6 Introduction to Chain Molecules a 160nm (b) Figure 1.1 (a)Individual molecules of DNA of various sizes,spread on a fluid positively charged surface, imaged by fluorescence.The scale bar is 10 um.(Reproduced from Maier,B.and Radler,J.O.Macromolecules 33,7185,2000.With permission.)(b)Atomic force microscopy images of three-arm star polymers,where each arm is a heavily branched comb.The circles indicate linear molecules.(Reproduced from Matyjaszewski,K., Qin,S.,Boyce,J.R.,Shirvanyants,D.,and Sheiko,S.S.Macromolecules 36,1843,2003.With permission.) the molecule in the environment.Relevant aspects of polymer solutions are taken up in Chapter 6 through Chapter 9. Figure 1.1a and Figure 1.1b are rather striking images of individual polymer molecules.Figure 1.la shows single molecules of DNA that have been heavily labeled with fluorescent dyes;the dyes
the molecule in the environment. Relevant aspects of polymer solutions are taken up in Chapter 6 through Chapter 9. Figure 1.1a and Figure 1.1b are rather striking images of individual polymer molecules. Figure 1.1a shows single molecules of DNA that have been heavily labeled with fluorescent dyes; the dyes Figure 1.1 (a) Individual molecules of DNA of various sizes, spread on a fluid positively charged surface, imaged by fluorescence. The scale bar is 10 mm. (Reproduced from Maier, B. and Ra¨dler, J.O. Macromolecules 33, 7185, 2000. With permission.) (b) Atomic force microscopy images of three-arm star polymers, where each arm is a heavily branched comb. The circles indicate linear molecules. (Reproduced from Matyjaszewski, K., Qin, S., Boyce, J.R., Shirvanyants, D., and Sheiko, S.S. Macromolecules 36, 1843, 2003. With permission.) Hiemenz/ Polymer Chemistry, 2nd Edition DK4670_C001 Final Proof page 6 5.11.2007 8:21pm Compositor Name: JGanesan 6 Introduction to Chain Molecules
Linear and Branched Polymers,Homopolymers,and Copolymers 7 intercalate between the base pairs along the chain,without seriously altering the conformation of the molecule.Under illumination the resulting fluorescence provides a good representation of the molecules themselves.In this particular image,the DNA molecules are spread out in two dimensions,on a cationically charged imitation lipid membrane.DNA,as it turns out,is an excellent example of a semiflexible chain,which can actually be inferred from these images;the molecules are not straight rods,but neither are they heavily coiled around themselves.The scale bar corresponds to 10 um,indicating that these molecules are of very high molecular weight indeed.In Figure 1.1b,the image is of a star-shaped polymer,but one in which each arm of the star is a heavily branched comb or"bottlebrush."The molecule is thus akin to a kind of starfish,with very hairy arms.This picture was obtained by atomic force microscopy(AFM), one of a series of surface-sensitive analysis techniques with exquisite spatial resolution.The molecules themselves were deposited from a Langmuir-Blodgett trough onto a mica substrate. Both situations depicted in Figure 1.1a and Figure 1.1b raise the question of the relationship between the conformation observed on the surface and that at equilibrium in solution.In Chapter 6 through Chapter 9 we will encounter several ways in which the solution conformation can be determined reliably,which can serve to confirm the impression derived from figures such as these. We conclude this section by questioning whether there is a minimum molecular weight or linear dimension that must be met for a molecule to qualify as a polymer.Although a dimer is a molecule for which N=2,no one would consider it a polymer.The term oligomer has been coined to designate molecules for which N<10.If they require a special name,apparently the latter are not full-fledged polymers either.At least as a first approximation,we shall take the attitude that there is ordinarily no discontinuity in behavior with respect to observed properties as we progress through a homologous series of compounds with different N values.At one end of the series,we may be dealing with a simple low molecular weight compound,and at the other end with a material that is unquestionably polymeric.The molecular weight and chain length increase monotonically through this series,and a variety of other properties vary smoothly also.This point of view emphasizes continuity with familiar facts concerning the properties of low molecular weight compounds.There are some properties,on the other hand,which follow so closely from the chain structure of polymers that the property is simply not observed until a certain critical molecular size has been reached.This critical size is often designated by a threshold molecular weight.The elastic behavior of rubber and several other mechanical properties fall into this latter category.In theoretical developments,large values of N are often assumed to justify neglecting end effects,using certain statistical methods and other mathematical approximations.With these ideas in mind,M=1000 seems to be a convenient round number for designating a compound to be a polymer,although it should be clear that this cutoff is arbitrary (and on the low side). 