Theory of thermal motion in helical chains

Thermal fluctuation in the conformation of helical polymers in the crystalline state is considered in order to explain the streak along the fifth layer line of the X-ray fiber pattern of polyoxymethylene that is observed at room temperature. It is assumed that the fluctuation is caused by thermal motion of the internal rotation angles of the chain, under the influence of the crystalline field. For a special mode of normal vibration, i.e., for the so-called E(Θ) mode, the amplitude of thermal vibration of the external coordinates of each atom on the helical chain has a rather sharp maximum of a resonance type. The period of normal vibration of this mode is the same as the turning period of the helix; thus this maximum seems to be due to a resonance in the geometric sense. Each chain in the crystal migrates in the ab-plane as a rigid helix, and general consideration of X-ray diffraction theory shows that this normal vibration causes the streak observed in the fiber pattern of POM, in which the helical molecule has five turns per repeat distance.