ORGANIC AND PHYSICAL CHEMISTRY OF POLYMERS phần 3 ppsx

All situations can exist between the amorphous state corresponding tothe maximum entropy for a macromolecular system and the single crystal whoseonly imperfections are due to chain foldi

POLYMER CHAINS WITH REGULAR CONFORMATIONS 117

Guanine(G)

NHN

N

O

NH2Cytosine(C)

HNNO

NH2

Chain moieties comprising these saccharide cycles and the bases are called osides (adenosine, guanosine, cytidine, and thymine in the case of DNA), and thephosphoric esters of these nucleosides are the nucleotides (adenylic acid, guanylicacid, cytidylic acid, and thymidylic acid)

nucle-Hence, DNA can be regarded as a statistical copolymer between four different

comonomers (hence it is called quaterpolymer ):

O

CH3H

Sugar Guanine-cytosine

NN

NO

N

HHH

Sugar

NNO

NHH

Sugar

NH H

Unlike ribonucleic acids, which are single-strand polymers, DNA form strand helices, a sort of twisted ladder, consisting of two complementary chains.This complementarity occurs through intermolecular hydrogen bonding betweentwo pairs of bases, between the adenosine of one strand and the thymidine ofanother, and likewise between cytidine and guanosine

double-This double helix was identified by Crick and Watson in 1954; the rungs

of the twisted ladder correspond to the pair of bases DNA is always formed

by replication/duplication upon separation of the double strands; the ate single strands are the matrices for the generation of new DNA chains Afterreplication, each double helix includes one old strand and a new one Threesuccessive nucleotides of DNA provide the code for one amino acid, and thegenetic code is determined by the sequence of these triplets

intermedi-Each nucleus in a living cell contains long, thread-like structures called mosomes, which carry bits of genes Both chromosomes and genes are made ofDNA, which is often called the blueprint for life; every living cell contains indeed

chro-a copy of the blueprint

Figure 5.15 shows the complexity of such a structure, underscoring the progressmade by biology to unveil it

C G

A T

A

T

T G

5.3.1 Assembly of Random Coils

Taken individually, random coils commonly exhibit a Gaussian distribution of theirconstitutive units if one considers the distance of the latter to the center of mass ofthe macromolecule under consideration The chains constituting a sample add theirdistributions and give an apparently homogeneous material down to the nanometerlevel Figure 5.16 schematizes the situation of an assembly of chains of differentsize, showing the interpenetration of random coils in the condensed state Such aninterpenetration leads to interchain entanglements and enhances the cohesion of thecorresponding material

For reasons that are related to the rigidity of constitutive units, atoms in certainpolymers do not occupy entirely the space available to them in spite of the apparent

homogeneity of the latter as illustrated by the horizontal straight line of the P = f (r)

diagram (line corresponding to the addition of the probabilities of presence ofmonomer units belonging to different chains) To account for this unfilled space,

CHAIN PACKING 119

P

r

Figure 5.16 Diagram showing the variation of the probability P of presence of monomeric units

belonging to an assembly of polymeric chains as a function of their distance R to a reference

point.

the concept of free volume was introduced The free volume (see Chapter 11) plays

an important role with respect to thermomechanical properties (glass transition) andtransfer properties (permeability, etc.)

5.3.2 Packing of Sequences of Regular Chains

Due to the possible existence of defects in the molecular structure of monomericunits and in their placement, an assembly of regular chains can be described onlyfor short sequences whose length is closely related to the extent of their regularity

In that respect, only linear and stereoregular sequences can be taken into accountsince branching points, junction points in networks, chain ends, and configurationalirregularities are structural defects that oppose the regular chain packing in theirtotality Given the difficulty for chains to organize on a large scale due to themacromolecular state, only assemblies made up of a limited number of constitutiveunits will be described

Three categories of assemblies can be arbitrarily distinguished whose geometry

is determined by the molecular structure of the constitutive unit, the relative size andbulkiness of side groups, and the conformation of the isolated chain This geometry

is governed by the tendency of these assemblies to minimize their potential energyand maximize their molecular interactions (intra- and interchain)

The first category of assemblies is that of chains which exhibit a cylindrical

overall shape and can be viewed as screws with small “threads.” For the maximumdevelopment of molecular interactions, the chains tend to minimize the distancebetween them (which corresponds to the maximum density), and it is the hexagonalpacking which complies best with this criterion as shown in Figure 5.17

A typical example of such a packing is that of polytetrafluoroethylene which

crystallizes in a hexagonal system with a = 0.554 nm and b = 1.680 nm and whose

regular conformation was previously described (see page 111)

Figure 5.17 Hexagonal packing of chains similar to cylinders.

The second group is that of chains with helical conformation, which are different

from cylinders: their “threads” are indeed more prominent, and the number ofconstitutive units per helix turn is fractional The chain packing takes a tetragonalsymmetry with an interpenetration of the “threads” of a left-handed helix withthose of the four right-handed helices which surround it and vice versa Figure 5.18represents an arrangement of such chains in which the size of the thread is measured

by the ratio R/r It also shows the way chains assemble and the relative direction

of the interpenetrated helices In this group, isotactic poly(4-methylpent-1-ene) isfound whose regular conformation is a 72 helix This means that the period ofidentity along the fiber axis of the chain is 7 repetitive units regularly placed on 2

helix turns; the parameters of the corresponding tetragonal cell are: a = b = 1.86 nm

and c= 13.7 nm

CH2CH

CH3

CH3

n

The third group includes chains similar to the preceding ones, whose number

of constitutive units per helix turn is a nonfractional number In this case, thesymmetry of the assembly reflects that of the individual chain: ternary symme-try for an assembly of chains with a ternary symmetry, and so on Figures 5.19and 5.20 show such an assembly with ternary and quaternary symmetries, respec-tively

It is worth stressing that the criteria that distinguish the above groups tolerate anumber of exceptions which can be found even for an usual polymer with a simplestructure

CHAIN PACKING 121

Figure 5.18 Diagram of the packing of helical chains exhibiting a tetragonal symmetry.

