POLYMER CHAINS WITH REGULAR CONFORMATIONS 117 Guanine ( G ) NH N N O NH 2 C y tosine ( C ) HN NO NH 2 Chain moieties comprising these saccharide cycles and the bases are called nucle- osides (adenosine, guanosine, cytidine, and thymine in the case of DNA), and the phosphoric esters of these nucleosides are the nucleotides (adenylic acid, guanylic acid, cytidylic acid, and thymidylic acid). Hence, DNA can be regarded as a statistical copolymer between four different comonomers (hence it is called quaterpolymer): Adenine-thymine N N N N Sugar N N O O CH 3 H Sugar Guanine-cytosine N N N O N H H H Sugar N N O NH H Sugar NH H Unlike ribonucleic acids, which are single-strand polymers, DNA form double- strand helices, a sort of twisted ladder, consisting of two complementary chains. This complementarity occurs through intermolecular hydrogen bonding between two pairs of bases, between the adenosine of one strand and the thymidine of another, and likewise between cytidine and guanosine. 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 intermedi- ate single strands are the matrices for the generation of new DNA chains. After replication, each double helix includes one old strand and a new one. Three successive nucleotides of DNA provide the code for one amino acid, and the genetic code is determined by the sequence of these triplets. Each nucleus in a living cell contains long, thread-like structures called chro- mosomes, which carry bits of genes. Both chromosomes and genes are made of DNA, which is often called the blueprint for life; every living cell contains indeed a copy of the blueprint. Figure 5.15 shows the complexity of such a structure, underscoring the progress made by biology to unveil it. 118 CONFORMATIONAL STRUCTURES AND MORPHOLOGIES C G A T A T T G G C A C Figure 5.15. Representation of the DNA double-helix organization showing A-T and C-G links. 5.3. CHAIN PACKING 5.3.1. Assembly of Random Coils Taken individually, random coils commonly exhibit a Gaussian distribution of their constitutive units if one considers the distance of the latter to the center of mass of the macromolecule under consideration. The chains constituting a sample add their distributions and give an apparently homogeneous material down to the nanometer level. Figure 5.16 schematizes the situation of an assembly of chains of different size, showing the interpenetration of random coils in the condensed state. Such an interpenetration leads to interchain entanglements and enhances the cohesion of the corresponding material. For reasons that are related to the rigidity of constitutive units, atoms in certain polymers 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 of monomer 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) and transfer properties (permeability, etc.). 5.3.2. Packing of Sequences of Regular Chains Due to the possible existence of defects in the molecular structure of monomeric units and in their placement, an assembly of regular chains can be described only for 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 account since branching points, junction points in networks, chain ends, and configurational irregularities are structural defects that oppose the regular chain packing in their totality. Given the difficulty for chains to organize on a large scale due to the macromolecular state, only assemblies made up of a limited number of constitutive units 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 and bulkiness of side groups, and the conformation of the isolated chain. This geometry is governed by the tendency of these assemblies to minimize their potential energy and 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 maximum development of molecular interactions, the chains tend to minimize the distance between them (which corresponds to the maximum density), and it is the hexagonal packing 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). 120 CONFORMATIONAL STRUCTURES AND MORPHOLOGIES 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 of constitutive units per helix turn is fractional. The chain packing takes a tetragonal symmetry with an interpenetration of the “threads” of a left-handed helix with those of the four right-handed helices which surround it and vice versa. Figure 5.18 represents 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) is found whose regular conformation is a 7 2 helix. This means that the period of identity 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. CH 2 CH CH 2 CH CH 3 CH 3 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, the symmetry 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 5.19 and 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 a number of exceptions which can be found even for an usual polymer with a simple structure. 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 3 1 ). Figure 5.20. Packing of quaternary symmetry chains: isotactic polyacetaldehyde (confor- mation 4 1 ). 122 CONFORMATIONAL STRUCTURES AND MORPHOLOGIES 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 configurational regularity) and by the treatment undergone by the sample prior to or being in the solid state. All situations can exist between the amorphous state corresponding to the maximum entropy for a macromolecular system and the single crystal whose only imperfections are due to chain folding and the molecular irregularity of their ends. 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 thor- oughly entangled. At the microscopic level, this brings about an apparent homo- geneity, which is responsible, in particular, for the transparency of these systems 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 to disentangle when cooling from the molten state. In the latter case, a fast cooling quenches the disordered molten state. Poly(methyl methacrylate) (PMMA) and polystyrene (PS) obtained by free radical polymerization are amorphous due to their atacticity. Poly(ethylene tereph- thalate) (PET) is also amorphous when quenched from the molten state but is potentially 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 a disordered state. 