In ceramics or metals, a crystalline solid comprises repeating unit cells that contain each of the component atoms in the material. Each unit cell is composed of one or more molecular units. In a polymer this is not possible; the molecules are chains containing potentially millions of formula units. There is, however a repeating unit in a polymer - the monomer from which it was made. This must be the basis of both long and short-range order in a polymeric material.
For example, a short section of linear poly(ethylene) looks like this:
However, the conformation of the bonds around each carbon atom can be represented schematically as follows:
These diagrams are called Newman projections. The circle is a single C-H bond; and this diagram represents a projection along it. These two structures thus represent one half of the backbone continuing on either side of a C-C bond (trans), or both halves on the same side (gauche). Note that there are two possible gauche states, labelled gauche (-) and gauche (+).
Whilst the trans conformation has a lower energy (since it's easier to position the hydrogen atoms on the carbon backbone further apart), an all-trans conformation would be a considerably more ordered structure than a random one - that is, it has a much lower entropy.
Amorphous polymers are generally found in a random coil conformation and have a disordered chain structure. This is the most common structure of many polymers. Crystalline polymers are predominantly in the all-trans conformation, and the chains are arranged in lamellae, as below:
The polymer crystal is made up from one-dimensional chain-folded sequences, shown on the above left, where the repeat distance is given by the chain spacing. To the above right is shown a schematic arrangement of folded chains into a two-dimensional lamella.
An amorphous polymer has the maximum entropy conformation (given by the Boltzmann distribution), and the chains are arrayed randomly throughout the material, making atomic positions quasi-random as in any other glassy material.
As a result of the difference between the amorphous and crystalline arrangements of polymer chains, the X-ray diffraction patterns of the two phases are very different. The amorphous phase contains no long-range order, meaning that there are no regular crystalline planes to diffract X-rays. Thus the incident X-rays are scattered randomly and there are no sharp peaks in the diffraction pattern. In the crystalline phase, the repeating lamellar chains provide a regular structure, thus the diffraction pattern will contain sharp, prominent signature peaks, the position of which depends on the exact spacing between chains.
As the degree of crystallinity of a polymer affects its properties, accurately determining it is important. X-ray diffraction can be used to determine the degree of crystallinity of a sample. Thermal analysis techniques such as differential scanning calorimetry (DSC) can also be used. The two determinations may not necessarily be in agreement, and the reasons for this are complex.