《高分子化学》课程教学资源（参考书籍）Paul C. Hiemenz&Timothy P. Lodge《Polymer Chemistry》第二版（Second Edition）.pdf_P36-P40

Structural Isomerism 21 Solution Begin by recognizing that a molecule containing x of the head-to-head links will be cleaved into x+1 molecules upon reaction.Hence if n is the number of polymer molecules in a sample of mass w,the following relations apply before and after cleavage:na=(x+1)np or w/Ma=(x+1) (w/Mp).Solving for x and dividing the latter by the total number of linkages in the original polymer gives the desired ratio.The total number of links in the original polymer is Mp/Mo Therefore the ratio is xMo/Mp=Mo(1/M-1/Mp).For poly(vinyl alcohol)Mo is 44,so the desired formula has been obtained.For the specific data given,x/np=44(10-3-10-5)=0.044,or about 4%of the additions are in the less favorable orientation.We shall see presently that the molecular weight of a polymer is an average,which is different depending on the method used for its determination.The present example used molecular weights as a means for counting the number of molecules present.Hence the sort of average molecular weight used should also be one which is based on counting. 1.6.2 Stereo Isomerism The second type of isomerism we discuss in this section is stereo isomerism.Again we consider the number of ways a singly substituted vinyl monomer can add to a growing polymer chain: (1.V (1.C) (1.X Structure (1.VIII)and Structure (1.IX)are not equivalent;they would not superimpose if the extended chains were overlaid.The difference has to do with the stereochemical configuration at the asymmetric carbon atoms.Note that the asymmetry is more accurately described as pseudoa- symmetry,since two sections of chain are bonded to these centers.Except near chain ends,which we ignore for high polymers,these chains provide local symmetry in the neighborhood of the carbon under consideration.The designations of D and L or R and S are used to distinguish these structures,even though true asymmetry is absent. We use the word configuration to describe the way the two isomers produced by Reaction(1.C) differ.It is only by breaking bonds,moving substituents,and reforming new bonds that the two structures can be interconverted.This state of affairs is most readily seen when the molecules are drawn as fully extended chains in one plane,and then examining the side of the chain on which substituents lie.The configurations are not altered if rotation is allowed to occur around the various bonds of the backbone to change the shape of the molecule to a jumbled coil.We shall use the term conformation to describe the latter possibilities for different molecular shapes. The configuration is not influenced by conformational changes,but the stability of different conformations may be affected by differences in configuration.We shall return to these effects in Chapter 6. In the absence of any external influence,such as a catalyst that is biased in favor of one configuration over the other,we might expect Structure (1.VIID)and Structure (1.IX)to occur at random with equal probability as if the configuration at each successive addition were determined by the toss of a coin.Such indeed is the ordinary case.However,in the early 1950s,stereospecific catalysts were discovered:Ziegler and Natta received the Nobel Prize for this discovery in 1963. Following the advent of these catalysts,polymers with a remarkable degree of stereoregularity have been formed.These have such a striking impact on polymer science that a substantial part of

Solution Begin by recognizing that a molecule containing x of the head-to-head links will be cleaved into x þ 1 molecules upon reaction. Hence if n is the number of polymer molecules in a sample of mass w, the following relations apply before and after cleavage: na ¼ (x þ 1) nb or w/Ma ¼ (x þ 1) (w/Mb). Solving for x and dividing the latter by the total number of linkages in the original polymer gives the desired ratio. The total number of links in the original polymer is Mb/M0. Therefore the ratio is xM0/Mb ¼ M0(1/Ma1/Mb). For poly(vinyl alcohol) M0 is 44, so the desired formula has been obtained. For the specific data given, x/nb ¼ 44(103 105 ) ¼ 0.044, or about 4% of the additions are in the less favorable orientation. We shall see presently that the molecular weight of a polymer is an average, which is different depending on the method used for its determination. The present example used molecular weights as a means for counting the number of molecules present. Hence the sort of average molecular weight used should also be one which is based on counting. 