Lecture notes on Polymers

what polymers occur naturally and what polymers are synthetic and what polymers is responsible for your inheritance, what polymers are biodegradable
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Published Date:03-08-2017
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Polymers 219 Chapter 21 Polymers Introduction Where people have, since the industrial revolution, used metals, nature uses polymers. Almost all biological systems are built of polymers which not only perform mechan- ical functions (like wood, bone, cartilage, leather) but also contain and regulate chem- ical reactions (leaf, veins, cells). People use these natural polymers, of course, and have done so for thousands of years. But it is only in this century that they have learned how to make polymers of their own. Early efforts (bakelite, celluloid, formaldehyde plastics) were floppy and not very strong; it is still a characteristic of most simple synthetic polymers that their stiffness (for a given section) is much less than that of metal or, indeed, of wood or bone. That is because wood and bone are composites: they are really made up of stiff fibres or particles, embedded in a matrix of simple polymer. People have learned how to make composites too: the industries which make high-performance glass, carbon, or Kevlar-fibre reinforced polymers (GFRP, CFRP, KFRP) enjoy a faster growth rate (over 10% per year) than almost any other branch of materials production. These new materials are stiff, strong and light. Though expens- ive, they are finding increasing use in aerospace, transport and sporting goods. And there are many opportunities for their wider application in other fields like hiking equipment, medical goods and even apparently insignificant things like spectacle frames: world-wide, at least 1,000,000,000 people wear spectacles. And the new polymers are as exciting as the new composites. By crystallising, or by cross-linking, or by orienting the chains, new polymers are being made which are as stiff as aluminium; they will quickly find their way into production. The new process- ing methods can impart resistance to heat as well as to mechanical deformation, open- ing up new ranges of application for polymers which have already penetrated heavily into a market which used to be dominated by metals. No designer can afford to neglect the opportunities now offered by polymers and composites. But it is a mistake to imagine that metal components can simply be replaced by components of these newer materials without rethinking the design. Polymers are less stiff, less strong and less tough than most metals, so the new component requires careful redesign. Composites, it is true, are stiff and strong. But they are often very anisotropic, and because they are bound by polymers, their properties can change radically with a small change in temperature. Proper design with polymers requires a good understanding of their properties and where they come from. That is the func- tion of the next four chapters.220 Engineering Materials 2 In this chapter we introduce the main engineering polymers. They form the basis of a number of major industries, among them paints, rubbers, plastics, synthetic fibres and paper. As with metals and ceramics, there is a bewilderingly large number of polymers and the number increases every year. So we shall select a number of “generic” polymers which typify their class; others can be understood in terms of these. The classes of interest to us here are: (a) Thermoplastics such as polyethylene, which soften on heating. (b) Thermosets or resins such as epoxy which harden when two components (a resin and a hardener) are heated together. (c) Elastomers or rubbers. (d) Natural polymers such as cellulose, lignin and protein, which provide the mechan- ical basis of most plant and animal life. Although their properties differ widely, all polymers are made up of long molecules with a covalently bonded backbone of carbon atoms. These long molecules are bonded together by weak Van der Waals and hydrogen (“secondary”) bonds, or by these plus covalent cross-links. The melting point of the weak bonds is low, not far from room temperature. So we use these materials at a high fraction of the melting point of the weak bonds (though not of the much stronger covalent backbone). Not surprisingly, they show some of the features of a material near its melting point: they creep, and the elastic deflection which appears on loading increases with time. This is just one import- ant way in which polymers differ from metals and ceramics, and it necessitates a different design approach (Chapter 27). Most polymers are made from oil; the technology needed to make them from coal is still poorly developed. But one should not assume that dependence on oil makes the polymer industry specially vulnerable to oil price or availability. The value-added when polymers are made from crude oil is large. At 1998 prices, one tonne of oil is about 150; 1 tonne of