystal growth initiated by primary nucleation, but also by secondary crystallization
(including annealing, perfection, filling growth behind the growth front, etc.).
Concerning the complicated details in the crystallization process, it is not
recommended to learn the details of crystal nucleation modes and the dimensions
of crystal growth purely from the Avrami index. However, it is reliable to assign the
change of the Avrami index with crystallization temperatures to the change of
nucleation and growth mechanisms.
In the practical processing of polymer materials, the crystallization process is
often non-isothermal, especially in the processes of plastic extrusion, injection
molding and fiber spinning. The study of non-isothermal crystallization is still at
the experiment-oriented stage, and the theoretical treatment is limited to the level of
the Avrami equation.
Jeziorny directly applied Avrami equation to treat the non-isothermal crystalli-
zation peak in DSC scanning measurement (Jeziorny 1971 ). He obtained the
Avrami indexnand made a correction toKwith the cooling ratea,as

logKc¼

logK

a

(10.41)

He found thatnhas a linear dependence on the cooling ratea. Whennchanges
from 2 to 3 with the increase of cooling rate, crystallization may change from two-
dimensional lamellar growth to three-dimensional spherulitic growth, while
Kckeeps constant. Compared to the following methods, The Jeziorny method
lacks of a necessary theoretical basis.
Ozawa proposed to study the overall crystallization kinetics from several simple
DSC scanning experiments (Ozawa 1971 ). Assuming that when the polymer sam-
ple is cooled fromT 0 with a fixed cooling ratea¼dT/dt, both the radial growth rate
v(T)of the spherulites and the nucleation rateI(T)will change with temperature. For
a spherulite nucleated at timet, its radius at timetwill be

r¼

ðt

t

vðTÞdt¼

dt

dT

½

ðT

Tm

vðTÞdT

ðT^0

Tm

vðTÞdTŠ¼

1

a

½RðTÞRðT 0 ފ (10.42)

Here, the initial temperatureT 0 corresponds to timet, andTmis the melting
point. The density of crystal nuclei is thus

m

V

¼

ðT^0

Tm

IðTÞdt¼

1

a

Tð 0

Tm

IðTÞdT¼

NðT 0 Þ

a

(10.43)

10.4 Kinetics of Polymer Crystallization 217