10.3.2 Unit Cells of Polymer Crystals
Let us first look at the unit cell structure of polymer crystals. The periodic lattice
structure of crystalline polymers has been well characterized by the wide-angle
X-ray diffraction (WAXD) spectrum. Early in 1928, Meyer and Mark proposed that
a certain segment of polymer helix can form the size of the unit cell (Meyer and
Mark 1928 ), instead of having the whole chain in the unit cell. Such a breakthrough
strongly supported the macromolecular concept proposed by Staudinger at that
time. The unit cell is constituted by three axes (abc) and the angles between them
(abg), as illustrated in Fig.10.8. Conventionally, thec-axis of the unit cell is defined
as being oriented along the chain direction, whilea-axis andb-axis are oriented
along the parallel packing directions of polymer chains.
The packing of polymer chains into the unit cell normally follows two basic
rules:
Rule No. 1, crystalline polymers intend to form the most stable conformation,
although sometimes they are compromised with Rule No. 2. As illustrated in
Fig.10.9, the most stable conformation of polyethylene is the all-trans conformation
TTTT, also known as the Zigzag conformation, withc¼2.534 A ̊.Incontrast,if
isotactic polypropylene forms the same all-trans conformations, their methyl-groups
would be overcrowding on the same sides, increasing the conformational potential
energy. By calculating the methyl-groups oriented with 120 angles, Natta and
Corradini first discovered the most stable TGTG helical conformation withc¼6.50
A ̊, called the H3/1 helix (Natta and Corradini 1960 ). H3/1 helix means that the
substitutes turning around one circle back to the same places go through three
repeating units. Accordingly, the zigzag conformation of polyethylene can be
Fig. 10.8 Illustration of the unit cell of polymer crystals
198 10 Polymer Crystallization