polyethylene is about 800. So doubling the price of oil does not double the price of the polymer. And the energy content of metals is large too: that of aluminium is nearly twice as great as that of most polymers. So polymers are no more sensitive to energy prices than are most other commodities, and they are likely to be with us for a very long time to come. The generic polymers Thermoplastics Polyethylene is the commonest of the thermoplastics. They are often described as linear polymers, that is the chains are not cross-linked (though they may branch occa- sionally). That is why they soften if the polymer is heated: the secondary bonds which bind the molecules to each other melt so that it flows like a viscous liquid, allowing it to be formed. The molecules in linear polymers have a range of molecular weights, and they pack together in a variety of configurations. Some, like polystyrene, are amorphous; others, like polyethylene, are partly crystalline. This range of molecular weights and packing geometries means that thermoplastics do not have a sharp meltingPolymers 221 point. Instead, their viscosity falls over a range of temperature, like that of an inor- ganic glass. Thermoplastics are made by adding together (“polymerising”) sub-units (“monomers”) to form long chains. Many of them are made of the unit H H C C H R repeated many times. The radical R may simply be hydrogen (as in polyethylene), or —CH (polypropylene) or —Cl (polyvinylchloride). A few, like nylon, are more com- 3 plicated. The generic thermoplastics are listed in Table 21.1. The fibre and film-forming polymers polyacrylonitrile (ACN) and polyethylene teraphthalate (PET, Terylene, Dacron, Mylar) are also thermoplastics. Thermosets or resins Epoxy, familiar as an adhesive and as the matrix of fibre-glass, is a thermoset (Table 21.2). Thermosets are made by mixing two components (a resin and a hardener) which react and harden, either at room temperature or on heating. The resulting polymer is usually heavily cross-linked, so thermosets are sometimes described as network polymers. The cross-links form during the polymerisation of the liquid resin and hardener, so the structure is almost always amorphous. On reheating, the addi- tional secondary bonds melt, and the modulus of the polymer drops; but the cross- links prevent true melting or viscous flow so the polymer cannot be hot-worked (it turns into a rubber). Further heating just causes it to decompose. The generic thermosets are the epoxies and the polyesters (both widely used as matrix materials for fibre-reinforced polymers) and the formaldehyde-based plastics (widely used for moulding and hard surfacing). Other formaldehyde plastics, which now replace bakelite, are ureaformaldehyde (used for electrical fittings) and melamine- formaldehyde (used for tableware). Elastomers Elastomers or rubbers are almost-linear polymers with occasional cross-links in which, at room temperature, the secondary bonds have already melted. The cross-links pro- vide the “memory” of the material so that it returns to its original shape on unloading. The common rubbers are all based on the single structure H H A D C C C C B E C F H H R H n with the position R occupied by H, CH or Cl. They are listed in Table 21.3. 3222 Engineering Materials 2 Table 21.1 Generic thermoplastics Thérmoplastic Composition Uses Polyethylene, PE H Tubing, film, bottles, cups, electrical insulation, A D packaging. B C E C F H n Partly crystalline. Polypropylene, PP H H Same uses as PE, but lighter, stiffer, more resistant to A D sunlight. B E C C C F H CH 3 n Partly crystalline. Polytetrafluoroethylene, F Teflon. Good, high-temperature polymer with very low A D PTFE friction and adhesion characteristics. Non-stick B E C saucepans, bearings, seals. C F F n Partly crystalline. Polystyrene, PS H H Cheap moulded objects. Toughened with butadiene to A D make high-impact polystyrene (HIPS). Foamed with B C C E CO to make common packaging. 2 C F H C H 6 5 n Amorphous. Polyvinylchloride, PVC Architectural uses (window frames, etc.). Plasticised to H H A D make artificial leather, hoses, clothing. B C C E C F H Cl n Amorphous. Polymethylmethacrylate, H CH Perspex, lucite. Transparent sheet and mouldings. 3 A D PMMA Aircraft windows, laminated windscreens. B C C E C F H COOCH 3 n Amorphous. Nylon 66 () C H NO Textiles, rope, mouldings. 6 11 n Partly crystalline when drawn. Natural polymers The rubber polyisoprene is a natural polymer. So, too, are cellulose and lignin, the main components of wood and straw, and so are proteins like wool or silk. We use cellulose in vast quantities as paper and (by treating it with nitric acid) we make celluloid and cellophane out of it. But the vast surplus of lignin left from wood process- ing, or available in straw, cannot be processed to give a useful polymer. If it could, itPolymers 223 Table 21.2 Generic thermosets or resins Thermoset Composition Uses CH OH Epoxy Fibreglass, adhesives. 