CallisterCh4
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CallisterCh4

Course Number: MECH ENG 083, Spring 2004

College/University: Duke

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Chapter 4 / Polymer Structures T ransmission electron mi- crograph showing the spherulite structure in a natural rubber specimen. Chain-folded lamellar crystallites approximately 10 nm thick extend in radial directions from the center; they appear as white lines in the micrograph. 30,000 . (Photograph supplied by P. J. Phillips. First published in R. Bartnikas and R. M. Eichhorn, Engineering Dielectrics, Vol....

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Polymer Chapter 4 / Structures T ransmission electron mi- crograph showing the spherulite structure in a natural rubber specimen. Chain-folded lamellar crystallites approximately 10 nm thick extend in radial directions from the center; they appear as white lines in the micrograph. 30,000 . (Photograph supplied by P. J. Phillips. First published in R. Bartnikas and R. M. Eichhorn, Engineering Dielectrics, Vol. IIA, Electrical Properties of Solid Insulating Materials: Molecular Structure and Electrical Behavior. Copyright ASTM. Reprinted with permission.) Why Study Polymer Structures? A relatively large number of chemical and structural characteristics affect the properties and behaviors of polymeric materials. Some of these inuences are as follows: 1. Degree of crystallinity of semicrystalline polymerson density, stiffness, strength, and ductility (Sections 4.11 and 8.18). 2. Degree of crosslinkingon the stiffness of rubber-like materials (Section 8.19). 3. Polymer chemistryon melting and glass-transition temperatures (Section 11.17). 76 Learning Objectives After careful study of this chapter you should be able to do the following: 1. Describe a typical polymer molecule in terms of its chain structure, and, in addition, how the molecule may be generated by repeating mer units. 2. Draw mer structures for polyethylene, polyvinyl chloride, polytetrauoroethylene, polypropylene, and polystyrene. 3. Calculate number-average and weight-average molecular weights, and number-average and weight-average degrees of polymerization for a specied polymer. 4. Name and briey describe: (a) the four general types of polymer molecular structures; (b) the three types of stereoisomers; (c) the two kinds of geometrical isomers; (d) the four types of copolymers. 5. Cite the differences in behavior and molecular structure for thermoplastic and thermosetting polymers. 6. Briey describe the crystalline state in polymeric materials. 7. Briey describe/diagram the spherulitic structure for a semicrystalline polymer. 4.1 INTRODUCTION Naturally occurring polymersthose derived from plants and animalshave been used for many centuries; these materials include wood, rubber, cotton, wool, leather, and silk. Other natural polymers such as proteins, enzymes, starches, and cellulose are important in biological and physiological processes in plants and animals. Modern scientic research tools have made possible the determination of the molecular structures of this group of materials, and the development of numerous polymers, which are synthesized from small organic molecules. Many of our useful plastics, rubbers, and ber materials are synthetic polymers. In fact, since the conclusion of World War II, the eld of materials has been virtually revolutionized by the advent of synthetic polymers. The synthetics can be produced inexpensively, and their properties may be managed to the degree that many are superior to their natural counterparts. In some applications metal and wood parts have been replaced by plastics, which have satisfactory properties and may be produced at a lower cost. As with metals and ceramics, the properties of polymers are intricately related to the structural elements of the material. This chapter explores molecular and crystal structures of polymers; Chapter 8 discusses the relationships between structure and some of the mechanical properties. 4.2 HYDROCARBON MOLECULES Since most polymers are organic in origin, we briey review some of the basic concepts relating to the structure of their molecules. First, many organic materials are hydrocarbons; that is, they are composed of hydrogen and carbon. Furthermore, the intramolecular bonds are covalent. Each carbon atom has four electrons that may participate in covalent bonding, whereas every hydrogen atom has only one bonding electron. A single covalent bond exists when each of the two bonding atoms contributes one electron, as represented schematically in Figure 2.10 for a molecule of methane (CH4). Double and triple bonds between two carbon atoms involve the sharing of two and three pairs of electrons, respectively. For example, in ethylene, which has the chemical formula C2H4 , the two carbon atoms are doubly bonded together, and each is also singly bonded to two hydrogen atoms, 77 78 Chapter 4 / Polymer Structures as represented by the structural formula HH FF CuC FF HH where U and u denote single and double covalent bonds, respectively. An example of a triple bond is found in acetylene, C2H2 : HUCICUH Molecules that have double and triple covalent bonds are termed unsaturated. That is, each carbon atom is not bonded to the maximum (or four) other atoms; as such, it is possible for another atom or group of atoms to become attached to the original molecule. Furthermore, for a saturated hydrocarbon, all bonds are single ones (and saturated), and no new atoms may be joined without the removal of others that are already bonded. Some of the simple hydrocarbons belong to the parafn family; the chainlike parafn molecules include methane (CH4), ethane (C2H6), propane (C3H8), and butane (C4H10). Compositions and molecular structures for parafn molecules are contained in Table 4.1. The covalent bonds in each molecule are strong, but only weak hydrogen and van der Waals bonds exist between molecules, and thus these hydrocarbons have relatively low melting and boiling points. However, boiling temperatures rise with increasing molecular weight (Table 4.1). Hydrocarbon compounds with the same composition may have different atomic arrangements, a phenomenon termed isomerism. For example, there are two iso- Table 4.1 Compositions and Molecular Structures for Some of the Parafn Compounds: CnH2n 2 Name Composition Structure H F HUCUH F H HH FF HUCUCUH FF HH HHH FFF HUCUCUCUH FFF HHH Boiling Point ( C) Methane CH4 164 Ethane C2H6 88.6 Propane C3H8 42.1 Butane Pentane Hexane C4H10 C5H12 C6H14 0.5 36.1 69.0 4.3 Polymer Molecules 79 mers for butane; normal butane has the structure HHHH FFFF HUCUCUCUCUH FFFF HHHH whereas a molecule of isobutane is represented as follows: H F HUCUH HFH F FFF HUCUCUCUH FFF HHH Some of the physical properties of hydrocarbons will depend on the isomeric state; for example, the boiling temperatures for normal butane and isobutane are 0.5 and 12.3 C (31.1 and 9.9 F), respectively. There are numerous other organic groups, many of which are involved in polymer structures. Several of the more common groups are presented in Table 4.2, where R and R represent organic radicalsgroups of atoms that remain as a single unit and maintain their identity during chemical reactions. Examples of singly bonded hydrocarbon radicals include the CH3 , C2H5 , and C6H5 (methyl, ethyl, and phenyl) groups. 