1 Introduction to Chain Molecules 1.1 Introduction "I am inclined to think that the development of polymerization is perhaps the biggest thing chemistry has done,where it has had the biggest impact on everyday life"[1].This assessment of the significance of polymer chemistry to modern society was offered 25 years ago by Lord Todd (President of the Royal Society and 1957 Nobel Laureate in Chemistry),and subsequent develop- ments have only reinforced this sentiment.There is hardly an area of modern life in which polymer materials do not play an important role.Applications span the range from the mundane (e.g.,packaging,toys,fabrics,diapers,nonstick cookware,pressure-sensitive adhesives,etc.)to demanding specialty uses (e.g.,bulletproof vests,stealth aircraft,artificial hip joints,resorbable sutures,etc.).In many instances polymers are the main ingredients,and the ingredients whose characteristic properties are essential to the success of a particular technology:rubber tires,foam cushions and insulation,high-performance athletic shoes,clothing,and equipment are good examples.In other cases,polymers are used as additives at the level of a few percent by volume, but which nevertheless play a crucial role in the properties of the final material;illustrations of this can be found in asphalt(to suppress brittle fracture at low temperature and flow at high tempera- ture),shampoo and other cosmetics (to impart "body"),automobile windshields (to prevent shattering),and motor oil (to reduce the dependence of viscosity on temperature,and to suppress crystallization). For those polymer scientists“of a certain age,”the 1967 movie“The Graduate”[2]provided an indelible moment that still resonates today.At his college graduation party,the hero Benjamin Braddock(played by Dustin Hoffman)is offered the following advice by Mr.McGuire(played by Walter Brooke): MR.McGUIRE.I want to say one word to you.Just one word. BENIAMIN.Yes,sir. MR.MCGUIRE.Are you listening? BENIAMIN.Yes I am. MR.MCGUIRE.Plastics. In that period,the term "plastic"was often accompanied by negative connotations,including “artificial,”as opposed to“natural,.”and“cheap,”as opposed to“valuable..”Today,in what we might call the "post-graduate era,"the situation has changed.To the extent that the advice offered to Benjamin was pointing him to a career in a particular segment of the chemical industry,it was probably very sound advice.The volume of polymer materials produced annually has grown rapidly over the intervening years,to the point where today several hundred pounds of polymer materials are produced each year for each person in the United States.More interesting than sheer volume,however,is the breadth of applications for polymers.Not only do they continue to encroach into the domains of "classical"materials such as metal,wood,and glass (note the inexorable transformation of polymers from minor to major components in automobiles),but they also play a central role in many emerging technologies.Examples include "plastic electronics," 1
1 Introduction to Chain Molecules 1.1 Introduction ‘‘I am inclined to think that the development of polymerization is perhaps the biggest thing chemistry has done, where it has had the biggest impact on everyday life’’ [1]. This assessment of the significance of polymer chemistry to modern society was offered 25 years ago by Lord Todd (President of the Royal Society and 1957 Nobel Laureate in Chemistry), and subsequent developments have only reinforced this sentiment. There is hardly an area of modern life in which polymer materials do not play an important role. Applications span the range from the mundane (e.g., packaging, toys, fabrics, diapers, nonstick cookware, pressure-sensitive adhesives, etc.) to demanding specialty uses (e.g., bulletproof vests, stealth aircraft, artificial hip joints, resorbable sutures, etc.). In many instances polymers are the main ingredients, and the ingredients whose characteristic properties are essential to the success of a particular technology: rubber tires, foam cushions and insulation, high-performance athletic shoes, clothing, and equipment are good examples. In other cases, polymers are used as additives at the level of a few percent by volume, but which nevertheless play a crucial role in the properties of the final material; illustrations of this can be found in asphalt (to suppress brittle fracture at low temperature and flow at high temperature), shampoo and other cosmetics (to impart ‘‘body’’), automobile windshields (to prevent shattering), and motor oil (to reduce the dependence of viscosity on temperature, and to suppress crystallization). For those polymer scientists ‘‘of a certain age,’’ the 1967 movie ‘‘The Graduate’’ [2] provided an indelible moment that still resonates today. At his college graduation party, the hero Benjamin Braddock (played by Dustin Hoffman) is offered the following advice by Mr. McGuire (played by Walter Brooke): MR. MCGUIRE. I want to say one word to you. Just one word. BENJAMIN. Yes, sir. MR. MCGUIRE. Are you listening? BENJAMIN. Yes I am. MR. MCGUIRE. Plastics. In that period, the term ‘‘plastic’’ was often accompanied by negative connotations, including ‘‘artificial,’’ as opposed to ‘‘natural,’’ and ‘‘cheap,’’ as opposed to ‘‘valuable.’’ Today, in what we might call the ‘‘post-graduate era,’’ the situation has changed. To the extent that the advice offered to Benjamin was pointing him to a career in a particular segment of the chemical industry, it was probably very sound advice. The volume of polymer materials produced annually has grown rapidly over the intervening years, to the point where today several hundred pounds of polymer materials are produced each year for each person in the United States. More interesting than sheer volume, however, is the breadth of applications for polymers. Not only do they continue to encroach into the domains of ‘‘classical’’ materials such as metal, wood, and glass (note the inexorable transformation of polymers from minor to major components in automobiles), but they also play a central role in many emerging technologies. Examples include ‘‘plastic electronics,’’ Hiemenz/ Polymer Chemistry, 2nd Edition DK4670_C001 Final Proof page 1 5.11.2007 8:21pm Compositor Name: JGanesan 1
2 Introduction to Chain Molecules gene therapy,artificial prostheses,optical data storage,electric cars,and fuel cells.In short,a reasonable appreciation of the properties of chain molecules,and how these result in the many desirable attributes of polymer-containing materials,is a necessity for a well-trained chemist, materials scientist,or chemical engineer today. Science tends to be plagued by cliches,which make invidious comparison of its efforts;"they can cure such and such a dreaded disease,but they cannot do anything about the common cold"or "we know more about the surface of the moon than the bottom of the sea."If such comparisons were popular in the 1920s,the saying might have been,"we know more about the structure of the atom than about those messy,sticky substances called polymers."Indeed,Millikan's determin- ation of the charge of an electron,Rutherford's idea of the nuclear atom,and Bohr's model of the hydrogen atom were all well-known concepts before the notion of truly covalent macromolecules was accepted.This was the case in spite of the great importance of polymers to human life and activities.Our bodies,like all forms of life,depend on polymer molecules:carbohydrates,proteins, nucleic acids,and so on.From the earliest times,polymeric materials have been employed to satisfy human needs:wood and paper;hides;natural resins and gums;fibers such as cotton,wool, and silk. Attempts to characterize polymeric substances had been made,of course,and high molecular weights were indicated,even if they were not too accurate.Early workers tended to be more suspicious of the interpretation of the colligative properties of polymeric solutions than to accept the possibility of high molecular weight compounds.Faraday had already arrived at CsHs as the empirical formula of "rubber"in 1826,and isoprene was identified as the product resulting from the destructive distillation of rubber in 1860.The idea that a natural polymer such as rubber somehow "contained"isoprene emerged,but the nature of its involvement was more elusive. During the early years of the 20th century,organic chemists were enjoying success in deter- mining the structures of ordinary-sized organic molecules,and this probably contributed to their reluctance to look beyond structures of convenient size.Physical chemists were interested in intermolecular forces during this period,and the idea that polymers were the result of some sort of association between low molecular weight constituent molecules prevailed for a long while. Staudinger is generally credited as being the father of modern polymer chemistry,although a foreshadowing of his ideas can be traced through older literature.In 1920,Staudinger proposed the chain formulas we accept today,maintaining that structures are held together by covalent bonds,which are equivalent in every way to those in low molecular weight compounds.There was a decade of controversy before this"macromolecular hypothesis"began to experience widespread acceptance.Staudinger was awarded the Nobel Prize in 1953 for his work with polymers.By the 1930s,Carothers began synthesizing polymers using well-established reactions of organic chemistry such as esterification and amidation.His