Fundamentals of Polymer Engineering Part 12 pptx

For cules, polymer mobility exists only above the glass transition temperature, andbecause the energetics are favorable only below the melting point, crystallizationcan take place only i

inFigure 11.1; the decrease in free energy with increasing temperature for bothphases is due to the relative increase in the temperature–entropy term The point

of intersection of the two curves is the equilibrium melting point T0

M, whereas thevertical difference between them represents the free-energy change,DGv, betweenthe two states at any temperature Note that many materials (such as iron) exhibitpolymorphism; that is, they exist in more than one crystalline form In such acase, each form has its own G versus temperature curve

Long-chain molecules can also crystallize, and they do so for the sameenergetic reasons as short-chain molecules However, for a polymer to becrystallizable, its chemical structure should be regular enough that the polymermolecule can arrange itself into a crystal lattice Thus, isotactic and syndiotacticpolypropylenes crystallize easily, but atactic polypropylene does not For thesame reason, the presence of bulky side groups (as in polystyrene) hinderscrystallization, but the possibility of hydrogen-bonding (as in polyamides)

437

promotes the process.Figure 11.2shows a schematic representation of nylon 66[1] A unit cell contains a total of one chemical repeat unit, and the molecules are

in the fully extended zigzag conformation The polymer chain direction isgenerally labeled the c axis of the cell The cell itself is triclinic, which meansthat magnitudes of the three axes and the three interaxial angles are all different

A sketch of the unit cell is shown in Figure 11.3, in which arrows are used todesignate hydrogen bonds Whether a crystallizable polymer actually crystallizes

or not, though, depends on the thermal history of the sample For cules, polymer mobility exists only above the glass transition temperature, andbecause the energetics are favorable only below the melting point, crystallizationcan take place only in a temperature range between Tm0 and Tg However,crystallization is not an instantaneous process; it takes place by nucleation andgrowth, and these steps take time If the rate of cooling from the melt is rapidenough, a completely amorphous polymer can result This is shown schematically

macromole-in Figure 11.4, which is a continuous-cooling transformation curve [2] If thecooling rate is such that we can go from T0

mto Tgwithout intersecting the curvelabeled ‘‘crystallization begins in quiescent melts,’’ no crystallization takes place.Therefore, it is possible to obtain completely amorphous samples of a slowlycrystallizing polymer such as polyethylene terephthalate, but it is not possible for

a rapidly crystallizing polymer such as polyethylene In addition to temperature,the extent of crystallization also depends on factors such as the applied stressduring processing, which tends to align polymer chains in the stress direction.This can alter the energetics of phase change and can lead to a very significantenhancement of the rate of crystallization The phenomenon can be understood as

a shift to the left in Figure 11.4, from the curve indicating the onset of quiescentcrystallization to the curve labeled ‘‘crystallization begins in stretched melts.’’Because polymers are rarely completely crystalline, they are called semicrystal-line

FIGURE11.1 Variation with temperature of the Gibbs free energy per unit volume

FIGURE11.2 Schematic representation of nylon 66 (From Ref 1.)

FIGURE11.3 Perspective drawing of a unit cell of nylon 66 The viewpoint is 11 A˚ up,

10 A˚ to the right, and 40 A˚ back from the lower left corner of the cell (From Ref 1.)

Crystallizable polymers that dissolve in a solvent can also be made tocrystallize from solution When this is done using dilute solutions, single crystalscan be obtained [3] The crystals can have a large degree of perfection and areusually in the form of lamellae or platelets having thickness of the order of 100 A˚and lateral dimensions of the order of microns The observed thickness depends

on the temperature of crystallization As shown in Figure 11.5, a single lamella iscomposed of chain-folded polymer molecules Lamellae of different polymershave been observed in the form of hollow pyramids and hexagonal structures.When crystallized from quiescent melts, though, spherical structures calledspherulites are observed These spheres, which can grow to a few hundredmicrons in diameter, are made up of lamellae that arrange themselves along the