1.3 Linear and Branched Polymers,Homopolymers,and Copolymers 1.3.1 Branched Structures Most of the preceding section was based on the implicit assumption that polymer chains are linear(with the striking exception of Figure 1.1b).In evaluating both the degree of polymeriza- tion and the extended chain length,we assumed that the chain had only two ends.While linear polymers are important,they are not the only type of molecules possible:branched and cross- linked molecules are also common.When we speak of a branched polymer,we refer to the presence of additional polymeric chains issuing from the backbone of a linear molecule.(Small substituent groups such as methyl or phenyl groups on the repeat units are generally not considered branches,or,if they are,they should be specified as "short-chain branches.") Branching can arise through several routes.One is to introduce into the polymerization reaction some monomer with the capability of serving as a branch.Consider the formation of a polyester
intercalate between the base pairs along the chain, without seriously altering the conformation of the molecule. Under illumination the resulting fluorescence provides a good representation of the molecules themselves. In this particular image, the DNA molecules are spread out in two dimensions, on a cationically charged imitation lipid membrane. DNA, as it turns out, is an excellent example of a semiflexible chain, which can actually be inferred from these images; the molecules are not straight rods, but neither are they heavily coiled around themselves. The scale bar corresponds to 10 mm, indicating that these molecules are of very high molecular weight indeed. In Figure 1.1b, the image is of a star-shaped polymer, but one in which each arm of the star is a heavily branched comb or ‘‘bottlebrush.’’ The molecule is thus akin to a kind of starfish, with very hairy arms. This picture was obtained by atomic force microscopy (AFM), one of a series of surface-sensitive analysis techniques with exquisite spatial resolution. The molecules themselves were deposited from a Langmuir–Blodgett trough onto a mica substrate. Both situations depicted in Figure 1.1a and Figure 1.1b raise the question of the relationship between the conformation observed on the surface and that at equilibrium in solution. In Chapter 6 through Chapter 9 we will encounter several ways in which the solution conformation can be determined reliably, which can serve to confirm the impression derived from figures such as these. We conclude this section by questioning whether there is a minimum molecular weight or linear dimension that must be met for a molecule to qualify as a polymer. Although a dimer is a molecule for which N ¼ 2, no one would consider it a polymer. The term oligomer has been coined to designate molecules for which N < 10. If they require a special name, apparently the latter are not full-fledged polymers either. At least as a first approximation, we shall take the attitude that there is ordinarily no discontinuity in behavior with respect to observed properties as we progress through a homologous series of compounds with different N values. At one end of the series, we may be dealing with a simple low molecular weight compound, and at the other end with a material that is unquestionably polymeric. The molecular weight and chain length increase monotonically through this series, and a variety of other properties vary smoothly also. This point of view emphasizes continuity with familiar facts concerning the properties of low molecular weight compounds. There are some properties, on the other hand, which follow so closely from the chain structure of polymers that the property is simply not observed until a certain critical molecular size has been reached. This critical size is often designated by a threshold molecular weight. The elastic behavior of rubber and several other mechanical properties fall into this latter category. In theoretical developments, large values of N are often assumed to justify neglecting end effects, using certain statistical methods and other mathematical approximations. With these ideas in mind, M ¼ 1000 seems to be a convenient round number for designating a compound to be a polymer, although it should be clear that this cutoff is arbitrary (and on the low side). 1.3 Linear and Branched Polymers, Homopolymers, and Copolymers 1.3.1 Branched Structures Most of the preceding section was based on the implicit assumption that polymer chains are linear (with the striking exception of Figure 1.1b). In evaluating both the degree of polymerization and the extended chain length, we assumed that the chain had only two ends. While linear polymers are important, they are not the only type of molecules possible: branched and crosslinked molecules are also common. When we speak of a branched polymer, we refer to the presence of additional polymeric chains issuing from the backbone of a linear molecule. (Small substituent groups such as methyl or phenyl groups on the repeat units are generally not considered branches, or, if they are, they should be specified as ‘‘short-chain branches.’’) Branching can arise through several routes. One is to introduce into the polymerization reaction some monomer with the capability of serving as a branch. Consider the formation of a polyester. Hiemenz/ Polymer Chemistry, 2nd Edition DK4670_C001 Final Proof page 7 5.11.2007 8:21pm Compositor Name: JGanesan Linear and Branched Polymers, Homopolymers, and Copolymers 7
