Mechanical Behaviour of Engineering Materials - Metals, Ceramics, Polymers and Composites 2010 Part 8 pot

log glass transistionsecondary transition energy elastic entropy elastic energy elastic amorphous regions: entropy elastic, crystalline regions: energy elastic d DuromersFig.. Due to the

Fig 8.9 Eyring plot of polycarbonate (after [97])

Figure 8.10(a) schematically shows the temperature dependence of Young’smodulus in an amorphous thermoplastic, measured at a typical, constant load-ing time (for example, one second) Increasing the loading time would cause

a reduction of Young’s modulus As can be seen from the figure, the stiffnessstrongly decreases at temperatures close to the glass temperature The elasticbehaviour will therefore be discussed separately in the temperature regimesbelow and above the glass temperature

Energy elasticity

The elasticity of thermoplastics below their glass temperature is mainly due

to the energy needed to displace atoms from their equilibrium position Onunloading, the atoms return to their original position which has the lowestenergy For this reason, this behaviour is called energy elasticity It is mostlythe weak, intermolecular van der Waals, dipole, or hydrogen bonds that arestrained The covalent bonds do not contribute significantly to the elasticproperties Their stiffness is so large that they nearly cannot be strained elas-tically as long as the other bonds can deform Only if the chain moleculesare aligned in parallel, as in polymer fibres like aramid (kevlar), the covalentbonds determine Young’s modulus which can then take very large values of

up to 440 GPa

We already saw in section 2.6 that Young’s modulus is approximately portional to the melting temperature and thus to the binding energy Foramorphous polymers, the relevant temperature is the glass transition temper-ature because this is the temperature where the bonds melt The rather lowvalues of the glass temperature (listed in table 1.3) thus also explain whyYoung’s modulus of polymers is smaller than for the other material classes.The strong decrease of Young’s modulus at the glass temperature (seefigure 8.10(a)) will be discussed in the next section More interesting in the

(log)

glass transistionsecondary transition

energy elastic entropy elastic

energy elastic

amorphous regions: entropy elastic, crystalline regions: energy elastic

(d) DuromersFig 8.10 Temperature dependence of Young’s modulus in different types of poly-mers (after [19]) Because a logarithmic scale is used, the reduction of Young’smodulus appears to be smaller than it is in reality More explanations in the text

present context is the fact that even below the glass temperature, there may

be temperature values at which Young’s modulus decreases markedly by about

a factor of approximately 2 These so-called secondary transitions are caused

by relaxation processes which enable a limited mobility of the chain moleculesand thus cause a stress relaxation by movement of molecule segments Becausesuch rearrangements always require overcoming some activation energy, theybecome more probable if the loading time increases They are responsible forthe viscoelastic behaviour of polymers

As the activation energies of different relaxation processes differ, theirrelaxation time also differs This is the reason why the simple spring-and-dashpot model from section 8.2.1 cannot be used to make quantitative predic-tions This would require coupling several such elements [97] with relaxationtimes chosen to fit their respective processes

We already saw in section 8.1.1 that the activation energy of some ation processes is so low that it can be overcome by thermal activation already

relax-at temperrelax-atures as low as a few kelvin At room temperrelax-ature, their relaxrelax-ation

Fig 8.11 Elastic deformation of a polymer above the glass temperature Themolecules are straightened between the entanglement points

times are thus very short (of the order of 10−8s) Relaxation is almost taneous so that these processes contribute to the initial deformation of thepolymer when the load is applied

instan-If the stressed polymer has deformed viscoelastically by relaxation, thedeformed configuration has a higher energy than the initial one Upon unload-ing, the molecules return to their initial positions This process again requiresthermal activation and is therefore time-dependent as well

Entropy elasticity

If the temperature exceeds the glass temperature, Young’s modulus stronglydecreases From what has been said so far, it could be surmised that the poly-mer should deform like a viscous liquid if heated beyond the glass temperature,exhibiting viscosity, but no elasticity This, however, is not the case