4.3 POLYMER MOLECULES The molecules in polymers are gigantic in comparison to the hydrocarbon molecules heretofore discussed; because of their size they are often referred to as macromolecules. Within each molecule, the atoms are bound together by covalent interatomic bonds. For most polymers, these molecules are in the form of long and exible chains, the backbone of which is a string of carbon atoms; many times each carbon atom singly bonds to two adjacent carbons atoms on either side, represented schematically in two dimensions as follows: FFFFFFF UCUCUCUCUCUCUCU FFFFFFF Each of the two remaining valence electrons for every carbon atom may be involved in side-bonding with atoms or radicals that are positioned adjacent to the chain. Of course, both chain and side double bonds are also possible. These long molecules are composed of structural entities called mer units, which are successively repeated along the chain. Mer originates from the Greek word meros, which means part; the term polymer was coined to mean many mers. We sometimes use the term monomer, which refers to a stable molecule from which a polymer is synthesized. 80 Chapter 4 / Polymer Structures Table 4.2 Some Common Hydrocarbon Groups Family Characteristic Unit Representative Compound H Alcohols R OH H C H OH Methyl alcohol H Ethers R O R H O C H H OH C O Acetic acid H C H H Dimethyl ether OH Acids R C O H C H R Aldehydes H C O H R OH a Phenol C O Formaldehyde H Aromatic hydrocarbons H a C C C C C H H The simplified structure denotes a phenyl group, C H H 4.4 THE CHEMISTRY OF POLYMER MOLECULES Consider again the hydrocarbon ethylene (C2H4), which is a gas at ambient temperature and pressure, and has the following molecular structure: HH FF CuC FF HH If the ethylene gas is subjected catalytically to appropriate conditions of temperature and pressure, it will transform to polyethylene (PE), which is a solid polymeric material. This process begins when an active mer is formed by the reaction between 4.4 The Chemistry of Polymer Molecules 81 an initiator or catalyst species (R ) and the ethylene mer unit, as follows: HH FF CuC FF HH HH FF RU C U C FF HH R (4.1) The polymer chain then forms by the sequential addition of polyethylene monomer units to this active initiator-mer center. The active site, or unpaired electron (denoted by ), is transferred to each successive end monomer as it is linked to the chain. This may be represented schematically as follows: HH FF RU C U C FF HH HH FF CuC FF HH HHHH FFFF RU C U C U C U C FFFF HHHH (4.2) The nal result, after the addition of many ethylene monomer units, is the polyethylene molecule, a portion of which is shown in Figure 4.1a. This representation is not strictly correct in that the angle between the singly bonded carbon atoms is not 180 as shown, but rather close to 109 . A more accurate three-dimensional model is one in which the carbon atoms form a zigzag pattern (Figure 4.1b), the CUC bond length being 0.154 nm. In this discussion, depiction of polymer molecules is frequently simplied using the linear chain model. If all the hydrogen atoms in polyethylene are replaced by uorine, the resulting polymer is polytetrauoroethylene (PTFE); its mer and chain structures are shown in Figure 4.2a. Polytetrauoroethylene (having the trade name Teon) belongs to a family of polymers called the uorocarbons. Polyvinyl chloride (PVC), another common polymer, has a structure that is a slight variant of that for polyethylene, in which every fourth hydrogen is replaced with a Cl atom. Furthermore, substitution of the CH3 methyl group . HUCUH F H FIGURE 4.1 For polyethylene, (a) a schematic representation of mer and chain structures, and (b) a perspective of the molecule, indicating the zigzag backbone structure. H C H H C H H C H H C H H C H H C H H C H H C H Mer unit (a) C (b) H 82 Chapter 4 / Polymer Structures FIGURE 4.2 Mer and chain structures for (a) polytetrauoroethylene, (b) polyvinyl chloride, and (c) polypropylene. F C F F C F F C F F C F F C F F C F F C F F C F Mer unit (a) H C H H C Cl H C H H C Cl H C H H C Cl H C H H C Cl Mer unit (b) H C H H C CH3 H C H H C CH3 H C H H C CH3 H C H H C CH3 Mer unit (c) for each Cl atom in PVC yields polypropylene (PP). Polyvinyl chloride and polypropylene chain structures are also represented in Figure 4.2. Table 4.3 lists mer structures for some of the more common polymers; as may be noted, some of them, for example, nylon, polyester, and polycarbonate, are relatively complex. Mer structures for a large number of relatively common polymers are given in Appendix D. When all the repeating units along a chain are of the same type, the resulting polymer is called a homopolymer. There is no restriction in polymer synthesis that prevents the formation of compounds other than homopolymers; and, in fact, chains may be composed of two or more different mer units, in what are termed copolymers (see Section 4.10). The monomers discussed thus far have an active bond that may react to covalently bond with other monomers, as indicated above for ethylene; such a monomer is termed bifunctional; that is, it may bond with two other units in forming the two-dimensional chainlike molecular structure. However, other monomers, such as phenol-formaldehyde (Table 4.3), are trifunctional; they have three active bonds, from which a three-dimensional molecular network structure results. 