Figure 5.19 Packing of ternary symmetry chains: isotactic polybut-1-ene (conformation 31).

Figure 5.20 Packing of quaternary symmetry chains: isotactic polyacetaldehyde

(confor-mation 41).

5.4 MORPHOLOGY OF MACROMOLECULAR SYSTEMS

The term morphology corresponds to the structure taken by polymers at the

micro-scopic level The morphology of a macromolecular system is primarily determined

by the molecular regularity (placement of the constitutive units and configurationalregularity) and by the treatment undergone by the sample prior to or being in thesolid state All situations can exist between the amorphous state corresponding tothe maximum entropy for a macromolecular system and the single crystal whoseonly imperfections are due to chain folding and the molecular irregularity of theirends The various situations will be successively examined

5.4.1 Homogeneous Amorphous State

The amorphous state can be depicted as a multitude of random coils being oughly entangled At the microscopic level, this brings about an apparent homo-geneity, which is responsible, in particular, for the transparency of these systems

thor-to the visible light; such polymers are often called organic glasses

The amorphous state results from the impossibility of chains to crystallize due

to the existence of defects at the molecular level or difficulty for the chains todisentangle when cooling from the molten state In the latter case, a fast coolingquenches the disordered molten state

Poly(methyl methacrylate) (PMMA) and polystyrene (PS) obtained by freeradical polymerization are amorphous due to their atacticity Poly(ethylene tereph-thalate) (PET) is also amorphous when quenched from the molten state but ispotentially crystallizable; the rigidity of the chains prevents them from disentan-gling rapidly enough so that they remain as in the molten state —that is, in adisordered state

5.4.2 Extended Chain Polymers

Due to the molecular agitation at the time of the transition, chains can hardly lize in an extended form and without folding However, chains that are highly rigid

crystal-such as aromatic polyamides —for example, poly(p-phenyleneterephthalamide)

HH

n

with their rigid phenylene moieties and interchain hydrogen bonds between amidefunctional groups (-CO-NH-)—crystallize almost unfolded Application of an exter-nal stress can also prevent chain folding For instance, poly(oxymethylene) (POM)[-(CH2-O)n-] obtained by solid-state radiation polymerization of cyclic trioxane(CH2-O)3 form extended crystalline chains In this case, the monomer is polymer-ized in its crystal form which affords directly stretched chains; the length of the

MORPHOLOGY OF MACROMOLECULAR SYSTEMS 123

Figure 5.21 Electron micrography of a fracture of a PE sample revealing zones comprising

extended chains.

extended crystalline part corresponds to the molar mass of the chain (chains intotal extension)

Extended chains whose folding occurs only beyond∼100 nm are also

consid-ered Such length corresponds to degrees of polymerization (for common vinylpolymers) higher than 500 Such structures are observed in “nascent” polytetraflu-oroethylene (PTFE), which forms partially extended highly rigid helical chains Inanother example, when polyethylene is crystallized under strong pressure (about

100 MPa), it can also give rise to extended chains of the type shown in Figure 5.21.Chains extended under stressed conditions do not exhibit the same attractive-ness applicationwise as those oriented monodimensionally (fibers and films) ortwo-dimensionally (films) stretched Section 5.5 will be devoted to the description

of orientated polymers

5.4.3 Single Crystals

Upon cooling slowly dilute solutions of a polymer of great molecular regularity,

it is possible to obtain single crystals with a morphology close to that of simplemolecules as shown in Figure 5.22a (electron diffraction)

These single crystals exhibit the most regular arrangement possibly formed in apolymer; they form lamellae (Figure 5.23) whose thickness (a few tens of nanome-ters) is determined by the nature of the polymer and the thermodynamic conditions

of crystallization

These lamellae can also pile up by means of screw dislocations (see Figure 5.28)and afford more complex structures such as those shown in Figure 5.22b Theirdimensions (about a few tens of micrometers) are such that optical or electronmicroscopies are essential techniques to visualize them By analysis of the elec-tron diffraction patterns of these single crystals, it could be established that they

(a) (b)

Figure 5.22 Electron diffraction pattern (a) and transmission electron micrography (b) of a

single crystal of polyethylene of pyramidal shape [Courtesy of J C Wittmann, ICS, CNRS Strasbourg (France).]

Figure 5.23 Transmission electron micrography of monolamellar single crystals of

From a thermodynamic point of view, the regular folding of the chains is theresult of a compromise between the increase of the free energy of the system related

to torsional and longitudinal oscillations of extended chains under the effect ofmolecular agitation and the tendency of the crystal to exhibit a minimum surfacefree energy The existence of such a compromise indicates that the dimension of theextended segments (thickness of the lamellae) is likely affected by the temperature

of crystallization

This is what is actually observed experimentally It is even possible to ment the thickness of a preexisting single crystal by means of a thermal treatment

aug-MORPHOLOGY OF MACROMOLECULAR SYSTEMS 125

Face 110

Figure 5.24 Schematic representation of an ideal polyethylene single crystal resulting from

the folding of chains planar zigzag conformation.

Figure 5.25 Polyethylene single crystal ‘‘reconditioned’’ in a different thermodynamic

envi-ronment from that of the initial crystallization and resulting in the formation of ‘‘holes.’’

