And second, the polymer has a glass temperature which is well below roomtemperature, so that at room temperature the secondary bonds have melted.. Other properties change discontinuously
Trang 1The 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 = C6H5 gives polystyrene The radical gives asymmetry to themonomer 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-groupsnestle into the regular concavities of the next molecule The irregular, atactic, moleculescannot: 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 anarrow spread of lengths Others (like the older, high-pressure, ICI process) are crudeand 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 reasonhas 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,
Trang 2Perspex, Plexiglas or lucite) is one of these: the two radicals are —CH3 and —COOCH3.Now the difficulties of getting regular arrangements increases, and most of thesepolymers 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 drawninto 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 dramaticwhen linear polymers are drawn to fibres: the high strength of nylon, Dacron andKevlar fibres reflects the near-perfect lining up of the macromolecules along the fibreaxis
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 giveH2O (a by-product), welding the two molecules together at the severed bonds Sinceone of the two molecules is polyfunctional, random three-dimensional networks arepossible Because of the cross-linking, thermosets do not melt when heated (thoughthey 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 thesame reason they are chemically more stable, are useful to a higher temperature, andare generally stiffer than thermoplastics The irreversible setting reaction makesthermosets 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 – sothat a molecule with a DP of 500 might have fewer than five cross-link points along itslength And second, the polymer has a glass temperature which is well below roomtemperature, so that (at room temperature) the secondary bonds have melted Whythese 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 EachC—C joint in its backbone has rotational freedom, so that the direction of the moleculechanges at each step along the chain, allowing it to spiral, twist and tangle in themost extravagant way When a linear polymer melts, its structure is that of a densespaghetti-like tangle of these meandering molecules Each is free to slither past theothers in the melt, so the chain-links bend in a random way (Fig 22.4) The averagedistance between the start of the chain and its end is then calculated in the same waythat 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.
Trang 3The 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 Themolecules have no side-groups or branches On cooling, secondary bonds tend to pullthe 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 arerarely as neatly folded as computer paper The folds are not perfectly even, and thetails 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
Trang 4Fig 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 muchsmaller 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 ofdisorder – 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 Morecrystallites nucleate on the bundle, and they, too, splay out as they grow The splayingcontinues until the crystallites bend back on themselves and touch; then it can go nofurther (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, nylonand many other linear polymers do the same thing
When a liquid crystallises to a solid, there is a sharp, sudden decrease of volume atthe melting point (Fig 22.8a) The random arrangement of the atoms or molecules inthe liquid changes discontinuously to the ordered, neatly packed, arrangement of thecrystal Other properties change discontinuously at the melting point also: the vis-cosity, for example, changes sharply by an enormous factor (1010 or more for a metal).Broadly speaking, polymers behave in the same way: a crystalline polymer has a fairlywell-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 (andthus melting points) as shown in Fig 22.8(b) For the same reason, other polymerproperties (like the viscosity) change rapidly at the melting point, but the true discon-tinuity of properties found in simple crystals is lost
Trang 5The 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 ) can be defined and measured.
Trang 6When, instead, the polymer solidifies to a glass (an amorphous solid) the blurring ismuch greater, as we shall now see.
Amorphous polymers
Cumbersome side-groups, atacticity, branching and cross-linking all hinder tion In the melt, thermal energy causes the molecules to rearrange continuously Thiswriggling of the molecules increases the volume of the polymer The extra volume
crystallisa-(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 linking prevent crystallisation, then the liquid structure is retained, and free-volume isnot all lost immediately (Fig 22.8c) As with the melt, flow can still occur, thoughnaturally 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, thoughsufficient 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)
cross-This is the glass transition temperature, Tg 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 Tg are given in Table 21.5) Below Tg, secondary bonds bind themolecules into an amorphous solid; above, they start to melt, allowing molecularmotion The glass temperature of PMMA is 100°C, so at room temperature it is a brittle
solid Above Tg, 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 inliquid 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 theorigins of the strength of polymers in more detail, seeking the criteria which must besatisfied 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 ismeant by each of the following:
Trang 7The structure of polymers 237
(a) a linear polymer;
(o) the glass transition temperature
22.2 The density of a polyethylene crystal is 1.014 Mg m–3 at 20°C The density ofamorphous 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%.