4.5 MOLECULAR WEIGHT Extremely large molecular weights1 are to be found in polymers with very long chains. During the polymerization process in which these large macromolecules are 1 Molecular mass, molar mass, and relative molecular mass are sometimes used and are really more appropriate terms than molecular weight in the context of the present discussion in actual fact, we are dealing with masses and not weights. However, molecular weight is most commonly found in the polymer literature, and thus will be used throughout this book. 4.5 Molecular Weight 83 Table 4.3 A Listing of Mer Structures for 10 of the More Common Polymeric Materials Polymer Repeating (Mer) Structure H Polyethylene (PE) H C H H C Cl F C F H C CH3 H C C H H Polyvinyl chloride (PVC) C H F Polytetrauoroethylene (PTFE) C F H Polypropylene (PP) C H H C Polystyrene (PS) H H Polymethyl methacrylate (PMMA) CH3 C C O O CH3 C H OH CH2 Phenol-formaldehyde (Bakelite) CH2 CH2 H Polyhexamethylene adipamide (nylon 6,6) O N 6 H C H 4 O C N H C H C H 84 Chapter 4 / Polymer Structures Table 4.3 (Continued ) Polymer Repeating (Mer) Structure Polyethylene terephthalate (PET, a polyester) O C b O C O H C H H C H O O C O b Polycarbonate CH3 C CH3 O H C b H C C C C H The symbol in the backbone chain denotes an aromatic ring as C H synthesized from smaller molecules, not all polymer chains will grow to the same length; this results in a distribution of chain lengths or molecular weights. Ordinarily, an average molecular weight is specied, which may be determined by the measurement of various physical properties such as viscosity and osmotic pressure. There are several ways of dening average molecular weight. The numberaverage molecular weight Mn is obtained by dividing the chains into a series of size ranges and then determining the number fraction of chains within each size range (Figure 4.3a). This number-average molecular weight is expressed as Mn x i Mi (4.3a) where Mi represents the mean (middle) molecular weight of size range i, and xi is the fraction of the total number of chains within the corresponding size range. A weight-average molecular weight Mw is based on the weight fraction of molecules within the various size ranges (Figure 4.3b). It is calculated according to Mw w i Mi (4.3b) where, again, Mi is the mean molecular weight within a size range, whereas wi denotes the weight fraction of molecules within the same size interval. Computations for both number-average and weight-average molecular weights are carried out in Example Problem 4.1. A typical molecular weight distribution along with these molecular weight averages are shown in Figure 4.4. An alternate way of expressing average chain size of a polymer is as the degree of polymerization n, which represents the average number of mer units in a chain. 4.5 Molecular Weight 0.3 0.3 85 Number fraction 0.1 Weight fraction 0.2 0.2 0.1 0 0 5 10 15 20 25 3 30 35 40 0 0 5 10 15 20 25 3 30 35 40 Molecular weight (10 g/mol) (a) Molecular weight (10 g/mol) (b) FIGURE 4.3 Hypothetical polymer molecule size distributions on the basis of (a) number and (b) weight fractions of molecules. Both number-average (nn) and weight-average (nw) degrees of polymerization are possible, as follows: nn Mn m (4.4a) nw Mw m (4.4b) where Mn and Mw are the number-average and weight-average molecular weights as dened above, while m is the mer molecular weight. For a copolymer (having Number-average, Mn FIGURE 4.4 Distribution of molecular weights for a typical polymer. Weight-average, Mw Amount of polymer Molecular weight 86 Chapter 4 / Polymer Structures two or more different mer units), m is determined from m f j mj (4.5) In this expression, fj and mj are, respectively, the chain fraction and molecular weight of mer j . EXAMPLE PROBLEM 4.1 Assume that the molecular weight distributions shown in Figure 4.3 are for polyvinyl chloride. For this material, compute (a) the number-average molecular weight; (b) the number-average degree of polymerization; and (c) the weightaverage molecular weight. S OLUTION (a) The data necessary for this computation, as taken from Figure 4.3a, are presented in Table 4.4a. According to Equation 4.3a, summation of all the xi Mi products (from the right-hand column) yields the number-average molecular weight, which in this case is 21,150 g/mol. (b) To determine the number-average degree of polymerization (Equation 4.4a), it rst becomes necessary to compute the mer molecular weight. For PVC, each mer consists of two carbon atoms, three hydrogen atoms, and a Table 4.4a Data Used for Number-Average Molecular Weight Computations in Example Problem 4.1 Molecular Weight Range ( g/mol ) 5,000 10,000 10,000 15,000 15,000 20,000 20,000 25,000 25,000 30,000 30,000 35,000 35,000 40,000 Mean Mi ( g/mol ) 7,500 12,500 17,500 22,500 27,500 32,500 37,500 xi 0.05 0.16 0.22 0.27 0.20 0.08 0.02 Mn xi M i 375 2000 3850 6075 5500 2600 750 21,150 Table 4.4b Data Used for Weight-Average Molecular Weight Computations in Example Problem 4.1 Molecular Weight Range ( g/mol ) 5,000 10,000 10,000 15,000 15,000 20,000 20,000 25,000 25,000 30,000 30,000 35,000 35,000 40,000 Mean Mi ( g/mol ) 7,500 12,500 17,500 22,500 27,500 32,500 37,500 wi 0.02 0.10 0.18 0.29 0.26 0.13 0.02 Mw wi Mi 150 1250 3150 6525 7150 4225 750 23,200 4.6 Molecular Shape 87 single chlorine atom (Table 4.3). Furthermore, the atomic weights of C, H, and Cl are, respectively, 12.01, 1.01, and 35.45 g/mol. Thus, for PVC m 2(12.01 g/mol) 62.50 g/mol and nn Mn m 21,150 g/mol 62.50 g/mol 338 3(1.01 g/mol) 35.45 g/mol (c) Table 4.4b shows the data for the weight-average molecular weight, as taken from Figure 4.3b. The wi Mi products for the several size intervals are tabulated in the right-hand column. The sum of these products (Equation 4.3b) yields a value of 23,200 g/mol for Mw . Various polymer characteristics are affected by the magnitude of the molecular weight. One of these is the melting or softening temperature; melting temperature is raised with increasing molecular weight (for M up to about 100,000 g/mol). At room temperature, polymers with very short chains (having molecular weights on the order of 100 g/mol) exist as liquids or gases. Those with molecular weights of approximately 1000 g/mol are waxy solids (such as parafn wax) and soft resins. Solid polymers (sometimes termed high polymers), which are of prime interest here, commonly have molecular weights ranging between 10,000 and several million g/mol. 4.6 MOLECULAR SHAPE There is no reason to suppose that polymer chain molecules are strictly straight, in the sense that the zigzag arrangement of the backbone atoms (Figure 4.1b) is disregarded. Single chain bonds are capable of rotation and bending in three dimensions. Consider the chain atoms in Figure 4.5a; a third carbon atom may lie at any point on the cone of revolution and still subtend about a 109 angle with the bond between the other two atoms. A straight chain segment results when 109 (a) (b) (c) FIGURE 4.5 Schematic representations of how polymer chain shape is inuenced by the positioning of backbone carbon atoms (solid circles). For (a), the rightmost atom may lie anywhere on the dashed circle and still subtend a 109 angle with the bond between the other two atoms. Straight and twisted chain segments are generated when the backbone atoms are situated as in (b) and (c), respectively. (From Science and Engineering of Materials, 3rd edition, by D. R. Askeland. 