products were not limited to single ester or amide linkages,however,but contained many such groups:they were polyesters and polyamides. Physical chemists also got in on the act.Kuhn,Guth,Mark,and others were soon applying statistics and crystallography to describe the multitude of forms a long-chain molecule could assume [3]. Our purpose in this introduction is not to trace the history of polymer chemistry beyond the sketchy version above;interesting and extensive treatments are available [4,5].Rather,the primary objective is to introduce the concept of chain molecules,which stands as the cornerstone of all polymer chemistry.In the next few sections we shall explore some of the categories of polymers, some of the reactions that produce them,and some aspects of isomerism which multiply the structural possibilities.A common feature of all synthetic polymerization reactions is the statistical nature of the individual polymerization steps.This leads inevitably to a distribution of molecular weights,which we would like to describe.As a consequence of these considerations,another important part of this chapter is an introduction to some of the statistical concepts that also play a central role in polymer chemistry
gene therapy, artificial prostheses, optical data storage, electric cars, and fuel cells. In short, a reasonable appreciation of the properties of chain molecules, and how these result in the many desirable attributes of polymer-containing materials, is a necessity for a well-trained chemist, materials scientist, or chemical engineer today. Science tends to be plagued by cliche´s, which make invidious comparison of its efforts; ‘‘they can cure such and such a dreaded disease, but they cannot do anything about the common cold’’ or ‘‘we know more about the surface of the moon than the bottom of the sea.’’ If such comparisons were popular in the 1920s, the saying might have been, ‘‘we know more about the structure of the atom than about those messy, sticky substances called polymers.’’ Indeed, Millikan’s determination of the charge of an electron, Rutherford’s idea of the nuclear atom, and Bohr’s model of the hydrogen atom were all well-known concepts before the notion of truly covalent macromolecules was accepted. This was the case in spite of the great importance of polymers to human life and activities. Our bodies, like all forms of life, depend on polymer molecules: carbohydrates, proteins, nucleic acids, and so on. From the earliest times, polymeric materials have been employed to satisfy human needs: wood and paper; hides; natural resins and gums; fibers such as cotton, wool, and silk. Attempts to characterize polymeric substances had been made, of course, and high molecular weights were indicated, even if they were not too accurate. Early workers tended to be more suspicious of the interpretation of the colligative properties of polymeric solutions than to accept the possibility of high molecular weight compounds. Faraday had already arrived at C5H8 as the empirical formula of ‘‘rubber’’ in 1826, and isoprene was identified as the product resulting from the destructive distillation of rubber in 1860. The idea that a natural polymer such as rubber somehow ‘‘contained’’ isoprene emerged, but the nature of its involvement was more elusive. During the early years of the 20th century, organic chemists were enjoying success in determining the structures of ordinary-sized organic molecules, and this probably contributed to their reluctance to look beyond structures of convenient size. Physical chemists were interested in intermolecular forces during this period, and the idea that polymers were the result of some sort of association between low molecular weight constituent molecules prevailed for a long while. Staudinger is generally credited as being the father of modern polymer chemistry, although a foreshadowing of his ideas can be traced through older literature. In 1920, Staudinger proposed the chain formulas we accept today, maintaining that structures are held together by covalent bonds, which are equivalent in every way to those in low molecular weight compounds. There was a decade of controversy before this ‘‘macromolecular hypothesis’’ began to experience widespread acceptance. Staudinger was awarded the Nobel Prize in 1953 for his work with polymers. By the 1930s, Carothers began synthesizing polymers using well-established reactions of organic chemistry such as esterification and amidation. His products were not limited to single ester or amide linkages, however, but contained many such groups: they were polyesters and polyamides. Physical chemists also got in on the act. Kuhn, Guth, Mark, and others were soon applying statistics and crystallography