FIGURE11.4 Schematic illustration of the concept of a ‘‘continuous-cooling formation curve’’ showing the anticipated effect of stress in shifting such curves (FromRef 2.)

trans-FIGURE11.5 A chain-folded crystal lamella

radial direction in the sphere, as shown in Figure 11.6 The interlamellar regions

as well as the region between spherulites are composed of amorphous ornoncrystallizable fractions of the polymer When crystallization takes placefrom a strained (deforming) solution or strained melt, the crystal shape canchange to that of a shish kebab in the former case and to a row-nucleated crystal

in the latter case; these are shown in Figure 11.7 [4] The chain orientation insolution initially results in the formation of extended chain crystals, which giverise to the central core or ‘‘shish’’; the ‘‘kebabs,’’ which are lamellar, then growradially outward from the shish If the polymer sample is polydisperse, the higher-molecular-weight fraction crystallizes first, and this results in fractionation.From this discussion, it should be clear that a solid semicrystalline polymer

is a two-phase structure consisting essentially of an amorphous phase with a

FIGURE11.6 Schematic diagram of a spherulite Each ray is a lamella

FIGURE11.7 Oriented morphologies appearing in polyethylene (Reprinted fromGedde, U W., Polymer Physics, Figure 7.38, copyright 1995, Chapman and Hall Withkind permission of Kluwer Academic.)

dispersed crystalline phase Each phase is characterized by different values of agiven physical property The density of the crystals, for instance, is always greaterthan that of the amorphous polymer Furthermore, process conditions determinethe volume fraction of crystals, their shape, size, and size distribution, theorientation of polymer chains within the two phases, and how the crystallineregions are connected to the amorphous regions Thus, whereas the properties of

an amorphous polymer can be described as glassy or rubbery (depending onwhether the temperature of measurement is below or above the glass transitiontemperature), the behavior of a semicrystalline polymer is much more compli-cated and is often anisotropic: If polymer chains are aligned in a particulardirection, the material will be very strong in that direction but weak in a directionperpendicular to it However, one of the two phases may be dominant in terms ofinfluencing a particular overall property of the polymer Thus, regarding mechan-ical properties, we find that increasing the spherulite size results in a decrease inthe impact strength, an increase in the yield stress, and a reduction in theelongation to break in a tensile experiment while the Young’s modulus goesthrough a maximum [5] The solubility of a molecule in a polymer and also itsdiffusivity, though, are determined by the amorphous phase As a consequence,the permeability, which is a product of these two quantities, decreases as theextent of crystallinity increases The breakdown of electrical insulation, on theother hand, depends on the properties of the interspherulitic region in the polymer[6] Other factors that are influenced by the structure include brittleness,environmental degradation, thermal properties, melting point, and glass transitiontemperature If the solid structure that is formed is a nonequilibrium one, it canchange later if conditions (especially temperature) are such that equilibrium can

be approached Thus, a polymer sample whose chains have been frozen in anextended position can shrink when chain alignment is lost on heating to atemperature above the glass transition temperature

Although some of the influence of structure on properties can be lized by thinking of crystallites either as filler particles in an amorphous matrix or

rationa-as permanent cross-links (rationa-as in vulcanized rubber), a proper understanding ofstructure development during processing is necessary to satisfy intellectualcuriosity and to utilize crystallization knowledge for economic gain As aresult, we need to know what structure arises from a given set of processingconditions, how we can characterize (or measure) this structure, and how it affects

a property of interest It is, of course, much more difficult to reverse the process

of thinking and inquire how we might obtain a particular structure in order to getspecified values of properties of interest This is the realm of engineered materialproperties and the subject of research of many industrial research laboratories.Before tackling greater problems, though, we must first get acquainted with somerather fundamental concepts

11.2 ENERGETICS OF PHASE CHANGE

If the temperature of a liquid is lowered to below the melting point, material tends

to solidify As mentioned previously, the process is neither sudden nor neous Indeed, it proceeds relatively slowly and on a small scale if the temperature

instanta-is only slightly below the melting point, and it involves two dinstanta-istinct steps.Initially, nuclei of the new phase must be formed, and the ease with which thishappens depends on the extent of supercooling This step is followed by growth

of the nuclei, a procedure that involves diffusion of material to the phaseboundary The combined process of nucleation and growth is the same regardless

of whether the crystallization behavior being observed is that of molten metals ormolten polymers