3 A D Expensive. B E O C H C C H O CH CH CH 6 4 6 4 2 2 C F CH 3 n Amorphous. Polyester O O CH OH Fibreglass, laminates. 2 A D Cheaper than epoxy. B E C (CH ) C O C 2 m C F CH OH 2 n Amorphous. Phenol-formaldehyde OH Bakelite, Tufnol, Formica. A D Rather brittle. B C H CH E 6 2 2 C F CH 2 n Amorphous. Table 21.3 Generic elastomers (rubbers) Elastomer Composition Uses Polyisoprene H H Natural rubber. A D B E C C C C C F H H CH H 3 n Amorphous except at high strains. Polybutadiene Synthetic rubber, car tyres. H H A D B C C C C E C F H H H H n Amorphous except at high strains. Polychloroprene H H Neoprene. An oil-resistant rubber used for seals. A D B C C C C E C F H H Cl H n Amorphous except at high strains.224 Engineering Materials 2 Table 21.4 Generic natural polymers Natural polymer Composition Uses Cellulose ( C H O ) Framework of all plant life, as the main structural 6 9 6 n Crystalline component in cell walls. Lignin Amorphous. The other main component in cell walls of all plant life. Protein Gelatin, wool, silk. R A D B E NH C C C F H O n R is a radical. Partly crystalline. Table 21.5 Properties of polymers Polymer Cost (UK£ Density Young’s Tensile −1 −3 (US) tonne ) (Mg m ) modulus strength (20°C 100 s) (MPa) (GPa) Thermoplastics Polyethylene, PE (low density) 560 (780) 0.91–0.94 0.15–0.24 7–17 Polyethylene, PE (high density) 510 (700) 0.95–0.98 0.55–1.0 20–37 Polypropylene, PP 675 (950) 0.91 1.2–1.7 50–70 Polytetrafluoroethylene, PTFE – 2.2 0.35 17–28 Polystyrene, PS 650 (910) 1.1 3.0–3.3 35–68 Polyvinyl chloride, PVC (unplasticised) 425 (595) 1.4 2.4–3.0 40–60 Polymethylmethacrylate, PMMA 1070 (1550) 1.2 3.3 80–90 Nylons 2350 (3300) 1.15 2–3.5 60–110 Resins or thermosets Epoxies 1150 (1600) 1.2–1.4 2.1–5.5 40–85 Polyesters 930 (1300) 1.1–1.4 1.3–4.5 45–85 Phenolformaldehyde 750 (1050) 1.27 8 35–55 Elastomers (rubbers) Polyisoprene 610 (850) 0.91 0.002–0.1 ≈10 Polybutadiene 610 (850) 1.5 0.004–0.1 Polychloroprene 1460 (2050) 0.94 ≈0.01 Natural polymers Cellulose fibres 1.5 25–40 ≈1000 Lignin 1.4 2.0 – Protein 1.2–1.4 ––Polymers 225 would form the base for a vast new industry. The natural polymers are not as complic- ated as you might expect. They are listed in Table 21.4. Material data Data for the properties of the generic polymers are shown in Table 21.5. But you have to be particularly careful in selecting and using data for the properties of polymers. Specifications for metals and alloys are defined fairly tightly; two pieces of Type 316L stainless steel from two different manufacturers will not differ much. Not so with polymers: polyethylene made by one manufacturer may be very different from polyethylene made by another. It is partly because all polymers contain a spectrum of molecular lengths; slight changes in processing change this spectrum. But it is also because details of the polymerisation change the extent of molecular branching and the degree of crystallinity in the final product; and the properties can be further changed by mechanical processing (which can, in varying degrees, align the molecules) and by proprietary additives. For all these reasons, data from compilations (like Table 21.5), or data books, are at best approximate. For accurate data you must use the manufacturers’ data sheets, or conduct your own tests. Fracture Glass Softening Specific heat Thermal Thermal −1 −1 toughness temperature expansion (J kg K ) conductivity coefficient −1 −1 −1 (20°C) T (K) temperature (W m K)(MK ) g 1/2 (MPa m ) T (K) s 1–2 270 355 2250 0.35 160–190 2–5 300 390 2100 0.52 150–300 3.5 253 310 1900 0.2 100–300 –– 395 1050 0.25 70–100 2 370 370 1350–1500 0.1–0.15 70–100 2.4 350 370 – 0.15 50–70 1.6 378 400 1500 0.2 54–72 3–5 340 350–420 1900 0.2–0.25 80–95 0.6–1.0 380 400–440 1700–2000 0.2–0.5 55–90 0.5 340 420–440 1200–2400 0.2–0.24 50–100 –– 370–550 1500–1700 0.12–0.24 26–60 – 220 ≈350 ≈2500 ≈0.15 ≈600 – 171 ≈350 ≈2500 ≈0.15 ≈600 – 200 ≈350 ≈2500 ≈0.15 ≈600 –– – – – – –– – – – – –– – – – –226 Engineering Materials 2 There are other ways in which polymer data differ from those for metals or ceram- ics. Polymers are held together by two sorts of bonds: strong covalent bonds which form the long chain backbone, and weak secondary bonds which stick the long chains together. At the glass temperature T , which is always near room temperature, the g secondary bonds melt, leaving only the covalent bonds. The moduli of polymers re- flect this. Below T most polymers have a modulus of around 3 GPa. (If the polymer is g drawn to fibres or sheet, the molecules are aligned by the drawing process, and the modulus in the draw-direction can be larger.) But even if T is below T , T will room g room still be a large fraction of T . Under load, the secondary bonds creep, and the modulus g falls. The table lists moduli for a loading time of 100 s at room temperature (20°C); for loading times of 1000 hours, the modulus can fall to one-third of that for the short (100 s) test. And above T , the secondary bonds melt completely: linear polymers g become very viscous liquids, and cross-linked polymers