to describe the multitude of forms a long-chain molecule could assume [3]. Our purpose in this introduction is not to trace the history of polymer chemistry beyond the sketchy version above; interesting and extensive treatments are available [4,5]. Rather, the primary objective is to introduce the concept of chain molecules, which stands as the cornerstone of all polymer chemistry. In the next few sections we shall explore some of the categories of polymers, some of the reactions that produce them, and some aspects of isomerism which multiply the structural possibilities. A common feature of all synthetic polymerization reactions is the statistical nature of the individual polymerization steps. This leads inevitably to a distribution of molecular weights, which we would like to describe. As a consequence of these considerations, another important part of this chapter is an introduction to some of the statistical concepts that also play a central role in polymer chemistry. Hiemenz/ Polymer Chemistry, 2nd Edition DK4670_C001 Final Proof page 2 5.11.2007 8:21pm Compositor Name: JGanesan 2 Introduction to Chain Molecules
How Big Is Big? 3 1.2 How Big Is Big? The term polymer is derived from the Greek words poly and meros,meaning many parts.We noted in the Section 1.1 that the existence of these parts was acknowledged before the nature of the interaction which held them together was known.Today we realize that ordinary covalent bonds are the intramolecular forces that keep the polymer molecule intact.In addition,the usual types of intermolecular forces-hydrogen bonds,dipole-dipole interactions,London forces,etc.-hold assemblies of these molecules together in the bulk state.The only thing that is remarkable about these molecules is their size,but that feature is remarkable indeed.Another useful term is macromolecule,which of course simply means "large (or long)molecule."Some practitioners draw a distinction between the two:all polymers are macromolecules,but not all macromolecules are polymers.For example,a protein is not made by repeating one or two chemical units many times,but involves a precise selection from among 20 different amino acids;thus it is a macro- molecule,but not a polymer.In this text we will not be sticklers for formality,and will use the terms rather interchangeably,but the reader should be aware of the distinction. 1.2.1 Molecular Weight One of the first things we must consider is what we mean when we talk about the "size"of a polymer molecule.There are two possibilities:one has to do with the number of repeat units and the other to the spatial extent.In the former case.the standard term is molecular weight (although again the reader must be aware that molar mass is often preferred).A closely related concept,the degree of polymerization is also commonly used in this context.A variety of experimental techniques are available for determining the molecular weight of a polymer.We shall discuss a few such methods in Section 1.8 and postpone others until the appropriate chapters.The expression molecular weight and molar mass should always be modified by the word average.This too is something we shall take up presently.For now,we assume that a polymer molecule has a molecular weight M,which can be anywhere in the range 10-10or more.(We shall omit units when we write molecular weights in this book,but the student is advised to attach the units g/mol to these quantities when they appear in problem calculations.) Since polymer molecules are made up of chains of repeat units,after the chain itself comes the repeat unit as a structural element of importance.Many polymer molecules are produced by covalently bonding together only one or two types of repeat units.These units are the parts from which chains are generated;as a class of compounds they are called monomers.Throughout this book,we shall designate the molecular weight of a repeat unit as Mo. The degree of polymerization of a polymer is simply the number of repeat units in a molecule. The degree of polymerization N is given by the ratio of the molecular weight of the polymer to the molecular weight of the repeat unit: N=M (1.2.1) Mo One type of polymerization reaction is the addition reaction in which successive repeat units add on to the chain.No other product molecules are formed,so the molecular weight of the monomer and that of the repeat unit are identical in this case.A second category of polymerization reaction is the condensation reaction,in which one or two small molecules such as water or HCI are eliminated for each chain linkage formed.In this case the molecular weight of the monomer and the repeat unit are somewhat different.For example,suppose an acid(subscript A)reacts with an alcohol (subscript B)to produce an ester linkage and a water molecule.The molecular weight of the ester-the repeat unit if an entire chain is built up this way-differs from the combined weight of the reactants by twice the molecular weight of the water;therefore, M M N= MoMA MB -2MH.o (1.2.2)