11.2.1 Homogeneous Nucleation

To understand the thermodynamics of nucleation, let us first consider geneous nucleation, also called sporadic nucleation, from an isothermal, quies-cent melt whose temperature T is kept below the melting point Tm0 Here,

homo-‘‘homogeneous’’ refers to the appearance of the new solid phase in the middle

of the old liquid phase

Based onFigure 11.1, we would expect nucleation to be accompanied by areduction in the Gibbs free energy equal to DGv per unit volume However, thesystem free energy is not reduced by the full amount of DGv This is becausesurface energy equal to g per unit area has to be expended in creating the surfacethat bounds the nuclei Thus, if the typical nucleus is a sphere of radius r, the netchange in the free energy due to the formation of this particle is

If we set the derivative ofDG with respect to r equal to zero, then using

Eq (11.2.1) we find that r*, the value of r corresponding to DG*, is

Because the magnitude ofDGv increases as the temperature is lowered, both r*and DG* decrease with decreasing temperature This variation can be madeexplicit by noting that, at the melting point,

ð11:2:5ÞNow,DSvand DHvdepend only weakly on temperature, so that

DGv¼ DHv 1
T

T0 m

ð11:2:6Þwhich, when introduced into Eqs (11.2.2) and (11.2.3), gives

r* ¼
2gT

0 m

DG* ¼16pg3ðTm0Þ2

3DH2

whereDT equals the amount of subcooling (T0

m
T) and DHvis physically thelatent heat of crystallization per unit volume and is a negative quantity Clearly,lower temperatures favor the process of nucleation, asDG* decreases rapidly withdecreasing temperature

Example 11.1: For a polyolefin it is found thatDHv¼
3  109ergs=cm3

and

g ¼ 90 ergs=cm2

If the equilibrium melting point is 145C, how do the radius r*

of a critical-sized nucleus and the associated energy changeDG* depend on theextent of subcooling, DT?

Solution: Using Eq (11.2.7), we find that

homogeneous nucleation to overall crystal growth is small compared to that ofheterogeneous or predetermined nucleation, unless the temperature is signifi-cantly below the melting point In the case of heterogeneous nucleation, crystalgrowth takes place on a pre-existing surface, which might be a dust particle, animpurity, part of the surface of the container, or an incompletely melted crystal If

we consider heterogeneous nucleation to take place on the surface of a existing lamella, as shown in Figure 11.8 [7], we discover that if the crystalvolume increases by an amount nabl, where abl is the volume of a single strand,the surface area increases by only 2bðl þ naÞ Had we considered primarynucleation, the surface area would have gone up by 2bðl þ naÞ þ 2nal Notethat due to chain folding, ge, the surface energy associated with the chain endscan be expected to be large compared to g, the surface energy of the lateralsurface

pre-In view of the foregoing, the free-energy change due to the deposition of npolymer strands is

and the free-energy change involved in laying down the (n þ 1)st strand isobtained from Eq (11.2.9) as

Clearly, for this process to be energetically favorable, the right-hand side of

Eq (11.2.10) has to be negative This condition requires that [8]

l>
2ge

FIGURE11.8 Crystal growth on a pre-existing surface

which, in view of Eq (11.2.6), implies that

with

l* ¼
2geT

0 m

and we find that, just as with r*, l* depends inversely onDT This is found to betrue experimentally Also, to a good approximation,

Example 11.2: Use the data given in Example 11.1 to confirm the validity of

Eq (11.2.15) DetermineDG* for DT ¼ 10 K and compare this value with that inExample 11.1 Assume that ge g