8 Introduction to Chain Molecules The presence of difunctional acids and difunctional alcohols allows the polymer chain to grow.These difunctional molecules are incorporated into the chain with ester linkages at both ends of each.Trifunctional acids or alcohols,on the other hand,produce a linear molecule by the reaction of two of their functional groups.If the third reacts and the resulting chain continues to grow,a branch has been introduced into the original chain.A second route is through adventitious branching,for example,as a result of an atom being abstracted from the original linear molecule,with chain growth occurring from the resulting active site.This is quite a common occurrence in the free-radical polymerization of ethylene,for example.A third route is grafting,whereby pre-formed but still reactive polymer chains can be added to sites along an existing backbone (so-called "grafting to"),or where multiple initiation sites along a chain can be exposed to monomer (so-called "grafting from"). The amount of branching introduced into a polymer is an additional variable that must be specified for the molecule to be fully characterized.When only a slight degree of branching is present,the concentration of junction points is sufficiently low that these may be simply related to the number of chain ends.For example,two separate linear molecules have a total of four ends.If the end of one of these linear molecules attaches itself to the middle of the other to form a T,the resulting molecule has three ends.It is easy to generalize this result.If a molecule has v branches,it has v+2 chain ends if the branching is relatively low.Two limiting cases to consider,illustrated in Figure 1.2,are combs and stars.In the former,a series of relatively uniform branches emanate from along the length of a common backbone;in the latter,all branches radiate from a central junction.Figure 1.1b gave an example of both of these features. If the concentration of junction points is high enough,even branches will contain branches. Eventually a point can be reached at which the amount of branching is so extensive that the polymer molecule becomes a giant three-dimensional network.When this condition is achieved, the molecule is said to be cross-linked.In this case,an entire macroscopic object may be considered to consist of essentially one molecule.The forces that give cohesiveness to such a body are covalent bonds,not intermolecular forces.Accordingly,the mechanical behavior of cross-linked bodies is much different from those without cross-linking.This will be discussed at length in Chapter 10.However,it is also possible to suppress cross-linking such that the highly branched molecules remain as discrete entities,known as hyperbranched polymers(see Figure 1.2). Another important class of highly branched polymers illustrated in Figure 1.2 are dendrimers,or treelike molecules.These are completely regular structures,with well-defined molecular weights, that are made by the successive condensation of branched monomers.For example,begin with a Hyperbranched Four-arm star Comb Dendrimer Figure 1.2 Illustration of various polymer architectures
The presence of difunctional acids and difunctional alcohols allows the polymer chain to grow. These difunctional molecules are incorporated into the chain with ester linkages at both ends of each. Trifunctional acids or alcohols, on the other hand, produce a linear molecule by the reaction of two of their functional groups. If the third reacts and the resulting chain continues to grow, a branch has been introduced into the original chain. A second route is through adventitious branching, for example, as a result of an atom being abstracted from the original linear molecule, with chain growth occurring from the resulting active site. This is quite a common occurrence in the free-radical polymerization of ethylene, for example. A third route is grafting, whereby pre-formed but still reactive polymer chains can be added to sites along an existing backbone (so-called ‘‘grafting to’’), or where multiple initiation sites along a chain can be exposed to monomer (so-called ‘‘grafting from’’). The amount of branching introduced into a polymer is an additional variable that must be specified for the molecule to be fully characterized. When only a slight degree of branching is present, the concentration of junction points