1.6.2 Stereo Isomerism The second type of isomerism we discuss in this section is stereo isomerism. Again we consider the number of ways a singly substituted vinyl monomer can add to a growing polymer chain: (1.VIII) ∗ X H H H X + ∗ X X ∗ X X (1:C) (1.IX) Structure (1.VIII) and Structure (1.IX) are not equivalent; they would not superimpose if the extended chains were overlaid. The difference has to do with the stereochemical configuration at the asymmetric carbon atoms. Note that the asymmetry is more accurately described as pseudoasymmetry, since two sections of chain are bonded to these centers. Except near chain ends, which we ignore for high polymers, these chains provide local symmetry in the neighborhood of the carbon under consideration. The designations of D and L or R and S are used to distinguish these structures, even though true asymmetry is absent. We use the word configuration to describe the way the two isomers produced by Reaction (1.C) differ. It is only by breaking bonds, moving substituents, and reforming new bonds that the two structures can be interconverted. This state of affairs is most readily seen when the molecules are drawn as fully extended chains in one plane, and then examining the side of the chain on which substituents lie. The configurations are not altered if rotation is allowed to occur around the various bonds of the backbone to change the shape of the molecule to a jumbled coil. We shall use the term conformation to describe the latter possibilities for different molecular shapes. The configuration is not influenced by conformational changes, but the stability of different conformations may be affected by differences in configuration. We shall return to these effects in Chapter 6. In the absence of any external influence, such as a catalyst that is biased in favor of one configuration over the other, we might expect Structure (1.VIII) and Structure (1.IX) to occur at random with equal probability as if the configuration at each successive addition were determined by the toss of a coin. Such indeed is the ordinary case. However, in the early 1950s, stereospecific catalysts were discovered; Ziegler and Natta received the Nobel Prize for this discovery in 1963. Following the advent of these catalysts, polymers with a remarkable degree of stereoregularity have been formed. These have such a striking impact on polymer science that a substantial part of Hiemenz/ Polymer Chemistry, 2nd Edition DK4670_C001 Final Proof page 21 5.11.2007 8:21pm Compositor Name: JGanesan Structural Isomerism 21

Chapter 5 is devoted to a discussion of their preparation and characterization. For now, only the terminology involved in their description concerns us. Three different situations can be distinguished along a chain containing pseudoasymmetric carbons: 1. Isotactic. All substituents lie on the same side of the extended chain. Alternatively, the stereoconfiguration at the asymmetric centers is the same, say, –DDDDDDDDD–. 2. Syndiotactic. Substituents on the fully extended chain lie on alternating sides of the backbone. This alternation of configuration can be represented as –DLDLDLDLDLDL–. 3. Atactic. Substituents are distributed at random along the chain, for example, DDLDLLLDLDLL–. Figure 1.3 shows sections of polymer chains of these three types; the substituent X equals phenyl for polystyrene and methyl for polypropylene. The general term for this stereoregularity is tacticity, a term derived from the Greek word meaning ‘‘to put in order.’’ Polymers of different tacticity have quite different properties, especially in the solid state. As we will see in Chapter 13, one of the requirements for polymer crystallinity is a high degree of microstructural regularity to enable the chains to pack in an orderly manner. Thus atactic polypropylene is a soft, tacky substance, whereas both isotactic and syndiotactic polypropylene are highly crystalline. 1.6.3 Geometrical Isomerism The final type of isomerism we take up in this section is nicely illustrated by the various possible structures that result from the polymerization of 1,3-dienes. Three important monomers of this type are 1,3-butadiene, 1,3-isoprene, and 1,3-chloroprene, Structure (1.X) through Structure (1.XII), respectively: H H H H (1:X) X XX X X X X XX XX X X X X XX X X X X X X XX X X (a) (b) (c) Figure 1.3 Sections of ‘‘polyvinyl X’’ chains of differing tacticity: (a) isotactic, (b) syndiotactic, and (c) atactic. Hiemenz/ Polymer Chemistry, 2nd Edition DK4670_C001 Final Proof page 22 5.11.2007 8:21pm Compositor Name: JGanesan 22 Introduction to Chain Molecules

