plastics, general surveystructures.dhu.edu.cn/_upload/article/files/f6/62/f5c... · 2019. 11....

� 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Article No : a20_543

Plastics, General Survey

HANS-GEORG ELIAS,MichiganMolecular Institute, Midland, MI 48 640, United States

1. Introduction. . . . . . . . . . . . . . . . . . . . . . . 36

1.1. Polymers . . . . . . . . . . . . . . . . . . . . . . . . . 37

1.1.1. Fundamental Terms . . . . . . . . . . . . . . . . . 37

1.1.2. Nomenclature . . . . . . . . . . . . . . . . . . . . . . 37

1.2. Plastics. . . . . . . . . . . . . . . . . . . . . . . . . . . 38

1.2.1. Fundamental Terms . . . . . . . . . . . . . . . . . 38

1.2.2. Designations . . . . . . . . . . . . . . . . . . . . . . 40

1.3. History of Plastics . . . . . . . . . . . . . . . . . . 45

1.4. Economic Importance . . . . . . . . . . . . . . . 47

2. Molecular Structure of Polymers . . . . . . 48

2.1. Constitution . . . . . . . . . . . . . . . . . . . . . . . 48

2.1.1. Homopolymers . . . . . . . . . . . . . . . . . . . . . 48

2.1.2. Copolymers. . . . . . . . . . . . . . . . . . . . . . . . 51

2.1.3. Branched Polymers . . . . . . . . . . . . . . . . . . 51

2.1.4. Ordered Chain Assemblies . . . . . . . . . . . . . 53

2.1.5. Unordered Networks . . . . . . . . . . . . . . . . . 54

2.2. Molar Masses and Molar Mass

Distributions . . . . . . . . . . . . . . . . . . . . . . 55

2.2.1. Molar Mass Average . . . . . . . . . . . . . . . . . 55

2.2.2. Determination of Molar Mass. . . . . . . . . . . 55

2.2.3. Molar Mass Distributions. . . . . . . . . . . . . . 57

2.2.4. Determination of Molar Mass Distributions. 59

2.3. Configurations . . . . . . . . . . . . . . . . . . . . . 59

2.4. Conformations . . . . . . . . . . . . . . . . . . . . . 61

2.4.1. Microconformations. . . . . . . . . . . . . . . . . . 61

2.4.2. Conformations in Ideal Polymer Crystals . . 62

2.4.3. Conformations in Polymer Solutions. . . . . . 63

2.4.4. Unperturbed Coils . . . . . . . . . . . . . . . . . . . 64

2.4.5. Perturbed Coils . . . . . . . . . . . . . . . . . . . . . 65

2.4.6. Wormlike Chains. . . . . . . . . . . . . . . . . . . . 65

3. Polymer Manufacture . . . . . . . . . . . . . . . 65

3.1. Raw Materials . . . . . . . . . . . . . . . . . . . . . 65

3.1.1. Wood . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.1.2. Coal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.1.3. Natural Gas. . . . . . . . . . . . . . . . . . . . . . . . 66

3.1.4. Petroleum . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.1.5. Other Natural Raw Materials . . . . . . . . . . . 66