1.2 How Big Is Big? The term polymer is derived from the Greek words poly and meros, meaning many parts. We noted in the Section 1.1 that the existence of these parts was acknowledged before the nature of the interaction which held them together was known. Today we realize that ordinary covalent bonds are the intramolecular forces that keep the polymer molecule intact. In addition, the usual types of intermolecular forces—hydrogen bonds, dipole–dipole interactions, London forces, etc.—hold assemblies of these molecules together in the bulk state. The only thing that is remarkable about these molecules is their size, but that feature is remarkable indeed. Another useful term is macromolecule, which of course simply means ‘‘large (or long) molecule.’’ Some practitioners draw a distinction between the two: all polymers are macromolecules, but not all macromolecules are polymers. For example, a protein is not made by repeating one or two chemical units many times, but involves a precise selection from among 20 different amino acids; thus it is a macromolecule, but not a polymer. In this text we will not be sticklers for formality, and will use the terms rather interchangeably, but the reader should be aware of the distinction. 1.2.1 Molecular Weight One of the first things we must consider is what we mean when we talk about the ‘‘size’’ of a polymer molecule. There are two possibilities: one has to do with the number of repeat units and the other to the spatial extent. In the former case, the standard term is molecular weight (although again the reader must be aware that molar mass is often preferred). A closely related concept, the degree of polymerization is also commonly used in this context. A variety of experimental techniques are available for determining the molecular weight of a polymer. We shall discuss a few such methods in Section 1.8 and postpone others until the appropriate chapters. The expression molecular weight and molar mass should always be modified by the word average. This too is something we shall take up presently. For now, we assume that a polymer molecule has a molecular weight M, which can be anywhere in the range 103 –107 or more. (We shall omit units when we write molecular weights in this book, but the student is advised to attach the units g/mol to these quantities when they appear in problem calculations.) Since polymer molecules are made up of chains of repeat units, after the chain itself comes the repeat unit as a structural element of importance. Many polymer molecules are produced by covalently bonding together only one or two types of repeat units. These units are the parts from which chains are generated; as a class of compounds they are called monomers. Throughout this book, we shall designate the molecular weight of a repeat unit as M0. The degree of polymerization of a polymer is simply the number of repeat units in a molecule. The degree of polymerization N is given by the ratio of the molecular weight of the polymer to the molecular weight of the repeat unit: N ¼ M M0 (1:2:1) One type of polymerization reaction is the addition reaction in which successive repeat units add on to the chain. No other product molecules are formed, so the molecular weight of the monomer and that of the repeat unit are identical in this case. A second category of polymerization reaction is the condensation reaction, in which one or two small molecules such as water or HCl are eliminated for each chain linkage formed. In this case the molecular weight of the monomer and the repeat unit are somewhat different. For example, suppose an acid (subscript A) reacts with an alcohol (subscript B) to produce an ester linkage and a water molecule. The molecular weight of the ester—the repeat unit if an entire chain is built up this way—differs from the combined weight of the reactants by twice the molecular weight of the water; therefore, N ¼ M M0 ¼ M MA þ MB 2MH2O (1:2:2) Hiemenz/ Polymer Chemistry, 2nd Edition DK4670_C001 Final Proof page 3 5.11.2007 8:21pm Compositor Name: JGanesan How Big Is Big? 3