(annealing); as the other dimensions remain constant, “holes” appear in the crystal

to compensate the increase of the lamellae thickness (Figure 5.25)

5.4.4 Semi-crystalline State

It corresponds to a state intermediate between the amorphous state and a stronglyordered one such as that of a single crystal All polymers that exhibit a sufficientlyhigh molecular regularity to generate crystalline zones organize in a semicrys-talline state when subjected to favorable thermal and kinetic conditions (see Section12.3) Before describing various morphologies referring to this physical state, it is

necessary to define the degree of crystallinity (X ) of semicrystalline polymers,

which is simply the proportion of crystalline matter; depending on whether thisproportion is expressed in mass or in volume, slightly different values will result

The degree of crystallinity (X v ) in volume is defined as

X v = V c /(V a + V c ) = V c /V

a relation in which Va, Vc, and V denote the respective volumes of the amorphous

and crystalline phases and the total volume phases of the sample studied

In the same way, the degree of crystallinity (X m ) in mass can be defined as

X m = m c /(m a + m c ) = m c /m

a relation in which ma, mc, and m denote the mass of the amorphous and crystalline

phases and the total mass phases, respectively

If V c , V ,ρc , andρ are the bulk volumes and the densities of the crystalline

phase and of the entire sample, one can write

It is worth emphasizing that the physical, chemical, mechanical, and so on, erties of amorphous and crystalline phases are very different In most cases, there

prop-is a proportional additivity of the specific properties If P a , P c , and P represent,

respectively, the specific property of the amorphous phases, the crystalline phases,and all the phases, one can write

P = XP c + (1 − X)P a

and this relation is used for the measurement of the degree of crystallinity (seeSection 6.5)

Depending upon the degree of crystallinity of a polymer, regardless of whether

it is low or high, two different types of morphology for semicrystalline systemscan be distinguished

For low degrees of crystallinity, the morphology can be described by the fringed

micelle model, with small-size crystallites being dispersed in an amorphous

poly-mer matrix The size and the degree of perfection of these crystallites are closelyrelated to the length of the regular—and thus crystallizable —sequences in thechains constituting the sample Figure 5.26 schematically represents a polymerexhibiting such a morphology In this representation the crystallites result fromthe packing of more or less long sequences belonging to different chains In addi-tion, the same chain can be involved in the formation of several crystallites; it

MORPHOLOGY OF MACROMOLECULAR SYSTEMS 127

Figure 5.26 Diagram showing the morphology of a semicrystalline polymer with a low degree

of crystallinity (crystallites are ringed).

is thus impossible to physically separate crystalline domains from the amorphousphase Crystallites are zones of high density of cohesive energy; they play the role

of physical cross-links and, even in small proportion, can significantly affect themechanical properties of polymers in the solid state For instance, the difficultiesencountered in the processing of PVC are of rheological origin and due to thecrystallization of short syndiotactic sequences

For high degrees of crystallinity, the crystalline zones give rise to an

organi-zation of higher order They represent the majority of the sample and self-organize

in lamellae made of folded chains as described in the case of monocrystals Bothimpurities present in the medium and noncrystallizable sequences or sequences thatcould not crystallize due to kinetic reasons are rejected into interlamellar zones andform the amorphous phase (Figure 5.27) Because the matter in such amorphouszones is less cohesive than that in the crystalline layers, its proportion and itsthermomechanical characteristics can considerably affect the overall mechanicalproperties of the whole sample

Figure 5.27 Diagram showing the detail of the lamellar structure of a spherulite in a polymer

with a high degree of crystallinity.

Figure 5.28 Representation of a screw dislocation: the arrow indicates the direction of growth

of the dislocation.

The examination of this structure shows that a same chain can be involved inthe formation of different lamellae, thus bringing about the cohesion between thevarious layers The three-dimensional filling of space by crystallized matter occurs

by means of dislocations (Figure 5.28) and various lamellae stuctures resultingfrom crystallographic defects

At the microscopic level a structure with an apparent spherical symmetry is

obtained, which is referred to as spherulite Figure 5.29 explains how the growth

of such lamellae (direction of the arrows) and the space filling by the crystallizedmatter in the perpendicular direction to the orientation of the chains occur.The electron microscopy image of Figure 5.30 clearly shows that the crystal-lization starts from a central nucleus and grows through the formation of layerswhose orientation corresponds to the representation of the Figure 5.29

In addition, the examination of spherulites in polarized light reveals textureswhich can be related to the orientation of lamellae and thus to that of the chains

Figure 5.29 Representation of the directions of the growth of the lamellae starting from a

microcrystalline nucleus (crystallization from the molten state).

MORPHOLOGY OF MACROMOLECULAR SYSTEMS 129

Figure 5.30 Electron micrography of a polyethylene spherulite at the beginning of growth.

[Courtesy of B Lotz, ICS-CNRS, Strasbourg (France).]

Figure 5.31 Microscopic texture of a polyethylene spherulite with radial lamellae Observation

between crossed nicols [Courtesy of B Lotz, ICS-CNRS, Strasbourg (France).]

Figure 5.31 is characteristic of a highly crystalline structure in which the lae are oriented along the radius of the spherulite; in Figure 5.32, the existence ofconcentric extinction lines in the texture shows that the lamellae are twisted asschematically represented in Figure 5.33

lamel-Crystallization from the molten state is an important phenomenon whose anism, thermodynamic aspects and kinetics will be described in Chapter 12

mech-Figure 5.32 Microscopic texture of a spherulite of poly(ethylene adipate) with twisted lamellae.

Observation between crossed nicols [Courtesy of B Lotz, ICS-CNRS, Strasbourg (France).]

a b

c

Figure 5.33 Schematical representation of a twisted lamella corresponding to a ringed texture

as shown in Figure 5.32.

