Polymer Physics

shaped lamellar growth front of PE crystals can be directly observed in the bulk
phase, as shown in Fig.10.28(Mullin and Hobbs 2011 ).
In 1960, Lauritzen and Hoffman proposed a theoretical model (Lauritzen and
Hoffman 1960 ; Hoffman and Lauritzen 1961 ) that elucidated the secondary nucle-
ation barrier in the formation of the first stem on a smooth growth front. In 2003, the
intramolecular crystal nucleation model has been proposed (Hu et al.2003c), which
assigned the secondary nucleation barrier to the two-dimensional intra-chain crystal
nucleation and thus explained the source of chain-folding. In the crystallization of a
single chain, regular folding can effectively minimize the surface free energy
barrier and maximize the parallel stacking of backbones, both favored by crystal
nucleation. The intramolecular nucleation model provides a better interpretation to
the regime phenomenon reproduced in molecular simulations (Hu and Cai 2008 ). In
addition, this model can explain the molecular segregation phenomenon, which
gives long-chain fractions a priority to crystallize, as the principle of crystallization
fractionation of polydisperse polymers (Hu 2005 ). To date, controversial arguments
on the crystal growth mechanism of polymers still remain, which demand further
experimental investigations and theoretical developments.

10.4.3 Overall Kinetic Analysis of Polymer Crystallization

The details of the polymer crystallization process can be quite complicated. Practi-
cally, one may not care about the details of crystal nucleation and the linear crystal
growth rates, but just want to characterize the overall crystallization kinetics. The
degree of crystallization process can be roughly defined ascrystallinity, regardless
of their detailed crystal morphologies. The conventional methods to characterize
the crystallinity include DSC, X-ray diffraction and dilatometer. Depending on the
measured quantity, crystallinity is also separated intothe weight crystallinity

fcw¼

Wc

WcþWa

 100 % (10.30)

andthe volume crystallinity

fcV¼

Vc

VcþVa

 100 % (10.31)

The subscriptscandarepresent crystalline and amorphous states, respectively. They
can be derived to each other with the densities of crystalline and amorphous states.
Since the crystallinity of polymers is commonly low, it is often convenient to
trace its time evolution usingthe relative crystallinity

Xc¼

fcðtÞ

fcð1Þ

(10.32)

214 10 Polymer Crystallization