4 Introduction to Chain Molecules The end units in a polymer chain are inevitably different from the units that are attached on both sides to other repeat units.We see this situation in the n-alkanes:each end of the chain is a methyl group and the middle parts are methylene groups.Of course,the terminal group does not have to be a hydrogen as in alkanes;indeed,it is often something else.Our interest in end groups is concerned with the question of what effect they introduce into the evaluation of N through Equation (1.2.2).The following example examines this through some numerical calculations. Example 1.1 As a polymer prototype consider an n-alkane molecule consisting of N-2 methylenes and 2 methyl groups.How serious an error is made in M for different Ns if the difference in molecular weight between methyl and methylene groups is ignored? Solution The effect of different end groups on M can be seen by comparing the true molecular weight with an approximate molecular weight,calculated on the basis of a formula(CH2)N.These Ms and the percentage difference between them are listed here for several values of N N M Mapprox. Difference 3 44 42 4.5 7 100 98 2.0 12 170 168 1.2 52 730 728 0.3 102 1.430 1,428 0.14 502 7.030 7.028 0.028 1002 14.030 14,028 0.014 Although the difference is almost 5%for propane,it is closer to 0.1%for the case of N100, which is about the threshold for polymers.The precise values of these numbers will be different,depending on the specific repeat units and end groups present.For example,if Mo=100 and Mend=80,the difference would be 0.39%in a calculation such as that above forN≈100. The example shows that the contribution of the ends becomes progressively less important as the number of repeat units in a structure increases.By the time polymeric molecular sizes are reached,the error associated with failure to distinguish between segments at the end and those within the chain is generally less than experimental error.In Section 1.8.2 we shall consider a method for polymer molecular weight determination based on chemical analysis for the end groups in a polymer.A corollary of the present discussion is that the method of end group analysis is applicable only in the case of relatively low molecular weight polymers. As suggested above,not all polymers are constructed by bonding together a single kind of repeat unit.For example,although protein molecules are polyamides in which N amino acid repeat units are bonded together,the degree of polymerization is a less useful concept,since an amino acid unit might be any one of the 20-odd molecules that are found in proteins.In this case the molecular weight itself,rather than the degree of polymerization,is generally used to describe the molecule.When the actual content of individual amino acids is known,it is their sequence that is of special interest to biochemists and molecular biologists
The end units in a polymer chain are inevitably different from the units that are attached on both sides to other repeat units. We see this situation in the n-alkanes: each end of the chain is a methyl group and the middle parts are methylene groups. Of course, the terminal group does not have to be a hydrogen as in alkanes; indeed, it is often something else. Our interest in end groups is concerned with the question of what effect they introduce into the evaluation of N through Equation (1.2.2). The following example examines this through some numerical calculations. Example 1.1 As a polymer prototype consider an n-alkane molecule consisting of N2 methylenes and 2 methyl groups. How serious an error is made in M for different Ns if the difference in molecular weight between methyl and methylene groups is ignored? Solution The effect of different end groups on M can be seen by comparing the true molecular weight with an approximate molecular weight, calculated on the basis of a formula (CH2)N. These Ms and the percentage difference between them are listed here for several values of N N MMapprox. % Difference 3 44 42 4.5 7 100 98 2.0 12 170 168 1.2 52 730 728 0.3 102 1,430 1,428 0.14 502 7,030 7,028 0.028 1002 14,030 14,028 0.014 Although the difference is almost 5% for propane, it is closer to 0.1% for the case of N 100, which is about the threshold for polymers. The precise values of these numbers will be different, depending on the specific repeat units and end groups present. For example, if M0 ¼ 100 and Mend ¼ 80, the difference would be 0.39% in a calculation such as that above for N 100. The example shows that the contribution of the ends becomes progressively less important as the number of repeat units in a structure increases. By the time polymeric molecular sizes are reached, the error associated with failure to distinguish between segments at the end and those within the chain is generally less than experimental error. In Section 1.8.2 we shall consider a method for polymer molecular weight determination based on chemical analysis for the end groups in a polymer. A corollary of the present discussion is that the method of end group analysis is applicable only in the case of relatively low molecular