The Structure of Materials
1.3 STRUCTURE OF POLYMERS
1.3.6 Polymer Crystallinity
general,Mn=Mw, but taken together as a ratio, they provide a measure of the breadth of the molecular weight distribution. This ratio is called thepolydispersity index, and it takes on values greater than or equal to 1.0:
Mw
Mn ≥1.0 (1.60)
If all chains have exactly the same weight and number of repeat units, then the system is termedmonodispersed, and the polydispersity index is exactly 1.0. Most real polymers have rather large polydispersity indexes, but some standards used for chromatogra- phy calibration, such as polystyrene, can have values approaching unity. Calculating molecular weights and determining which form of Eqs. (1.55), (1.58), and (1.59) to use requires some practice and patience. A Cooperative Learning Exercise is provided below, but you are encouraged to consult any of the excellent textbooks on polymer science listed at the end of this chapter for further information on molecular weight calculations and determination.
Cooperative Learning Exercise 1.6 Consider the following collection of polymer chains:
10 molecules 2800 MW 5 molecules 3000 MW 4 molecules 1200 MW 2 molecules 3600 MW 1 molecule 1000 MW Person 1: Calculate the number average molecular weight.
Person 2: Calculate the weight average molecular weight.
Combine your answers to determine the polydispersity index.
Answer :
M
= w
28,000(2800) + 15,000(3000)
+ 4800(
1200) + 7200(3600)
+ 1000(
100)
56,000
1.56 =
×
8 10 56,000
= 2787
M
= n
10(2800) + 5(3000) + 4(1200) + 2(3600) + 1(1000)
22
56,000 =
= 22 2545
M /M w
= n
2787/2545
= 1.095
STRUCTURE OF POLYMERS 87
which generally need a great deal of energy to devitrify (crystallize), or metals that require nonequilibrium conditions to form amorphous structures, many polymers have amorphous to crystalline transition temperatures that are near room temperature. Not all polymers crystallize readily, however. Intuitively, we would expect that a jumbled mass of spaghetti-like strands that make up a polymer solution or melt would tend to be amorphous, and this is indeed the case. But there are a number of structural factors that contribute to the ability of the amorphous polymer chains to rearrange themselves into an ordered structure. These factors include chain architecture (the chemical constituents and bond angles of the backbone and side groups), order and regularity (e.g., tacticity), intermolecular forces (both within an individual chain and between adjacent chains, such as hydrogen bonding), and steric effects (the size of side groups and branches).
1.3.6.1 Types of Bulk Polymer Crystallinity. Polymer crystallinity is a com- plicated subject, to which numerous books and symposia are devoted; but for our purposes, we can classify crystallinity in bulk polymers into two general categories:
extended chain and folded chain.Extended chain crystallinity arises in many polymers with highly regular structures, such as polyethylene, poly(vinyl alcohol), syndiotactic polymers of poly(vinyl chloride) and poly(1,2-butadiene), most polyamides, and cellu- lose. In these molecules, the so-called “planar zigzag” structure shown in Figure 1.60a possesses the minimum energy for an isolated section of the chain and is therefore the thermodynamically favored conformation. Side groups, if they are small enough and arranged in a regular fashion, as in the syndiotactic structure, need not prevent crystallinity (see Figure 1.60b), but as the bulkiness and irregularity of the side groups grow, crystallization becomes more and more difficult. As a result, highly branched molecules, such as branched polyethylene, do not crystallize, even though polyethylene itself is easily crystallized. Similarly, networked polymers do not have the freedom to move in a way such that extended chain crystallinity can occur.
As with the other classes of materials, polymers can be either single crystals or polycrystalline. Polycrystalline polymers are more appropriately termedsemicrystalline polymers, since the region between crystalline domains in polymers can be quite large and result in a significant amorphous component to the polymer. The crystalline regions in semicrystalline polymers are called crystallites, which have dimensions of several hundred angstroms, but the length of polymer chains is generally much larger than this. For example, a polyethylene chain with the extended chain structure shown in Figure 1.60a with molecular weight 50,000 has an end-to-end length of about 4500 ˚A.
How can this be? The second type of crystalline structure in polymers chain folding gives as an explanation. Polymer chains can fold in a regular fashion to form plate-like crystallites calledlamellae, as shown schematically in the insert of Figure 1.61. Notice that the polymer chains not only fold, but can extend from one lamella to another to form amorphous regions. In polymers crystallized from the melt, these lamellae often radiate from a central nucleation site, forming three-dimensional spherical structures calledspherulites (see Figures 1.61 and 1.62). In cross-polarized light, the spherulites form a characteristicMaltese cross pattern due to birefringent effects associated with the lamellar structures.