5.4.2. Extended Chain Polymers Due to the molecular agitation at the time of the transition, chains can hardly crystal- lize in an extended form and without folding. However, chains that are highly rigid such as aromatic polyamides—for example, poly(p-phenyleneterephthalamide) NN HH OO n with their rigid phenylene moieties and interchain hydrogen bonds between amide functional groups (-CO-NH-)—crystallize almost unfolded. Application of an exter- nal stress can also prevent chain folding. For instance, poly(oxymethylene) (POM) [-(CH 2 -O) n -] obtained by solid-state radiation polymerization of cyclic trioxane (CH 2 -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 in total extension). Extended chains whose folding occurs only beyond ∼100 nm are also consid- ered. Such length corresponds to degrees of polymerization (for common vinyl polymers) higher than 500. Such structures are observed in “nascent” polytetraflu- oroethylene (PTFE), which forms partially extended highly rigid helical chains. In another 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) or two-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 simple molecules as shown in Figure 5.22a (electron diffraction). These single crystals exhibit the most regular arrangement possibly formed in a polymer; 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. Their dimensions (about a few tens of micrometers) are such that optical or electron microscopies are essential techniques to visualize them. By analysis of the elec- tron diffraction patterns of these single crystals, it could be established that they 124 CONFORMATIONAL STRUCTURES AND MORPHOLOGIES (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 polyethy- lene. comprise regularly folded linear chains, as schematically shown in Figure 5.24, and that the chain axes are perpendicular to the surface of the lamellae. The existence of such folding is proved by the fact that the thickness of the lamellae is generally much lower than the length of totally stretched chains. Due to this folding, irregu- larities related to the dispersion in the molar masses of the chains forming a same single crystal can be somehow compensated. From a thermodynamic point of view, the regular folding of the chains is the result 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 of molecular agitation and the tendency of the crystal to exhibit a minimum surface free energy. The existence of such a compromise indicates that the dimension of the extended 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 aug- ment the thickness of a preexisting single crystal by means of a thermal treatment 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 strongly ordered one such as that of a single crystal. All polymers that exhibit a sufficiently high molecular regularity to generate crystalline zones organize in a semicrys- talline state when subjected to favorable thermal and kinetic conditions (see Section 12.3). Before describing various morphologies referring to this physical state, it is 126 CONFORMATIONAL STRUCTURES AND MORPHOLOGIES necessary to define the degree of crystallinity (X) of semicrystalline polymers, which is simply the proportion of crystalline matter; depending on whether this proportion 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 V a ,V c ,andV denote the respective volumes of the amorphous and crystalline phases and the total volume phases of the sample studied. Inthesameway,thedegree 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 m a ,m c ,andm denote the mass of the amorphous and crystalline phases and the total mass phases, respectively. If V c , V,ρ c , and ρ are the bulk volumes and the densities of the crystalline phase and of the entire sample, one can write X v = V c m c Vm = V a V X m = ρ ρ c X m For the majority of polymers, both mass and volume degrees of crystallinity are not very different; both are thus used indifferently, depending upon the method utilized to carry out the measurement. It is worth emphasizing that the physical, chemical, mechanical, and so on, prop- erties of amorphous and crystalline phases are very different. In most cases, there 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 (see Section 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 systems can 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 closely related to the length of the regular—and thus crystallizable—sequences in the chains constituting the sample. Figure 5.26 schematically represents a polymer exhibiting such a morphology. In this representation the crystallites result from the 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 [...]... 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... 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 the identification and titration of the functional groups located at one or each of the two Organic and Physical. .. presence of a phase separation in a system consists of the observation of two glass transition temperatures Techniques of microscopy are also widely used to characterize heterogeneous systems (Figures 5 .34 and 5 .38 ) because they afford extremely precise information with respect to the phase dispersion and the structure of the interphase zones 5.5 ORIENTED POLYMERS 5.5.1 Intrinsic and Shape Anisotropy of Polymers. .. block The system self-organizes in a centered cubic symmetry (Figures 5 .35 a and 5 .35 e) With the increase of the proportion of the minority phase and for compositions [A]/[B] ranging between 20% and 35 %, the spheres self-assemble into cylinders exhibiting a hexagonal symmetry (Figures 5 .35 b and 5 .35 d) In the case of block copolymers with a balanced composition ([A]/[B] from 40% to 60%), the cylinders... as compared to that of common polymers as a result of the dispersion of micron-size nodules of elastomers in a rigid phase High-impact polystyrene (HIPS) and ABS (acrylonitrile, butadiene, and styrene copolymers) are the best-known examples HIPS is obtained by free radical polymerization of styrene in the presence of polybutadiene The labile character of the allylic hydrogen atom of polybutadiene favors... 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 condensation polymers (see Chapter 7) It is also used when the polymers. .. (in general the fiber axis in the case of an uniaxial drawing): Fher = 1 (3 cos 2 2 − 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 a random orientation 5.5.2 .3 Effect of Biaxial Drawing Such a biaxial drawing... mechanical properties of polymers in the solid state For instance, the difficulties encountered in the processing of PVC are of rheological origin and due to the crystallization of short syndiotactic sequences For high degrees of crystallinity, the crystalline zones give rise to an organization of higher order They represent the majority of the sample and self-organize in lamellae made of folded chains as... 5 .33 Crystallization from the molten state is an important phenomenon whose mechanism, thermodynamic aspects and kinetics will be described in Chapter 12  130 CONFORMATIONAL STRUCTURES AND MORPHOLOGIES 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).] c b a Figure 5 .33 ... concentration of the solute (C2 ) can be related: C2 = m2 /(V1 + V2 ) ∼ m2 /V1 which can be also expressed as C2 = N2 M2 /V1 = N2 M2 /N1 V10 ∼ f2 M2 /V10 where m2 represents the mass of the solute, V1 and V2 are the volumes occupied by the solvent and the solute, N1 and N2 are the number of molecules of solvent and solute, and M2 is the molar mass of the solute One thus obtains the Van’t Hoff law, which . 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. Representation of the DNA double-helix organization showing A-T and C-G links. 5 .3. CHAIN PACKING 5 .3. 1. Assembly of Random Coils Taken individually, random coils commonly exhibit a Gaussian distribution of. interpenetration of the “threads” of a left-handed helix with those of the four right-handed helices which surround it and vice versa. Figure 5.18 represents an arrangement of such chains in which the size of