5.4.5 Morphology of Phase-Separated Polymer Systems

Even if the heterogeneity of their structure is well established, semicrystallinehomopolymers are generally not included in the category of heterogeneous systems.This term is reserved to polymers subject to a clear phase separation in which thenonmiscibility is due to the presence of different molecular structures The thermo-dynamic aspect of the nonmiscibility of polymers is discussed in Section 4.4, where

it is shown that this phenomenon is practically general, with the only exception

of polymers with strong specific molecular interactions Upon mixing two miscible polymers molecular interactions develop within each phase but interphaseinteractions remain weak It results in poor mechanical characteristics for the cor-responding materials The electron micrography of Figure 5.34 clearly shows thelack of interphase cohesion between two nonmiscible homopolymers

non-The situation is different when a covalent link can be established between thephases In block copolymers the various blocks are also nonmiscible, but the dyadlinking the two blocks ensures the cohesion of the system and the phase dispersion

MORPHOLOGY OF MACROMOLECULAR SYSTEMS 131

Figure 5.34 Scanning electron micrography of a polystyrene– polybutadiene blend in absence

of a compatibilizing agent [Courtesy of BASF Cy (Ludwigshaffen Germany).]

5.4.5.1 Morphology of Block Copolymers — ‘‘Self-Organized Polymers’’.

Two situations have to be considered in the case of block copolymers, dependingupon their situation with respect to the limit of segregation If the system is far fromthis limit, the segregation is clear and the morphology is determined only by themolecular composition of the block copolymer In the second case, an increase (inabsolute value) of the entropy of mixing with the temperature can result in a certaincompatibility at high temperature (see Section 4.4) For the sake of simplicity, onlysystems that are far from the limit of segregation will be described

When block copolymers exhibit a relatively well-defined molecular structure(uniform composition and molar mass), four types of morphologies are observed,

depending upon their composition Such systems are referred to as self-organized polymers.

For a poly(A-b-B) copolymer whose mass ratio [A]/[B] (or [B]/[A]) is lower

than approximately 20%, the minority phase forms spherical domains that are larly dispersed in the matrix based on the majority block The system self-organizes

regu-in a centered cubic symmetry (Figures 5.35a and 5.35e) With the regu-increase of theproportion of the minority phase and for compositions [A]/[B] ranging between20% and 35%, the spheres self-assemble into cylinders exhibiting a hexagonalsymmetry (Figures 5.35b and 5.35d) In the case of block copolymers with a bal-anced composition ([A]/[B] from 40% to 60%), the cylinders self-assemble inlamellae whose thickness is determined by the composition (Figure 5.35c) Forintermediate compositions [A]/[B] (or [B]/[A]) ranging from 35% to 40%, struc-

tures such as bicontinuous phases are observed These biphasic morphologies (not

represented in the Figure 5.35) are intermediate between cylinder ones and lae ones The minor phase can form a sort of “network” (or two interpenetrated

lamel-(a) (b) (c) (d) (e)

< 15% 15–35% 35–65% 65–85% > 85%

0.5 m m

Figure 5.35 Morphologies and micrographies of poly (styrene-b-butadiene) organized

poly-mers: (a, e) Spheres; (b, d) cylinders; (c) lamellae (Percentages are those of styrene).

“networks”) regularly distributed in the matrix constituted by the major phase Starblock copolymers also give rise to this type of structure

Morphologies of self-organized copolymers are observed not only in diblockcopolymers but also in copolymers with a higher number of blocks However, as

the number of blocks increases and their individual length decreases (segmented

polymers), it is more difficult to obtain a clear phase separation

Triblock copolymers comprising a central block of polybutadiene (BR) and two

external blocks of polystyrene (PS) are commonly used as thermoplastic tomers.

elas-Their composition induces the formation of a morphology in which polystyrenespheres are distributed with a cubic symmetry in an elastomeric matrix of polybu-tadiene At the service temperature the spherical polystyrene nodules are in theglassy state, whereas the polybutadiene chains connecting them are in the elas-tomeric state Figure 5.36 shows the rigid nodules of PS in their role of physicalcross-links, which are responsible for the reversibility of the deformations under-gone by the sample

When the temperature of the system is increased beyond the glass transitiontemperature of polystyrene, the material becomes plastic and can be processed as

a viscous liquid Upon lowering the temperature, the PS nodules become glassyagain and the elastomeric character of the material is restored

5.4.5.2 ‘‘Compatibilization’’ of Polymer Mixtures— High Impact mers In block copolymers that are ill-defined (heterogeneity in composition, dis-

Poly-persity of molar masses, etc.) phase separation occurs with no defined order This

is also observed in graft copolymers and polymer blends that are “compatibilized”

by means of a block (or graft) copolymer consisting of the same monomeric units

as those of the homopolymers to be mixed

MORPHOLOGY OF MACROMOLECULAR SYSTEMS 133

Figure 5.36 Diagram of the morphology of relaxed S-B-S thermoplastic elastomers revealing

the physical cross-linking of the system by the glassy nodules of polystyrene.

