Frustration and Frustrated Crystal Structures of Polymers and Biopolymers

Abstract

The manifestations of frustration are widespread in materials science. The more specific geometrical frustration in crystalline materials is created when physical interactions between nearest neighbors induce packing modes (e.g., the slight twist between neighboring DNA strands) that cannot propagate indefinitely throughout space. The structure is made of small domains separated by dislocation lines or other less ordered walls (e.g., in DNA blue phases). A second type of geometrical frustration, compatible with crystallographic symmetry, may arise in hexagonal close-packed crystals of helices with 3-fold symmetry. If favorable pair–pair interactions exist between helices, they can propagate only in a honeycomb pattern. The resulting unit cell is trigonal and contains three independent helices, one of which interacts less favorably with its neighbors—thus the frustration. Recognition of this type of geometrical frustration in polymer crystallography is relatively recent, although some crystal structures determined long ago displayed what amounts to frustration. This frustration is widespread: a number of chiral crystal structures of polymers and biopolymers conform to, and probably many more will fit in, this packing scheme. Frustration in polymers manifests itself by specific diffraction and morphological features (e.g., triangular single crystals) and, in one case, could be imaged by AFM. The frustrated structures provide, in view of their unusual characteristics, an exceptional investigation material to further elucidate the finer details of polymer crystallography and polymer crystallization processes.