The reason for this is the strong entanglement of the chain molecules Asdiscussed in section 1.4.2, the chain molecules are strongly folded Differentchain molecules are thus ‘tied together’ like a knot in many places On load-ing, the molecules are straightened Directly above the glass temperature, theycannot slide past each other because this movement is hampered by the sur-rounding molecules (see figure 8.11) The molecules thus straighten betweentheir entanglement points During sliding, energy barriers have to be overcomebecause the chain molecules are straightened, rotate, and because side groupshave to move Due to the higher temperature and the larger distance betweenthe molecules, this process is much easier at temperatures above the glasstemperature The deformation of the material is still time-dependent due tothe required thermal activation

If the load is removed, there is no force on the straightened molecules,

so there seems to be no reason why they should return to their initial tion Because of the stochastic thermal movements of the molecules in thepolymer, the molecule will probably return from the straightened to a foldedgeometry because there are a lot more possibilities for a folded molecule thanfor a straightened one The arbitrary thermal collisions with the surroundingmolecules thus fold up the molecule again Thus, there is a thermodynamicdriving force because the entropy of the molecule is larger in the folded than

posi-in the straightened state This behaviour is therefore called entropy elasticity.The entanglement points between the chain molecules remain in a fixed posi-tion on the molecules during elastic deformation so that the molecule returns

to its initial shape In contrast to the deformation below the glass ture, it is not the smaller energy of the initial configuration that drives thereturn to this form, but its larger entropy As before, the movement of themolecules is time-dependent.3

tempera-The viscoelasticity of amorphous polymers is most pronounced near theglass temperature in the transition regime between energy-elastic and entropy-elastic behaviour At lower temperatures, only smaller parts of the moleculescan slide past each other as explained above As we approach the glass tem-perature, more and more sliding processes become possible As the slidingprocesses can be more easily thermally activated the higher the temperaturebecomes, the relaxation time decreases At temperatures well above the glasstemperature, relaxation times are small, and the system returns quickly to itsinitial state

So far, we only considered amorphous thermoplastics Semi-crystalline moplastics show a different behaviour as shown in figure 8.10(b) Due to thestronger intermolecular bonds in the crystalline regions, their elastic stiffness

ther-is usually larger than that of amorphous polymers The decrease in Young’smodulus on reaching the glass temperature is smaller because only the amor-phous regions become entropy-elastic, whereas the crystalline regions remain

in the energy-elastic state The cohesion between the crystalline and the phous regions is ensured because most chain molecules extend over severalcrystalline and amorphous regions

amor-8.3.2 Elastic properties of elastomers and duromers

Elastomers and duromers are characterised by additional covalent cross-linksbetween the chain molecules In the energy-elastic regime, these additionalbonds do not influence the elastic properties significantly; Young’s modulusonly increases slightly

At temperatures above the glass temperature, the additional bonds becomeimportant Elastomers are entropy-elastic at these temperatures The covalentbonds between the molecules increase the linking between them compared tothermoplastics where molecules are linked by geometric entanglement only.These additional links cannot be broken during sliding of the molecules andthus increase the effect of entropy elasticity With increasing number of cross-links, the covalent bonds are loaded more heavily during elastic deformation sothat Young’s modulus increases with the cross-linking density as can be seen

3

Above the glass temperature, there is always plastic deformation as well If theloading time is sufficiently short, the plastic strain rate is small enough to beneglected; at larger loading times, it has to be taken into account (see also sec-tion 8.4.1)

from figure 8.10(c) Because the restoring force in entropy-elastic deformation

is the entropy, which becomes more important the larger the temperature

is (see equation (C.3)), Young’s modulus of elastomers often increases withincreasing temperature

Contrary to metals and ceramics, the elastic strains in elastomers canbecome very large and attain values of several hundred percent The reason

is that the molecules are straightened during deformation, but the cross-linksprevent the molecules from sliding past each other and thus inhibit plasticdeformation Upon unloading, entropy-elasticity completely restores the initialarrangement of the molecules This behaviour is called hyperelasticity

During deformation of hyperelastic materials, large strains of 100% ormore can occur The material behaviour is strongly non-linear There-fore, the theory of large deformations has to be used to describe thematerial behaviour (see section 3.1)