24 Introduction to Chain Molecules a (b) Figure 1.4 1,4-Polyisoprene (a)all-cis isomer (natural rubber)and (b)all-trans isomer(gutta-percha). as isoprene;the extra combinations afforded by copolymer composition and structure in SBR offset the fact that Structure (1.XIII and Structure (1.XIV)are identical for butadiene. Although the conditions of the polymerization reactions may be chosen to optimize the formation of one specific isomer,it is typical in these systems to have at least some contribution of all possible isomers in the polymeric product,except in the case of polymers of biological origin,like natural rubber and gutta-percha. Example 1.4 Suppose you have just ordered a tank car of polybutadiene from your friendly rubber company.By some miracle,all the polymers in the sample have M=54,000.The question we would like to consider is this:what are the chances that any two molecules in this sample have exactly the same chemical structure? Solution We will not attempt to provide a precise answer to such an artificial question;what we really want to know is whether the probability is high(approximately 1),vanishing(approximately 0),or finite. From the discussion above,we recognize three geometrical isomers:trans-1,4,cis-1,4,and 1,2. We will ignore the stereochemical possibilities associated with the 1,2 linkages.Assuming all three isomers occur with equal probability,the total number of possible structures is 3 x 3 x 3x ...x 3=3,where N is the degree of polymerization.(Recall that the combined probability of a sequence of events is equal to the products of the individual probabilities.)In this case N=54,000/ 54=1000,and thus there are about 3100010s00 possible structures.Now we need to count how many molecules we have.Assuming for simplicity that the tank car is 3.3 m x 3.3 m x 10 m=100 m3=10%cm3,and the density of the polymer is 1 g/cm3(it is actually closer to 0.89 g/cm2),we have 10g of polymer.As M=54,000 g/mol,we have about 2000 moles,or 2000 x 6 x 10231027 molecules.Clearly,therefore,there is essentially no chance that any two molecules have the identical structure,even without taking the molecular weight distribution into account. This example,as simplistic as it is,actually underscores two important points.First,polymer chemists have to get used to the idea that while all carbon atoms are identical,and all 1,3-butadiene molecules are identical,polybutadiene actually refers to an effectively infinite number of distinct chemical structures.Second,almost all synthetic polymers are heterogeneous in more than one variable:molecular weight,certainly;isomer and tacticity distribution,probably;composition and sequence distribution,for copolymers;and branching structure,when applicable. 1.7 Molecular Weights and Molecular Weight Averages Almost every synthetic polymer sample contains molecules of various degrees of polymerization. We describe this state of affairs by saying that the polymer shows polydispersity with respect to molecular weight or degree of polymerization.To see how this comes about,we only need to think of the reactions between monomers that lead to the formation of polymers in the first place. Random encounters between reactive species are responsible for chain growth,so statistical

as isoprene; the extra combinations afforded by copolymer composition and structure in SBR offset the fact that Structure (1.XIII) and Structure (1.XIV) are identical for butadiene. 4. Although the conditions of the polymerization reactions may be chosen to optimize the formation of one specific isomer, it is typical in these systems to have at least some contribution of all possible isomers in the polymeric product, except in the case of polymers of biological origin, like natural rubber and gutta-percha. Example 1.4 Suppose you have just ordered a tank car of polybutadiene from your friendly rubber company. By some miracle, all the polymers in the sample have M ¼ 54,000. The question we would like to consider is this: what are the chances that any two molecules in this sample have exactly the same chemical structure? Solution We will not attempt to provide a precise answer to such an artificial question; what we really want to know is whether the probability is high (approximately 1), vanishing (approximately 0), or finite. From the discussion above, we recognize three geometrical isomers: trans-1,4, cis-1,4, and 1,2. We will ignore the stereochemical possibilities associated with the 1,2 linkages. Assuming all three isomers occur with equal probability, the total number of possible structures is 3 3 3 3 ¼ 3N, where N is the degree of polymerization. (Recall that the combined probability of a sequence of events is equal to the products of the individual probabilities.) In this case N ¼ 54,000/ 54 ¼ 1000, and thus there are about 31000 10500 possible structures. Now we need to count how many molecules we have. Assuming for simplicity that the tank car is 3.3 m 3.3 m 10 m ¼ 100 m3 ¼ 108 cm3 , and the density of the polymer is 1 g/cm3 (it is actually closer to 