Solution: As ge g, l* ¼ r* ¼ 250:8 A˚ Because a cannot be more than a fewangstroms, a  l* and we can neglect the last term on the right-hand side of Eq.(11.2.13) in comparison with the first term The second term in Eq (11.2.13) canalso be neglected, provided that the following holds:

aDGv 2g

or

aDHvDT

2gT0 m

 1Introducing numbers, aDHvDT=2gT0

m¼ að3  109 10Þ=ð2  90  418Þ ¼3:98  105a, which is much less than unity because a< 10
7cm Consequently,DG* ¼ 2bl*g ¼ 4bggeT0

m=DHvDT / 1=DT For homogeneous nucleation, DG*

is equal to 2:37  10
9ergs For heterogeneous nucleation, DG* ¼4:51b  10
4ergs Because b< 10
7cm, the energy barrier for heterogeneousnucleation is much smaller than that for homogeneous nucleation when thetemperature is close to the equilibrium melting point

11.3 OVERALL CRYSTALLIZATION RATE

Even when a phase transformation is thermodynamically possible, the rate atwhich it happens is controlled by the existence of any barriers retarding anapproach to equilibrium; the activation energy DG* calculated in the previoussection represents just such a barrier for crystallization The probability that agroup of molecules has an energy DG* greater than the average energy at aspecified temperature T is given by the Boltzmann relation

Probability / exp
DG*

kT

ð11:3:1Þwhich, when applied to the process of nucleation, means that if the total number

of solid particles at any instant is N0, the number N * that actually possess theexcess energyDG* is given by

N * ¼ N0exp
DG*

kT

ð11:3:2ÞNuclei form by the addition of molecules; this is a process of diffusion for whichthe following relation holds:

Rate / exp
ED

kT

ð11:3:3Þwhere EDis the activation energy for diffusion A combination of Eqs (11.3.2)and (11.3.3) then implies that the rate of nucleation _NN in units of nuclei per unittime is given by [9]

be proportional to some product of _NN and n Thus,

ED

where c1 is a constant with units of energy per mole, and c2 is a constant withunits of temperature Also, if Eq (11.2.15) is used for DG*, we have

FIGURE11.9 Qualitative temperature dependence of the linear growth rate G

Solution: Taking the natural logarithm of both sides of Eq (11.3.9) andrearranging gives

ln G þ c1

RðT
T1Þ¼ ln G0
A

TDTand a plot of the left-hand side of this equation versus 1=TDT should be a straightline This is, indeed, found to be the case when known values of 365 K and503.8 K are used for Tg and T0

m, respectively, and c1and c2 are considered to beadjustable parameters The final result is

ln G ¼ 15:11
2073

T
290
9:25  104

T ð503:8
TÞThis equation is plotted (on linear coordinates) in Figure 11.10 and givesexcellent agreement with experimental growth rates

In closing this section, we note that the size of spherulites is large whencrystallization takes place near the melting point This is because few nuclei areformed due to the large value ofDG* However, once formed, nuclei grow easily

By contrast, when crystallization occurs near the glass transition temperature, alarge number of small spherulites are observed; here, nuclei are formed readily,but they do not grow because the rate of diffusion is low A common technique of

FIGURE11.10 Comparison of experimentally determined growth rates of spherulites

of i-polystyrene with (d) experimental (—) theoretical values (From J Polym Sci Polym.Phys Ed., 21, Kennedy, M A., G Turturro, G R Brown, and L E St.-Pierre: Retardation

of spherulitic growth rate in the crystallization of isotatic polystyrene due to the presence

of a nucleant, Copyright#1983 by John Wiley & Sons, Inc Reprinted by permission ofJohn Wiley & Sons, Inc.)

increasing the rate of crystallization is to intentionally add a fine powder such assilica or titanium dioxide to act as a nucleating agent.