The basis of the description is the energy of the deformation: cause it is elastic (i e., reversible), energy is stored in the material andcan be regained on unloading Hyperelastic materials can therefore bedescribed by specifying the energy density as a function of strain Thestress in the material can be calculated as the derivative of the energydensity with respect to the strain This description is useful for tworeasons: On the one hand, the energy density in the material can becalculated using methods of thermodynamics, on the other hand, it en-sures that the stored energy does not depend on the material history,but only on the current state of deformation This is necessary becausehyperelastic processes do not dissipate energy; it would be difficult toaccomplish by defining a stress-dependent Young’s modulus

Be-If the cross-linking density of a polymer is increased further, the elastic behaviour vanishes nearly completely because the large number of cross-links prevent the straightening of the molecules For this reason, duromersshow only a small decrease of Young’s modulus with temperature (see fig-ure 8.10(d)) caused by relaxation processes They are energy elastic even abovethe glass temperature

entropy-Table 8.1 lists the magnitude of Young’s modulus for the different polymergroups as a function of their cross-linking density This quantity is normalised

by assigning a value of 1 to diamond in which all atoms contribute to thecross-linking

8.4 Plastic behaviour

Polymer elasticity is determined by the reversible deformation of the chainmolecules as we saw in the previous section Polymers can also deform plas-tically, with chain molecules sliding past each other over large distances as

Table 8.1 Cross-linking density and Young’s modulus of different types of polymers(cf section 1.4.2)

type of material cross-linking density E/GPa

As in the previous section, we start by discussing amorphous tics and afterwards discuss how things change in semi-crystalline thermoplas-tics Elastomers and duromers only allow for a small amount of plastic defor-mation because the cross-links prevent molecule sliding as explained above.Elastomers used above their glass temperature can be deformed with largeelastic strains instead; duromers are brittle, with the covalent bonds betweenthe chain molecules breaking in brittle failure

thermoplas-8.4.1 Amorphous thermoplastics

We start this section by discussing the plastic behaviour of amorphous moplastics The stated temperature regions are, due to the time-dependence

ther-of plastic deformation, valid for rather large strain rates (with testing times

of a few seconds) Increasing the testing time i e., decreasing the strain rate,

is equivalent to increasing the temperature (see section 8.2)

Far below the glass temperature

At temperatures lower than about 80% of the glass temperature Tg, the bondsbetween the molecules are so strong and the specific volume is so small thatchain molecules cannot move by sliding On loading, the molecules are straight-ened viscoelastically If the load is raised further, as sketched in figure 8.12(a),brittle failure ensues, mainly breaking the intermolecular bonds

Slightly below the glass temperature

At temperatures of about 80% of the glass temperature Tg, amorphous moplastics have a limited ductility (see figure 8.12(b)) At these higher temper-atures, the mean distance between the chain molecules is larger and enables

"elastic

ob-a metob-al with ob-an ob-appob-arent yield point (see section 6.4.3) Only if the plob-as-tic strain becomes larger does some hardening occur because the moleculesbecome aligned in the direction of the applied stress

plas-A typical microstructure of an amorphous thermoplastic loaded in tensionslightly below the glass temperature is shown in figure 8.13(a) There are mi-croscopically small, lens-shaped cavities, called crazes They have a thickness

of about 1µm to 10 µm and a diameter of about 10 µm to 1000 µm and arebridged by fibrils The fibrils comprise several chain molecules and have adiameter of approximately 10 nm to 100 nm Their volume fraction within thecraze is between 10% and 50% Although the crazes do look crack-like, thestrength of the material is only slightly reduced in this region compared tothe strength of the undeformed material since the chain molecules within thefibrils are straightened and thus can bear a higher load The thickness of acraze is almost independent of the applied stress, but it increases with increas-ing temperature If the applied stress is large, a large number of small crazesform, if it is small, their number is smaller

Usually, crazes are initiated at surface defects, for example scratches orimpurities Plastic deformation starts in these regions due to the slight stressconcentration caused by these defects Because the material softens as ex-plained above, plastic deformation concentrates in this region, resulting in

a slight local necking This, in turn, causes the stress state to become axial and increases the hydrostatic tension Small cavities with a diameter

tri-of a few nanometres form (figure 8.14) Because tri-of the stress concentration,the material between the cavities is heavily loaded and deforms plastically,

(b) Scaled partial view of the edge of a craze

Fig 8.13 Microstructure of a craze (after [82, 128])

straightening the molecules in this region Fibrils between the cavities emergeand a craze is formed

