identical to the chain axis appears much smaller than the chain length, so he
proposed theadjacent chain-folding modelto explain this structural feature of
lamellar crystals (Keller 1957 ). The idea of chain-folding in polymer crystals was
first discussed by Storks in 1938 in his analysis of electron diffraction data on gutta-
percha films (a natural rubber trans-polyisoprene) (Storks 1938 ), but it was incon-
ceivable at that time because the lamellar crystals had not yet been recognized as a
native structure. The wide observation of the native lamellar crystals formed by
chain-folding is a milestone discovery in the history of polymer science (Keller
1957 ; Till 1957 ; Fischer 1957 ). The lamellar crystals serve as the building blocks to
assemble into spherulites.
In comparison to the crystallization in dilute solutions, the melt crystallization
appears more complicated. In 1962, Fischer and Schimdt proposed the long period
of alternating amorphous and lamellar crystals as monitored by the X-ray scattering
of stretched polyethylene (Fischer and Schmidt 1962 ). Almost in the same period,
Flory suggested that polymer chains may not be able to fold up quickly into the
regularly adjacent chain-folding state in lamellar crystals, and many chains will
form loops and cilia (Flory 1962 ). In 1978, Fischer proposed thesolidification
model(Erstarrungsmodell) for polymer chains to crystallize in the nearby regions
without a large-scale reorganization (Fischer 1978 ). In the mean time, Flory and
Yoon used the“telephone-switchboard” modelto emphasize the coexistence of
loops, cilia and tie molecules at the lamellar surfaces (Flory and Yoon 1978 ), to
explain the observation from neutron scattering experiments. The explanation was
argued to reconcile both switchboard model and the adjacent folding model, into
thevariable-cluster modelto describe the single chain conformation in the lamellar
crystals formed in the melt-crystallization process (Hoffman et al. 1979 , 1983 ), as
illustrated also in Fig.10.11.
Why does polymer crystallization spontaneously select the adjacent chain fold-
ing? If one looks at the nucleus formation of polymer crystals, there are two basic
types: one is called the inter-chain nucleation, as described by the fringed-micelle
model, with a bundle of chains parallel stacked on the normal directions; another is
called the intra-chain nucleation, as described by the adjacent chain folding model,
with chains parallel packed and folded back in time to avoid overcrowding at the
lamellar surfaces. In the case of inter-chain nucleation, since a large fraction of
amorphous chains connected with the crystal stems on the lamellar surfaces, the
amorphous chains will lose the conformational entropy due to their overcrowding.
This raises the surface free energy, and the nucleation barrier will be very high. In
contrast, in the case of intra-chain nucleation, since a large fraction of adjacent
chain-folding on the lamellar surfaces, the amorphous chains are relatively free.
This selection lowers the surface free energy, and the nucleation barrier is thus
relatively low. According to this kinetic selection of nucleation mechanisms, the
intra-chain nucleation dominates not only the primary crystal nucleation but also
the secondary crystal nucleation at the lateral growth front of lamellar polymer
crystals. The latter process generates a large amount of adjacent chain-folds at the
surfaces of polymer crystals, which fabricates naturally the metastable lamellar
crystals as the native morphological structure of polymer crystals. The above
10.3 Crystalline Structures of Polymers 201