A polymer crystal structure related to chain folding is called the fringed micelle model, in which the polymer chains do not fold in a regular fashion but extend from one crystalline region to another, again forming amorphous regions between the crystallites (see Figure 1.63). While the fringed micelle model is no longer the preferred one for
(a)
(b)
Figure 1.60 Schematic illustration of extended chain crystallinity in polymers (a) polyethylene and (b) polypropylene.
Amorphous material Tie molecule
Spherulite surface z
x
y
Lamellar chain-folded
crystallite
Figure 1.61 Schematic illustration of chain folding leading to lamellar crystallites (inset) and lamellar stacking to form spherulites.
STRUCTURE OF POLYMERS 89
100 µ
Figure 1.62 Cross-polarized micrograph of polyethylene showing spherulitic structure. From K. M. Ralls, T. H. Courtney, and J. Wulff,Introduction to Materials Science and Engineering.
Copyright 1976 by John Wiley & Sons, Inc. This material is used by permission of John Wiley & Sons, Inc.
Figure 1.63 The fringed-micelle model of polymer crystallinity. From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright
1976 by John Wiley & Sons, Inc. This material is used by permission of John Wiley &
Sons, Inc.
describing crystallinity in most polymers, it is still used to describe the structure of highly oriented polymers, such as occurs in the stretching of rubber, viscose rayon, and Kevlar.
The amorphous and crystalline regions each have different densities, with the crys- talline densityρc being higher than the amorphous densityρa due to a more compact structure. The percent crystallinity in a semicrystalline polymer with bulk density ρs
can then be calculated from the respective crystalline and amorphous densities:
% crystallinity= ρc(ρs−ρa)
ρs(ρc−ρa)×100 (1.61)
2 µm
Figure 1.64 Polyethylene single crystals. Reprinted, by permission, from P. Heimenz,Polymer Chemistry: The Basic Concepts, p. 239. Copyright1984 by Marcel Dekker, Inc.
(a) (b)
b H
H C H H
c
a H
C H H
H b
C a
Figure 1.65 (a) Crystal structure of polyethylene unit cell shown in relation to chains. (b) View of unit cell perpendicular to chain axis. Reprinted, by permission, from Heimenz, P.,Polymer Chemistry: The Basic Concepts, p. 236. Copyright1984 by Marcel Dekker, Inc.
STRUCTURE OF POLYMERS 91
Polymer single crystals possess the density of the crystal,ρc. Though polymer single crystals do not usually form in the bulk, but rather from more carefully controlled formation techniques such as vapor deposition, we will describe them here since they generally have the folded-chain crystal structure. An example of a polymer single crystal is shown in Figure 1.64. One would expect that the regular array of folded chains in a single crystal, or in a semicrystalline polymer for that matter, leads to diffraction phenomena when bombarded with X rays, in much the same way that lower-molecular-weight materials like sodium chloride or aluminum do. This is indeed the case, and the study of X-ray diffraction phenomena in polymers is a large field of interest. The primary difference in the diffraction patterns of polymer crystals is due to the fact that molecules, in this case polymer chains, rather than atoms, make up the lattice points of the unit cells. For example, the unit cell of polyethylene is orthorhombic, with polyethylene chains forming the lattice points, as illustrated in Figure 1.65. As a result, the dimensions of the unit cells in polymer crystals tend to be much bigger than those for ceramics and metals. The orthorhombic unit cell for polyethylene in Figure 1.65 has dimensions a=7.42 ˚A,b=4.95 ˚A,c=2.55 ˚A, with two chains per unit cell: one in the center and 4×(1/4) at each corner where four unit cells come together. The larger lattice parameters and increased interplanar spacings mean that the diffraction angles for polymers are generally much smaller than for ceramics and metals [recall thatθ∝1/d, see Eq. (1.35)]. Hence,small-angle X-ray scattering (SAXS) is often used for polymer structural characterization instead of the traditionalwide-angle X-ray scattering (WAXS).
As with ceramics and metals, polymer crystals can have multiple crystal forms.