Despite the load-bearing capacity of the fibrils, there is a stress tion near the edges of a craze, easing its further growth The growth mech-anism is a so-called meniscus instability: Near the edge of the craze, finger-shaped extensions evolve and contract, forming new fibrils (figure 8.15) Fibrilswithin the crazes initially elongate further by drawing other chain moleculesfrom the bulk material Cross-links between the fibrils may form if opposite

A polymer can deform not only by crazing, but also by forming shear bands,created at an angle between 45° and 60° [44, 82, 132] to the loading direction(figure 8.16) Formation of shear bands is especially important under com-pressive loads Within the shear bands, large localised plastic deformations

of 100% or more can occur, whereas the deformation is very small outside ofthem Shear band formation has not been studied as closely as crazing A sim-ple mechanical model is based on the shearing of chain molecules (figure 8.17).The shear stress component causes the chain molecules to either straighten or

to form two kinks, resulting in a region with aligned chain molecules If eral shear bands converge, a crack can be initiated if one shear band reachesthe already straightened molecules Because these cracks are now loaded un-der shear where, according to section 5.1.1, the fracture toughness is larger(KIIc  KIc), the fracture strain is significantly larger than under tensileloading

sev-Several factors determine whether a polymer deforms by shear bands orcrazing The crucial factor is that crazes, which are initiated by cavitation,

can only form under hydrostatic tensile stress.4 The larger the hydrostatictensile stress is, the stronger is the tendency for crazing Figure 8.18 showsthe yield surface of a polymer in plane stress, illustrating this.

The yield strength of polymers generally depends on hydrostatic stressbecause hydrostatic compression decreases the specific volume and thus ham-pers sliding of the molecules This was already discussed phenomenologically

in section 3.3.3 However, the criteria discussed there did not take crazing intoaccount

Apart from the multiaxiality of the stress state, the temperature and theloading time also play a role in determining the deformation mechanism Largestrain rates (and small temperatures) make shear band formation more diffi-cult, thus favouring crazing

4

Even in a uniaxial stress state, there is a hydrostatic stress according to tion (3.25): σ = σ/3

Fig 8.19 Stress-strain curve of an amorphous thermoplastic closely below the glasstemperature (after [9])

Fig 8.20 Configuration of a drawn thermoplastic made

of fibre bundles (after [35])

Close to the glass temperature

If the temperature approaches the glass temperature, the chain molecules come more and more mobile and may rearrange on loading Figure 8.19 showsthe stress-strain curve for this case After the yield strength has been reached,the specimen starts to neck in some region because of local softening as ex-plained in the previous section If deformation continues, more and more chainmolecules are drawn and straightened in parallel The more pronounced thedrawing of the chain molecules is, the more are the covalent bonds loaded,causing a local hardening This eventually overcompensates for the reduction

be-in cross section and forecloses further neckbe-ing be-in this region Instead, the ing region grows until the whole specimen comprises drawn chain molecules

neck-In this process, strains can be as high as 300%

By drawing a thermoplastic, it is thus possible to manufacture a materialwith chain molecules arranged mainly in parallel Figure 8.20 schematicallyshows the structure of such a polymer: The chain molecules are arranged

in bundles, being parallel within them The material deforms by sliding ofthese fibre bundles As the fibre bundles are very long, even a small interfacial

strength between them is sufficient to exploit the strength of the covalentbonds.5 The force on a fibre bundle can become so large that the covalentbonds break The fracture surface splices, exposing the fibre bundles Fibresmanufactured this way have a very large stiffness and strength compared toamorphous thermoplastics.