become rubbers. Then the modulus can fall dramatically, from 3 GPa to 3 MPa or less. You can see that design with polymers involves considerations which may differ from those for design with metals or ceramics. And there are other differences. One of the most important is that the yield or tensile strength of a polymer is a large fraction of its modulus; typically, σ = E/20. This means that design based on general yield y (plastic design) gives large elastic deflections, much larger than in metals and ceramics. The excessive “give” of a poorly designed polymer component is a common experi- ence, although it is often an advantage to have deflections without damage – as in polyethylene bottles, tough plastic luggage, or car bumpers. The nearness of T to room temperature has other consequences. Near T most g g polymers are fairly tough, but K can drop steeply as the temperature is reduced. IC (The early use of polymers for shelving in refrigerators resulted in frequent fractures at +4°C. These were not anticipated because the polymer was ductile and tough at room temperature.) The specific heats of polymers are large – typically 5 times more than those of metals 3 when measured per kg. When measured per m , however, they are about the same because of the large differences in density. The coefficients of thermal expansion of polymers are enormous, 10 to 100 times larger than those of metals. This can lead to problems of thermal stress when polymers and metals are joined. And the thermal conductivities are small, 100 to 1000 times smaller than those of metals. This makes polymers attractive for thermal insulation, particularly when foamed. In summary, then, design with polymers requires special attention to time-dependent effects, large elastic deformation and the effects of temperature, even close to room tem- perature. Room temperature data for the generic polymers are presented in Table 21.5. As emphasised already, they are approximate, suitable only for the first step of the design project. For the next step you should consult books (see Further reading), and when the choice has narrowed to one or a few candidates, data for them should be sought from manufacturers’ data sheets, or from your own tests. Many polymers contain additives – plasticisers, fillers, colourants – which change the mechanical prop- erties. Manufacturers will identify the polymers they sell, but will rarely disclose their Remember that the modulus E = σ/ε. ε will increase during creep at constant σ. This will give a lower apparent value of E. Long tests give large creep strains and even lower apparent moduli.Polymers 227 additives. So it is essential, in making a final choice of material, that both the polymer and its source are identified and data for that polymer, from that source, are used in the design calculations. Further reading F. W. Billmeyer, Textbook of Polymer Science, 3rd edition, Wiley Interscience, 1984. J. A. Brydson, Plastics Materials, 6th edition, Butterworth-Heinemann, 1996. C. Hall, Polymer Materials, Macmillan, 1981. International Saechtling, Plastics Handbook, Hanser, 1983. R. M. Ogorkiewicz (ed.), Thermoplastics: Properties and Design, Wiley, 1974. R. M. Ogorkiewicz, Engineering Design Guide No. 17: The Engineering Properties of Plastics, Oxford University Press, 1977. Problems 21.1 What are the four main generic classes of polymers? For each generic class: (a) give one example of a specific component made from that class; (b) indicate why that class was selected for the component. 21.2 How do the unique characteristics of polymers influence the way in which these materials are used?228 Engineering Materials 2 Chapter 22 The structure of polymers Introduction If the architecture of metal crystals is thought of as classical, then that of polymers is baroque. The metal crystal is infused with order, as regular and symmetrical as the Parthenon; polymer structures are as exotic and convoluted as an Austrian altarpiece. Some polymers, it is true, form crystals, but the molecular packing in these crystals is more like that of the woven threads in a horse blanket than like the neat stacking of spheres in a metal crystal. Most are amorphous, and then the long molecules twine around each other like a bag full of tangled rope. And even the polymers which can crystallise are, in the bulk form in which engineers use them, only partly crystalline: segments of the molecules are woven into little crystallites, but other segments form a hopeless amorphous tangle in between. The simpler polymers (like polyethylene, PMMA and polystyrene) are linear: the chains, if straightened out, would look like a piece of string. These are the thermoplastics: if heated, the strings slither past each other and the polymer softens and melts. And, at least in principle, these polymers can be drawn in such a way that the flow orients the strings, converting the amorphous tangle into sheet or fibre in which the molecules are more or less aligned. Then the properties are much changed: if you pull on the fibre (for example) you now stretch the molecular strings instead of merely unravelling them, and the stiffness and strength you measure are much larger than before. The less simple polymers (like the epoxies, the polyesters and the formaldehyde- based resins) are networks: each chain is cross-linked in many places to other chains, so that, if stretched out, the array would look like a piece of Belgian lace, somehow woven in three dimensions. These are the thermosets: if heated, the structure softens but it does not melt; the cross-links prevent viscous flow. Thermosets are usually a bit stiffer than amorphous thermoplastics because of the cross-links, but they cannot easily be crystallised or oriented, so there is less scope for changing their properties by processing. In this chapter we review, briefly, the essential features of polymer structures. They are more complicated than those of metal crystals, and there is no formal framework (like that of crystallography) in which to describe them exactly. But a looser, less precise description is possible, and is of enormous value in understanding the propert- ies that polymers exhibit. Molecular length and degree of polymerisation Ethylene, C H , is a molecule. We can represent it as shown in Fig. 22.1(a), where the 2 4 square box is a carbon atom, and the small circles are hydrogen. Polymerisation breaksThe structure of polymers 229 Fig. 22.1. (a) The ethylene molecule or monomer; (b) the monomer in the activated state, ready to polymerise with others; (c)–(f) the ethylene polymer (“polyethylene”); the chain length is limited by the addition of terminators like —OH. The DP is the number of monomer units in the chain. the double bond, activating the ethylene monomer (Fig. 22.1b), and allowing it to link to others, forming a long chain or macromolecule (Fig. 22.1c). The ends of the chain are a problem: they either link to other macromolecules, or end with a terminator (such as an —OH group), shown as a round blob. If only two or three molecules link, we have created a polymer. But to create a solid with useful mechanical properties, the chains must be longer – at least 500 monomers long. They are called high polymers (to distinguish them from the short ones) and, obviously, their length, or total molecular weight, is an important feature of their structure. It is usual to speak of the degree of polymerisation or DP: the number of 3 5 monomer units in a molecule. Commercial polymers have a DP in the range 10 to 10 . The molecular weight of a polymer is simply the DP times the molecular weight of the monomer. Ethylene, C H , for example, has a molecular weight of 28. If the DP for 2 4 4 a batch of polyethylene is 10 , then the molecules have an average molecular weight of 280,000. The word “average” is significant. In all commercial polymers there is a range of DP, and thus of molecular lengths (Fig. 22.2a). Then the average is simply ∞ DP = DPP(DP)d(DP) (22.1)  0 where P(DP)d(DP) is the fraction of molecules with DP values between DP and DP + d(DP). The molecular weight is just mDP where m is the molecular weight of the monomer. Most polymer properties depend on the average DP. Figure 22.2(b, c), for poly- ethylene, shows two: the tensile strength, and the softening temperature. DPs of less than 300 give no strength because the short molecules slide apart too easily. The strength rises with DP, but so does the viscosity; it is hard to mould polyethylene if 230 Engineering Materials 2 Fig. 22.2. (a) Linear polymers are made of chains with a spectrum of lengths, or DPs. The probability of a given DP is P(DP); (b) and (c) the strength, the softening temperature and many other properties depend on the average DP. 3 the DP is much above 10 . The important point is that a material like polyethylene does not have a unique set of properties. There are many polyethylenes; the properties of a given batch depend on (among other things) the molecular length or DP . The molecular architecture Thermoplastics are the largest class of engineering polymer. They have linear molecules: they are not cross-linked, and for that reason they soften when heated, allowing them to be formed (ways of doing this are described in Chapter 24). Monomers which form linear chains have two active bonds (they are bifunctional). A molecule with only one active bond can act as a chain terminator, but it cannot form a link in a chain. Monomers with three or more active sites (polyfunctional monomers) form networks: they are the basis of thermosetting polymers, or resins. The simplest linear-chain polymer is polyethylene (Fig. 22.3a). By replacing one H atom of the monomer by a side-group or radical R (sausages on Fig. 22.3b, c, d) we obtain the vinyl group of polymers: R = Cl gives polyvinyl chloride; R = CH gives 3The structure of polymers 231 Fig. 22.3. (a) Linear polyethylene; (b) an isotactic linear polymer: the side-groups are all on the same side; (c) a sindiotactic linear polymer: the side-groups