Polyethylene has a metastable monoclinic form and a orthohexagonal high pressure form. A list of some of the more common polymers and their corresponding crystal structures is given in Table 1.24. Finally, X-ray diffraction can be used to determine the amorphous to crystalline ratio in semicrystalline polymers in much the same way that Eq. (1.61) can be used. Figure 1.66 shows a schematic illustration of the X-ray diffraction patterns for semicrystalline and amorphous polyethylene. The estimation of crystalline content is based upon a ratio of the peak areas in the two samples.
More so than in metals, glasses, and ceramics, the microstructure in polymers is easily altered and within the operating temperature and pressure of many industrial and biological processes, transitions between the amorphous and crystalline state, and the ratio between the amorphous and crystalline components, can easily take place. As we mentioned in the previous section, the amorphous component of a polymer is less dense than the crystalline component. Conversely, thespecific volume, or volume per mole in cubic centimeters, is lower for polymer crystals than it is for amorphous polymers. This distinction is best understood by observing the volume change of a polymer melt as it cools. Consider a molten polymer at point A in Figure 1.67. If we cool the polymer melt slowly, as in pathABG, the polymer chains have sufficient time to rearrange, fold, and form lamellar structures, resulting in a crystalline polymer, provided, of course, that they have the propensity to fold in the first place, and are not prevented from doing so by such factors as steric effects. The point at which the melt solidifies in the form of crystals is called the crystalline melting point,Tm, and is characterized by a sharp decrease in the specific volume and an increase in the density. If the same polymer melt is cooled rapidly, as in the pathABCD, a supercooled liquid is first obtained at point C, followed by an amorphous solid, orglassy polymer, at point D, due to insufficient time for the large molecules to arrange themselves in an ordered structure. The point
Table 1.24 The Crystal Structures of Selected Polymers
Lattice Constants, ˚A
Crystal Density
Polymer Crystal System a b c (g/cm3)
Polyethylene Orthorhombic 7.417 4.945 2.547 1.00
Polytetrafluoroethylene Trigonal(>19◦C) 5.66 — 19.50 2.30
Isotactic α-Monoclinic 6.65 20.96 6.50 0.936
polypropylene β-Hexagonal 19.08 — 6.49 0.922
Syndiotactic polypropylene
Orthorhombic 14.50 5.60 7.40 0.93
Isotactic polystyrene Trigonal 21.90 — 6.65 1.13
Poly(vinyl chloride) Orthorhombic 10.6 5.4 5.1 1.42
Poly(vinyl alcohol) Monoclinic 7.81 2.25 5.51 1.35
Poly(vinyl fluoride) Orthorhombic 8.57 4.95 2.52 1.430
Poly(vinylidine α-Monoclinic 4.96 9.64 4.62 1.925
fluoride) β-Orthorhombic 8.58 4.91 2.56 1.973
Isotactic poly(methyl methacrylate)
Orthorhombic 20.98 12.06 10.40 1.26
trans-1,4-Polybutadiene Monoclinic 8.63 9.11 4.83 1.04
cis-1,4-Polybutadiene Monoclinic 4.60 9.50 8.60 1.01
Poly(ethylene oxide) Monoclinic 8.05 13.04 19.48 1.228
triclinic 4.71 4.44 7.12 1.197
Isotactic
poly(propylene oxide)
Orthorhombic 10.46 4.66 7.03 1.126
Nylon 66 α-Triclinic 4.9 5.4 17.2 1.24
β-Triclinic 4.9 8.0 17.2 1.248
2,6-Polyurethane Triclinic 4.93 4.58 16.8 1.27
Triclinic 4.59 5.14 13.9 1.33
3,6-Polyurethane Monoclinic 4.70 8.66 33.9 1.34
Polyketone Orthorhombic 7.97 4.76 7.57 1.296
Poly(ethylene sulfide) Orthorhombic 8.50 4.95 6.70 1.416
Polyisobutylene Orthorhombic 6.88 11.91 18.60 0.972
Poly(isobutylene oxide) Orthorhombic 10.76 5.76 7.00 1.10
Poly(ethylene sulfide) Orthorhombic 8.50 4.95 6.70 1.60
Isotactic poly(vinyl methyl ether)
Trigonal 16.25 — 6.50 1.168
Source: Tadokoro,Structure of Crystalline Polymers.
