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attractive forces, showing properties characteristic of nanoparticles rather than molecules.

      The strong covalent (σ) bonds due to the sp² hybrid orbitals, delocalized electrons of the π bonds due to the overlapping p orbitals in the hexagonally arranged carbon atoms and small size endow graphenes, carbon nanotubes, and fullerenes with unique physico‐chemical properties. These structures have received an enormous amount of scientific and technological interest since their discovery and are now receiving considerable interest for potential biomedical applications, such as drug delivery, gene delivery, biomedical imaging, biosensing, and tissue engineering (Eatemadi et al. 2014; Zhao et al. 2017).

      As carbon is chemically inert and hydrophobic, a related area of investigation is the functionalization of graphenes, carbon nanotubes, and fullerenes with appropriate molecules for optimal use in these applications (Chapter 13). In common with nanostructured materials such as nanoparticles intended for use in vivo, the possible toxicity of graphenes, carbon nanotubes, and fullerenes has been widely studied. While the vast majority of studies have shown no serious adverse response from cells and tissues, some questions still remain about possible toxic effects.

      

      3.3.5 Structure of Polymers

      Polymers are composed of long molecules (macromolecules) in which hundreds or thousands of atoms are joined together by covalent bonds to form a chain. The chain backbone in the vast majority of polymers is composed of carbon atoms, as in polyethylene (PE), for example (Figure 2.10), but many polymers have a chain backbone that contains atoms other than carbon, such as silicon, or in addition to carbon, such as silicon, nitrogen, or oxygen. Macromolecules of commonly used degradable polymers such as polylactic acid (PLA), polyglycolic acid (PGA), and polycaprolactone (PCL), for example, contain carbon‐oxygen bonds in addition to carbon–carbon bonds (Chapter 9).

Intermolecular forces resulting from van der Waals bonding, hydrogen bonding or a combination of these two types of physical bonding are present in all polymers. On the other hand, depending on the chemical composition of the polymer and how it is synthesized, neighboring chains can also be joined chemically at various points, that is, cross‐linked by covalent bonds. The elasticity of synthetic rubbers used in engineering applications and elastin, a component of skin and other tissues, is due to the presence of chemical crosslinks between the molecules. Macromolecules in the vast majority of polymers are also more complex than the simple linear structure of PE (Chapter 8). Instead of just hydrogen atoms bonded to carbon atoms in the chain backbone, the side groups can have a variety of composition, structure and size, and they can be bonded to carbon atoms of the chain backbone at regular or random intervals. These factors influence the way in which the macromolecules pack together in a solid.

In the majority of solid polymers, when the macromolecules pack together they do so in a random manner, giving an amorphous structure (Figure 3.15a). In other polymers, commonly those in which the macromolecules have a rather simple structure with little or no crosslinking, the chains can pack in an ordered pattern by folding backward and forward (Figure 3.15b). This regular repeating pattern of chain folding leads to the formation of crystalline regions. As long as the macromolecular structure allows this type of ordered arrangement, the formation of crystalline regions is possible because there is a driving force for it. This is because a crystal has a lower energy than an amorphous structure of the same composition due to the ordered and closer packing of the polymer chains. However, it is difficult for a macromolecule to pack completely into a crystalline pattern even for the simplest structure. Consequently, these polymers are composed of crystalline regions interspersed with amorphous regions (Figure 3.15b). The term semicrystalline has often been used to describe these polymers, in a sense to indicate that they are not totally composed of crystals. Generally, formation of crystalline regions is more favorable when the side groups are less bulky, are bonded at regular intervals to the chain backbone, or allow substantial intermolecular bonding such as hydrogen bonding to stabilize the ordered arrangement of the macromolecules.

Figure 3.15 Schematic representation of (a) random arrangement of macromolecules in a polymer to give an amorphous structure and (b) ordered packing of macromolecule in crystalline regions of a semicrystalline polymer. For clarity, only the chain backbone of the macromolecules are shown.

      Whether a polymer is amorphous or semicrystalline has significant consequences for its properties and applications. The crystalline regions typically have better mechanical properties than the amorphous regions, such as higher strength, higher elastic modulus and better wear resistance. Improvement in the percentage of crystalline regions in PE, for example, has resulted in reduced wear of ultrahigh molecular weight polyethylene (UHMWPE) bearings in hip and knee implants. In degradable polymers such as PLA and PGA, for example, the crystalline regions have a lower degradation rate than the amorphous regions. Consequently, amorphous copolymers of PLA and PGA, referred to as polylactic‐co‐glycolic acid (PLGA), are often preferred in drug delivery devices because they provide a more predictable degradation rate than semicrystalline PLA or PGA.

3.4 Defects in Crystalline Solids

      A perfect crystal is an idealization. Imperfections, often called defects, are present at random positions in the structure. These defects play an important role because they control several physico‐chemical properties of the solid. Metals, for example, would not show the attractive mechanical property of ductility when subjected to an applied stress were it not for the presence of a particular type of defect in the crystals called dislocations. Defects in crystals occur for two main reasons. Structurally, atoms in the pure material do not pack perfectly in a crystal due to thermal fluctuations during their processing or growth. Chemically, other atoms can be added accidentally or deliberately during production of the material, which disrupt the regular‐repeating pattern of the host atoms. As this type of compositional modification can influence the defect structure to a far larger extent than purely packing irregularities in the pure material, it is a widely used approach to modify or improve the properties of metals and ceramics.

Defects in crystalline solids are commonly divided into three types, described as point defects, line defects, and planar defects. Three‐dimensional defects, such as microcracks, pores, and fine particulate inclusions can be accidentally incorporated into a solid, whether crystalline or amorphous, during its production or use. These three‐dimensional defects have a significant effect on the bulk properties of a solid, such as its strength and the way it fractures under an applied mechanical stress (Chapter 4).

      3.4.1 Point Defects

Point defects are defects associated with one or a few atomic sites in the crystal. The major types of point defects are illustrated in Figure 3.16. A different atom, called a foreign atom, that occupies the site of a regular atom in the pure crystal, called a host atom, is said to be a substitutional defect. A vacant atomic site is called a vacancy. Foreign atoms and host atoms can occupy the interstitial sites between the regular atomic positions, giving foreign interstitial defects and self‐interstitial defects, respectively.

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