is sufficiently low that these may be simply related to the number of chain ends. For example, two separate linear molecules have a total of four ends. If the end of one of these linear molecules attaches itself to the middle of the other to form a T, the resulting molecule has three ends. It is easy to generalize this result. If a molecule has n branches, it has n þ 2 chain ends if the branching is relatively low. Two limiting cases to consider, illustrated in Figure 1.2, are combs and stars. In the former, a series of relatively uniform branches emanate from along the length of a common backbone; in the latter, all branches radiate from a central junction. Figure 1.1b gave an example of both of these features. If the concentration of junction points is high enough, even branches will contain branches. Eventually a point can be reached at which the amount of branching is so extensive that the polymer molecule becomes a giant three-dimensional network. When this condition is achieved, the molecule is said to be cross-linked. In this case, an entire macroscopic object may be considered to consist of essentially one molecule. The forces that give cohesiveness to such a body are covalent bonds, not intermolecular forces. Accordingly, the mechanical behavior of cross-linked bodies is much different from those without cross-linking. This will be discussed at length in Chapter 10. However, it is also possible to suppress cross-linking such that the highly branched molecules remain as discrete entities, known as hyperbranched polymers (see Figure 1.2). Another important class of highly branched polymers illustrated in Figure 1.2 are dendrimers, or treelike molecules. These are completely regular structures, with well-defined molecular weights, that are made by the successive condensation of branched monomers. For example, begin with a Linear Cycle Four-arm star Comb Hyperbranched Dendrimer Figure 1.2 Illustration of various polymer architectures. Hiemenz/ Polymer Chemistry, 2nd Edition DK4670_C001 Final Proof page 8 5.11.2007 8:21pm Compositor Name: JGanesan 8 Introduction to Chain Molecules
Linear and Branched Polymers,Homopolymers,and Copolymers 9 trifunctional monomer"B3,"or "generation 0."This is reacted with an excess of AB2 monomers, leading to a generation 1 dendrimer with 6 B groups.A second reaction with AB2 leads to generation 2 with 12 pendant B groups.Eventually,perhaps at generation 6 or 7,the surface of the molecule becomes so congested that addition of further complete generations is impossible. Note that the "B"part of the AB2 monomer needs to be protected in some way so that only one generation can be added at one time. A final class of nonlinear polymers to consider are cycles or rings,whereby the two ends of the molecule react to close the loop.Such polymers are currently more of academic interest than commercial importance,as they are tricky to prepare,but they can shed light on various aspects of polymer behavior.Interestingly,nature makes use of this architecture;the DNA of the Lambda bacteriophage reversibly cyclizes and uncyclizes during gene expression. 1.3.2 Copolymers Just as it is not necessary for polymer chains to be linear,it is also not necessary for all repeat units to be the same.We have already mentioned proteins,where a wide variety of different repeat units are present.Among synthetic polymers,those with a single kind of repeat unit are called homopolymers,and those containing more than one kind of repeat unit are copolymers.Note that these definitions are based on the repeat unit,not the monomer.An ordinary polyester is not really a copolymer,even though two different monomers,acids and alcohols,are its monomers. By contrast,copolymers result when different monomers bond together in the same way to produce a chain in which each kind of monomer retains its respective substituents in the polymer molecule. The unmodified term copolymer is generally used to designate the case where two different repeat units are involved.Where three kinds of repeat units are present,the system is called a terpolymer. where there are more than three,the system is called a multicomponent copolymer.The copoly- mers we discuss in this book will be primarily two-component molecules.We shall explore aspects of the synthesis and characterization of copolymers in both Chapter 4 and Chapter 5. The moment we admit the possibility of having more than one kind of repeat unit,we require additional variables to describe the polymer.First,we must know how many kinds of repeat units are present and what they are.To describe the copolymer quantitatively,the relative amounts of the different kinds of repeat units must be specified.Thus the empirical formula of a copolymer may be written A By.where A and B signify the individual repeat units and x and y indicate the relative number of each.From a knowledge of the molecular weight of the polymer,the molecular weights of A and B,and the values ofx and y,it is possible to calculate the number of each kind of