Background and a brief survey of polymer crystallography

It is important to emphasize that the types of polymer dealt with in this chapter have flexible chains. Rigid-rod polymers forming mesomorphic phases are not discussed here. Most of the material presented comes from extensive studies of polyethylene. This polymer should be considered as a model for other flexible-chain polymers and not as a special case. 

Periodic arrangements of any motif (e.g. group of atoms) are generated by placing the motif at points located such that each point has identical surroundings. Such infinite arrangements are called lattices. Bravais (1850) showed that there are only 14 different ways (so-called Bravais or space lattices) of arranging points in space (Fig. 7.1). 

The repeating period of the space lattice that most simply describes the nature of the space lattice when it is repeated by three-dimensional translation is called the unit cell of the space lattice. Note the analogy between a, b and c in the unit cell and the corresponding quantities of the crystal system. Cells with only one unique motif are referred to as primitive. It is always possible to generate a primitive cell from a given lattice but in many cases end-, face- or body-centred representations are preferred because they may show greater symmetry than the primitive cells. 

Crystals exhibit symmetry. A number of different symmetry operations are possible  

Systems Axes Axial angles Minimum symmetry 

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