at which the slope of the specific volume with temperature curve decreases (between C and D), representing solidification, is called the glass transition temperature, Tg. The reasoning behind the term “glass transition temperature” becomes more apparent if we turn around and begin slowly heating the glassy polymer. At some point, there is sufficient mobility in the polymer chains for them to begin to align themselves in a regular array and form crystallites. The polymer is not yet molten—there is simply short range chain movement that results in an amorphous to crystalline transformation in the solid state. This point is alsoTg. As we continue to heat the sample, the now- crystalline polymer eventually reachesTmand melts. Most polymers are a combination
STRUCTURE OF POLYMERS 93
Amorphous 110
200
Intensity
Diffraction angle Background
Figure 1.66 Resolution of the X-ray scattering curve of a semicrystalline polyethylene sample into contributions from crystalline (110 and 200 planes) and amorphous components. From F. W. Billmeyer, Textbook of Polymer Science, 3rd ed. Copyright 1984 by John Wiley &
Sons, Inc. This material is used by permission of John Wiley & Sons, Inc.
of amorphous and crystalline components and are the result of intermediate cooling paths such asABEF in Figure 1.67. Keep in mind that some polymers, no matter how slowly we cool them, cannot crystallize, and they follow the glassy pathABCD all the time. We will have more to say about the glass transition temperature in Section 1.3.7.
1.3.6.2 Liquid Crystalline Polymers. One class of polymers that requires some special attention from a structural standpoint is liquid crystalline polymers, or LCPs.
Liquid crystalline polymers are nonisotropic materials that are composed of long molecules parallel to each other in large clusters and that have properties intermediate between those of crystalline solids and liquids. Because they are neither completely liquids nor solids, LCPs are called mesophase (intermediate phase) materials. These mesophase materials have liquid-like properties, so that they can flow; but under cer- tain conditions, they also have long-range order and crystal structures. Because they are liquid-like, LCPs have a translational degree of freedom that most solid crystals we have described so far do not have. That is, crystals have three-dimensional order, whereas LCPs have only one- or two-dimensional order. Nevertheless, they are called
“crystals,” and we shall treat them as such in this section.
In many cases, these polymer chains take on a rod-like (calamitic LCPs) or even disc-like (discotic LCPs) conformation, but this does not affect the overall structural classification scheme. There are many organic compounds, though not polymeric in nature, that exhibit liquid crystallinity and play important roles in biological processes.
For example, arteriosclerosis is possibly caused by the formation of a cholesterol containing liquid crystal in the arteries of the heart. Similarly, cell wall membranes are generally considered to have liquid crystalline properties. As interesting as these examples of liquid crystallinity in small, organic compounds are, we must limit the current discussion to polymers only.
Tg T V
D
F
E
G C
B A
Tm
Figure 1.67 Specific volume as a function of temperature on cooling from the melt for a poly- mer that tends to crystallize. RegionA is liquid,B liquid with elastic response,C supercooled liquid,D glass,E crystallites in a supercooled liquid matrix,F crystallites in a glassy matrix, andG completely crystalline. PathsABCD, ABEF, andABG represent fast, intermediate, and very slow cooling rates, respectively. From K. M. Ralls, T. H. Courtney, and J. Wulff,Intro- duction to Materials Science and Engineering. Copyright1976 by John Wiley & Sons, Inc.
This material is used by permission of John Wiley & Sons, Inc.
There are three categories of LCPs, grouped according to the arrangement of the molecules: smectic, nematic, and cholesteric. Nematic (from the Greek term mean- ing “thread-like”) LCPs have their molecules aligned along the chain axis, as shown schematically in Figure 1.68. Nematic liquids have low viscosity, and tend to be turbid, or “cloudy.”Smectic (from the Greek term for “soap”) LCPs have an additional level of structure, in that the polymer chains are also aligned along the chain axis, but they also segregate into layers. Smectic liquids are also turbid, but tend to be highly viscous.
Finally,cholesteric(from the Greek term for “bile”) LCPs have layered structures, but the aligned polymer chains in one layer are rotated from the aligned polymer chains in adjacent layers. Cholesteric LCPs are also highly viscous, but often possess novel photochromic, optical, thermochromic, and electro-optical properties.
