Fibrous and crystal structures of a helical polymer, poly-L-lactic acid (PLLA), were analyzed by using x-ray diffraction experiments. It was confirmed that the molecular residues were arranged on a nonintegral 10/3 helix as De Santis and Kovacs [Biopolymers 6, 299 (1968)] reported. The atomic positions in a monomeric unit, which were proposed by Hoogsteen, Postema, Pennings, ten Brinke, and Zugenmaier [Macromolecules 23, 634 (1990)], were validated. However, the previous reports on the positions of the two helical chains were found to be in error. The correct positions were determined. The second helical chain shifts from the base center by 0.45, 0.25, and 0.61 Å along a, b, and c axes. Besides, the second chain rotates by 2.46° with respect to the first. Distribution function of the crystallites in various drawn fibers were determined as a function of spiral angle. Optical gyrations of PLLA and poly-D-lactic acid fibers were successfully measured by using high accuracy universal polarimeter, as functions of temperature and drawing ratio. By using x-ray data of the change of the fibrous structure by drawing treatments, the gyration tensor components of PLLA could be calculated. It is of great interest that gyration tensor component g33 along the helical axis is extremely large, ∼(3.85±0.69)×10-2, which corresponds to a rotatory power of (9.2±1.7)×103°/ mm, about two orders of magnitude larger than those of ordinary crystals. This is the first experimental evidence that helical polymers will produce enormous optical activity in the solid state. Helical polymers will be important for the elucidation of gyro-optical properties of solids and promising for new optical applications utilizing their large optical activity.
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