The development of early knowledge about crystals of flexible macromolecules (usually called simply “polymers”) and their defects was reviewed in Reference. Much of the initial research followed the information gathered on crystals of small molecules, metals, salts, and ceramics. Very quickly, however, the special nature of polymers became obvious. It was suggested some time ago to describe semicrystalline polymers with the help of zero- to three-dimensional defects. The present status of this scheme is summarized in this article.

Crystallized polymers are rarely in equilibrium. Therefore, the phase rule, which permits the presence of only one phase with two degrees of freedom (temperature and pressure) for a onecomponent material, does not apply. This nonequilibrium state is kept metastable by restrictions caused by the molecules that cross the interfaces (two-dimensional defects). The strain propagated to the noncrystalline areas produces three-dimensional defects of limited mobility. The overall structure can also be described as being microphase-separated.

Often the sizes of the different phases can be as small as the nanometer scale. One-dimensional or line defects, also called dislocations, became obvious in polymers with the first observations of solution-grown crystals of polyethylene that showed frequent growth spirals. Because of the molecular chain struc ture, many of these dislocations are sessile (immobile) and cannot participate for example, in deformation mecha nisms. Until recently, zero-dimensiona or point defects were understood largely because of molecular-mechanics calculations.

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.

The liquid crystal phase is an anisotropic mesophase, intermediate in order between the liquid and crystal phases. Liquid crystals have less translational order than crystals and more rotational order than isotropic liquids. The liquid crystal phase does not support finite shear stresses and thus behaves like a fluid. Molecules that display a liquid crystal phase are referred to as mesogenic. Mesogenic molecules exhibit shape anisotropy: either large length to diameter ratio (needlelike) or large diameter to thickness ratio (disklike). Because of their shape anisotropy, all liquid crystals display orientational order of their molecular axes.

Until 1956, all known examples of liquid crystals were low molecular weight compounds. Robinson was the first to identify liquid crystallinity in a liquid crystalline polymer (LCP) as the explanation for “a birefringent solution” of a polymeric material, poly-y-benzyl-L-glutamate, in chloroform, previously observed by Elliott and Ambrose. Chemists soon discovered that LCPs may be readily synthesized by covalently stitching small mesogenic units (e.g., rigid monomers) together into a chain using short flexible spacers. Mainchain or sidechain liquid crystal polymers may be formed (Figure 1). An example of a polymer molecule possessing a liquid crystal phase is shown in Figure 2. Liquid crystals may be thermotropic, where liquid crystallinity is exhibited over a range of temperatures, or lyotropic, where nonmesogenic solvent molecules are present in addition to the mesogens, and liquid crystallinity is observed over a range of concentrations as well.

Conventionally, the term “defects” in liquid-crystalline systems refers to microscopic faults in the orientational order, which are usually visible optically. These are discussed in other articles in this issue. Our use of the term defect is entirely different. The defects we shall be considering, “hairpins,” occur on the scale of several angstroms and are abrupt reversals in the trajectory of a single liquid-crystalline-polymer (LCP) chain (Figure 1). In comparison to conventional defects, the direct observation of hairpin defects is much more difficult, yet their presence has important effects. Among the affected properties are the dimensions and the elasticity of the chains, the elastic behavior of the bulk nematic, and its dielectric response. Their presence should also give rise to a family of interfacial phase transitions in solutions of LCPs in nematic solvents. In turn, these are of interest in the design of liquid-crystalline displays. Hairpins in LCPs are superficially reminiscent of similar configurations in proteins and in homopolymers that undergo fold crystallization. These similarities are misleading because hairpins in proteins are permanent structures due to the chemical bonds. The folds in crystalline polymers are also fixed structures. In marked contrast, hairpin defects are mobile topological excitations that are created and annihilated continuously. Our emphasis in this article is on main-chain, semiflexible, nematic LCPs, consisting of mesogenic monomers joined by flexible spacer chains (Figure la). These polymers combine the orientational order of monomeric nematics with the flexibility and randomness inherent in polymers. The appearance of an oriented, nematic phase can be controlled either by temperature or by concentration.

