the PET transparency and Coke bottles. High transparency does not mean that there
is no crystalline domain in materials. As a matter of fact, the crystallinity in PET
transparency can be as high as 50 %, but the crystallite sizes are smaller than the
wavelengths of visible lights. Two key factors characterize the efficiency of nucle-
ation agents: one is whether they can effectively decrease the interface free energy
of the crystallites, as the research has found that surface epitaxy is an effective way
to initiate crystal nucleation; another is whether they can provide large amount of
homogeneously dispersed foreign surfaces to initiate crystal nucleation on time.
In 1926, Volmer and Weber found that the nucleation rate shows a negative
exponential dependence on critical free energy barrier (Volmer and Weber 1926 ).
Becker and Do ̈ring further proposed that the activation energy for the short-distance
diffusion of molecules molecules to enter the crystalline phase should be considered
as well (Becker and Do ̈ring 1935 ). Turnbull and Fisher derived the prefactor for the
rate equation of crystal nucleation (Turnbull and Fisher 1949 ). The rate of polymer
crystal nucleationiwith the change of critical free energy barrier can be expressed as
i¼i 0 expðDU
kTÞexpðDG^
kTÞ (10.28)
Herei 0 is the prefactor,DUis the activation energy for short-distance diffusion
of molecules at interfaces. According to the VFT relaxation mode (6.10),DU/kT/
1/(TTV). With the increase of crystallization temperatures, molecular diffusion
will be enhanced, andDUwill be decreased. On the other hand,DGis the critical
free energy barrier for crystal nucleation. For the primary nucleation,DG/DT^2.
With increase of the crystallization temperatures,DTwill become smaller, andDG*
will rise, accordingly the nucleation rate will be decreased. Thus, at high
temperatures, the nucleation rate is mainly dominated by the critical free energy
barrier for crystal nucleation, the higher the temperature, the smaller the nucleation
rate; at low temperatures, the nucleation rate will be mainly dominated by the
Fig. 10.25 Illustration of (a) the temperature dependence of two key factors controlling the
nucleation rate; (b) the resulting bell-shape nucleation rate versus temperature
10.4 Kinetics of Polymer Crystallization 211