The properties of imperfections (or defects) of the atomic or molecular order in condensed matter can be conveniently described under two headings: (1) Topological properties—Defects break a specific symmetry of the ordered system at a local scale, that is, along a point defect, a line defect (a dislocation or a disclination), or a surface defect (a wall). (2) Elastic properties—Defects are sources of two types of distortions of the order: long-range distortions, which depend crucially on the broken symmetry but also on the material constants, and short-range distortions in the “core” region of the defect where the order parameter of the ordered phase is broken. These distortions are irreversible in the sense that defects appear during plastic deformation (in solids) or rheological flow (in liquid crystals).
To illustrate this classification, let us recall the example of dislocation lines in solids. These defects break translational symmetries (henceforth a dislocation is defined topologically by the translation b it breaks, the so-called Burgers vector). They are at the origin of rather weak, long-range, internal distortions and stresses that depend on the elastic constants (in the region of the good crystal) and rather strong, short-range distortions and stresses in the “core” region, implying a complete rearrangement of the molecular order. These stresses are different in the static and dynamic states, and the shape of the dislocation line, as well as its size, etc., depend on the history of the sample.
In this article, we will focus on defects in liquid-crystalline polymers. A synthetic polymer that displays mesomorphic order (intermediate between crystalline and liquid) is usually made of units that are themselves mesogenic and that align coherently when in contact.