Commercially, polymeric fibers are perhaps the most important of all, covering as they do a vast range of applications. There are two broad categories of polymeric fibers: natural and synthetic. Natural fibers can be from the vegetable kingdom such as cotton, sisal and jute or from the animal kingdom such as wool, silk, etc. Natural fibers are mostly polymeric in nature. There are, however, some natural fibers that occur in rock formations. These fibers are minerals and can therefore be treated as a ceramic, e.g. asbestos and basalt. We describe these natural mineral fibers in Chapter 6. In this and the following chapter, we describe polymeric fibers. We first briefly review some of the fundamental aspects of polymers and then describe the natural polymeric fibers. We devote Chapter 4 to the synthetic polymeric fibers, which have seen tremendous advancement in the last half of the twentieth century. A vast range of natural polymeric fibers is available and they find large-scale commercial applications. Much research effort is focused on a very special natural fiber originating in the animal kingdom, spider silk. The idea here is to learn about the processing, structure, and properties of silk fibers which are very strong and stiff. More about this later in this chapter. The volume of other natural fibers such cotton, jute, sisal, ramie, etc. in industrial and non-industrial applications has always been quite large because of their many attributes such as the wear-comfort of cotton and the fact that all natural fibers represent a renewable resource.

In this chapter we describe synthetic polymeric fibers, which saw tremendous advancement in the last half of the twentieth century. In fact, a reasonable case can be made that the so-called age of fibers began with the advent of synthetic fibers such as nylon, polyester, etc. in the late 1930s and early 1940s. Many companies such as Du Pont, Monsanto, BASF, Hoechst, ICI, etc. contributed significantly in this area. For a historical account of the scientific and technological progress made in this area, the reader is referred to a study of research and development activities at Du Pont during the period 1902–1980 (Hounshell and Smith, 1988). Most of these synthetic polymeric fibers such as polyester, nylon, etc. have very uniform and reproducible properties. They, however, have a rather low elastic modulus, which restricts them mostly to the apparel or textile market. It was the research work aimed at making strong and stiff synthetic polymeric fibers for use as reinforcements in polymers, which started sometime in the late 1950s and early 1960s, that resulted in the commercial availability of strong and stiff fibers such as aramid and extended-chain polyethylene. We describe below the processing, structure, and properties of some important synthetic polymeric fibers in some detail.

Brief history of organic fibers

A brief historical review of the work in the area of organic fibers will be helpful in placing things in perspective.

In this chapter, we define some important terms and parameters that are commonly used with fibers and fiber products such as yarns, fabrics, etc., and then describe some general features of fibers and their products. These definitions, parameters, and features serve to characterize a variety of fibers and products made from them, excluding items such as fiber reinforced composites. These definitions and features are generally independent of fiber type, i.e. polymeric, metallic, glass or ceramic fibers. They depend on the geometry rather than any material characteristics.

Fiber is the fundamental unit in making textile yarns and fabrics. Fibers can be naturally occurring or synthetic, i.e. man-made. There are many natural fibers, organic and inorganic. Examples include organic fibers such as silk, wool, cotton, jute, sisal and inorganic fibers such as asbestos and basalt. There is a large variety of synthetic fibers available commercially. Polymer fibers such as polypropylene, polyethylene, polyamides, polyethyleneterephthalate (PET), polyacrylonitrile (PAN), polytetrafluoroethylene (PTFE), aramid, etc. are wellestablished fibers. Metallic wires or filaments have been available for a long time. Examples include steel, aluminum, copper, tungsten, molybdenum, gold, silver, etc. Among ceramic and glass fibers, glass fiber for polymer reinforcement has been available since the 1940s; optical glass fiber for telecommunication purposes made its debut in the 1950s, while ceramic fibers such as carbon, silicon carbide, alumina, etc. became available from the 1960s onward.

In this chapter we provide a description of the processing, structure, and properties of high temperature ceramic fibers, excluding glass and carbon, which are dealt with in separate chapters because of their greater commercial importance. Before we do that, however, we review briefly some fundamental characteristics of ceramics (crystalline and noncrystalline). Once again, readers already familiar with this basic information may choose to go directly to Section 6.5.

Some important ceramics

We provide a summary of the characteristics of some important ceramic materials that have been converted into a fibrous form.