weight polymers. As suggested above, not all polymers are constructed by bonding together a single kind of repeat unit. For example, although protein molecules are polyamides in which N amino acid repeat units are bonded together, the degree of polymerization is a less useful concept, since an amino acid unit might be any one of the 20-odd molecules that are found in proteins. In this case the molecular weight itself, rather than the degree of polymerization, is generally used to describe the molecule. When the actual content of individual amino acids is known, it is their sequence that is of special interest to biochemists and molecular biologists. Hiemenz/ Polymer Chemistry, 2nd Edition DK4670_C001 Final Proof page 4 5.11.2007 8:21pm Compositor Name: JGanesan 4 Introduction to Chain Molecules
How Big Is Big? 5 1.2.2 Spatial Extent We began this section with an inquiry into how to define the size of a polymer molecule.In addition to the molecular weight or the degree of polymerization,some linear dimension that characterizes the molecule could also be used for this purpose.As an example,consider a hydrocarbon molecule stretched out to its full length but without any bond distortion.There are several features to note about this situation: 1. The tetrahedral geometry at the carbon atoms gives bond angles of 109.5. 2.The equilibrium bond length of a carbon-carbon single bond is 0.154 nm or 1.54 A. 3.Because of the possibility of rotation around carbon-carbon bonds,a molecule possessing many such bonds will undergo many twists and turns along the chain. 4. Fully extended molecular length is not representative of the spatial extension that a molecule actually displays.The latter is sensitive to environmental factors,however,so the extended length is convenient for our present purposes to provide an idea of the spatial size of polymer molecules. A fully extended hydrocarbon molecule will have the familiar all-trans zigzag profile in which the hydrogens extend in front of and in back of the plane containing the carbons,with an angle of 109.5 between successive carbon-carbon bonds.The chain may be pictured as a row of triangles resting corner to corner.The length of the row equals the product of the number of triangles and the length of the base of each.Although it takes three carbons to define one of these triangles,one of these atoms is common to two triangles;therefore the number of triangles is the same as the number of pairs of carbon atoms,except where this breaks down at the ends of the molecule.If the chain is sufficiently long,this end effect is inconsequential. The law of cosines can be used to calculate the length of the base of each of these triangles: [2(0.154)2(1-cos 109.]2=0.252 nm.If the repeat unit of the molecule contributes two carbon atoms to the backbone of the polymer-as is the case for vinyl polymers-the fully extended chain length is given by N(0.252)nm.For a polymer with N=103,this corresponds to 2.52 um. Objects which actually display linear dimensions of this magnitude can be seen in an ordinary microscope,provided that they have suitable optical properties to contrast with their surroundings; an example will be given in Figure 1.1a.Note that the distance between every other carbon atom we have used here is also the distance between the substituents on these carbons for the fully extended chains. We shall see in Chapter 6 that,because of all the twists and turns a molecule undergoes, the actual average end-to-end distance of the jumbled molecules increases as N2.With the same repeat distance calculated above,but the square root dependence on N,the actual end-to- end distance of the coiled chain with N=104 is closer to (104)2x0.252 nm25 nm.If we picture one end of this jumbled chain at the origin of a coordinate system,the other end might be anywhere on the surface of a sphere whose radius is given by this end-to-end distance.This spherical geometry comes about because the random bends occurring along the chain length can take the end of the chain anywhere in a spherical domain whose radius depends on N The above discussion points out the difficulty associated with using the linear dimensions of a molecule as a measure of its size:it is not the molecule alone that determines its dimensions,but also the shape or conformation in which it exists.Fully extended,linear arrangements of the sort described above exist in polymer crystals,at least for some distance,although usually not over the full length of the chain.We shall take up the structure of polymer crystals in Chapter 13.In the solution and bulk states,many polymers exist in the coiled form we have also described.Still other structures are important,notably the rod or semiflexible chain,which we shall discuss in Chapter 6. The overall shape assumed by a polymer molecule can be greatly affected by the environment.The shape of a molecule in solution plays a key role in determining many properties of polymer solutions.From a study of these solutions,some conclusions can be drawn regarding the shape of