Block or graft copolymers used in the latter case act as compatibilizers

(surfac-tants) of the polymer blend so as to “emulsify” the two homopolymers (Figure 5.38)and thus improve its mechanical characteristics

Remark It is important to distinguish between miscibility and

compatibil-ity : the miscibilcompatibil-ity is a thermodynamic characteristic, whereas the bility is a phenomenon affecting a service property.

compati-Upon thoroughly blending two homopolymers, such compatibilizers can times be generated Indeed, such a mechanical mixing can cause the homolyticbreaking ofσ bonds and generate macromolecular free radicals that can give rise

some-to block copolymers by random recombination

A particularly interesting case of polymer systems with heterogeneous phology is that of polymers with high-impact strength These polymers exhibit astrongly improved impact resistance as compared to that of common polymers as

mor-a result of the dispersion of micron-size nodules of elmor-astomers in mor-a rigid phmor-ase.High-impact polystyrene (HIPS) and ABS (acrylonitrile, butadiene, and styrenecopolymers) are the best-known examples

HIPS is obtained by free radical polymerization of styrene in the presence ofpolybutadiene The labile character of the allylic hydrogen atom of polybutadienefavors radical transfer from the growing polystyrene chains (see section 8.5.6.4),which generates graft copolymers along with homopolystyrene:

R + Styrene Polystyrene

Polybutadiene

+ StyreneCH-CH=CH-CH2

CH-CH=CH-CH2Polystyrene

sol-of the polybutadiene phase in the PS matrix Figure 5.37 shows the various steps

of such a process

The covalent links between the elastomeric nodules and the matrix are ble for the cohesion of the whole material and the dispersed soft phase for stoppingthe propagation of cracks resulting from an impact (Figure 5.38)

(e)

Figure 5.37 Scanning electron micrographies carried out at various steps of the formation of

a HIPS (a– d) The given percentages correspond to the yield in styrene (e) Final state; dark parts consist of polybutadiene phase [Courtesy of BASF Cy (Ludwigshaffen Germany).]

ORIENTED POLYMERS 135

Figure 5.38 Scanning electron micrography of a high-impact polystyrene showing the

cohe-sion between the polybutadiene nodules and the polystyrene matrix [Courtesy of BASF Cy (Ludwigshaffen Germany).]

Terpolymers referred to as ABS are obtained in the same way as HIPS, astyrene/acrylonitrile mixture replacing styrene The copolymerization of acryloni-trile with styrene gives rise to a material with better cohesive properties

It is worth mentioning that in heterogeneous multiphase systems, each phaseretains its characteristics The best method to check the presence of a phase sepa-ration in a system consists of the observation of two glass transition temperatures.Techniques of microscopy are also widely used to characterize heterogeneoussystems (Figures 5.34 and 5.38) because they afford extremely precise infor-mation with respect to the phase dispersion and the structure of the interphasezones

5.5 ORIENTED POLYMERS

5.5.1 Intrinsic and Shape Anisotropy of Polymers

A system consisting of oriented molecules generates anisotropic properties Thisanisotropy can take various facets —for example, an anisotropy of the refractiveindex (i.e., birefringence)

The anisotropy of a material depends on the degree of orientation of its

con-stitutive molecules and on the molecular anisotropy of the latter Both a shape anisotropy and the molecule intrinsic anisotropy contribute to this molecular

anisotropy

The shape anisotropy results from the molecular asymmetry: when placed in anexternal electric field, an object of refractive index ˜n modifies it in a nonisotropic

way due to an asymmetrical polarization of its charges This shape anisotropy,which is proportional to (˜n − ˜n0)2, can be only positive Due to their asymme-try, macromolecular chains are characterized by a shape anisotropy that can onlyincrease with the deformation applied.

As for the intrinsic anisotropy of molecules, it depends on their chemical ture and more particularly on their polarizability Double bonds and more particu-larly conjugated ones —mainly in aromatic cycles —contribute to the anisotropy ofmolecules For a macromolecule to exhibit an intrinsic anisotropy, it has to consist

struc-of anisotropic groups organized in a very regular manner along the chain Indeed, anassembly of anisotropic molecules, which would be randomly oriented, would gen-erate a macroscopically isotropic system Polymers forming double helixes (DNA)

or which are rigid [poly(benzyl glutamate)] are among the best-known examples ofpolymers with strong intrinsic anisotropy Macromolecular coils exhibit an intrin-sic anisotropy that is less pronounced than that of highly organized polymers; itdepends essentially on differences in the polarizabilities of the backbone and of theside-chain substituents This difference is minimum in the case of the poly(methylmethacrylate) whose main chain anisotropy is almost completely counterbalanced

by that of the side groups

In the case of polystyrene, the contribution of the aromatic moieties lar to the chain results in a negative intrinsic anisotropy of its segments As observedfor the shape anisotropy, the intrinsic anisotropy of macromolecules is also expected

perpendicu-to strongly increase upon orientation of each of their anisotropic segments In thesolid state, this orientation can be obtained by a mechanical solicitation (stretch-ing); in the liquid state, it can be obtained by (a) an elongational flow (extrusion,spinning) or (b) an electric (Kerr effect) or magnetic effect (Colton–Sheep effect)when the chemical structure of the macromolecules is appropriate

All macromolecules are not prone to undergo an orientation by one of themeans previously mentioned The structural criteria determining the “orientability”

of polymer chains are almost the same as those required for manufacturing fibers.Highly symmetrical and stereoregular chains that possess groups with a strongenergy of interaction [poly(vinyl chloride) (PVC), polyacrylonitrile (PAN), etc.]are the best suited to retain an orientation upon drawing or in an elongational flow

5.5.2 Orientation of Polymers

5.5.2.1 Uniaxial Drawing in a Solid State Upon drawing, initially disordered

chains in an amorphous polymer undergo a phenomenon of orientation The factthat macromolecular coils are oriented upon application of an elongational stress

is materialized by the phenomenon of necking (point B of Figure 5.39); in the

subsequent step (B-C), the stretched chains self-organize in fibrillae, which reducesthe intermolecular distances and contributes to reinforce the interactions betweenchains and the density of the cohesive energy of the system PVC is an example

of an amorphous polymer whose mechanical properties can be improved to givetextile fibers after undergoing such a drawing

Drawing also orientates the crystalline zones (when they exist) inducing thetransformation of spherulites into lamellar structures (see Figure 5.40) However,

ORIENTED POLYMERS 137

B A

C

Figure 5.39 Schematic presentation of the necking phenomenon (B) obtained by the drawing

of an amorphous polymer sample.