Trang 8The mechanical state of a polymer depends on its molecular weight and on thetemperature; or, more precisely, on how close the temperature is to its glass temper-
ature Tg Each mechanical state covers a certain range of normalised temperature T/Tg
(Fig 23.1) Some polymers, like PMMA, and many epoxies, are brittle at room perature because their glass temperatures are high and room temperature is only
tem-0.75 Tg Others, like the polyethylenes, are leathery; for these, room temperature is about 1.0 Tg Still others, like polyisoprene, are elastomers; for these, room temperature is well above Tg (roughly 1.5 Tg) So it makes sense to plot polymer properties not against temperature T, but against T/Tg 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.
Trang 9Mechanical behaviour of polymers 239
state The modulus diagrams and strength diagrams described in this chapter areplotted 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 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 complicatedorigins, which we will now explain
re-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 σdivided by the elastic strain ε
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 oflinear-amorphous polymers, examining the reasons for the enormous range of modu-lus, and digressing occasionally to explain how cross-linking, or crystallisation, changethings
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 toaround 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
Trang 10Fig 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 isrecovered on unloading But there are two sorts of bonds: the taut, muscular, covalentbonds that form the backbone of the chains; and the flabby, soft, secondary bondsbetween them Figure 23.2 illustrates this: the covalent chain is shown as a solid lineand the side groups or radicals as full circles; they bond to each other by secondarybonds shown as dotted lines (this scheme is helpful later in understanding elasticdeformation)
The modulus of the polymer is an average of the stiffnesses of its bonds But itobviously is not an arithmetic mean: even if the stiff bonds were completely rigid, thepolymer would deform because the weak bonds would stretch Instead, we calculatethe modulus by summing the deformation in each type of bond using the methods ofcomposite theory (Chapter 25) A stress σ produces a strain which is the weighted sum
of the strains in each sort of bond
f E
Trang 11Mechanical behaviour of polymers 241
Fig 23.3. The way in which the modulus of polymers changes with the fraction of covalent bonds in the loading direction Cross-linking increases this fraction a little; drawing increases it much more.
Substituting this information into the last equation gives an equation for the glassymodulus as a function of the fraction of covalent bonding
3
1
This function is plotted in Fig 23.3 The glassy modulus of random, linear
poly-mers ( f = 1) is always around 3 GPa Heavily cross-linked polymers have a higher
modulus because f is larger – as high as 0.75 – giving E = 8 GPa Drawn polymersare different: they are anisotropic, having the chains lined up along the draw direc-tion Then the fraction of covalent bonds in the loading direction is increased dramatic-ally In extreme drawing of fibres like nylon or Kevlar this fraction reaches 98%, and
the modulus rises to 100 GPa, about the same as that of aluminium This orientation
strengthening is a potent way of increasing the modulus of polymers The stiffness
normal to the drawing direction, of course, decreases because f falls towards zero in
that direction
You might expect that the glassy modulus (which, like that of metals and ceramics,
is just due to bond-stretching) should not depend much on temperature At very lowtemperatures this is correct But the tangled packing of polymer molecules leavessome “loose sites” in the structure: side groups or chain segments, with a little helpfrom thermal energy, readjust their positions to give a little extra strain These second-ary relaxations (Fig 23.1) can lower the modulus by a factor of 2 or more, so theycannot be ignored But their effect is small compared with that of the visco-elastic, orglass transition, which we come to next
Trang 12Fig 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 T g , each molecule can move (reptate) in its tube, giving strain.
The glass, or visco-elastic transition
As the temperature is raised, the secondary bonds start to melt Then segments of thechains can slip relative to each other like bits of greasy string, and the modulus fallssteeply (Fig 23.1) It is helpful to think of each polymer chain as contained within atube made up by the surrounding nest of molecules (Fig 23.4) When the polymer isloaded, bits of the molecules slide slightly in the tubes in a snake-like way (called
“reptation”) giving extra strain and dissipating energy As the temperature rises past
T g, the polymer expands and the extra free volume (Chapter 22) lowers the packingdensity, allowing more regions to slide, and giving a lower apparent modulus But thereare still non-sliding (i.e elastic) parts On unloading, these elastic regions pull thepolymer back to its original shape, though they must do so against the reverse viscous
sliding of the molecules, and that takes time The result is that the polymer has leathery
properties, as do low-density polyethylene and plasticised PVC at room temperature
Within this regime it is found that the modulus E at one temperature can be related
to that at another by a change in the time scale only, that is, there is an equivalence
between time and temperature This means that the curve describing the modulus at one
temperature can be superimposed on that for another by a constant horizontal
dis-placement log (a T ) along the log (t) axis, as shown in Fig 23.5.