1994. Reprinted with permission of Brooks/Cole, a division of Thomson Learning. Fax 800 730-2215.) 88 Chapter 4 / Polymer Structures FIGURE 4.6 Schematic representation of a single polymer chain molecule that has numerous random kinks and coils produced by chain bond rotations. (From L. R. G. Treloar, The Physics of Rubber Elasticity, 2nd edition, Oxford University Press, Oxford, 1958, p. 47.) r successive chain atoms are positioned as in Figure 4.5b. On the other hand, chain bending and twisting are possible when there is a rotation of the chain atoms into other positions, as illustrated in Figure 4.5c.2 Thus, a single chain molecule composed of many chain atoms might assume a shape similar to that represented schematically in Figure 4.6, having a multitude of bends, twists, and kinks.3 Also indicated in this gure is the end-to-end distance of the polymer chain r ; this distance is much smaller than the total chain length. Polymers consist of large numbers of molecular chains, each of which may bend, coil, and kink in the manner of Figure 4.6. This leads to extensive intertwining and entanglement of neighboring chain molecules, a situation similar to that of a shing line that has experienced backlash from a shing reel. These random coils and molecular entanglements are responsible for a number of important characteristics of polymers, to include the large elastic extensions displayed by the rubber materials. Some of the mechanical and thermal characteristics of polymers are a function of the ability of chain segments to experience rotation in response to applied stresses or thermal vibrations. Rotational exibility is dependent on mer structure and chemistry. For example, the region of a chain segment that has a double bond (CuC) is rotationally rigid. Also, introduction of a bulky or large side group of atoms restricts rotational movement. For example, polystyrene molecules, which have a phenyl side group (Table 4.3), are more resistant to rotational motion than are polyethylene chains. 4.7 MOLECULAR STRUCTURE The physical characteristics of a polymer depend not only on its molecular weight and shape, but also on differences in the structure of the molecular chains. Modern 2 For some polymers, rotation of carbon backbone atoms within the cone may be hindered by bulky side group elements on neighboring chains. 3 The term conformation is often used in reference to the physical outline of a molecule, or molecular shape, that can only be altered by rotation of chain atoms about single bonds. 4.7 Molecular Structure 89 polymer synthesis techniques permit considerable control over various structural possibilities. This section discusses several molecular structures including linear, branched, crosslinked, and network, in addition to various isomeric congurations. LINEAR POLYMERS Linear polymers are those in which the mer units are joined together end to end in single chains. These long chains are exible and may be thought of as a mass of spaghetti, as represented schematically in Figure 4.7a, where each circle represents a mer unit. For linear polymers, there may be extensive van der Waals and hydrogen bonding between the chains. Some of the common polymers that form with linear structures are polyethylene, polyvinyl chloride, polystyrene, polymethyl methacrylate, nylon, and the uorocarbons. BRANCHED POLYMERS Polymers may be synthesized in which side-branch chains are connected to the main ones, as indicated schematically in Figure 4.7b; these are ttingly called branched polymers. The branches, considered to be part of the main-chain molecule, result from side reactions that occur during the synthesis of the polymer. The chain packing efciency is reduced with the formation of side branches, which results in a lowering of the polymer density. Those polymers that form linear structures may also be branched. FIGURE 4.7 Schematic representations of (a) linear, (b) branched, (c) crosslinked, and (d ) network (three-dimensional) molecular structures. Circles designate individual mer units. 90 Chapter 4 / Polymer Structures CROSSLINKED POLYMERS In crosslinked polymers, adjacent linear chains are joined one to another at various positions by covalent bonds, as represented in Figure 4.7c. The process of crosslinking is achieved either during synthesis or by a nonreversible chemical reaction that is usually carried out at an elevated temperature. Often, this crosslinking is accomplished by additive atoms or molecules that are covalently bonded to the chains. Many of the rubber elastic materials are crosslinked; in rubbers, this is called vulcanization, a process described in Section 8.19. NETWORK POLYMERS Trifunctional mer units, having three active covalent bonds, form three-dimensional networks (Figure 4.7d ) and are termed network polymers. Actually, a polymer that is highly crosslinked may be classied as a network polymer. These materials have distinctive mechanical and thermal properties; the epoxies and phenol-formaldehyde belong to this group. It should be pointed out that polymers are not usually of only one distinctive structural type. For example, a predominantly linear polymer might have some limited branching and crosslinking. 4.8 MOLECULAR CONFIGURATIONS (CD-ROM) By way of summary of the preceding sections, polymer molecules may be characterized in terms of their size, shape, and structure. Molecular size is specied in terms of molecular weight (or degree of polymerization). Molecular shape relates to the degree of chain twisting, coiling, and bending. Molecular structure depends on the manner in which structural units are joined together. Linear, branched, crosslinked, and network structures are all possible, in addition to several isomeric congurations (isotactic, syndiotactic, atactic, cis, and trans). These molecular characteristics are presented in the taxonomic chart, Figure 4.8. It should be noted that some of the structural elements are not mutually exclusive of one another, and, in fact, it may be necessary to specify molecular structure in terms of more than one. For example, a linear polymer may also be isotactic. 