High-strength polymer fibres with drawn chain molecules can be produced

by spinning Aramid fibres with drawn molecules, for example, can have aYoung’s modulus in fibre direction of up to 450 GPa and an axial tensilestrength of 4700 MPa These fibres are frequently used in composites (seechapter 9)

Above the glass temperature

If the temperature significantly exceeds the glass temperature, the chainmolecules can easily slide past each other because the strong increase in thespecific volume (see section 8.1.2) and the melting of the intermolecular bondsstrongly increases the mobility of the molecules During plastic deformation,thermoplastics behave similar to highly viscous liquids Their strength is there-fore very low

8.4.2 Semi-crystalline thermoplastics

The bond strength between the chain molecules is higher in the crystallineregions of a semi-crystalline thermoplastic than in the amorphous regionsbecause of the smaller bond length This increases Young’s modulus and alsothe strength, even at temperatures above the glass temperature

Plastic deformation starts by lengthening the amorphous regions (seefigure 8.21(b)) At larger strains, the crystalline regions rotate the chainmolecules into the loading direction (figure 8.21(c)) On further deformation,the crystalline regions separate into different blocks (figure 8.21(d) and (e))

In those crystalline regions where the molecules are directed transversely tothe loading direction, the molecules may also rearrange to a vertical orienta-tion, not by rotating block-wise, but by forming new layers in the verticaldirection

One problem of semi-crystalline thermoplastics is that impurities andshort-chained molecules are concentrated in the amorphous regions becausethey are pushed from the crystalline regions on crystallisation The interfacebetween amorphous and crystalline regions is therefore weak and cracks mayinitiate there

Nature frequently uses polymers for load-bearing applications as well(see also section 9.4.4) One particularly interesting example for a bio-logical polymer is the silk of spiders or some insects, for example the

5 This will be explained in detail in section 9.3.2 for the case of fibre composites

F

(c)Rearrangement

of crystallineregions

F

F

(d)Separationinto blocks

F

F

(e) Formation

of microscopicfibres

(microfibrils)Fig 8.21 Stages of plastic deformation of a semi-crystalline thermoplastic (after [44,82])

larvae of the silk moth Bombyx mori [144] Silks are made of proteinfibres, spun to strings with a diameter between about 2µm and 10 µm

in spider silk and 10µm and 50 µm in silk of the silk moth

Proteins are polymers comprising amino acids as monomers (seealso section 9.4.4) Their structure is similar to polyamide (see fig-ure 1.23), with the chain ‘R’ consisting of a carbon atom with a sidegroup 20 different amino acids commonly exist in nature, resulting in

a huge number of possible protein structures In contrast to technicalpolymers, the structure of a protein i e., the sequence of its constitut-ing amino acids, is defined exactly This sequence determines how theprotein molecule folds up to form a three-dimensional structure

Most silks are semi-crystalline polymers Due to the exactly definedthree-dimensional structure, proteins can be aligned exactly in the crys-talline regions, with different side chains precisely interlocking The silk

of the silk moth, for example, contains large regions of two alternatingamino acids, one of them (glycin) with a very small, the other (alanine

or serine) with a slightly larger side group These side groups interlock

as shown in figure 8.22 and thus create crystalline regions with veryhigh strength

Silk properties vary strongly, depending on their structure A singlespider can possess up to seven different types of silks which may be used,for example, as dragline, for orb-spinning, or to encase prey or the eggs

in an egg cocoon Each type of silk is produced by its own silk gland.The mechanical properties of spider dragline silk are especially well-studied, mostly for the common garden spider Araneus diadematus and

A A A A

G G G G A A

A A A A A

Fig 8.22 Crystalline structure of the proteins in the silk of the silk moth The sidegroups of neighbouring molecule chains interlock and cause a high strength In eachprotein, the amino acids glycin and alanine with different side groups alternate Inthe amorphous regions (not shown here), other amino acids are used, inhibiting thiscrystalline structure

the golden silk spider Nephila clavipes Draglines are almost always duced by a spider during moving, serving as a safety rope for the casethat it falls during climbing As the dragline must not break, its frac-ture toughness has to be large The tensile strength of a dragline cantake values of up to 1.1 GPa, approximately one third of that of aramidfibres Their fracture strain is about 30%, much larger than in aramid(with a fracture strain of about 2.7%) Thus, they can absorb largeamounts of energy without breaking Because it is impossible to per-form crack propagation experiments with these microscopic specimens,the fracture toughness is characterised by measuring the energy absorp-tion to fracture This can take values of 1.5 × 108J/m3, more than fourtimes higher than in aramid fibres

pro-Similar silks are also used during orb spinning in those lines that runradially outwards from the centre The circumferential lines, formingthe viscid net for capturing prey, are made from a completely differenttype These have to absorb large amounts of energy to prevent preyhitting the orb from bouncing back and they have to cling to the prey

to retain it To achieve this, their fracture strain is especially large,with values of up to 800% and a tensile strength of about 500 MPa.The energy to fracture can be as high as 109J/m3, larger than in anyother known material