Clearly, not all polymeric molecules possess the ability to form LCPs. Generally, LCPs have a molecular structure in which there are two regions with dissimilar chemical properties. For example, chains that consist of aliphatic–aromatic, dipo- lar–nonpolar, hydrophobic–hydrophilic, flexible –rigid, or hydrocarbon–fluorocarbon combinations of substantial size have a propensity to form LCPs. The two different por- tions of the chains can interact locally with similar regions of adjacent chains, leading to ordering. Liquid crystalline polymers that rely on structural units in the backbone, or main chain, to impart their crystallinity are calledmain-chain LCPs. The building blocks of typical main-chain LCPs are shown in Figure 1.69. Side-chain LCPs crys- tallize due to interaction of the side chains, or branches, as shown in Figure 1.69. Side
STRUCTURE OF POLYMERS 95
(a)
(b)
Figure 1.68 The structure of liquid crystalline polymers (a) nematic, (b) smectic and (c) cholesteric. Reprinted, by permission, from J. L. Fergason,Scientific American,211(2), pp. 78, 80. Copyright1964 by Scientific American, Inc.
(c)
Figure 1.68 (continued).
chains play an important role in determining not only the liquid crystalline activity of polymers, but the type of structure that will form as well. For example, in Table 1.25, we see that the number of hydrocarbon units in the side chain (not the backbone repeat unit) affects whether the resulting LCP is nematic or smectic.
We have used the general term “liquid” to describe this special class of polymers, but we know that a liquid can be either a melt or a solution. In the case of LCPs, both
STRUCTURE OF POLYMERS 97
Table 1.25 Effect of the Flexible Tail on the Structure of a Side-Chain LCP
C CH2
CH3 COO (CH2)n O COO R
Number n R Structure
1 2 OCH3 Nematic
2 2 OC3H7 Smectic
3 6 OCH3 Nematic
4 6 OC6H13 Smectic
Flexible Tail S.C. LCPs
M.C. LCPs
Flexible Tail
none none none none
R O R C N
Cholesteryl Cyclic Unit
Cyclic Unit Cyclic Unit
Bridging Group Bridging Group Bridging Group
Cyclic Unit Cyclic Unit
Functional Unit Functional Unit Functional Unit
Spacer
Spacer n
n
Spacer
Functional Unit
Flexible Backbone
Flexible Backbone
X
1, 3 CO
1, 4
1, 4 1, 5 2, 6
n=1, 2, 3 X=Me
Ph Cl
O CR CR CR NO CO NH NO N
C C
CR N N CR
O CO O O CO
(CH2)n
S R S
SiR2 O (CH2 CHR)n NR' R NR'
CH CHR
SiR O SiR2 O SiR O
Figure 1.69 General structure of main-chain (M.C.) and side-chain (S.C.) LCPs. Adapted from T. S. Chung, The recent developments of thermotropic liquid crystalline polymers, Polymer Engineering and Science, 26(13), p. 903. Copyright1986, Society of Plastics Engineers.
types of liquids can occur. A polymer that exhibits crystallinity in the melt and that undergoes an ordered–disordered transformation as a result of thermal effects is called athermotropic LCP. A polymer requiring a small molecule solvent in order to exhibit crystallinity is termed alyotropicLCP. All three types of LCP structures can occur in either thermotropic or lyotropic polymers, and both are industrially relevant materials.
N H C O
C O N H
N H C O
Figure 1.70 The repeat structure of Kevlar.
Perhaps the most widely utilized (and studied) lyotropic LCP is poly p-phenylene terephthalamide (PPTA), more commonly known as Kevlar(see Figure 1.70). Kevlar belongs to the class of aramids that are well known for their LCP properties. Because these polymers are crystalline in solution, they are often spun into filaments, from which the solvent is subsequently removed in order to retain the aligned polymer structure.
The result is a highly oriented, strong filament that can be used for a wide variety of structural applications. Most thermotropic LCPs are polyesters or copolymers that can be melted and molded into strong, durable objects.
200 300 400 500 600
100 200 300 400
Tm (K ) Tg (K)
Region having no physical meaning
Tg = 0.5Tm
Branched polyethylene
Block copolymers Linear polyethylene
Nylon 66 x
xx x
x
x x
x
Polyvinylidene chloride Isotactic
polypropylene
Polyvinyl chloride Isotactic polystyrene
Nylon 6 Semicrystalline
random copolymers
Tg = Tm
Tg = 0.74 Tm
Homopolymers Neoprene
Natural rubber Silicone rubber
Figure 1.71 The glass transition temperature,Tg, as a function of crystalline melting point, Tm, for homopolymers. Filled circles are addition homopolymers, open circles are elastomers, and crosses are condensation homopolymers. From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright1976 by John Wiley & Sons, Inc. This material is used by permission of John Wiley & Sons, Inc.