4.9 THERMOPLASTIC AND THERMOSETTING POLYMERS The response of a polymer to mechanical forces at elevated temperatures is related to its dominant molecular structure. And, in fact, one classication scheme for these materials according is to behavior with rising temperature. Thermoplasts (or thermoplastic polymers) and thermosets (or thermosetting polymers) are the two subdivisions. Thermoplasts soften when heated (and eventually liquefy) and harden when cooled processes that are totally reversible and may be repeated. On a molecular level, as the temperature is raised, secondary bonding forces are diminished (by increased molecular motion) so that the relative movement of adjacent chains is facilitated when a stress is applied. Irreversible degradation results when the temperature of a molten thermoplastic polymer is raised to the point at which molecular vibrations become violent enough to break the primary covalent bonds. In addition, thermoplasts are relatively soft. Most linear polymers and those having 4.10 Copolymers FIGURE 4.8 Classication scheme for the characteristics of polymer molecules. Chemistry (mer composition) Molecular characteristics 91 Size (molecular weight) Shape (chain twisting, entanglement, etc.) Structure Linear Branched Crosslinked Network Isomeric states Stereoisomers Geometrical isomers Isotactic Syndiotactic Atactic cis trans some branched structures with exible chains are thermoplastic. These materials are normally fabricated by the simultaneous application of heat and pressure. Thermosetting polymers become permanently hard when heat is applied and do not soften upon subsequent heating. During the initial heat treatment, covalent crosslinks are formed between adjacent molecular chains; these bonds anchor the chains together to resist the vibrational and rotational chain motions at high temperatures. Crosslinking is usually extensive, in that 10 to 50% of the chain mer units are crosslinked. Only heating to excessive temperatures will cause severance of these crosslink bonds and polymer degradation. Thermoset polymers are generally harder and stronger than thermoplastics, and have better dimensional stability. Most of the crosslinked and network polymers, which include vulcanized rubbers, epoxies, and phenolic and some polyester resins, are thermosetting. 4.10 COPOLYMERS Polymer chemists and scientists are continually searching for new materials that can be easily and economically synthesized and fabricated, with improved properties or better property combinations than are offered by the homopolymers heretofore discussed. One group of these materials are the copolymers. Consider a copolymer that is composed of two mer units as represented by and in Figure 4.9. Depending on the polymerization process and the relative fractions of these mer types, different sequencing arrangements along the polymer chains are possible. For one, as depicted in Figure 4.9a, the two different units are randomly dispersed along the chain in what is termed a random copolymer. For an alternating copolymer, as the name suggests, the two mer units alternate chain 92 Chapter 4 / Polymer Structures FIGURE 4.9 Schematic representations of (a) random, (b) alternating, (c) block, and (d ) graft copolymers. The two different mer types are designated by black and colored circles. (a) (b) (c) (d) positions, as illustrated in Figure 4.9b. A block copolymer is one in which identical mers are clustered in blocks along the chain (Figure 4.9c). And, nally, homopolymer side branches of one type may be grafted to homopolymer main chains that are composed of a different mer; such a material is termed a graft copolymer (Figure 4.9d ). Synthetic rubbers, discussed in Section 13.13, are often copolymers; chemical repeat units that are employed in some of these rubbers are contained in Table 4.5. Styrene butadiene rubber (SBR) is a common random copolymer from which automobile tires are made. Nitrile rubber (NBR) is another random copolymer composed of acrylonitrile and butadiene. It is also highly elastic and, in addition, resistant to swelling in organic solvents; gasoline hoses are made of NBR. 4.11 POLYMER CRYSTALLINITY The crystalline state may exist in polymeric materials. However, since it involves molecules instead of just atoms or ions, as with metals and ceramics, the atomic arrangements will be more complex for polymers. We think of polymer crystallinity as the packing of molecular chains so as to produce an ordered atomic array. Crystal structures may be specied in terms of unit cells, which are often quite complex. For example, Figure 4.10 shows the unit cell for polyethylene and its relationship 4.11 Polymer Crystallinity 93 Table 4.5 Chemical Repeat Units That Are Employed in Copolymer Rubbers Repeat Unit Name Repeat Unit Structure Repeat Unit Name Repeat Unit Structure H Acrylonitrile H C C N cis-Isoprene H CH3 H C H H Isobutylene H C H C H C C H C Styrene H C CH3 C CH3 H C H H Butadiene H C H C H C H Dimethylsiloxane CH3 Si CH3 O C H H Cl H H C H Chloroprene C H C C FIGURE 4.10 Arrangement of molecular chains in a unit cell for polyethylene. (Adapted from C. W. Bunn, Chemical Crystallography, Oxford University Press, Oxford, 1945, p. 233.) 0.255 nm 0.741 nm 0.494 nm C H 94 Chapter 4 / Polymer Structures to the molecular chain structure; this unit cell has orthorhombic geometry (Table 3.6). Of course, the chain molecules also extend beyond the unit cell shown in the gure. Molecular substances having small molecules (e.g., water and methane) are normally either totally crystalline (as solids) or totally amorphous (as liquids). As a consequence of their size and often complexity, polymer molecules are often only partially crystalline (or semicrystalline), having crystalline regions dispersed within the remaining amorphous material. Any chain disorder or misalignment will result in an amorphous region, a condition that is fairly common, since twisting, kinking, and coiling of the chains prevent the strict ordering of every segment of every chain. Other structural effects are also inuential in determining the extent of crystallinity, as discussed below. The degree of crystallinity may range from completely amorphous to almost entirely (up to about 95%) crystalline; by way of contrast, metal specimens are almost always entirely crystalline, whereas many ceramics are either totally crystalline or totally noncrystalline. Semicrystalline polymers are, in a sense, analogous to twophase metal