Block copolymer melts with a near-symmetric composition can microphase-separate to form a lamellar morphology where unfavorable monomeric interactions are reduced by an antiparallel layering of the polymer chains (see Figure 2, discussed later). The symmetry of such a block copolymer is the same as for small-molecule, smectic-A liquid crystals, which also exhibit (parallel or antiparallel) layering. Because of their shared symmetry, their quasistatic mechanical properties are of the same form. To lowest order, the energy of distortion of the lamellar pattern can be expressed as a sum of a compressional/dilational and a bend energy (see, for example, Reference 2):

where n is a unit vector normal to the layers, and ε and ∇ n are the layer dilational and bending strain, respectively. B and K are the corresponding moduli. These have been measured only recently for block copolymers. The ratio of these moduli yields a characteristic microscopic length:

which is calculated to be a fraction of the layer spacing d0.

Similarities are also found in the dynamic properties of polymeric and smallmolecule smectics. These similarities are found at low strain rate and amplitude where the rheological response is controlled by their similar layered structures and associated defects. During either steady or dynamic shear, certain defect and domain motions are induced such that a steady-state alignment of the director has been observed. In this report, we discuss defect structure and how the much more viscous nature of these polymeric layered materials influences the distribution and relative population of each defect type. We also discuss how these defects can control material stress-relaxation behavior.

Understanding the influence of local variations in symmetry (“defects”) on the macroscopic properties of polymers in the condensed state is an ongoing experimental and theoretical challenge. Studies of defects in solids require the most information-intensive description of microstructure since it is not possible to describe a “defect” without understanding the morphology of the majority phase as well.

The nature of defects in polymers has been discussed elsewhere, including other articles in this issue of the MRS Bulletin. The structure, properties, and mobility of defects in polymers are all profoundly influenced by the covalently bonded chain backbone. In polymers, there are unique defects such as chain folds and twists that have no obvious analogue in materials of small molar mass. Here, we examine a particular type of defect that is present in all polymer systems with finite molecular weight: chain ends. Our interest will focus on chain ends in polymers that are essentially fully extended parallel to a certain preferred orientation axis.

The extended-chain microstructure was originally envisioned by Staudinger as a “continuous crystal” in which high-molecular-weight polymers would be perfectly oriented and close-packed together laterally. Extended-chain polymer fibers such as poly(paraphenylene terephthalamide) (PPTA or Kevlar®), gelspun polyethylene (Spectra®), and the rigid-rod polymers poly(paraphenylene benzobisthiazole) (PBZT) and poly(paraphenylene benzobisoxazole (PBZO or PBO) (Structure 1) closely approach this conceptual limit. The outstanding tensile moduli (100–400 GPa) and tensile strengths (2–4 GPa or higher) of these fibers have generated considerable interest for lightweight structural applications. Extendedchain polymers can also be prepared by solid-state polymerizations of appropriate monomer precursors. Perhaps the most familiar of this latter class of materials are the polydi-acetylenes, first developed by Wegner.

Defects play a significant role in determining the physical and thermodynamic behaviors of a material. This precept can be especially helpful when one attempts to interpret the engineering properties of a biological material in the context of its complex, hierarchical microstructure. An excellent example of an impressive engineering material used by nature is silk, which has a composite microstructure assembled from one or more protein polymers. Spiders, aided by several million years of evolution, have succeeded in producing a polymer fiber [major ampullate silk (MAS)] with a strength-to-weight ratio exceeding that of nearly all synthetic materials. Even the exceptions—specialty fibers such as carbon, silica, and some variants of Kevlar—pale in comparison when toughness (energy required to bring about failure) is taken into account; they are relatively brittle and lack the viscoelastic extensibility of MAS. When one considers that spiders produce this naturally biodegradable material under ambient conditions and with an aqueous solvent, the feat becomes even more impressive. It is clear that the spider could be an excellent instructor in both polymer processing and microstructural design.

where the α-carbon is bonded to a functional “R” group that distinguishes the monomer as being one of the 20 commonly occurring natural a-amino acids.