0.89 g/cm3 ), we have 108 g of polymer. As M ¼ 54,000 g/mol, we have about 2000 moles, or 2000 6 1023 1027 molecules. Clearly, therefore, there is essentially no chance that any two molecules have the identical structure, even without taking the molecular weight distribution into account. This example, as simplistic as it is, actually underscores two important points. First, polymer chemists have to get used to the idea that while all carbon atoms are identical, and all 1,3-butadiene molecules are identical, polybutadiene actually refers to an effectively infinite number of distinct chemical structures. Second, almost all synthetic polymers are heterogeneous in more than one variable: molecular weight, certainly; isomer and tacticity distribution, probably; composition and sequence distribution, for copolymers; and branching structure, when applicable. 1.7 Molecular Weights and Molecular Weight Averages Almost every synthetic polymer sample contains molecules of various degrees of polymerization. We describe this state of affairs by saying that the polymer shows polydispersity with respect to molecular weight or degree of polymerization. To see how this comes about, we only need to think of the reactions between monomers that lead to the formation of polymers in the first place. Random encounters between reactive species are responsible for chain growth, so statistical (a) (b) Figure 1.4 1,4-Polyisoprene (a) all-cis isomer (natural rubber) and (b) all-trans isomer (gutta-percha). Hiemenz/ Polymer Chemistry, 2nd Edition DK4670_C001 Final Proof page 24 5.11.2007 8:21pm Compositor Name: JGanesan 24 Introduction to Chain Molecules

Molecular Weights and Molecular Weight Averages 25 descriptions are appropriate for the resulting product.The situation is reminiscent of the distribu- tion of molecular velocities in a sample of gas.In that case,also,random collisions impart extra energy to some molecules while reducing the energy of others.Therefore,when we talk about the molecular weight of a polymer,we mean some characteristic average molecular weight.It turns out there are several distinct averages that may be defined,and that may be measured experimentally;it is therefore appropriate to spend some time on this topic.Furthermore,one might well encounter two samples of a particular polymer that were equivalent in terms of one kind of average,but different in terms of another;this,in turn,can lead to the situation where the two polymers behave identically in terms of some important properties,but differently in terms of others. In Chapter 2 through Chapter 4 we shall examine the expected distribution of molecular weights for condensation and addition polymerizations in some detail.For the present,our only concern is how such a distribution of molecular weights is described.We will define the most commonly encountered averages,and how they relate to the distribution as a whole.We will also relate them to the standard parameters used for characterizing a distribution:the mean and standard deviation. Although these are well-known quantities,many students are familiar with them only as results provided by a calculator,and so we will describe them in some detail. 1.7.1 Number-,Weight-,and z-Average Molecular Weights Suppose we have a polymer sample containing many molecules with a variety of degrees of polymerization.We will call a molecule with degree of polymerization i an "i-mer",and the associated molecular weight Mi=iMo.where Mo is the molecular weight of the repeat unit. (Conversion between a discussion couched in terms of i or in terms of Mi is therefore straightfor- ward,and we will switch back and forth when convenient.)The number of i-mers we will denote as n;(we could also refer to n;as the number of moles of i-mer,but again this just involves a factor of Avogadro's number).The first question we ask is this:if we choose a molecule at random from our sample,what is the probability of obtaining an i-mer?The answer is straightforward.The total number of molecules is >ini,and thus this probability is given by ni Xi= ∑i (1.7.1) The probability x;is the number fraction or mole fraction of i-mer.We can use this quantity to define a particular average molecular weight,called the number-average molecular weight,Mn. We do this by multiplying the probability of finding an i-mer with its associated molecular weight, xMi,and adding all these up: M=∑M=4=M, ∑im (1.7.2) ∑ ii The other expressions on the right-hand side of Equation 1.7.2 are equivalent,and will prove useful subsequently.You should convince yourself that this particular average is the one you are familiar with in everyday life:take the value of the property of interest,M;in this case,add it up for all the (n)objects that possess that value of the property,and divide by the total number of objects. So far,so good.We return for a moment to our hypothetical sample,but instead of choosing a molecule at random,we choose a repeat unit or monomer at random,and ask about the molecular weight of the molecule to which it belongs.We will get a different answer,as a simple argument illustrates.Suppose we had two molecules,one a 10-mer and another a 20-mer.If we choose molecules at random,we would choose each one 50%of the time.However,if we choose mono- mers at random,2/3 of the monomers are in the 20-mer,so we would pick the larger molecule twice as often as the smaller.The total number of monomers in a sample is ini,and the chance of