Spider silks are produced in silk glands in which the constitutingproteins are dissolved in water [85] During drawing of the thread, thetensile stress straightens and aligns the molecules although the material

is still dissolved in a liquid Shortly before it leaves the gland, the talline regions are arranged as discussed above and water is removed.Although no chemical reaction occurs at this stage, the silk is not sol-

crys-uble in water after it has left the gland How the spider accomplishesthis is not known To achieve the correct microstructure, it is crucialthat the silk is drawn from the gland because this is required to alignthe molecules Silks cannot be pressed or squirted out of the gland.

The silk of the silk moth has been technically used for thousands

of years Because of their excellent mechanical properties and also cause of their biocompatibility, spider silks are especially attractive formany technical applications, for example for wound dressing, sutures,

be-or in microtechnics Contrary to the larvae of the silk moth, spiders arehighly territorial and have a strong tendency for cannibalism so that it

is impossible to keep many of them in a confined space Nowadays, it

is tried to manufacture spider silk biotechnologically, using bacteria toproduce the silk proteins

8.5 Increasing the thermal stability

The thermal stability of polymers is inferior to that of metals and ceramics.Near the glass temperature, the stiffness and strength of amorphous thermo-plastics strongly decrease Above the glass temperature, viscous flow is thedominant deformation mechanism in amorphous thermoplastics Therefore,amorphous thermoplastics can only be used at service temperatures markedlybelow their glass temperature in load-bearing applications because Young’smodulus strongly decreases before the glass temperature is reached (see fig-ure 8.10(a)) Semi-crystalline polymers can also be used above their glasstemperature Their strength is smaller here than below Tg, but their ductilityincreases Elastomers are always used above the glass temperature, becausethey are rubbery only in this temperature regime Duromers can be used be-low or above the glass temperature, depending on the application Althoughthe stiffness is smaller above the glass temperature, they do not flow viscouslyabove Tg and are thus still serviceable

Due to this temperature dependence, any means of increasing the thermalstability are of extreme importance, especially as they usually also increasethe strength and stiffness One can either increase the glass or, in a semi-crystalline polymer, the melting temperature, or the volume fraction of thecrystalline regions This will be discussed in the following

8.5.1 Increasing the glass and the melting temperature

On reaching the glass temperature, the mobility of the chain molecules comes large enough to allow them to slide past each other, as we saw in sec-tion 8.1.2 Figure 8.4 on page 261 visualises the movement of a chain molecule

be-during sliding It shows that, in the process, the molecule has to move through

an intricately shaped tunnel formed by the surrounding molecules If thismovement can be impeded, the glass temperature will increase

Because of the intricate shape of the tunnel, sliding through it is onlypossible if the chain molecule can rotate One way to reduce the mobility

of the molecules is thus to impede these rotations In principle, the carbon bond can rotate freely (see also section 8.1.1), enabling the molecule totwist slide through the tunnel If the rotation is impeded, sliding is impeded

carbon-as well.6 There are several ways to achieve this If, for example, the simplecarbon-carbon bond is replaced by a more complicated structure with less ro-tatable bonds, the glass temperature increases markedly Among the polymerswith the highest glass temperature are the polyimides (see table 1.3), with amolecular backbone formed not from a single carbon chain, but from a linkbetween a benzene ring, two amide groups, and a carbon chain As the ring-shaped part of the backbone is rigid, a rotation is not possible here, and themobility is strongly reduced The more mobile carbon chains between the ringsserve to reduce the brittleness of the material and improve its processibility

If large side groups are added to the molecule, they can also impede tation On the one hand, these side groups cannot penetrate each other andthus make sliding the molecule through the tunnel formed by the surroundingmolecules more difficult On the other hand, the energy required to rotate theside groups increases with their size (see figure 8.1) because the side groups on

ro-a single molecule interfere with ero-ach other due to their spro-atiro-al extension ro-andtheir electrostatic repulsion.7 The glass temperature thus increases with thesize of the side groups If we compare the glass temperature of polyethylene(−110℃ −20℃) without side groups, polypropylene (−20℃ 0℃) with

a simple methyl group, and polystyrene (100℃), we immediately see how thesize of the side group influences the glass temperature

