Engineering Materials Vol II (microstructures processing design) 2nd ed. - M. Ashby_ D. Jones (1999) Episode 9 potx

The 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 6 H 5 gives polystyrene. The radical gives asymmetry to the 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 3 and —COOCH 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 2 O (a by-product), welding the two molecules together at the severed bonds. Since 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 n λ 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. 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. 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 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- cosity, for example, changes sharply by an enormous factor (10 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 m ; (b) the spread of molecular weights blurs the melting point when polymers crystallise; (c) when a polymer solidifies to a glass the melting point disappears completely, but a new temperature at which the free volume disappears (the glass temperature, T g ) can be defined and measured. 236 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 g . Below this temperature the polymer is a glass. The glass transition temperature is as important for polymers as the melting point is for metals (data for T g are given in Table 21.5). Below T g , secondary bonds bind the 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 g , a polymer becomes first leathery, then rubbery, capable of large elastic 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. 22.2 The density of a polyethylene crystal is 1.014 Mg m –3 at 20°C. The density of amorphous polyethylene at 20°C is 0.84 Mg m –3 . Estimate the percentage crystal- linity in: (a) a low-density polyethylene with a density of 0.92 Mg m –3 at 20°C; (b) a high-density polyethylene with a density of 0.97 Mg m –3 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 strength can change by a factor of 10 3 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 g . Each mechanical state covers a certain range of normalised temperature T/T 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 g . Others, like the polyethylenes, are leathery; for these, room temperature is about 1.0 T g . Still others, like polyisoprene, are elastomers; for these, room temperature is well above T g (roughly 1.5 T g ). So it makes sense to plot polymer properties not against temperature T, but against T/T g since that is what really determines the mechanical 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. Mechanical behaviour of polymers 239 state. The modulus diagrams and strength diagrams described in this chapter are plotted in this way. It is important to distinguish between the stiffness and the strength of a polymer. The stiffness describes the resistance to elastic deformation, the strength describes the re- sistance to collapse by plastic yielding or by fracture. Depending on the application, one or the other may be design-limiting. And both, in polymers, have complicated origins, which we will now explain. Stiffness: the time- and temperature-dependent modulus Much engineering design – particularly with polymers – is based on stiffness: the designer aims to keep the elastic deflections below some critical limit. Then the mater- ial property which is most important is Young’s modulus, E. Metals and ceramics have Young’s moduli which, near room temperature, can be thought of as constant. Those of polymers cannot. When a polymer is loaded, it deflects by an amount which increases with the loading time t and with the temperature T. The deflection is elastic – on unloading, the strain disappears again (though that, too, may take time). So it is usual to speak of the time- and temperature-dependent modulus, E(t, T) (from now on simply called E). It is defined, just like any other Young’s modulus, as the stress σ divided by the elastic strain ε E tT (, ) .= σ ε (23.1) The difference is that the strain now depends on time and temperature. The modulus E of a polymer can change enormously – by as much as a factor of 1000 – when the temperature is changed. We will focus first on the behaviour of linear-amorphous polymers, examining the reasons for the enormous range of modu- lus, and digressing occasionally to explain how cross-linking, or crystallisation, change things. Linear-amorphous polymers (like PMMA or PS) show five regimes of deformation in each of which the modulus has certain characteristics, illustrated by Fig. 23.1. They are: (a) the glassy regime, with a large modulus, around 3 GPa; (b) the glass-transition regime, in which the modulus drops steeply from 3 GPa to around 3 MPa; (c) the rubbery regime, with a low modulus, around 3 MPa; (d) the viscous regime, when the polymer starts to flow; (e) the regime of decomposition in which chemical breakdown starts. We now examine each regime in a little more detail. The glassy regime and the secondary relaxations The glass temperature, T g , you will remember, is the temperature at which the second- ary bonds start to melt. Well below T g the polymer molecules pack tightly together, either in an amorphous tangle, or in poorly organised crystallites with amorphous 240 Engineering Materials 2 Fig. 23.2. A schematic of a linear-amorphous polymer, showing the strong covalent bonds (full lines) and the weak secondary bonds (dotted lines). When the polymer is loaded below T g , it is the secondary bonds which stretch. material in between. Load stretches the bonds, giving elastic deformation which is recovered on unloading. But there are two sorts of bonds: the taut, muscular, covalent bonds that form the backbone of the chains; and the flabby, soft, secondary bonds between them. Figure 23.2 illustrates this: the covalent chain is shown as a solid line and the side groups or radicals as full circles; they bond to each other by secondary bonds shown as dotted lines (this scheme is helpful later in understanding elastic deformation). The modulus of the polymer is an average of the stiffnesses of its bonds. But it obviously is not an arithmetic mean: even if the stiff bonds were completely rigid, the polymer would deform because the weak bonds would stretch. Instead, we calculate the modulus by summing the deformation in each type of bond using the methods of composite theory (Chapter 25). A stress σ produces a strain which is the weighted sum of the strains in each sort of bond ε σσ σ ( ) ( ) .