descriptions are appropriate for the resulting product. The situation is reminiscent of the distribution of molecular velocities in a sample of gas. In that case, also, random collisions impart extra energy to some molecules while reducing the energy of others. Therefore, when we talk about the molecular weight of a polymer, we mean some characteristic average molecular weight. It turns out there are several distinct averages that may be defined, and that may be measured experimentally; it is therefore appropriate to spend some time on this topic. Furthermore, one might well encounter two samples of a particular polymer that were equivalent in terms of one kind of average, but different in terms of another; this, in turn, can lead to the situation where the two polymers behave identically in terms of some important properties, but differently in terms of others. In Chapter 2 through Chapter 4 we shall examine the expected distribution of molecular weights for condensation and addition polymerizations in some detail. For the present, our only concern is how such a distribution of molecular weights is described. We will define the most commonly encountered averages, and how they relate to the distribution as a whole. We will also relate them to the standard parameters used for characterizing a distribution: the mean and standard deviation. Although these are well-known quantities, many students are familiar with them only as results provided by a calculator, and so we will describe them in some detail. 1.7.1 Number-, Weight-, and z-Average Molecular Weights Suppose we have a polymer sample containing many molecules with a variety of degrees of polymerization. We will call a molecule with degree of polymerization i an ‘‘i-mer’’, and the associated molecular weight Mi ¼ iM0, where M0 is the molecular weight of the repeat unit. (Conversion between a discussion couched in terms of i or in terms of Mi is therefore straightforward, and we will switch back and forth when convenient.) The number of i-mers we will denote as ni (we could also refer to ni as the number of moles of i-mer, but again this just involves a factor of Avogadro’s number). The first question we ask is this: if we choose a molecule at random from our sample, what is the probability of obtaining an i-mer? The answer is straightforward. The total number of molecules is Si ni, and thus this probability is given by xi ¼ P ni i ni (1:7:1) The probability xi is the number fraction or mole fraction of i-mer. We can use this quantity to define a particular average molecular weight, called the number-average molecular weight, Mn. We do this by multiplying the probability of finding an i-mer with its associated molecular weight, xiMi, and adding all these up: Mn ¼ X i xiMi ¼ P i P niMi i ni ¼ M0 P i P ini i ni (1:7:2) The other expressions on the right-hand side of Equation 1.7.2 are equivalent, and will prove useful subsequently. You should convince yourself that this particular average is the one you are familiar with in everyday life: take the value of the property of interest, Mi in this case, add it up for all the (ni) objects that possess that value of the property, and divide by the total number of objects. So far, so good. We return for a moment to our hypothetical sample, but instead of choosing a molecule at random, we choose a repeat unit or monomer at random, and ask about the molecular weight of the molecule to which it belongs. We will get a different answer, as a simple argument illustrates. Suppose we had two molecules, one a 10-mer and another a 20-mer. If we choose molecules at random, we would choose each one 50% of the time. However, if we choose monomers at random, 2/3 of the monomers are in the 20-mer, so we would pick the larger molecule twice as often as the smaller. The total number of monomers in a sample is Si ini, and the chance of Hiemenz/ Polymer Chemistry, 2nd Edition DK4670_C001 Final Proof page 25 5.11.2007 8:21pm Compositor Name: JGanesan Molecular Weights and Molecular Weight Averages 25