If the side chains are long and flexible, they may also decrease the glasstemperature On the one hand, the number of freely movable chain endsincreases and thus causes an effect similar to a reduction in the chainlength (see section 8.1.3), on the other hand, the side groups tend toincrease the distance between the chain molecules and thus reduce thebond strength If the chains become very long, the glass temperaturerises again because the side chains can be arranged regularly, similar

Fig 8.23 Spatial structure of a ptfe chain molecule The strong repulsion betweenthe fluorine atoms results in a twisted and rigid molecule

126℃ The large electron affinity of fluorine causes the fluorine atoms to bepartially negatively charged They thus repel each other and cause a twist

in the molecule to maximise the distance between them (figure 8.23) In arotation of the chain, the charged atoms approach each other and thus needadditional energy, resulting in an increase in the glass temperature

Furthermore, the glass temperature is affected by the bond strength tween the chain molecules To increase the glass temperature, the bonds can

be-be made stronger This can be-be achieved, for example, by adding polar sidegroups which can form stronger dipole bonds between the molecules This isthe reason why the glass temperature of polyvinyl chloride is larger than that

of polyethylene Replacing a single hydrogen atom by chlorine increases theglass temperature from between −110℃ and −20℃ to approximately +80℃.This is due to the dipole bond being much stronger than the van der Waalsbond as explained in chapter 1

Because the electron affinity of fluorine is even larger than that of chlorineand because each monomer of ptfe contains four fluorine atoms, it might besurmised that the glass temperature of ptfe is much larger than that of pvc.This, however, is not the case because the dipole bonds in pvc are in factstronger than those in ptfe One reason for this is that the dipole moments

of neighbouring regions of ptfe cancel each other due to the spatial structure

of the molecule (see figure 8.23) which possesses only negative charges on theoutside Furthermore, fluorine is a much smaller atom than chlorine, resulting

in a shorter bond length between carbon and fluorine The strength of adipole is directly proportional to its length, giving the carbon bond withthe chlorine atom a larger dipole moment Altogether, ptfe behaves like anonpolar molecule, making it suitable for low-adhesion coatings

Hydrogen bonds can also strongly bond the molecules in a polymer Oneexample is polyamide (see table 1.3) which contains hydrogen bonds formed

by the hydrogen atoms of the amino groups of neighbouring molecules.All methods discusses so far can also serve to increase the melting temper-ature in a semi-crystalline polymer However, to achieve a high crystallinity,the chain molecules must be sufficiently mobile to allow them to arrange in

an ordered alignment Stiffening the molecules therefore may decrease thecrystallinity A further problem is that a polymer made of stiff molecules has

a large viscosity at high temperatures, making manufacturing processes likeinjection moulding more difficult

8.5.2 Increasing the crystallinity

The strength of semi-crystalline polymers is larger than that of amorphouspolymers If the crystallinity of a polymer can be increased, the mechanicalproperties are improved accordingly

The crystallinity of a polymer can be changed by the manufacturing cess and by the structure of the chain molecules Upon cooling from the melt,crystalline regions can only form if there is sufficient time to arrange themolecules in the energetically favourable more densely packed crystal struc-ture Crystallinity is thus a function of the cooling speed If this speed is toohigh, the polymer is purely amorphous This is analogous to the production

pro-of glasses or to precipitation and transformation processes (see section 6.4.4).The crystallinity can also be increased by orienting the chain moleculesunder mechanical loads This was already discussed in section 8.4.1 for theplastic deformation of an amorphous thermoplastic close to the glass tem-perature By applying a tensile load, the fibres are drawn and straightened,forming crystalline fibres bundles

The size of the side chains and thus the mobility of the chain moleculesalso influences the crystallinity The more immobile the molecules are, themore difficult it is to arrange them in a closely packed and regular manner.For this reason, polyethylene is well-suited to form high-strength fibresbecause the polymer chain is very mobile due to its simple structure andcan be easily drawn in fibre direction Depending on the straightening ofthe molecules, Young’s modulus can reach values of up to 200 GPa [107] Intechnically used fibres, values between 62 GPa and 175 GPa are characteristic(see also table 9.1) These are rather high values, especially so if the lowdensity of slightly less than 1 g/cm3 is taken into account They are due tothe covalent carbon bonds along the backbone