11.4 EMPIRICAL RATE EXPRESSIONS: THE

AVRAMI EQUATION

Equation (11.3.9) and its derivation are very useful in understanding how crystalsnucleate and grow in a stagnant melt However, the knowledge gained does notpermit us to predict, a priori, the time dependence of the extent of crystallinityand the size distribution of spherulites in a polymer sample kept at a specifiedtemperature between Tg and T0

m This information about the microstructure iscrucial if we want to know in advance the mechanical properties likely to beobserved in plastic parts produced by methods such as injection molding (see

Chapter 15 for a description of the process) Because some of the very volume polymers such as polyethylene, polypropylene, and various nylons areinjection molded, the question of the microstructure of semicrystalline polymershas received a considerable amount of attention [12] This has led to theformulation of empirical expressions based on the theory originally developed

large-by Avrami [13–15], Johnson and Mehl [16] and Evans [17] to explain thesolidification behavior of crystallizable metals

11.4.1 Isothermal Quiescent Crystallization

If we consider the isothermal crystallization of a quiescent polymer melt—whether by homogeneous or heterogeneous nucleation—then at time t, thevolume of a spherulite that was nucleated at time t ðt< tÞ will be Vðt; tÞ As aconsequence, the weight fraction, X0, of material transformed will be as follows[18]:

X0ðtÞ ¼

ðt 0

In order to make further progress, it is necessary to specify the time dependence

of V and _NN This is done by appealing to observed crystallization behavior It isnow well established that, under isothermal conditions, the radius of a spheruliteincreases linearly with time [see also Eq (11.3.9)], with the following result:

V ðt; tÞ ¼4

3pG

where G is the constant time rate of change of the spherulite radius

For sporadic or homogeneous nucleation, _NN ðtÞ is usually a constant, and acombination of Eqs (11.4.3) and (11.4.4) yields

The corresponding result for the mass fraction crystallinity is given by

dX

where dX is the actual amount of material transformed in time dt and dX0is theamount of material that would be transformed in the same time interval in theabsence of impingement This equation simply expresses the fact that the effect ofimpingement is small when the amount of crystallization is small, and the rate ofcrystallization must decrease to zero as X tends to unity

Equation (11.4.7) is easily integrated because X0 is given either by

Eq (11.4.5) or Eq (11.4.6) For homogeneous nucleation the result is

which is known as the Avrami equation All of the temperature dependence isembodied in the rate constant k, whereas the Avrami exponent, n, is usuallyconsidered to be the sum p þ q, with p being 0 or 1 depending on predetermined

or sporadic nucleation and q being 1, 2, or 3 depending on the dimensionality ofcrystal growth Thus, n would equal 3 for the growth of disklike crystals byhomogeneous nucleation but would only be 2 if the nucleation were hetero-geneous

For most polymers, crystallinity is never complete and Eq (11.4.10) ismodified by defining an effective fraction of transformed material X=X1, where

X1is the mass fraction crystallized at the end of the transformation The result ofthis modification is given as follows [20]:

1
X

X1¼ exp
k

X1tn

ð11:4:11Þor

a certain induction time is needed before crystallization commences and that X1the ultimate crystallinity at very long times depends on the temperature ofcrystallization

When the data of Figure 11.11 are plotted on logarithmic coordinates, assuggested by Eq (11.4.12), a set of parallel lines is obtained, shown in Figure

11.12 The slope of each of the lines is approximately 3, suggesting geneous nucleation and three-dimensional spherulitic growth Note, though, that

hetero-in the latter stages of crystallization, growth slows and the Avrami expression isnot obeyed This phase of crystallization is called secondary crystallization, and

it is characterized by the thickening of crystal lamellae and an increase in crystalperfection rather than an increase in spherulite radius

Example 11.4: It is often found (see Fig 11.13) that primary isothermalcrystallization data at various temperatures superpose when X=X1 is plotted as

a function of t=t1 =2, where t1 =2 is the time for the percent crystallinity to reach50% of the final value [22] If the Avrami theory is valid, how is kðT Þ related to

t1 =2?