alternate regularly; (d) an atactic linear polymer: the side- groups alternate irregularly. polypropylene; R = C H gives polystyrene. The radical gives asymmetry to the 6 5 monomer unit, and there is then more than one way in which the unit can be attached to form a chain. Three arrangements are shown in Fig. 22.3. If all the side-groups are on the same side, the molecule is called isotactic. If they alternate in some regular way round the chain it is called sindiotactic. If they alternate randomly it is called atactic. These distinctions may seem like splitting hairs (protein, another linear polymer), but they are important: the tacticity influences properties. The regular molecules (Figs 22.3a,b,c) can stack side-by-side to form crystals: the regularly spaced side-groups nestle into the regular concavities of the next molecule. The irregular, atactic, molecules cannot: their side-groups clash, and the molecules are forced into lower-density, non- crystalline arrangements. Even the type of symmetry of the regular molecules matters: the isotactic (one-sided) molecules carry a net electric dipole and can be electroactive (showing piezoelectric effects, for instance), and others cannot. Some polymerisation processes (such as the Ziegler process for making polyethylene) are delicate and precise in their operation: they produce only linear chains, and with a narrow spread of lengths. Others (like the older, high-pressure, ICI process) are crude and violent: side-groups may be torn from a part-formed molecule, and other growing molecules may attach themselves there, giving branching. Branching hinders crystallisa- tion, just as atacticity does. Low-density polyethylene is branched, and for that reason has a low fraction of crystal (≈50%), a low density, and low softening temperature (75°C). High-density PE is not branched: it is largely crystalline (≈80%), it is 5% denser, and it softens at a temperature which is 30°C higher. The next simplest group of linear polymers is the vinylidene group. Now two of the hydrogens of ethylene are replaced by radicals. Polymethylmethacrylate (alias PMMA,232 Engineering Materials 2 Perspex, Plexiglas or lucite) is one of these: the two radicals are —CH and —COOCH . 3 3 Now the difficulties of getting regular arrangements increases, and most of these polymers are amorphous. Linear-chain thermoplastics are the most widely used of polymers, partly because of the ease with which they can be formed. Their plasticity allows them to be drawn into sheet, and in so doing, the molecules become aligned in the plane of the sheet, increasing the modulus and strength in this plane. Alignment is even more dramatic when linear polymers are drawn to fibres: the high strength of nylon, Dacron and Kevlar fibres reflects the near-perfect lining up of the macromolecules along the fibre axis. Most thermosets start from large polyfunctional monomers. They react with each other or with small, linking molecules (like formaldehyde) in a condensation reaction – one which plucks an —OH from one molecule and an —H from the other to give H O (a by-product), welding the two molecules together at the severed bonds. Since 2 one of the two molecules is polyfunctional, random three-dimensional networks are possible. Because of the cross-linking, thermosets do not melt when heated (though they ultimately decompose), they do not dissolve in solvents (as linear polymers do), and they cannot be formed after polymerisation (as linear polymers can). But for the same reason they are chemically more stable, are useful to a higher temperature, and are generally stiffer than thermoplastics. The irreversible setting reaction makes thermosets particularly good as adhesives, as coatings, and as the matrix for composites. Elastomers are a special sort of cross-linked polymer. First, they are really linear polymers with just a few cross-links – one every hundred or more monomer units – so that a molecule with a DP of 500 might have fewer than five cross-link points along its length. And second, the polymer has a glass temperature which is well below room temperature, so that (at room temperature) the secondary bonds have melted. Why these two features give an elastomer is explained later (Chapter 23). Packing of polymer molecules and the glass transition Although we have drawn them as straight, a free polymer molecule is never so. Each C—C joint in its backbone has rotational freedom, so that the direction of the molecule changes at each step along the chain, allowing it to spiral, twist and tangle in the most extravagant way. When a linear polymer melts, its structure is that of a dense spaghetti-like tangle of these meandering molecules. Each is free to slither past the others in the melt, so the chain-links bend in a random way (Fig. 22.4). The average distance between the start of the chain and its end is then calculated in the same way that you calculate the distance a drunk staggers from the pub: if steps (of length λ) are equally likely in all directions (a “random walk”), the distance from the pub after n steps is ( n )λ. So, if the polymer has n units of length λ, the distance from its head to its tail is, on average, ( n )λ, not nλ as you might at first think. When the melt is cooled, the spaghetti tangle may simply freeze without rearrang- ing; the resulting solid polymer then has an amorphous structure. But during cooling molecules can move, and (depending on their architecture) they may partly line up to form crystallites. We now consider each of the structures, starting with the crystallites.The structure of polymers 233 Fig. 22.4. The random walk of a chain in a polymer melt, or in a solid, glassy polymer means that, on average, one end of the molecule is ( n )l away from the other end. Very large strains (≈4) are needed to straighten the molecule out. Polymer crystals Linear-chain molecules can crystallise. High-density polyethylene is an example. The molecules have no side-groups or branches. On cooling, secondary bonds tend to pull the molecules together into parallel bundles, not perfectly crystalline, but not amorph- ous (that is, devoid of all order) either. Under some circumstances, well-defined chain- folded crystals form (Fig. 22.5): the long molecules fold like computer paper into a stack with a width much less than the length of the molecule. Actually, the crystals are rarely as neatly folded as computer paper. The folds are not perfectly even, and the tails of the molecules may not tuck in properly; it is more like a badly woven carpet. Nonetheless, the crystallinity is good enough for the polymer to diffract X-rays like a Fig. 22.5. A chain-folded polymer crystal. The structure is like that of a badly woven carpet. The unit cell, shown below, is relatively simple and is much smaller than the polymer chain.234 Engineering Materials 2 Fig. 22.6. A schematic drawing of a largely crystalline polymer like high-density polyethylene. At the top the polymer has melted and the chain-folded segments have unwound. metal crystal, and a unit cell can be defined (Fig. 22.5). Note that the cell is much smaller than the molecule itself. But even the most crystalline of polymers (e.g. high-density PE) is only 80% crystal. The structure probably looks something like Fig. 22.6: bundles, and chain-folded seg- ments, make it largely crystalline, but the crystalline parts are separated by regions of disorder – amorphous, or glassy regions. Often the crystalline platelets organise them- selves into spherulites: bundles of crystallites that, at first sight, seem to grow radially outward from a central point, giving crystals with spherical symmetry. The structure is really more complicated than that. The growing ends of a small bundle of crystallites (Fig. 22.7a) trap amorphous materials between them, wedging them apart. More crystallites nucleate on the bundle, and they, too, splay out as they grow. The splaying continues until the crystallites bend back on themselves and touch; then it can go no further (Fig. 22.7b). The spherulite then grows as a sphere until it impinges on others, to form a grain-like structure. Polythene is, in fact, like this, and polystyrene, nylon and many other linear polymers do the same thing. When a liquid crystallises to a solid, there is a sharp, sudden decrease of volume at the melting point (Fig. 22.8a). The random arrangement of the atoms or molecules in the liquid changes discontinuously to the ordered, neatly packed, arrangement of the crystal. Other properties change discontinuously at the melting point also: the vis- 10 cosity, for example, changes sharply by an enormous factor (10 or more for a metal). Broadly speaking, polymers behave in the same way: a crystalline polymer has a fairly well-defined melting point at which the volume changes rapidly, though the sharp- ness found when metals crystallise is blurred by the range of molecular weights (and thus melting points) as shown in Fig. 22.8(b). For the same reason, other polymer properties (like the viscosity) change rapidly at the melting point, but the true discon- tinuity of properties found in simple crystals is lost.The structure of polymers 235 Fig. 22.7. The formation and structure of a spherulite. Fig. 22.8. (a) The volume change when a simple melt (like a liquid metal) crystallises defines the melting point, T ; (b) the spread of molecular weights blurs the melting point when polymers crystallise; (c) when a m polymer solidifies to a glass the melting point disappears completely, but a new temperature at which the free volume disappears (the glass temperature, T ) can be defined and measured. g236 Engineering Materials 2 When, instead, the polymer solidifies to a glass (an amorphous solid) the blurring is much greater, as we shall now see. Amorphous polymers Cumbersome side-groups, atacticity, branching and cross-linking all hinder crystallisa- tion. In the melt, thermal energy causes the molecules to rearrange continuously. This wriggling of the molecules increases the volume of the polymer. The