alloys, discussed in subsequent chapters. The density of a crystalline polymer will be greater than an amorphous one of the same material and molecular weight, since the chains are more closely packed together for the crystalline structure. The degree of crystallinity by weight may be determined from accurate density measurements, according to % crystallinity c( s s( c a) a) 100 (4.10) where s is the density of a specimen for which the percent crystallinity is to be determined, a is the density of the totally amorphous polymer, and c is the density of the perfectly crystalline polymer. The values of a and c must be measured by other experimental means. The degree of crystallinity of a polymer depends on the rate of cooling during solidication as well as on the chain conguration. During crystallization upon cooling through the melting temperature, the chains, which are highly random and entangled in the viscous liquid, must assume an ordered conguration. For this to occur, sufcient time must be allowed for the chains to move and align themselves. The molecular chemistry as well as chain conguration also inuence the ability of a polymer to crystallize. Crystallization is not favored in polymers that are composed of chemically complex mer structures (e.g., polyisoprene). On the other hand, crystallization is not easily prevented in chemically simple polymers such as polyethylene and polytetrauoroethylene, even for very rapid cooling rates. For linear polymers, crystallization is easily accomplished because there are virtually no restrictions to prevent chain alignment. Any side branches interfere with crystallization, such that branched polymers never are highly crystalline; in fact, excessive branching may prevent any crystallization whatsoever. Most network and crosslinked polymers are almost totally amorphous; a few crosslinked polymers are partially crystalline. With regard to stereoisomers, atactic polymers are difcult to crystallize; however, isotactic and syndiotactic polymers crystallize much more easily because the regularity of the geometry of the side groups facilitates the process of tting together adjacent chains. Also, the bulkier or larger the sidebonded groups of atoms, the less tendency there is for crystallization. For copolymers, as a general rule, the more irregular and random the mer arrangements, the greater is the tendency for the development of noncrystallinity. 4.12 Polymer Crystals 95 For alternating and block copolymers there is some likelihood of crystallization. On the other hand, random and graft copolymers are normally amorphous. To some extent, the physical properties of polymeric materials are inuenced by the degree of crystallinity. Crystalline polymers are usually stronger and more resistant to dissolution and softening by heat. Some of these properties are discussed in subsequent chapters. 4.12 POLYMER CRYSTALS We shall now briey discuss some of the models that have been proposed to describe the spatial arrangement of molecular chains in polymer crystals. One early model, accepted for many years, is the fringed-micelle model (Figure 4.11). It was proposed that a semicrystalline polymer consists of small crystalline regions (crystallites, or micelles), each having a precise alignment, which are embedded within the amorphous matrix composed of randomly oriented molecules. Thus a single chain molecule might pass through several crystallites as well as the intervening amorphous regions. More recently, investigations centered on polymer single crystals grown from dilute solutions. These crystals are regularly shaped, thin platelets (or lamellae), approximately 10 to 20 nm thick, and on the order of 10 m long. Frequently, these platelets will form a multilayered structure, like that shown in the electron micrograph of a single crystal of polyethylene, Figure 4.12. It is theorized that the molecular chains within each platelet fold back and forth on themselves, with folds occurring at the faces; this structure, aptly termed the chain-folded model, is illustrated schematically in Figure 4.13. Each platelet will consist of a number of molecules; however, the average chain length will be much greater than the thickness of the platelet. Many bulk polymers that are crystallized from a melt form spherulites. As implied by the name, each spherulite may grow to be spherical in shape; one of them, as found in natural rubber, is shown in the transmission electron micrograph of the chapter-opening photograph for this chapter. The spherulite consists of an aggregate of ribbonlike chain-folded crystallites (lamellae) approximately 10 nm thick that radiate from the center outward. In this electron micrograph, these Region of high crystallinity Amorphous region FIGURE 4.11 Fringed-micelle model of a semicrystalline polymer, showing both crystalline and amorphous regions. (From H. W. Hayden, W. G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior. Copyright 1965 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.) 96 Chapter 4 / Polymer Structures FIGURE 4.12 Electron micrograph of a polyethylene single crystal. 20,000 . (From A. Keller, R. H. Doremus, B. W. Roberts, and D. Turnbull, Editors, Growth and Perfection of Crystals. General Electric Company and John Wiley & Sons, Inc., 1958, p. 498.) FIGURE 4.13 The chain-folded structure for a plateshaped polymer crystallite. ~ 10 nm FIGURE 4.14 Schematic representation of the detailed structure of a spherulite. (From John C. Coburn, Dielectric Relaxation Processes in Poly(ethylene terephthalate), Dissertation, University of Utah, 1984.) Spherulite surface z Lamellar chain-folded crystallite Tie molecule Amorphous material y x Summary FIGURE 4.15 A transmission photomicrograph (using cross-polarized light) showing the spherulite structure of polyethylene. Linear boundaries form between adjacent spherulites, and within each spherulite appears a Maltese cross. 525 . (Courtesy F. P. Price, General Electric Company.) 