Solution: Allowing X=X1to equal 0.5 in Eq (11.4.12) gives

ln 0:5 ¼
ktn

=2or

kðT Þ ¼ln 2

tn

1 =2Although the Avrami equation is obeyed exactly by a large number ofpolymers, noninteger values of the exponent n are often observed [23] Also notethat, for heterogeneous crystallization, the constant k in Eq (11.4.12) is related tothe linear growth rate G of Eq (11.3.6) as

Reprinted from Polymer, vol 27, Cebe, P., and S D Hong: ‘‘Crystallization Behaviour ofPoly(ether-ether-ketone),’’ pp 1183–1192, Copyright 1986, with kind permission fromElsevier Science Ltd., The Boulevard, Langford Lane, Kidlington OX5 1GB, UK

according to the original theory of Hoffman and Lauritzen [7], along withsupporting experimental data, may be found in the book by Gedde [4], whoalso discusses some of the more recent theoretical developments.

11.4.2 Nonisothermal Quiescent Crystallization

During the processing of any crystallizable polymer, crystallization never occurs

at a fixed, constant temperature Instead, the polymer cools from the molten state

to the solid state at some rate that is determined by the processing conditions, and

FIGURE11.12 Avrami plot of the data shown in Figure 11.11 Plot oflogf
ln½1
XcðtÞ=Xcð1Þg versus time for isothermal crystallization at 315C (u),

312C (s), 308C (n), 164C (j), and 160C (d) (From Ref 21.)

Reprinted from Polymer, vol 27, Cebe, P., and S D Hong: ‘‘Crystallization Behaviour ofPoly(ether-ether-ketone),’’ pp 1183–1192, Copyright 1986, with kind permission fromElsevier Science Ltd., The Boulevard, Langford Lane, Kidlington OX5 1GB, UK

the structure that results is due to crystallization that takes place over the entiretemperature range between the melting point and the glass transition temperature.

In principle, the final crystallinity at the end of the cooling process can again becalculated by combining Eqs (11.4.3) and (11.4.7), with the result that

X ¼ 1
exp
rs

rL

ðt 0

Crys-T Amano: Some aspects of nonisothermal crystallization of polymers: II Consideration ofthe isokinetic condition, Copyright # 1973 by John Wiley & Sons, Inc Reprinted bypermission of John Wiley & Sons, Inc

Now, G and _NN are no longer constants They may, however, be evaluated from aknowledge of the temperature dependence of the isothermal rate constants [24]._NNðtÞ ¼ðt

0

d _NdT

dTds

drds

dGdT

 dTdt

 

Insertion of these expressions into Eq (11.4.14) then makes it possible tocompute X ðtÞ However, it is obvious that an analytical result cannot be obtainedunless gross assumptions are made One such assumption involves allowing theratio _N=G to be constant, independent of temperature, resulting in an isokineticprocess [25] This is justified based on the fact that the shapes of both functionsare similar when they are plotted in terms of temperature [see Eqs (11.3.4) and(11.3.6)] A consequence of this assumption, as demonstrated by Nakamura andco-workers [22, 26] is that Eq (11.4.12), the Avrami equation, is modified to

ð11:4:19Þwhere

and n is the Avrami exponent determined from data on isothermal crystallization

It has been shown that the modified Avrami equation represents the mal crystallization behavior of high-density polyethylene very well [22]

nonisother-11.5 POLYMER CRYSTALLIZATION IN BLENDS

AND COMPOSITES

As discussed in Section 9.6 ofChapter 9, polymers are blended together with theexpectation of obtaining a material having enhanced thermal, mechanical, orsolvent-resistance properties relative to the blend constituents If one of thecomponents is crystallizable, the presence of the other component can influencethe nature, rate, extent, and temperature range of crystallization If the twopolymers are immiscible, crystallization may occur in the domain of one polymerunaffected by the presence of the other polymer, or the other polymer may act as a

nucleating agent, depending on which component solidifies first However, themore interesting situation, from a theoretical viewpoint, is one in which thepolymers are thermodynamically compatible and only one component is crystal-lizable An example is the blending of PEEK with poly(etherimide) (PEI), anamorphous polymer with a high thermal resistance (Tg 215C) The amor-phous polymer acts as a diluent for the crystallizable polymer, and the result is alowering of the equilibrium melting point; this effect is similar to the depression

in freezing point (see Sect 8.3 of Chap 8) of a liquid upon addition of anonvolatile solute If we use the Flory–Huggins theory developed in Section 9.3

of Chapter 9, it is possible to show the following [27]:

1

Tm
1

T0 m

A further effect of polymer blending is that the blend’s glass transitiontemperature is bounded by the glass transition temperatures of the blendconstituents; this intermediate value is given by Eq (9.6.1) of Chapter 9 Thus,because crystallization takes place only in a temperature range between Tmand

Tg, the addition of high-Tg amorphous diluent can serve to significantly contractthe range of available crystallization temperatures

Example 11.5: Estimate the lowering in melting point and the elevation in theglass transition temperature of PVF2 (T0

m¼ 170:6C, Tg ¼
50C) when it ismixed with PMMA (Tg ¼ 90C) such that the blend contains 60% by weight ofPVF2 According to Nishi and Wang [27], v1¼ 84:9 cm3=mol,

v2¼ 36:4 cm3=mol, DH2¼ 1:6 kcal=mol, and w12¼
0:295

Solution: Using Eq (11.5.1) gives

Tm¼ 438:7 K

ðT0

m
TmÞ ¼ 4:89 KUsing Eq (9.6.1) again gives

1

Tg¼ 0:4

363þ0:6223

or Tg ¼ 263:7 K, and Tg increases by 40.7 K

When a polymer crystallizes in the presence of a noncrystallizablecomponent, the crystal growth rates can be significantly affected due to theinevitable rejection of the noncrystallizable material from the growing crystal.This effect becomes increasingly important at large undercoolings, where growthrates are dominated by diffusion Thus, the maximum isothermal radial growthrate of isotactic polystyrene falls by almost a third on adding a 15% atacticpolymer [28] In this situation, the spherulite radius still increases linearly withtime because the mixture composition at the crystal growth front remainsunchanged as crystallization proceeds However, if the rejected polymer diffusesmore rapidly than the rate at which spherulites grow, the concentration of diluent

at the growth front can increase sufficiently, to further reduce the rate ofcrystallization and make the spherulite radius change nonlinearly with time Anadditional significant reduction in the growth rate can occur if the change in meltcomposition is accompanied by an increase in melt viscosity This is especiallyimportant when the two components have widely separated glass transitiontemperatures Furthermore, these kinetic effects can be accompanied by changes

in crystal morphology, depending on where the amorphous polymer segregatesitself [29] Additionally, when crystallization takes place in the presence ofcooling, the solidified blend may have very low levels of crystallinity due to all ofthe effects mentioned Nadkarni and Jog [30] have summarized the crystallizationbehavior of commonly encountered crystalline=amorphous as well as crystal-line=crystalline polymer blend systems

An important effect that is observed during the melt processing of blends ofcondensation polymers, such as two polyamides or two polyesters, is theoccurrence of interchange reactions [31] The result of these transamidation ortransesterification reactions is the formation of a block copolymer Initially, adiblock copolymer is produced, but, with increasing processing time, this givesway to blocks of progressively smaller size; ultimately, a random copolymerresults This ‘‘processing’’ route to the synthesis of copolymers is often simplerand more economical than making the copolymers in a chemical reactor, and

‘‘reactive extrusion’’ is a major industry today [32] If one homopolymer is

semicrystalline and the other amorphous, noncrystallizable sequences will bebuilt in between the crystallizable sequences of the semicrystalline polymer Thishas a profound effect on the crystallization behavior of the semicrystallinepolymer [33] In particular, there is a reduction in the melting point of thecrystals and a change in the glass transition temperature; the Tg of the resultingrandom copolymer can be estimated using Eq (9.6.1) of Chapter 9 that wasearlier shown to be valid for miscible polymer blends There is also a decreaseboth in the crystallization rate and the total crystallinity of the blend, as comparedwith the crystallizable homopolymer.