Figure 5.40 Deformation under stretching of spherulites in a semicrystalline polymer.

more than the latter phenomenon, it is the orientation of the amorphous parts whichcontributes to the increase of the Young modulus of such a stretched material inthe direction of drawing and to the increase of its fracture strength Indeed, aninitially stretched sample that is subjected to a new drawing test exhibits a higherYoung modulus in the direction of stretching and a lower one in the perpendiculardirection Such a drawing should be imperatively carried out at a temperature close

to, but lower than, the melting point (Tm) of the crystalline zones to favor the

chain rearrangement and prevent their immediate relaxation as soon as the stress issuppressed When treated under such conditions, semicrystalline polymers such asaromatic polyamides can exhibit a Young modulus equal to 130 GPa and a fracturestrength of 2.8 GPa

5.5.2.2 Orientation by Elongational Flow Crystallizable polymers can

undergo an orientation of their chains in dilute solutions When subjected to anelongational flow, these chains are forced to be oriented in the parallel direction and

thus form fibrillae; this phenomenon is referred to as fibrous crystallization Inside

these fibrous parts which behave as nuclei for the epitaxial growth of remainingmacromolecules, shear stresses are low This growth results in crystalline lamellaethat are perpendicular to the fiber axis As for the axis of the chains folded in theselamellae, it is parallel to that of the fibers: one speaks of “shish-kebab” (skewerstructures) as shown in Figure 5.41

Dilute solutions of either polyethylene in toluene or isotactic polypropene inchloronaphthalene afford such “shish-kebab” structures when crystallized in anelongational flow In the case of polyethylene of high molar mass spun from a vis-cous solution, fibers of 3-GPa fracture strength and of 90-GPa Young modulus could

be obtained These are very high values if one considers that only London-typemolecular interactions are responsible for the cohesion of the material

(b) fibrillar zone lamellar zone

Figure 5.41 (a) Representation and (b) scanning electron microscopy of a ‘‘shish-kebab’’

structure obtained in an elongating flow.

Whatever the method used to obtain the orientation of the macromolecular

sys-tems, an orientation function (referred to as “Hermans function” and indicated by

Fher) can be defined to characterize the chain alignment with the reference direction(in general the fiber axis in the case of an uniaxial drawing):

Fher= 1

2(3cos2  − 1)

where  is the angle between the direction of drawing and that of the chains axis.

If all the chains are completely oriented, then = 0 and Fher= 1 The orientation

function is equal to 0.5 for a perpendicular orientation of the chains and 0 for arandom orientation

5.5.2.3 Effect of Biaxial Drawing Such a biaxial drawing is observed in

film-forming processes It can be carried out on either amorphous or talline polymers The two-dimensional orientation can be described using the angles

semicrys-X and Y between the chain direction and those (X and Y) of drawing erally orthogonal) The Hermans functions relative to each reference direction aregiven by

(gen-FherX = 2cos2X + cos2Y − 1

F = 2cos2  + cos2  − 1

LIQUID CRYSTALLINE POLYMERS 139 5.6 LIQUID CRYSTALLINE POLYMERS

5.6.1 Molecular Liquid Crystals

Between the crystalline state (characterized by a long-range three-dimensionalorder), and the amorphous isotropic state, there is an intermediate state of matterreferred to as liquid crystal It is specific to certain molecules, which simultane-ously exhibit order like crystals and flow like fluids Reinitzer, who observed thatcholesteric esters form opaque liquids that become transparent upon raising the tem-perature, is considered as the precursor of this field In addition to the term liquid

crystal, mesomorphic or mesophase can also be used (from Greek mesos meaning

“median”) to name this intermediate state between an isotropic liquid state and

the three-dimensional crystalline order as first proposed by Friedel Molecules that

adopt a preferential orientation and result in an anisotropy are called mesogens Liquid crystalline molecules are classified in two families referred to as ther- motropic and lyotropic, respectively In thermotropic liquid crystals, the formation

of mesophases is temperature-dependent; as for lyotropic liquid crystals, they

necessitate the use of a solvent for forming mesophases Liquid crystals are alsosensitive to other stimuli such as magnetic or electric fields, pressure, and so on.Molecules that are prone to generate mesophases exhibit either “rod-like” or

“disk-like” rigid structures:

n n

n

(b) smectic C

Figure 5.42 Representation of the organization of mesogens in smectic phases (Sa, Sc) and nematic one (N).

are called smectic (S) As lateral forces between the molecules of a mesophase

are quite larger than those between the layers, the fluid character results from therelative slipping of the layers

At least eight different smectic phases are known; they can be distinguished fromone another by adding alphabetical index to the letter S The phase corresponding

to the highest degree of order and to a hexagonal ordering of mesogens within

a layer is referred to as smectic B (SB) In addition to SB phases, which exhibit

a three-dimensional arrangement of the mesogen groups, smectic mesophases E,

G, and H are also characterized by a similar degree of order, but in SG and SH

the direction of alignment of mesogens is tilted with respect to the axis dicular to the layer plane SA mesophases are the least-ordered smectic structuresthat are characterized by a random lateral distribution of mesogens even if theirlongitudinal axis is perpendicular to the layer plane SC mesophases possess thesame characteristics as SA ones, but in the latter case the mesogens are tilted by

perpen-an perpen-angle θ with respect to the axis perpendicular to the layer plane Mesophases