1.2.2 Spatial Extent We began this section with an inquiry into how to define the size of a polymer molecule. In addition to the molecular weight or the degree of polymerization, some linear dimension that characterizes the molecule could also be used for this purpose. As an example, consider a hydrocarbon molecule stretched out to its full length but without any bond distortion. There are several features to note about this situation: 1. The tetrahedral geometry at the carbon atoms gives bond angles of 109.58. 2. The equilibrium bond length of a carbon–carbon single bond is 0.154 nm or 1.54 A˚ . 3. Because of the possibility of rotation around carbon–carbon bonds, a molecule possessing many such bonds will undergo many twists and turns along the chain. 4. Fully extended molecular length is not representative of the spatial extension that a molecule actually displays. The latter is sensitive to environmental factors, however, so the extended length is convenient for our present purposes to provide an idea of the spatial size of polymer molecules. A fully extended hydrocarbon molecule will have the familiar all-trans zigzag profile in which the hydrogens extend in front of and in back of the plane containing the carbons, with an angle of 109.58 between successive carbon–carbon bonds. The chain may be pictured as a row of triangles resting corner to corner. The length of the row equals the product of the number of triangles and the length of the base of each. Although it takes three carbons to define one of these triangles, one of these atoms is common to two triangles; therefore the number of triangles is the same as the number of pairs of carbon atoms, except where this breaks down at the ends of the molecule. If the chain is sufficiently long, this end effect is inconsequential. The law of cosines can be used to calculate the length of the base of each of these triangles: [2(0.154)2 (1 cos 109.58)]1/2 ¼ 0.252 nm. If the repeat unit of the molecule contributes two carbon atoms to the backbone of the polymer—as is the case for vinyl polymers—the fully extended chain length is given by N(0.252) nm. For a polymer with N ¼ 104 , this corresponds to 2.52 mm. Objects which actually display linear dimensions of this magnitude can be seen in an ordinary microscope, provided that they have suitable optical properties to contrast with their surroundings; an example will be given in Figure 1.1a. Note that the distance between every other carbon atom we have used here is also the distance between the substituents on these carbons for the fully extended chains. We shall see in Chapter 6 that, because of all the twists and turns a molecule undergoes, the actual average end-to-end distance of the jumbled molecules increases as N1/2. With the same repeat distance calculated above, but the square root dependence on N, the actual end-toend distance of the coiled chain with N ¼ 104 is closer to 104 ð Þ1=2 0:252 nm 25 nm. If we picture one end of this jumbled chain at the origin of a coordinate system, the other end might be anywhere on the surface of a sphere whose radius is given by this end-to-end distance. This spherical geometry comes about because the random bends occurring along the chain length can take the end of the chain anywhere in a spherical domain whose radius depends on N1/2. The above discussion points out the difficulty associated with using the linear dimensions of a molecule as a measure of its size: it is not the molecule alone that determines its dimensions, but also the shape or conformation in which it exists. Fully extended, linear arrangements of the sort described above exist in polymer crystals, at least for some distance, although usually not over the full length of the chain. We shall take up the structure of polymer crystals in Chapter 13. In the solution and bulk states, many polymers exist in the coiled form we have also described. Still other structures are important, notably the rod or semiflexible chain, which we shall discuss in Chapter 6. The overall shape assumed by a polymer molecule can be greatly affected by the environment. The shape of a molecule in solution plays a key role in determining many properties of polymer solutions. From a study of these solutions, some conclusions can be drawn regarding the shape of Hiemenz/ Polymer Chemistry, 2nd Edition DK4670_C001 Final Proof page 5 5.11.2007 8:21pm Compositor Name: JGanesan How Big Is Big? 5