Bonding and crystalline structure

Ceramics are primarily compounds. Ceramics other than glasses generally have a crystalline structure, while silica-based glasses, a subclass of ceramic materials, are noncrystalline. In crystalline ceramic compounds, stoichiometry dictates the ratio of one element to another. Nonstoichiometric ceramic compounds, however, occur frequently. Some important ceramic materials are listed in Table 6.1. Physical and mechanical characteristics of some ceramic materials are given in Table 6.2. It should be noted that the values shown in Table 6.2 are more indicative than absolute.

In terms of bonding, ceramics have mostly ionic bonding and some covalent bonding. Ionic bonding means there occurs a transfer of electrons between atoms that make the compound. Generally, positively charged ions balance the negatively charged ions to give an electrically neutral compound, for example, NaCl. In covalent bonding, the electrons are shared between atoms.

Fracture of brittle materials, in general, involves statistical considerations. Materials have randomly distributed defects on their surfaces or in their interior. Fibrous materials, as we saw in Chapter 2, have a large surface area per unit volume. This makes it more likely for them to have surface defects than bulk materials. The presence of defects at random locations can lead to scatter in the experimentally determined strength values of fibers, which calls for a statistical treatment of fiber strength. Clearly, such scatter will be much more pronounced in brittle fibers than in ductile fibers such as metallic filaments. This is because ductile metals will yield plastically rather than fracture at a flaw of a critical size. Thus, most high performance fibers, with the exception of ductile metallic filaments, shows a rather broad distribution of strength because they are highly flaw sensitive. Since the distribution of flaws is of statistical nature, the strength of a fiber must be treated as a statistical variable. To bring home this important point of variation in strength of a fiber as a function of fiber length, we show, in Figs. 10.1–10.3, the variation of tensile strength of some fibers as a function of gage length: high modulus carbon fiber (Fig. 10.1), boron fiber (Fig. 10.2), and Kevlar 49 aramid fiber (Fig. 10.3). Intuitively, one can see that the probability of finding a critical flaw (which corresponds to the failure strength) increases as the volume of brittle material increases.

The term fiber conjures up an image of flexible threads, beautiful garments and dresses, and perhaps even some lowly items such as ropes and cords for tying things, and burlap sacks used for transporting commodities, etc. Nature provides us with an immense catalog of examples where materials in a fibrous form are used to make highly complex and multifunctional parts. Protein, which is chemically a variety of complexes of amino acids, is frequently found in nature in a fibrous form. Collagen, for example, is a fibrous protein that forms part of both hard and soft connective tissues. A more well-known natural fiber that is essentially pure protein, is silk fiber. Silk is a very important natural, biological fiber produced by spider and silkworm. It is a solution spun fiber, with the solution, in this case, being produced by the silkworm or the spider. The silkworm silk has been commercialized for many years while scientists and engineers are beginning to realize the potential of spidersilk.

Indeed, materials in a fibrous form have been used by mankind for a long time. Fiber yarns have been used for making fabrics, ropes, and cords, and for many other uses since prehistoric times, long before scientists had any idea of the internal structure of these materials. Weaving of cloth has been an important part of most ancient societies. The term fabric is frequently employed as a metaphor for society.

Carbon fibers have become established engineering materials. In view of their commercial importance, we devote a separate chapter to them. Carbon is a very versatile element. It is very light, with a theoretical density of 2.27 gcm–3. It can exist in a variety of forms, glassy or amorphous carbon, graphite, and diamond. Carbon in all these forms can be found in nature. Carbon in the graphitic form has a hexagonal structure and is highly anisotropic. The diamond form of carbon has a covalent structure and is an extremely hard material. The latest addition to the variety of forms of carbon is the Buckminster Fullerene, or the Buckyball with a molecular composition such as C60 or C70. In this chapter, we follow the same sequence as in previous chapters; processing, structure, properties and applications of carbon fibers. However, in order to understand these aspects of carbon fiber, it is helpful to review the basic structure and properties of graphite.

Structure and properties of graphite

Carbon fiber is a generic name representing a family of fibers. Over the years, it has become one of the most important reinforcement fibers in many different types of composites, especially in polymer matrix composites. It is an unfortunate fact that the terms carbon and graphite are used interchangeably in commercial practice as well as in some scientific literature. Rigorously speaking, graphite fiber is a form of carbon fiber that is obtained when we heat the carbon fiber to a temperature greater than 2400°C.