SF and SI correspond to an intermediate degree of order between SB and SA

mesophases

Nematic mesophases (N) are less ordered than smectic ones because they exhibitonly a monodimensional order In this case, even if the orientation order is retainedwith respect to a directing axis —which can thus be regarded as the main directionalaxis of the molecule —the centers of mass are not necessarily within a layer but can

be distributed in a random way Within these domains, whose size is in general inthe micron range, the average degree of alignment with respect to a preferential axis

is described by the Hermans orientation factor (Fher) (order parameter) The closerthis factor to 1, the higher the degree of order of the phase Nematic mesophasesare more fluid than their smectic homologs

The family of cholesteric mesophases is also part of the family of nematic

mesophases (N*) (Figure 5.43) Only mesogens carrying a chiral center (denoted

by the presence of * next to the letter N) and ordering themselves in nematic phasescan generate such phases The presence of this chiral center forces mesogen groups

to adopt a screw-type structure corresponding to a helical variation of the nematicdirecting axis Smectic structures SC and SAcan also afford chiral phases insofar

as the mesogenic group carries a chiral center Chiral smectic phases C (SC ∗) areknown for their ferro- and piezoelectric properties

Z

P

Figure 5.43 Representation of a chiral nematic phase known as ‘‘cholesteric.’’

LIQUID CRYSTALLINE POLYMERS 141

Finally, it is worth mentioning that a molecule can undergo several transitionsand experience successively the highly ordered state of a crystal (the nematic andthen smectic) and finally go to the isotropic states upon raising the temperature(SB→ SC→ SA→ N → I)

5.6.2 Liquid Crystalline (Mesomorphic) Polymers (LCP)

The association of simple molecular groups exhibiting mesomorphic properties withpolymers was considered soon after Flory predicted in 1956 that concentrated solu-tions of “rod”-type rigid polymers could form ordered structures Investigations ofthe behavior of polymers with helical conformation such as those of poly(methyl

and/or benzyl glutamate) type showed that they self-align in a given direction,

thus corroborating this prediction By associating polymers and mesogenic groupswithin the same structure, one can design materials exhibiting simultaneously theanisotropic characteristics of liquid crystals and the thermoplastic behavior of cer-tain liquids These mesogenic groups can be incorporated either in the main chain

or as side chains —that is, laterally grafted onto the backbone (Figure 5.44)

(a)

Figure 5.44 Representation of liquid crystalline polymers with main-chain (a) and side-chain

(b, c) mesogenic groups and combination of both types of chains (d).

Certain liquid crystalline polymers comprise both main-chain and side-chain genic groups Polymers that include mesogenic groups in the main chain aregenerally obtained by step-growth polymerization (see Chapter 8) Depending uponthe nature and the size of the links which connect the mesogenic groups together,main-chain mesomorphic polymers form either very rigid or semiflexible struc-tures

meso-Polymers carrying side-chain mesogenic groups can be prepared in various ways:

• By chemical modification of a flexible polymeric backbone as in the case ofpolysiloxanes

• By chain polymerization of a vinyl or related monomer carrying a mesogenicgroup

• By step-growth polymerization of mesomorphic monomers

In the latter case, the polymeric backbone and the mesogens are separated by a

bivalent flexible molecular group called spacer

5.6.2.1 Main-Chain Liquid Crystalline Polymers. Of the two types ofmain-chain liquid crystalline polymers, it is those containing mesogenic groups inthe main-chain that have generated most of the applications Indeed, such structuresexhibit exceptional mechanical properties When the mesogenic units forming thebackbone are connected to one another by small-size molecular species, the result-ing materials exhibit strong rigidity and decompose before melting and expressingtheir liquid crystalline properties.

For lyotropic polymers, the factor  (anisotropy ratio) which denotes the ratio

of the length L of the mesogen to its diameter is high ( > 6) The attractive forces

generated byπ–π-type interactions between the mesogens aligned in a parallel way

can consequently develop and contribute to the rigidity of the material Only theaddition of a highly polar solvent (dimethylsulfoxide, dimethylformamide, etc.) canweaken these intermolecular interactions and reveal the liquid crystalline behavior

of such materials Such birefringent solutions are referred to as lyotropic The

best-known and commercially available example is that of “Kevlar,” which is an

aromatic polyamide, poly(p-phenylene terephtalamide):

concentra-whereas the least concentrated phase is isotropic The higher the factor , the lower

the critical volume fraction at which phase separation occurs

At the critical concentration, the viscosity of the medium increases dramatically.Along with aromatic polyamides, some cellulosic derivatives (hydroxypropylcellu-lose, etc.) and polypeptides belong to the category of lyotropic polymers Fibers can

be produced from lyotropic solutions of these polymers at a concentration lowerthan their critical concentration

To reduce the melting point of rigid structures corresponding to main-chainmesogen-containing polymers, it is necessary to break the symmetry of these assem-blies by introducing either bulky lateral substituents or semiflexible connections Bythis means it is possible to increase the molecular mobility and attain the properties

of liquid crystals without the contribution of a solvent In other words, the liquidcrystals behavior becomes observable at temperatures lower than that of degrada-

tion; such structures are known as thermotropic This strategy was successfully

utilized, in particular, in the case of aromatic polyesters Many thermotropic mers have been obtained by “altering” the chain symmetry of polyesters Polyesterssuch as

poly-O

O

CH2)(

n m

[

]

LIQUID CRYSTALLINE POLYMERS 143

form nematic mesophases for odd values of m and smectic mesophases for even values of m.