A well-known example of this time–temperature equivalence is the steady-statecreep of a crystalline metal or ceramic, where it follows immediately from the kinetics
of thermal activation (Chapter 6) At a constant stress σ the creep rate varies withtemperature as
ε˙ ss = ε = exp (− / )
Trang 13Mechanical behaviour of polymers 243
1
0 0
This result says that a simple shift along the time axis by log (a T) will bring the
response at T into coincidence with that at T (see Fig 23.5)
Fig 23.5. Schematic of the time–temperature equivalence for the modulus Every point on the curve for temperature T 1 lies at the same distance, log (a T ), to the left of that for temperature T 0
Trang 14Polymers are a little more complicated The drop in modulus (like the increase increep rate) is caused by the increased ease with which molecules can slip past eachother In metals, which have a crystal structure, this reflects the increasing number ofvacancies and the increased rate at which atoms jump into them In polymers, whichare amorphous, it reflects the increase in free volume which gives an increase in therate of reptation Then the shift factor is given, not by eqn (23.11) but by
predict the effect of temperature on polymer behaviour If T0 is taken to be the glass
temperature, then C1 and C2 are roughly constant for all amorphous polymers (and
inorganic glasses too); their values are C1= 17.5 and C2= 52 K
Rubbery behaviour and elastomers
As the temperature is raised above T g, one might expect that flow in the polymershould become easier and easier, until it becomes a rather sticky liquid Linear poly-mers with fairly short chains ( DP < 103) do just this But polymers with longer chains( DP > 104) pass through a rubbery state.
The origin of rubber elasticity is more difficult to picture than that of a crystal orglass The long molecules, intertwined like a jar of exceptionally long worms, form
entanglements – points where molecules, because of their length and flexibility, become
knotted together (Fig 23.6) On loading, the molecules reptate (slide) except at ment points The entanglements give the material a shape-memory: load it, and thesegments between entanglements straighten out; remove the load and the wriggling of
entangle-the molecules (being above T g) draws them back to their original configuration, and
Fig 23.6. A schematic of a linear-amorphous polymer, showing entanglement points (marked “E”) which act like chemical cross-links.
Trang 15Mechanical behaviour of polymers 245
thus shape Stress tends to order the molecules of the material; removal of stress allows
it to disorder again The rubbery modulus is small, about one-thousandth of the glassy modulus, T g, 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 entanglementsare 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, and this makes the polymer above T g into a true elastomer, capable of elastic
extensions of 300% or more (the same as the draw ratio of the polymer in the plasticstate – see the next section) which are recovered completely on unloading Over-frequent cross-links destroy the rubbery behaviour If every unit on the polymerchain has one (or more) cross-links to other chains, then the covalent bonds form athree-dimensional network, and melting of the secondary bonds does not leave longmolecular spans which can straighten out under stress So good elastomers, likepolyisoprene (natural rubber) are linear polymers with just a few cross-links, well
above their glass temperatures (room temperature is 1.4 T g for polyisoprene) If they
are cooled below T g, the modulus rises steeply and the rubber becomes hard andbrittle, with properties like those of PMMA at room temperature
Viscous flow
At yet higher temperatures (>1.4Tg) the secondary bonds melt completely and even theentanglement points slip This is the regime in which thermoplastics are moulded:linear polymers become viscous liquids The viscosity is always defined (and usuallymeasured) in shear: if a shear stress σs produces a rate of shear ˙γ then the viscosity(Chapter 19) is
Its units are poise (P) or 10−1 Pa s
Polymers, like inorganic glasses, are formed at a viscosity in the range 104 to 106poise, when they can be blown or moulded (When a metal melts, its viscosity dropsdiscontinuously to a value near 10−3 poise – about the same as that of water; that iswhy metals are formed by casting, not by the more convenient methods of blowing ormoulding.) The viscosity depends on temperature, of course; and at very high tem-peratures the dependence is well described by an Arrhenius law, like inorganic glasses
(Chapter 19) But in the temperature range 1.3–1.5 Tg, where most thermoplastics are
formed, the flow has the same time–temperature equivalence as that of the viscoelasticregime (eqn 23.12) and is called “rubbery flow” to distinguish it from the higher-
temperature Arrhenius flow Then, if the viscosity at one temperature T0 is η0, the viscosity at a higher temperature T1 is