97 lamellae appear as thin white lines. The detailed structure of a spherulite is illustrated schematically in Figure 4.14; shown here are the individual chain-folded lamellar crystals that are separated by amorphous material. Tie-chain molecules that act as connecting links between adjacent lamellae pass through these amorphous regions. As the crystallization of a spherulitic structure nears completion, the extremities of adjacent spherulites begin to impinge on one another, forming more or less planar boundaries; prior to this time, they maintain their spherical shape. These boundaries are evident in Figure 4.15, which is a photomicrograph of polyethylene using cross-polarized light. A characteristic Maltese cross pattern appears within each spherulite. Spherulites are considered to be the polymer analogue of grains in polycrystalline metals and ceramics. However, as discussed above, each spherulite is really composed of many different lamellar crystals and, in addition, some amorphous material. Polyethylene, polypropylene, polyvinyl chloride, polytetrauoroethylene, and nylon form a spherulitic structure when they crystallize from a melt. SUMMARY Most polymeric materials are composed of very large molecules chains of carbon atoms, to which are side-bonded various atoms or radicals. These macromolecules may be thought of as being composed of mers, smaller structural entities, which are repeated along the chain. Mer structures of some of the chemically simple polymers (e.g., polyethylene, polytetrauoroethylene, polyvinyl chloride, and polypropylene) were presented. Molecular weights for high polymers may be in excess of a million. Since all molecules are not of the same size, there is a distribution of molecular weights. Molecular weight is often expressed in terms of number and weight averages. Chain length may also be specied by degree of polymerization, the number of mer units per average molecule. Several molecular characteristics that have an inuence on the properties of polymers were discussed. Molecular entanglements occur when the chains assume 98 Chapter 4 / Polymer Structures twisted, coiled, and kinked shapes or contours. With regard to molecular structure, linear, branched, crosslinked, and network structures are possible, in addition to isotactic, syndiotactic, and atactic stereoisomers, and the cis and trans geometrical isomers. The copolymers include random, alternating, block, and graft types. With regard to behavior at elevated temperatures, polymers are classied as either thermoplastic or thermosetting. The former have linear and branched structures; they soften when heated and harden when cooled. In contrast, thermosets, once having hardened, will not soften upon heating; their structures are crosslinked and network. When the packing of molecular chains is such as to produce an ordered atomic arrangement, the condition of crystallinity is said to exist. In addition to being entirely amorphous, polymers may also exhibit varying degrees of crystallinity; for the latter case, crystalline regions are interdispersed within amorphous areas. Crystallinity is facilitated for polymers that are chemically simple and that have regular and symmetrical chain structures. Polymer single crystals may be grown from dilute solutions as thin platelets and having chain-folded structures. Many semicrystalline polymers form spherulites; each spherulite consists of a collection of ribbonlike chain-folded lamellar crystallites that radiate outward from its center. IMPORTANT TERMS AND CONCEPTS Alternating copolymer Atactic conguration Bifunctional mer Block copolymer Branched polymer Chain-folded model Cis (structure) Copolymer Crosslinked polymer Crystallite Degree of polymerization Graft copolymer Homopolymer Isomerism Isotactic conguration Linear polymer Macromolecule Mer Molecular chemistry Molecular structure Molecular weight Monomer Network polymer Polymer Polymer crystallinity Random copolymer Saturated Spherulite Stereoisomerism Syndiotactic conguration Thermoplastic polymer Thermosetting polymer Trans (structure) Trifunctional mer Unsaturated REFERENCES Baer, E., Advanced Polymers, Scientic American, Vol. 255, No. 4, October 1986, pp. 178 190. Bovey, F. A. and F. H. Winslow (Editors), Macromolecules: An Introduction to Polymer Science, Academic Press, New York, 1979. Cowie, J. M. G., Polymers: Chemistry and Physics of Modern Materials, 2nd edition, Chapman and Hall (USA), New York, 1991. Engineered Materials Handbook, Vol. 2, Engineering Plastics, ASM International, Materials Park, OH, 1988. McCrum, N. G., C. P. Buckley, and C. B. Bucknall, Principles of Polymer Engineering, 2nd edition, Oxford University Press, Oxford, 1997. Chapters 0 6. Rodriguez, F., Principles of Polymer Systems, 3rd edition, Hemisphere Publishing Company (Taylor & Francis), New York, 1989. Rosen, S. L., Fundamental Principles of Polymeric Materials, 2nd edition, John Wiley & Sons, New York, 1993. Rudin, A., The Elements of Polymer Science and Engineering: An Introductory Text for Engineers and Chemists, Academic Press, New York, 1982. Questions and Problems 99 Schultz, J., Polymer Materials Science, PrenticeHall, Englewood Cliffs, NJ, 1974. Seymour, R. B. and C. E. Carraher, Jr., Polymer Chemistry, An Introduction, 3rd edition, Marcel Dekker, Inc., New York, 1992. Sperling, L. H., Introduction to Physical Polymer Science, 2nd edition, John Wiley & Sons, New York, 1992. Young, R. J. and P. Lovell, Introduction to Polymers, 2nd edition, Chapman and Hall, London, 1991. QUESTIONS AND PROBLEMS Note: To solve those problems having an asterisk (*) by their numbers, consultation of supplementary topics [appearing only on the CD-ROM (and not in print)] will probably be necessary. 4.1 Differentiate between polymorphism and isomerism. 4.2 On the basis of the structures presented in this chapter, sketch mer structures for the following polymers: (a) polyvinyl uoride, (b) polychlorotriuoroethylene, and (c) polyvinyl alcohol. 4.3 Compute mer molecular weights for the following: (a) polyvinyl chloride, (b) polyethylene terephthalate, (c) polycarbonate, and (d) polydimethylsiloxane. 4.4 The number-average molecular weight of a polypropylene is 1,000,000 g/mol. Compute the number-average degree of polymerization. 4.5 (a) Compute the mer molecular weight of polystyrene. (b) Compute the weight-average molecular weight for a polystyrene for which the weight-average degree of polymerization is 25,000. 