The term glass or a glassy material represents a rather large family of materials with the common characteristic that their structure is noncrystalline. Thus, rigorously speaking, one can produce a glassy material from a polymer, metal or ceramic. An amorphous structure is fairly common in polymeric materials. It is less so in metals, although metallic glass, generally in the form a ribbon, can be produced by rapid solidification, i.e. by not giving enough time for crystallization to occur. In this chapter we describe silica-based inorganic glasses because of their great commercial importance, as a reinforcement fiber for polymer matrix composites and as an optical fiber for communications. Communication via optical glass fibers is a well established field. Crude optical glass fiber bundles were used to examine the insides of the human body as far back as 1960. Since then tremendous progress has been made in making ultra pure, controlled composition fibers with very low optical attenuation. It is estimated that the total worldwide shipment of optical fibers is over US$5 billion per year. Before we describe the processing, structure, and properties of glass fiber, it would be appropriate to digress slightly and describe for the uninitiated, albeit very briefly, the basic physics behind the process of communication via optical glass fibers.

Basic physics of optical communication

Optical glass fiber has many desirable characteristics for communication such as:

1. ▪ large bandwidth over great distances;

2. ▪ protection against electrical interference and crosstalk;

3. ▪ galvanically protected signal transmission;

4. ▪ safety and reliability.

Metals in bulk form are quite common materials and extensively used in engineering and other applications. Metals can provide an excellent combination of mechanical and physical properties at a very reasonable cost. One of the important attributes of metals is their ability to undergo plastic deformation. This allows the use of plastic deformation as a means to process them into a variety of simple and complex shapes and forms, from airplane fuselages to huge oil and gas pipelines to commonplace aluminum soda pop cans and foil for household use. What is less well appreciated, however, is the fact that metals in the form of fibers or wire have also been in use for a long time. Examples of the use of metallic filaments include: tungsten filaments for lamps, copper and aluminum wire for electrical applications, steel wire for tire reinforcement, cables for use in suspension bridges, niobium-based filamentary superconductors, and, of course, strings for various musical instruments such as violin, piano, etc. Highly ductile metals such as gold and silver can be drawn into extremely thin filaments. Filaments of such noble metals have long been used as threads in making Indian women's traditional dress called the saree.

Let us first review some of the important characteristics of metals, in particular, the ones that allow metals and their alloys to be drawn into fine filaments, and then describe the processing, structure, properties and applications of some important metallic filaments.

Few problems in physics and engineering can be solved exactly, and one has to resort to approximate or numerical methods. Consider, for example, an electron in a square well whose potential is tilted by applying an electric field. The energy and wave function of its states change only slightly if the field is small. The lowest state becomes polarized to the deeper part of the well, causing a quadratic reduction in its energy. Perturbation theory provides a framework for calculating such changes, and this example is discussed in Section 7.2.

This approach works well if the potential can be divided into a ‘large’ part that can be solved exactly and a ‘small’ perturbation. Other methods must be used if this is not the case. The WKB method described in Section 7.4 is applicable to potentials that vary slowly in space, and is closely related to classical mechanics. The variational method (Section 7.5) gives only the energy of the ground state but has unrivalled accuracy and can include electron–electron interaction and other complications.

There are many applications to band structure. The k · p method in Section 7.3 gives the form of energy bands near a gap, the most important region in a semiconductor. Two general methods take opposite points of view. The tight-binding method (Section 7.7) is based on a picture of isolated atoms brought together to form the solid, where the bands originate from atomic levels.

Real electrons are three-dimensional but can be made to behave as though they are only free to move in fewer dimensions. This can be achieved by trapping them in a narrow potential well that restricts their motion in one dimension to discrete energy levels. If the separation between these energy levels is large enough, the electrons will appear to be frozen into the ground state and no motion will be possible in this dimension. The result is a two-dimensional electron gas (2DEG). The same effect can be achieved with a two-dimensional potential well, which leaves the electrons free to move in one dimension only – a quantum wire.

In the first part of this chapter we shall study some simple one-dimensional potential wells used to trap electrons. The infinitely deep square well cannot be made in practice, but its simplicity makes it a frequently used model. A well of finite depth provides a much better description of a real quantum well. Parabolic wells can be grown by changing the composition of the semiconductor continuously, but this potential proves to be most relevant for the study of magnetic fields. The final example is a triangular well, which can be used as a rough description of the two-dimensional electron gas formed at a doped heterojunction. Next we shall see how these potential wells make electrons behave as though they are two-dimensional.