DG¼
4 p
3r^3 Dgþ 4 pr^2 s (10.25)This equation is similar with (9.43). One can derive the critical free energy
barrier for the critical size nucleiDG*as
DG^ /DT^2 (10.26)
whereDTTmTc, closely proportional toDg(see (10.22)). The critical size of
nucleir*is
r^ /DT^1 (10.27)There are three basic situations for crystal nucleation, as illustrated in Fig.10.23.
The first situation corresponds to the genesis of new phase, supposed to generate a
cubic crystallite from the amorphous bulk polymer phase, which contains six square
interfaces. Such a genesis process is calledprimary nucleation. The second situa-
tion corresponds to the initiation of the growth of new layer on a smooth growth
front of the crystal, supposed to generate four additional square faces of the new
lateral interfaces. Such a two-dimensional nucleation process is calledsecondary
nucleation, which can be quite slow at the growth front and thus becomes a rate-
determining step. The third situation is not easy to be observed, as one-dimensional
nucleation at the edge of terrace for spreading on the growth front, supposed to
generate only two additional square faces at the top and down interfaces. Such a
one-dimensional nucleation process is calledtertiary nucleation. Primary nucle-
ation generates the largest new interface, so its free energy barrier will be the
highest, and its initiation will be the slowest. This process requires the largest
supercooling to initiate crystallization. The free energy barrier for secondary
nucleation will be lower. After the incubation period for the initiation of crystal
nucleation, crystal growth appears to be a self-acceleration process. Tertiary
Fig. 10.22 Illustration of the free energy curve for crystal nucleation with the change of crystal
size. The highest position reflects the height of the critical nucleation barrier at the critical size of
nuclei. Theleft bottomis the amorphous bulk polymer and theright upis the emergence of an
ordered domain
10.4 Kinetics of Polymer Crystallization 209