extra volume (over and above that needed by tightly packed, motionless molecules) is called the free- volume. It is the free-volume, aided by the thermal energy, that allows the molecules to move relative to each other, giving viscous flow. As the temperature is decreased, free-volume is lost. If the molecular shape or cross- linking prevent crystallisation, then the liquid structure is retained, and free-volume is not all lost immediately (Fig. 22.8c). As with the melt, flow can still occur, though naturally it is more difficult, so the viscosity increases. As the polymer is cooled fur- ther, more free volume is lost. There comes a point at which the volume, though sufficient to contain the molecules, is too small to allow them to move and rearrange. All the free volume is gone, and the curve of specific volume flattens out (Fig. 22.8c). This is the glass transition temperature, T . Below this temperature the polymer is a glass. g The glass transition temperature is as important for polymers as the melting point is for metals (data for T are given in Table 21.5). Below T , secondary bonds bind the g g molecules into an amorphous solid; above, they start to melt, allowing molecular motion. The glass temperature of PMMA is 100°C, so at room temperature it is a brittle solid. Above T , a polymer becomes first leathery, then rubbery, capable of large elastic g extensions without brittle fracture. The glass temperature for natural rubber is around −70°C, and it remains flexible even in the coldest winter; but if it is cooled to −196°C in liquid nitrogen, it becomes hard and brittle, like PMMA at room temperature. That is all we need to know about structure for the moment, though more informa- tion can be found in the books listed under Further reading. We now examine the origins of the strength of polymers in more detail, seeking the criteria which must be satisfied for good mechanical design. Further reading D. C. Bassett, Principles of Polymer Morphology, Cambridge University Press, 1981. F. W. Billmeyer, Textbook of Polymer Science, 3rd edition, Wiley Interscience, 1984. J. A. Brydson, Plastics Materials, 6th edition, Butterworth-Heinemann, 1996. J. M. C. Cowie, Polymers: Chemistry and Physics of Modern Materials, International Textbook Co., 1973. C. Hall, Polymer Materials, Macmillan, 1981. R. J. Young, Introduction to Polymers, Chapman and Hall, 1981. Problems 22.1 Describe, in a few words, with an example or sketch where appropriate, what is meant by each of the following:The structure of polymers 237 (a) a linear polymer; (b) an isotactic polymer; (c) a sindiotactic polymer; (d) an atactic polymer; (e) degree of polymerization; (f) tangling; (g) branching; (h) cross-linking; (i) an amorphous polymer; (j) a crystalline polymer; (k) a network polymer; (l) a thermoplastic; (m) a thermoset; (n) an elastomer, or rubber; (o) the glass transition temperature. –3 22.2 The density of a polyethylene crystal is 1.014 Mg m at 20°C. The density of –3 amorphous polyethylene at 20°C is 0.84 Mg m . Estimate the percentage crystal- linity in: –3 (a) a low-density polyethylene with a density of 0.92 Mg m at 20°C; –3 (b) a high-density polyethylene with a density of 0.97 Mg m at 20°C. Answers: (a) 46%, (b) 75%.238 Engineering Materials 2 Chapter 23 Mechanical behaviour of polymers Introduction All polymers have a spectrum of mechanical behaviour, from brittle-elastic at low temperatures, through plastic to viscoelastic or leathery, to rubbery and finally to viscous at high temperatures. Metals and ceramics, too, have a range of mechanical behaviour, but, because their melting points are high, the variation near room temperature is unimportant. With polymers it is different: between −20°C and +200°C a polymer can pass through all of the mechanical states listed above, and in doing so its modulus and 3 strength can change by a factor of 10 or more. So while we could treat metals and ceramics as having a constant stiffness and strength for design near ambient temper- atures, we cannot do so for polymers. The mechanical state of a polymer depends on its molecular weight and on the temperature; or, more precisely, on how close the temperature is to its glass temper- ature T . Each mechanical state covers a certain range of normalised temperature T/T g g (Fig. 23.1). Some polymers, like PMMA, and many epoxies, are brittle at room tem- perature because their glass temperatures are high and room temperature is only 0.75 T . Others, like the polyethylenes, are leathery; for these, room temperature is g about 1.0 T . Still others, like polyisoprene, are elastomers; for these, room temperature is g well above T (roughly 1.5 T ). So it makes sense to plot polymer properties not against g g temperature T, but against T/T since that is what really determines the mechanical g Fig. 23.1. Schematic showing the way in which Young’s modulus E for a linear polymer changes with temperature for a fixed loading time.

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