regarded as H2/1 helix. Therefore, the most stable internal rotation for a helical
conformation determines the symmetric structure of the unit cell, i.e. the azimuths for
the most stable packing, corresponding to the angles between two axes of the unit
cell.
Rule No. 2, the helix chains prefer the most compact packing. Note that the
compact packing is the main driving force for crystallization of small molecules.
Viewing along the chain axis, the zigzag conformation of polyethylene appears as
an oval. As illustrated in Fig.10.10, the parallel packing of the chains with
alternating orientations determines the unit-cell structure in the orthorhombic
crystal series, witha¼7.36 A ̊ andb¼4.92 A ̊, so the lowest parallel packing
potential between polymer chains can be reached.
The survey over about 150 polymer crystals shows their distribution among
seven crystal series. The number in the cubic crystal series is zero, because the
c-axis contains completely different interactions (covalent bonds along the chain
axis) from the other two axes (sub-valence interactions). The orthorhombic and the
Fig. 10.9 Illustration of all-trans TTTT conformation of polyethylene and TGTG 3/1 helix
conformation of polypropylene
Fig. 10.10 Illustration of polyethylene chains viewed as ovals along the chains, alternately
changing orientations to pack into the orthorhombic crystal structure, which determines the
quantity of cell parameteraandb
10.3 Crystalline Structures of Polymers 199