=+− = + −      f E f E f E f E 1212 1 1 (23.2) Here f is the fraction of stiff, covalent bonds (modulus E 1 ) and 1 − f is the fraction of weak, secondary bonds (modulus E 2 ). The polymer modulus is E f E f E ( ) .== + −      − σ ε 12 1 1 (23.3) If the polymer is completely cross-linked ( f = 1) then the modulus (E 1 ) is known: it is that of diamond, 10 3 GPa. If it has no covalent bonds at all, then the modulus (E 2 ) is that of a simple hydrocarbon like paraffin wax, and that, too, is known: it is 1 GPa. [...]... Handbook, Hanser, 198 3 P C Powell and A J Ingen Honsz, Engineering with Polymers, 2nd edition, Chapman and Hall, 199 8 D W Van Krevlin, Properties of Polymers, Elsevier, 197 6 I M Ward, Mechanical Properties of Solid Polymers, 2nd edition, Wiley, 198 4 R J Young, Introduction to Polymers, Chapman and Hall, 198 1 Problems 23.1 Estimate the loading time needed to give a modulus of 0.2 GPa in low-density polyethylene... because the molecules are more densely packed) but it does not suppress melting, so crystalline linear-polymers (like high-density PE) can be formed by heating and moulding them, just like linear-amorphous polymers; cross-linked polymers cannot 248 Engineering Materials 2 Strength: cold drawing and crazing Engineering design with polymers starts with stiffness But strength is also important, sometimes... circumspection In an engineering application the stress-state may be multiaxial, not simple tension; and the environment (even simple sunlight) may attack and embrittle the polymer, reducing its strength These, and other, aspects of design with polymers, are discussed in the books listed under Further reading Further reading J A Brydson, Plastics Materials, 6th edition, Butterworth-Heinemann, 199 6 International... give a compact summary of the small-strain behaviour of polymers, and are helpful in seeing how a given polymer will behave in a given application Cross-linking raises and extends the rubbery plateau, increasing the rubber-modulus, and suppressing melting Figure 23.8 shows how, for a single loading time, the contours of the modulus diagram are pushed up as the cross-link density is increased Crystallisation... is small compared with that of the visco-elastic, or glass transition, which we come to next 242 Engineering Materials 2 Fig 23.4 Each molecule in a linear polymer can be thought of as being contained in a tube made up by its surroundings When the polymer is loaded at or above Tg , each molecule can move (reptate) in its tube, giving strain The glass, or visco-elastic transition As the temperature... are brittle (Fig 23 .9) Unless special care is taken to avoid it, a polymer sample has small surface cracks (depth c) left by machining or abrasion, or caused by environmental attack Then a tensile stress σ will cause brittle failure if Fig 23 .9 Brittle fracture: the largest crack propagates when the fast-fracture criterion is satisfied Mechanical behaviour of polymers σ = K IC πc 2 49 (23.15) where KIC... typical of linear polymers 252 Engineering Materials 2 stiffness but the diagram is broadly typical of other linear polymers The diagram is helpful in giving a broad, approximate, picture of polymer strength The vertical axis is the strength of the polymer: the stress at which inelastic behaviour becomes pronounced The right-hand scale gives the strength in MPa; the left-hand scale gives the strength... is small, about one-thousandth of the glassy modulus, Tg , but it is there nonetheless, and gives the plateau in the modulus shown in Fig 23.1 Much more pronounced rubbery behaviour is obtained if the chance entanglements are replaced by deliberate cross-links The number of cross-links must be small – about 1 in every few hundred monomer units But, being strong, the covalent cross-links do not melt,... Overfrequent cross-links destroy the rubbery behaviour If every unit on the polymer chain has one (or more) cross-links to other chains, then the covalent bonds form a three-dimensional network, and melting of the secondary bonds does not leave long molecular spans which can straighten out under stress So good elastomers, like polyisoprene (natural rubber) are linear polymers with just a few cross-links, well... block copolymer (Fig 24.1b) 256 Engineering Materials 2 Fig 24.1 (a) A copolymer of vinyl chloride and vinyl acetate; the “alloy” packs less regularly, has a lower Tg , and is less brittle than simple polyvinylchloride (PVC) (b) A block copolymer: the two different molecules in the alloy are clustered into blocks along the chain Fig 24.2 A two-phase polymer alloy, made by co-polymerising styrene and butadiene . 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. summarised in the modulus diagram for a poly- mer. Figure 23.7 shows an example: it is a modulus diagram for PMMA, and is typical of linear-amorphous polymers (PS, for example, has a very similar. the other may be design-limiting. And both, in polymers, have complicated origins, which we will now explain. Stiffness: the time- and temperature-dependent modulus Much engineering design – particularly