In this chapter we turn to chemical products whose value is strongly connected to their microstructure. By “microstructure,” we mean chemical organization on the scale of micrometers. Some microstructured products are listed in Table 9.0–1. To understand how large such structures are, we remember that hair and beards grow about one millimeter in three days, or 300 μm per day. Thus, beard growth in eight hours – a “five o'clock shadow” – is about 100 μm. We can just feel this size. On the other hand, blood cells are discs 8 μm across and 3 μm thick, and we cannot feel individual blood cells. In many cases, the microstructures which we make will be between these sizes. Because they will be smaller than 100 μm, they will feel like continua, but because they are often the size of blood cells, they are not in reality homogeneous.

Another way to judge these products is their size on a logarithmic scale, shown earlier in Figure 1.5–1. On such a scale, the relative size of microstructures lies midway between the sizes of us and of individual molecules. Our little fingers are about 1 cm, or 10,000 μm, across. A microstructure of 1 μm, or 10,000 Å, is much larger than a molecule 3 Å in diameter. Microstructures are around the wavelength of visible light.

Products with microstructure supply added value because of the physical and chemical properties of the microstructure.

The distribution of copolymerized units in the polymer chain

General principles

If a mixture is made of two or more types of monomer which polymerize by similar mechanisms, e.g. the free radical process, they may be polymerized to form chains in which the structural units of the respective homopolymers are present to varying extents and in sequences whose lengths depend on the polymerization conditions. Such copolymers are important commercially and they are also the source of a considerable amount of information on polymerization processes. Their commercial importance is that they provide the means for modifying to advantage the physical properties of the parent homopolymers. They may provide a higher tensile strength, a greater impact strength, a superior stress crack resistance, an improved resistance to thermal and photochemical degradation or a modified crystallization behaviour. At the fundamental level, the molecular structure of the copolymer can often provide information on the polymerization mechanism, such as the factors which determine the reactivity of a particular radical. It is also possible to prepare polymers with known structural defects in order to study their effects. For example, the copolymerization of small amounts of ally1 chloride, CH2=CH—CH2CI, or acetylene, CH≡CH, with viny1 ch1oride may be used to introduce ch1oromethy1 branches, —CH2C1, or double bonds, respectively, into the viny1 chain in order to assess whether these types of defect are the sites of the initiation process for thermal degradation.

We have thus far dealt with the resistance to crack propagation at opposite extremes of material representation, continuum solid and atomic lattice. It is now appropriate to investigate the problem at an intermediate level, that of the microstructure. By ‘microstructure’ we mean the compositional configuration of discrete structural ‘defects’: voids, inclusions, secondphase particles (volume defects); secondary crack surfaces, grain boundaries, stacking faults, twin or phase boundaries (surface defects); dislocations (line defects). It is principally at this intermediate level that significant improvements in the mechanical properties of traditional brittle polycrystalline ceramics (cf. table 3.1) may be realised. By tailoring the microstructure it is possible to introduce an interactive defect structure that acts as an effective restraint on crack propagation and thus enhances the material toughness.

In this chapter we examine some of these ‘toughening’ interactions. We identify two classes of restraint. The first involves purely geometrical processes, deflections along or across weak interfaces, etc. The responsible microstructural elements may be regarded as ‘transitory obstacles’, in the sense that their impeding influence lasts only for the duration of crackfront intersection. Because of their ephemeral nature such interactions are relatively ineffective as sources of toughening, accounting at very most for increases of a factor of four in crack-resistance energy R or, equivalently, a factor of two in toughness T.

The second class of restraint comprises shielding processes. The critical interactions occur away from the tip, within a ‘frontal zone’ ahead or at a ‘bridged interface’ behind.

Overview

The previous chapter outlined an approach to asset price determination that focuses on stocks. In summary: the realized market price is such that the existing stock of each asset is willingly held by investors in the aggregate – the demand to hold the stock is equal to its supply. A second approach to price determination focuses on flows: the asset price is such that the flow of purchases over a short interval of time equals the flow of sales. That is, the total demand from all those investors who seek to add to their holdings of the asset equals the total supply of all those investors who seek to reduce their holdings. The two paradigms are not necessarily incompatible. Neither is necessarily right or wrong. They are just different ways of analysing the same thing – namely, what determines asset prices.

This chapter, unlike most that follow, adopts the second paradigm. Viewing prices as determined by flows of assets is particularly useful in exploring the details of how prices are set in practice and the behaviour of those who set them. Following a brief review of some basic features of market activity in section 2.1, section 2.2 studies the commonest trading mechanisms found in asset markets. Section 2.3 considers asset markets from the perspective of industrial organization and reviews the nature of competition within and between the markets.

Dislocation structure and behaviour

Plastic deformation in the matrix of a composite is never completely homogeneous. The reinforcement interrupts flow, giving rise to distinctive dislocation structures. As well as having immediate implications for the flow properties of the matrix, these structures also indirectly influence flow behaviour via changes in the precipitation and aging response.

The influence of thermal stress on dislocation structure

In many MMCs, thermal stresses can give rise to dislocation densities which are 10–100 times greater than those for comparable unreinforced alloys. The conditions under which the creation of thermally stimulated dislocations is energetically favourable were first studied by Ashby and Johnson, who found that, for incoherent particles, the critical misfit decreases with increasing particle size. For short fibres and particles, the simplest mechanism of stress relief is to punch out a dislocation loop (a disc of vacancies or interstitials) into the matrix (Fig. 10.1(a,b)). This mechanism, illustrated schematically in Fig. 4.16, is well understood in terms of a relaxation in the local stress field.

Firms create and manage markets by acting as intermediaries between buyers and sellers. An intermediary is an economic agent who purchases from suppliers for resale to buyers or who helps buyers and sellers meet and transact. Intermediaries seek out suppliers, find and encourage buyers, select buy and sell prices, define the terms of transactions, manage the payments and record keeping for transactions, and hold inventories to provide liquidity or availability of goods and services.

This book is concerned with the economic role of firms and the functioning of markets in general. In finance, the study of intermediation and the institutions of exchange is called market microstructure. I apply the term market microstructure generically to refer to the operation of markets for all types of goods and services. I show that there are basic similarities between a broad range of intermediation models in economics and finance. Throughout the book, the main results are derived within a common framework, with similar notation and related economic reasoning.

Just as producing goods and services consumes resources, so does the establishment and operation of markets to allocate those goods and services. Companies incur costs in adjusting prices and communicating price information to buyers and sellers. The types of information imperfections that are present determine the intermediation activities of firms. When there is demand and supply randomness, intermediaries provide liquidity or immediacy by standing ready to buy and sell. Given uncertainty about the willingness to pay or opportunity costs of trading partners, intermediaries coordinate transactions by matchmaking and brokering activities.