Polymers with stiff chain molecules usually have a lower crystallinity thanthose made of mobile chains Exceptions from this rule do occur, however:Due to its very stiff and straight chain molecules, ptfe can reach crystallinityvalues of up to 90% This is only possible if the cooling speed is very low; intechnical applications, the crystallinity is therefore usually less

The molecules can also be oriented during cooling from the melt by ing the melt with high speeds because this will also align the molecules Thishas to be kept in mind when designing polymer components manufactured

shear-by injection moulding to avoid a strong fluctuation of the crystallinity in thefinal component

Aramid is one example for a polymer that can be manufactured with highcrystallinity in this way This is mainly used to produce aramid fibres Due tothe aromatic rings on the backbone (see figure 1.23), the molecule is extremelystiff It thus does not fold up, but usually exists in rod-like form (similar toptfe) Well above the melting temperature, these rods are disordered in the

(a) Isotactic; all side groups are positioned on the same side

(b) Syndiotactic; the side group positions alternate

(c) Atactic; random positions of the side groups

Fig 8.24 Configuration of side groups in polyvinyl chloride (pvc)

melt If the temperature falls below a certain ordering temperature (which islarger than Tm), the molecules start to align themselves in parallel becausethis increases their binding energy They now possess a preferential orientation,although their positions are still unordered.8If fibres are drawn from the melt,the molecules in the fibres orient themselves in the drawing direction.9Especially important in determining the crystallinity of a polymer is thetacticity, the way the side groups of the monomers are arranged within thechain We distinguish the isotactic arrangement (figure 8.24(a)), in which allside groups are regularly arranged on one side of the chain molecule, thesyndiotactic arrangement with alternating side groups (figure 8.24(b)), andthe irregular atactic arrangement with random orientation of the side groups(figure 8.24(c)) The more regular the arrangement of the side groups is, theeasier it is to arrange the chain molecules in a crystalline structure If thestructure is the same otherwise, isotactic polymers thus have the largest, atac-

8

In this state, the molecules thus form a liquid crystal Liquid crystals are terised by molecules that have a preferential orientation but unordered positionslike the molecules of a liquid

charac-9 This is similar to the drawing of silk, see page 281

(a) Linear (b) Branched

Fig 8.25 Linear and branched chain molecules Side chains impede the formation

of crystalline structures

tic polymers the lowest crystallinity The isotactic structure is also superior tothe syndiotactic because the latter can only be crystalline if the side groupsmatch and interlock exactly

Although thermoplastics comprise un-linked chain molecules, they can ertheless have a branched structure In contrast to elastomers and duromers,these branches do not cause cross-linking between the chains, but they caninhibit a geometrically dense packing necessary to form crystalline regions.This is sketched in figure 8.25

nev-8.6 Increasing strength and stiffness

The most important methods to increase the strength or stiffness of a polymerare a direct consequence from what we saw in the previous section They are:

• Increasing the bond strength, for example by adding polar side groups(section 8.5.1),

• impeding the sliding of the chains, for example by adding large side groups

or by stiffening the chain molecule (section 8.5.1),

• increasing the crystallinity, for example during manufacturing or by usingisotactic structures (section 8.5.2),

• orienting the chain molecules in load direction (section 8.4.1)

Table 8.2 contains a survey of the mechanical properties of different polymers.The effect of the different mechanisms to increase strength or stiffness can

be clearly seen from the table Low-density polyethylene (ldpe), containingbranched polymer chains and thus possessing a low crystallinity of about 45%,has the lowest Young’s modulus and the lowest tensile strength because itconsists only of simple and mobile molecules with weak intermolecular bonds.Increasing the crystallinity to 75% and thus the density (creating high-densitypolyethylene, hdpe), markedly improves the properties because the largercrystallinity strongly increases the number and strength of the intermolecularbonds If side groups are added, as it is done in polypropylene and polyvinylchloride, the mechanical properties improve accordingly as already discussed