4.6 Below, molecular weight data for a polypropylene material are tabulated. Compute (a) the number-average molecular weight, (b) the weight-average molecular weight, (c) the number-average degree of polymerization, and (d) the weight-average degree of polymerization. Molecular Weight Range ( g/mol ) 8,000 16,000 16,000 24,000 24,000 32,000 32,000 40,000 40,000 48,000 48,000 56,000 xi 0.05 0.16 0.24 0.28 0.20 0.07 wi 0.02 0.10 0.20 0.30 0.27 0.11 4.7 Below, molecular weight data for some polymer are tabulated. Compute (a) the numberaverage molecular weight, and (b) the weightaverage molecular weight. (c) If it is known that this materials weight-average degree of polymerization is 780, which one of the polymers listed in Table 4.3 is this polymer? Why? (d) What is this materials number-average degree of polymerization? Molecular Weight Range ( g/mol ) 15,000 30,000 30,000 45,000 45,000 60,000 60,000 75,000 75,000 90,000 90,000 105,000 105,000 120,000 120,000 135,000 xi 0.04 0.07 0.16 0.26 0.24 0.12 0.08 0.03 wi 0.01 0.04 0.11 0.24 0.27 0.16 0.12 0.05 4.8 Is it possible to have a polymethyl methacrylate homopolymer with the following molecular weight data and a weight-average degree of polymerization of 585? Why or why not? Molecular Weight Range ( g/mol ) 8,000 20,000 20,000 32,000 32,000 44,000 44,000 56,000 56,000 68,000 68,000 80,000 80,000 92,000 xi 0.04 0.10 0.16 0.26 0.23 0.15 0.06 wi 0.01 0.05 0.12 0.25 0.27 0.21 0.09 4.9 High-density polyethylene may be chlorinated by inducing the random substitution of chlorine atoms for hydrogen. 100 Chapter 4 / Polymer Structures (a) Determine the concentration of Cl (in wt%) that must be added if this substitution occurs for 5% of all the original hydrogen atoms. (b) In what ways does this chlorinated polyethylene differ from polyvinyl chloride? 4.10 What is the difference between conguration and conformation in relation to polymer chains? 4.11 For a linear polymer molecule, the total chain length L depends on the bond length between chain atoms d, the total number of bonds in the molecule N, and the angle between adjacent backbone chain atoms , as follows: L Nd sin 2 (4.11) 4.17* Sketch cis and trans mer structures for (a) butadiene, and (b) chloroprene. 4.18 Sketch the mer structure for each of the following alternating copolymers: (a) poly (butadiene-chloroprene), (b) poly(styrenemethyl methacrylate), and (c) poly(acrylonitrile-vinyl chloride). 4.19 The number-average molecular weight of a poly(styrene-butadiene) alternating copolymer is 1,350,000 g/mol; determine the average number of styrene and butadiene mer units per molecule. 4.20 Calculate the number-average molecular weight of a random nitrile rubber [poly(acrylonitrile-butadiene) copolymer] in which the fraction of butadiene mers is 0.30; assume that this concentration corresponds to a number-average degree of polymerization of 2000. 4.21 An alternating copolymer is known to have a number-average molecular weight of 250,000 g/mol and a number-average degree of polymerization of 3420. If one of the mers is styrene, which of ethylene, propylene, tetrauoroethylene, and vinyl chloride is the other mer? Why? 4.22 (a) Determine the ratio of butadiene to styrene mers in a copolymer having a weightaverage molecular weight of 350,000 g/mol and weight-average degree of polymerization of 4425. (b) Which type(s) of copolymer(s) will this copolymer be, considering the following possibilities: random, alternating, graft, and block? Why? 4.23 Crosslinked copolymers consisting of 60 wt% ethylene and 40 wt% propylene may have elastic properties similar to those for natural rubber. For a copolymer of this composition, determine the fraction of both mer types. 4.24 A random poly(isobutylene-isoprene) copolymer has a weight-average molecular weight of 200,000 g/mol and a weight-average degree of polymerization of 3000. Compute the fraction of isobutylene and isoprene mers in this copolymer. 4.25 (a) Compare the crystalline state in metals and polymers. Furthermore, the average end-to-end distance for a series of polymer molecules r in Figure 4.6 is equal to r d N (4.12) A linear polytetrauoroethylene has a number-average molecular weight of 500,000 g/mol; compute average values of L and r for this material. Using the denitions for total chain molecule length L (Equation 4.11) and average chain end-to-end distance r (Equation 4.12), for a linear polyethylene determine (a) the number-average molecular weight for L 2500 nm; and (b) the number-average molecular weight for r 20 nm. Make comparisons of thermoplastic and thermosetting polymers (a) on the basis of mechanical characteristics upon heating, and (b) according to possible molecular structures. Some of the polyesters may be either thermoplastic or thermosetting. Suggest one reason for this. (a) Is it possible to grind up and reuse phenol-formaldehyde? Why or why not? (b) Is it possible to grind up and reuse polypropylene? Why or why not? Sketch portions of a linear polystyrene molecule that are (a) syndiotactic, (b) atactic, and (c) isotactic. 4.12 4.13 4.14 4.15 4.16* Questions and Problems 101 (b) Compare the noncrystalline state as it applies to polymers and ceramic glasses. 4.26 Explain briey why the tendency of a polymer to crystallize decreases with increasing molecular weight. 4.27* For each of the following pairs of polymers, do the following: (1) state whether or not it is possible to determine if one polymer is more likely to crystallize than the other; (2) if it is possible, note which is the more likely and then cite reason(s) for your choice; and (3) if it is not possible to decide, then state why. (a) Linear and syndiotactic polyvinyl chloride; linear and isotactic polystyrene. (b) Network phenol-formaldehyde; linear and heavily crosslinked cis-isoprene. (c) Linear polyethylene; lightly branched isotactic polypropylene. (d) Alternating poly(styrene-ethylene) copolymer; random poly(vinyl chloride-tetrauoroethylene) copolymer. 4.28 Compute the density of totally crystalline polyethylene. The orthorhombic unit cell for polyethylene is shown in Figure 4.10; also, the equivalent of two ethylene mer units is contained within each unit cell. 4.29 The density of totally crystalline polypropylene at room temperature is 0.946 g/cm3. Also, at room temperature the unit cell for this material is monoclinic with lattice parameters a b c 0.666 nm 2.078 nm 0.650 nm 90 99.62 90 If the volume of a monoclinic unit cell, Vmono , is a function of these lattice parameters as Vmono abc sin determine the number of mer units per unit cell. 4.30 The density and associated percent crystallinity for two polytetrauoroethylene materials are as follows: ( g / cm3 ) 2.144 2.215 Crystallinity (%) 51.3 74.2 (a) Compute the densities of totally crystalline and totally amorphous polytetrauoroethylene. (b) Determine the percent crystallinity of a specimen having a density of 2.26 g/cm3. 4.31 The density and associated percent crystallinity for two nylon 6,6 materials are as follows: ( g / cm3 ) 1.188 1.152 Crystallinity (%) 67.3 43.7 (a) Compute the densities of totally crystalline and totally amorphous nylon 6,6. (b) Determine the density of a specimen having 55.4% crystallinity.

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