Preferred orientation in polymer fiber scattering

Fiber symmetry is one of the most important sample geometries encountered in both wide-angle x-ray scattering (WAXS) and small-angle x-ray scattering (SAXS) of polymers, applicable both to natural polymers like collagen or cellulose and to many synthetic polymers that come in fiber form or otherwise exhibit cylindrical rotational symmetry. The structural information to be determined in scattering experiments from such fiber systems includes both the structure of the individual structural unit and qualitative and quantitative information about the preferred orientation state of the ensemble. Existing approaches and new developments to analyze fiber scattering patterns are rigorously reviewed. Special emphasis is placed on the calculation of complete SAXS and WAXS fiber scattering patterns, and various practical examples including collagen and cellulose fibers as well as fibers based on copolymers of polyethylene and polypropylene are discussed.