monomer unit in the copolymer.The sum of these values gives the degree of polymerization of the copolymer.The following example illustrates some of the ways of describing a copolymer. Example 1.2 A terpolymer is prepared from vinyl monomers A,B,and C;the molecular weights of the repeat units are 104.184,and 128,respectively.A particular polymerization procedure yields a product with the empirical formula A3.s5 B220 C1oo.The authors of this research state that the terpolymer has "an average unit weight of 134"and "the average molecular weight per angstrom of 53.5." Verify these values. Solution The empirical formula gives the relative amounts of A,B,and C in the terpolymer.The total molecular weight of this empirical formula unit is given by adding the molecular weight contri- butions of A,B,and C:3.44(104)+2.20(184)+1.00(128)=902 g/mol per empirical formula unit. tA.Ravve and J.T.Khamis,Addition and Condensation Polymerization Processes,Advances in Chemistry Series,Vol.91, American Chemical Society Publications,Washington,DC.1969
trifunctional monomer ‘‘B3,’’ or ‘‘generation 0.’’ This is reacted with an excess of AB2 monomers, leading to a generation 1 dendrimer with 6 B groups. A second reaction with AB2 leads to generation 2 with 12 pendant B groups. Eventually, perhaps at generation 6 or 7, the surface of the molecule becomes so congested that addition of further complete generations is impossible. Note that the ‘‘B’’ part of the AB2 monomer needs to be protected in some way so that only one generation can be added at one time. A final class of nonlinear polymers to consider are cycles or rings, whereby the two ends of the molecule react to close the loop. Such polymers are currently more of academic interest than commercial importance, as they are tricky to prepare, but they can shed light on various aspects of polymer behavior. Interestingly, nature makes use of this architecture; the DNA of the Lambda bacteriophage reversibly cyclizes and uncyclizes during gene expression. 1.3.2 Copolymers Just as it is not necessary for polymer chains to be linear, it is also not necessary for all repeat units to be the same. We have already mentioned proteins, where a wide variety of different repeat units are present. Among synthetic polymers, those with a single kind of repeat unit are called homopolymers, and those containing more than one kind of repeat unit are copolymers. Note that these definitions are based on the repeat unit, not the monomer. An ordinary polyester is not really a copolymer, even though two different monomers, acids and alcohols, are its monomers. By contrast, copolymers result when different monomers bond together in the same way to produce a chain in which each kind of monomer retains its respective substituents in the polymer molecule. The unmodified term copolymer is generally used to designate the case where two different repeat units are involved. Where three kinds of repeat units are present, the system is called a terpolymer; where there are more than three, the system is called a multicomponent copolymer. The copolymers we discuss in this book will be primarily two-component molecules. We shall explore aspects of the synthesis and characterization of copolymers in both Chapter 4 and Chapter 5. The moment we admit the possibility of having more than one kind of repeat unit, we require additional variables to describe the polymer. First, we must know how many kinds of repeat units are present and what they are. To describe the copolymer quantitatively, the relative amounts of the different kinds of repeat units must be specified. Thus the empirical formula of a copolymer may be written AxBy, where A and B signify the individual repeat units and x and y indicate the relative number of each. From a knowledge of the molecular weight of the polymer, the molecular weights of A and B, and the values of x and y, it is possible to calculate the number of each kind of monomer unit in the copolymer. The sum of these values gives the degree of polymerization of the copolymer. The following example illustrates some of the ways of describing a copolymer. Example 1.2 A terpolymer is prepared from vinyl monomers A, B, and C; the molecular weights of the repeat units are 104, 184, and 128, respectively. A particular polymerization procedure yields a product with the empirical formula A3.55B2.20C1.00. The authors of this research state that the terpolymer has ‘‘an average unit weight of 134’’ and ‘‘the average molecular weight per angstrom of 53.5.’’ Verify these values.y Solution The empirical formula gives the relative amounts of A, B, and C in the terpolymer. The total molecular weight of this empirical formula unit is given by adding the molecular weight contributions of A, B, and C: 3.44(104) þ 2.20(184) þ 1.00(128) ¼ 902 g/mol per empirical formula unit. y A. Ravve and J.T. Khamis, Addition and Condensation Polymerization Processes, Advances in Chemistry Series, Vol. 91, American Chemical Society Publications, Washington, DC, 1969. Hiemenz/ Polymer Chemistry, 2nd Edition DK4670_C001 Final Proof page 9 5.11.2007 8:21pm Compositor Name: JGanesan Linear and Branched Polymers, Homopolymers, and Copolymers 9