5.6.2.2 Side-Chain Liquid Crystalline Polymers Contrary to main-chain

LCP, those carrying side-chain mesogens did not find significant applications untilrecently, although many studies were devoted to them In 1978 the first polymerswith side-chain mesogens were prepared by Finkelman et al To reveal the liquidcrystalline behavior of such structures, these authors introduced a spacer betweenthe backbone and the side-chain mesogens They could uncouple in this way themovements of the main chain from those of the mesogenic groups In addition tothe nature of the mesogen, the type of polymer chosen as the backbone and thelength of the spacer play a vital role in the formation of mesophases

The more flexible the main chain, the broader the range of thermal stability ofsuch mesophases As for the size of the spacer, it determines to a large extent thetype of resulting mesophases, with their degree of order increasing with the length

of the spacer

Liquid crystalline polymers with side-chain mesogenic groups are also ing materials, but for totally different reasons than those mentioned for main-chainmesogenic structures Because the mesogen groups and the backbone are uncou-pled, these structures exhibit a behavior close to that of simple mesogenic molecules(Figure 5.45) Attempts have been made to prepare by this means materials with thecharacteristics of processability and mechanical resistance characteristic of poly-mers and the same sensitivity to stimuli (magnetic or electric field) as that of simplemesogenic molecules Such properties are of considerable interest in electro-opticaltechnologies

Molecules that self-organize in chiral nematic or smectic mesophases and prise a permanent dipole exhibit ferroelectric properties This means that they arespontaneously polarized and are able to orient themselves under the effect of anelectric field Polymers with chiral mesogens could be used for the manufacture oflarge-size video screens and more generally for displays To this end, they require

com-a response time (i.e., the time required for mesogens to flip from one position toanother) that is comparable to that of molecular liquid crystals This response time

t depends on the electric field (E ), the polarization (P ), and the viscosity (η):

t = η/PE

These materials are the subject of very active studies

Polymers with side-chain mesogens are also useful for applications in the field

of optical information storage (Figure 5.46) Using a mesomorphic polymer whosemesogenic groups would be aligned in a homeotropic way by application of a fieldand upon retaining this orientation by cooling, it is possible to produce localizedisotropic domains with a laser beam These domains scatter the light and lose theirtransparency; thus, information can be “written” on a film and subsequently erased

by simple increase of the temperature

Figure 5.46 Application of the liquid crystalline polymers in information technologies.

To identify mesophases, the experimenter can use a polarizing microscope toanalyze the characteristic textures of the various mesophases; he can also make use

of differential scanning calorimetry and of X-ray diffraction

LITERATURE 145 LITERATURE

P Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, 1971 P-G De Gennes, Introduction to Polymer Dynamics, Cambridge University Press, Cam-

C Booth and C Price (Eds.), Comprehensive Polymer Science, Vol 2: Polymer Properties,

Pergamon Press, Oxford, 1989

B Wunderlich, Macromolecular Physics, Vol 1 (1973), Vol 2 (1976), Vol 3 (1980),

Aca-demic Press, New York

F A., Bovey and L W Jelinski, Chain Structure and Conformation of Macromolecules,

Academic Press, New York, 1982

DETERMINATION OF MOLAR

MASSES AND STUDY OF CONFORMATIONS AND MORPHOLOGIES BY PHYSICAL METHODS

After the polymer synthesis step (see Chapters 7–10) comes that of their structuralcharacterization The methods available for this can be grouped into two categories:

• The first category includes methods used for the identification of any organic(simple or macromolecular) molecule, primarily spectroscopic ones; the study

of polymer tacticity by NMR spectroscopy described in Chapter 3 is anexample

• The second category includes methods that correlate the variation of a propertycharacteristic of the macromolecular state with structural parameters; they aredescribed in this chapter

6.1 DETERMINATION OF MOLAR MASSES BY COLLIGATIVE

METHODS

Colligative methods are those that involve the determination of the number of

macromolecules present in a polymer sample of given mass; it is then easy to

deduce the number average molar mass (M n) of the sample analyzed

6.1.1 End-Group Titration

Due to the low concentration of the chain ends and the lack of precision of titration,this method is well-suited for polymers of relatively low molar mass It involves theidentification and titration of the functional groups located at one or each of the two

Organic and Physical Chemistry of Polymers, by Yves Gnanou and Michel Fontanille

Copyright  2008 John Wiley & Sons, Inc.

147

148 DETERMINATION OF MOLAR MASSES AND STUDY OF CONFORMATIONS & MORPHOLOGIES

ends of strictly linear polymers Chemical titration requires only simple equipment,which is why it is still frequently used for the characterization of condensationpolymers (see Chapter 7) It is also used when the polymers analyzed are obtained

by “living” polymerization and functionalized at their terminal positions (that is,either through the initiator or through a functional deactivator) by a reactive groupeasy to titrate using spectrophotometric techniques

An example is the characterization of a polyamide sample whose solubility islimited to highly polar solvents, preventing it from being characterized by othermethods for the measurement of molar masses The titration of a primary amine

in a polyamide can be carried out in m-cresol solution using perchloric acid as the

reagent and can be monitored by potentiometry For the titration of carboxylic acids,

it is preferable to use a solution in benzyl alcohol and operate at high temperaturewith sodium hydroxide as the base and an indicator For polyamides grown from

α-amino,ω-carboxylic acids, only one titration is required but a double titration

can serve to confirm the values obtained in the first instance The accuracy of thetitration is approximately 3× 10−6moles of titrated functional groups per gram of

corre-ppm 1 2

3 4

5 6

7 8

1

2 3

1

4

Figure 6.1. 1H NMR spectrum of a polystyrene (with M n= 1800 g·mol −1) activated by twodifferent acetal functional groups.