In order to modify polymer properties, we commonly add fillers andreinforcements to plastics The dimensions of these additives are usually nosmaller than a few microns, and the fillers influence the behavior of crystallizablepolymers only to the extent that they provide sites for nucleation; polymermorphology is generally not affected In the recent past, though, it has becomepossible to add solids whose smallest dimension is of the order of 1 nm (10 A˚ ).These materials are called nanomers, and the mixture is known as a nanocompo-site [34] The most extensively researched filler is montmorillonite (MMT), a claythat is a layered silicate made up of platelets or sheets that are each about 1 nmthick and which have an aspect ratio ranging from 100 to 300 MMT has a largesurface area of about 750 m2=g, and the addition of just 1 wt% of well-dispersedclay to a polymer such as nylon 6 results in very significant property improve-ments: The Young’s modulus, dimensional stability, heat-distortion temperature,solvent resistance, and flame resistance all increase The extent of increase iswhat might normally be expected on adding more than 10 wt% glass fibers, say.Also, there is a reduction in gas and moisture permeability, and all this happenswithout loss of any other property of interest Not surprisingly, nanocompositesare being researched for a wide variety of applications, including the originalautomotive applications In terms of the crystallization behavior of polymerscontaining nanofillers, it has been found that the presence of silicate layersenhances the rate of isothermal crystallization [35]; this is not surprising becausethe clay platelets act as nucleating agents What is surprising, though, is that forpolymers such as polypropylene and nylon 6, the polymer morphology changesfrom spherulitic, in the absence of MMT, to fibrillar, in the presence of MMT—the fibrous structures grow in both length and diameter as crystallizationproceeds Also, crystallization can occur at high temperatures where the neatpolymers do not crystallize [35]

11.6 MELTING OF CRYSTALS

When the temperature of a polymeric crystal is raised above the glass transitiontemperature, it can begin to melt This process is the reverse of crystallization,

but, surprisingly (and in contrast to the behavior of low-molecular-weightsubstances), melting takes place over a range of temperatures even for crystals

of a monodisperse polymer Furthermore, the melting point changes if the rate ofheating is changed These phenomena, although ostensibly unusual, can beexplained in a straightforward manner using the theory developed in this chapter

A polymer single crystal of the type shown inFigure 11.5will actually melt

at a temperature Tm, where Tmis less than T0

m, when the net change in the Gibbsfree energy is zero Thus,

ð11:6:2Þwhich, when introduced into Eq (11.6.1), allows us to solve for the melting point

do not have a single, sharply defined melting point Indeed, it is even possible toheat a semicrystalline polymer to a temperature above Tg and to melt somecrystals while allowing other crystals to form! Furthermore, because crystals tend

to thicken on annealing (being held at a temperature above the glass transitiontemperature), slow heating of a crystal gives rise to a higher melting point thandoes fast heating Finally, a conceptually easy way to measure the equilibriummelting point is to plot Tm against 1=l and extrapolate to a zero value of theabscissa A more practical way is to plot Tmas a function of Tc, the temperature of

crystallization, and extend the plot until it intersects the graph of Tm¼ Tc Thepoint of intersection yields T0

m This procedure is known as a Hoffman–Weeksplot, and it is illustrated in Figure 11.14 for a 90=10 blend of nylon 66 with anamorphous nylon [33] Also shown in this figure are data on block copolymers ofthese two plastics Copolymerization takes place simply on holding the blend inthe melt state for an extended period of time, and as time in the melt increases, itresults in the formation of progressively smaller blocks The progressively smallerblocks lead to progressively less perfect crystals that have a progressively lowermelting point

Information generated about the melting point and the heat of fusion of asemicrystalline polymer by melting tiny samples in a differential scanningcalorimeter can generally be applied to predict the melting behavior of largeamounts of the same polymer in processing equipment Such a heat transfermodel for polymer melting in a single screw extruder is presented inChapter 15;

the rate of melting is determined by the sum of the heat generated in unit time byviscous dissipation and that which is provided by band heaters attached to theextruder barrel When one goes to progressively larger extruders, though, the ratio

of the surface area available for heat transfer to the volume of polymer in the

FIGURE11.14 Hoffman–Weeks plots for a 90=10 nylon 66=amorphous nylon blendannealed in the melt state for different periods of time (From Ref 33.)