10 Introduction to Chain Molecules The total amount of chain repeat units possessing this total weight is 3.55+2.20+1.00=6.75 repeat units per empirical formula unit.The ratio of the total molecular weight to the total number of repeat units gives the average molecular weight per repeat unit: 902 6.75 =134 g/mol per repeat unit Since the monomers are specified to be vinyl monomers,each contributes two carbon atoms to the polymer backbone,with the associated extended length of 0.252 nm per repeat unit.Therefore,the total extended length of the empirical formula unit is 6.75(0.252nm)=1.79nm=17.0A The ratio of the total weight to the total extended length of the empirical formula unit gives the average molecular weight per length of chain: 902 17 =53 g/mol per A Note that the average weight per repeat unit could be used to evaluate the overall degree of polymerization of this terpolymer.For example,if the molecular weight were 43,000,the corre- sponding degree of polymerization would be 43,000 134 =321 repeat units per molecule With copolymers,it is far from sufficient merely to describe the empirical formula to charac- terize the molecule.Another question that must be asked concems the location of the different kinds of repeat units within the molecule.Starting from monomers A and B,the following distribution patterns can be obtained in linear polymers: 1.Random (or statistical).The A-B sequence is governed strictly by chance,subject only to the relative abundances of repeat units.For equal proportions of A and B,we might have structures like -AAABABAABBABBB- Such a polymer could be called poly(A-stat-B)or poly(A-ran-B). 2.Alternating.A regular pattern of alternating repeat units in poly(A-alt-B): -ABABABABABAB- 3.Block.Long,uninterrupted sequence of each monomer is the pattern: -AAAAAAAAAAAAAABBBBBBBBBBBBBBBAAAAAAAAA- The above structure has three blocks,and is called poly(A-block-B-block-A),or an ABA triblock copolymer.If a copolymer is branched with different repeat units occurring in the branches and the backbone,we can have the following: 4.Graft.This segregation is often accomplished by first homopolymerizing the backbone.This is dissolved in the second monomer,with sites along the original chain becoming the origin of the comonomer side-chain growth: BBBBBBBBBB- -AAAAAAAAAAAAAAAAA- -BBBBBBBBBB BBBBBBB-
The total amount of chain repeat units possessing this total weight is 3.55 þ 2.20 þ 1.00 ¼ 6.75 repeat units per empirical formula unit. The ratio of the total molecular weight to the total number of repeat units gives the average molecular weight per repeat unit: 902 6:75 ¼ 134 g=mol per repeat unit Since the monomers are specified to be vinyl monomers, each contributes two carbon atoms to the polymer backbone, with the associated extended length of 0.252 nm per repeat unit. Therefore, the total extended length of the empirical formula unit is 6:75(0:252 nm) ¼ 1:79 nm ¼ 17:0 A The ratio of the total weight to the total extended length of the empirical formula unit gives the average molecular weight per length of chain: 902 17 ¼ 53 g=mol per A Note that the average weight per repeat unit could be used to evaluate the overall degree of polymerization of this terpolymer. For example, if the molecular weight were 43,000, the corresponding degree of polymerization would be 43,000 134 ¼ 321 repeat units per molecule With copolymers, it is far from sufficient merely to describe the empirical formula to characterize the molecule. Another question that must be asked concerns the location of the different kinds of repeat units within the molecule. Starting from monomers A and B, the following distribution patterns can be obtained in linear polymers: 1. Random (or statistical). The A–B sequence is governed strictly by chance, subject only to the relative abundances of repeat units. For equal proportions of A and B, we might have structures like –AAABABAABBABBB– Such a polymer could be called poly(A-stat-B) or poly(A-ran-B). 2. Alternating. A regular pattern of alternating repeat units in poly(A-alt-B): –ABABABABABAB– 3. Block. Long, uninterrupted sequence of each monomer is the pattern: –AAAAAAAAAAAAAABBBBBBBBBBBBBBBAAAAAAAAA– The above structure has three blocks, and is called poly(A-block-B-block-A), or an ABA triblock copolymer. If a copolymer is branched with different repeat units occurring in the branches and the backbone, we can have the following: 4. Graft. This segregation is often accomplished by first homopolymerizing the backbone. This is dissolved in the second monomer, with sites along the original chain becoming the origin of the comonomer side-chain growth: BBBBBBBBBB– j –AAAAAAAAAAAAAAAAA– j j –BBBBBBBBBB BBBBBBB– Hiemenz/ Polymer Chemistry, 2nd Edition DK4670_C001 Final Proof page 10 5.11.2007 8:21pm Compositor Name: JGanesan 10 Introduction to Chain Molecules