3.2. Polymer Syntheses: Overview . . . . . . . . . 67

3.2.1. Classifications . . . . . . . . . . . . . . . . . . . . . . 67

3.2.2. Functionality . . . . . . . . . . . . . . . . . . . . . . . 69

3.2.3. Cyclopolymerizations . . . . . . . . . . . . . . . . 69

3.3. Chain Polymerizations and

Polyeliminations. . . . . . . . . . . . . . . . . . . . 70

3.3.1. Thermodynamics . . . . . . . . . . . . . . . . . . . . 70

3.3.2. Free-Radical Polymerizations . . . . . . . . . . . 71

3.3.3. Anionic Polymerizations . . . . . . . . . . . . . . 75

3.3.4. Cationic Polymerizations . . . . . . . . . . . . . . 75

3.3.5. Ziegler – Natta Polymerizations . . . . . . . . . 76

3.3.6. Copolymerizations. . . . . . . . . . . . . . . . . . . 77

3.4. Polycondensations and Polyadditions. . . . 79

3.4.1. Bifunctional Polycondensations . . . . . . . . . 79

3.4.2. Multifunctional Polycondensations . . . . . . . 80

3.4.3. Polyaddition . . . . . . . . . . . . . . . . . . . . . . . 82

3.5. Polymer Reactions . . . . . . . . . . . . . . . . . . 82

3.5.1. Polymer Transformations . . . . . . . . . . . . . . 82

3.5.2. Block and Graft Formations . . . . . . . . . . . . 83

3.5.3. Cross-Linking Reactions . . . . . . . . . . . . . . 83

3.5.4. Degradation Reactions . . . . . . . . . . . . . . . . 83

4. Plastics Manufacture . . . . . . . . . . . . . . . . 84

4.1. Homogenization and Compounding . . . . . 84

4.2. Additives . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.2.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.2.2. Chemofunctional Additives . . . . . . . . . . . . 85

4.2.3. Processing Aids. . . . . . . . . . . . . . . . . . . . . 86

4.2.4. Extending and Reinforcing Fillers . . . . . . . 86

4.2.5. Plasticizers . . . . . . . . . . . . . . . . . . . . . . . . 87

4.2.6. Colorants . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.2.7. Blowing Agents. . . . . . . . . . . . . . . . . . . . . 88

4.3. Processing . . . . . . . . . . . . . . . . . . . . . . . . 88

5. Supermolecular Structures . . . . . . . . . . . 89

5.1. Noncrystalline States . . . . . . . . . . . . . . . . 89

5.1.1. Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.1.2. Orientation . . . . . . . . . . . . . . . . . . . . . . . . 89

5.2. Polymer Crystals . . . . . . . . . . . . . . . . . . 90

5.2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . 90

5.2.2. Crystal Structures . . . . . . . . . . . . . . . . . . . 91

5.2.3. Crystallinity . . . . . . . . . . . . . . . . . . . . . . . 92

5.2.4. Morphology . . . . . . . . . . . . . . . . . . . . . . . 92

5.3. Mesophases . . . . . . . . . . . . . . . . . . . . . . . 94

5.3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . 94

5.3.2. Types of Liquid Crystals . . . . . . . . . . . . . . 95

5.3.3. Mesogens . . . . . . . . . . . . . . . . . . . . . . . . . 96

5.3.4. Lyotropic Liquid Crystalline Polymers . . . . 98

5.3.5. Thermotropic Liquid Crystal Polymers . . . . 99

5.3.6. Block Copolymers . . . . . . . . . . . . . . . . . . . 99

5.3.7. Ionomers. . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.4. Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.5. Polymer Surfaces . . . . . . . . . . . . . . . . . . . 102

5.5.1. Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.5.2. Interfacial Tension. . . . . . . . . . . . . . . . . . . 102

5.5.3. Adsorption . . . . . . . . . . . . . . . . . . . . . . . . 103

6. Thermal Properties . . . . . . . . . . . . . . . . . 103

DOI: 10.1002/14356007.a20_543

6.1. Molecular Motion . . . . . . . . . . . . . . . . . . 103

6.1.1. Thermal Expansion . . . . . . . . . . . . . . . . . . 103

6.1.2. Heat Capacity . . . . . . . . . . . . . . . . . . . . . . 104

6.1.3. Heat Conductivity . . . . . . . . . . . . . . . . . . . 104

6.2. Thermal Transitions and Relaxations . . . 104

6.2.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . 104

6.2.2. Crystallization . . . . . . . . . . . . . . . . . . . . . . 106

6.2.3. Melting . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

6.2.4. Liquid Crystal Transitions . . . . . . . . . . . . . 108

6.2.5. Glass Transitions . . . . . . . . . . . . . . . . . . . . 109

6.2.6. Other Transitions and Relaxations . . . . . . . 110

6.2.7. Technical Methods . . . . . . . . . . . . . . . . . . 110

6.3. Transport. . . . . . . . . . . . . . . . . . . . . . . . . 110

6.3.1. Self-Diffusion . . . . . . . . . . . . . . . . . . . . . . 110

6.3.2. Permeation . . . . . . . . . . . . . . . . . . . . . . . . 111

7. Rheological Properties . . . . . . . . . . . . . . . 113

7.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . 113

7.2. Shear Viscosities at Rest . . . . . . . . . . . . . 113

7.2.1. Fundamentals . . . . . . . . . . . . . . . . . . . . . . 113

7.2.2. Molar Mass Dependence . . . . . . . . . . . . . . 113

7.2.3. Concentrated Solutions . . . . . . . . . . . . . . . 114

7.3. Non-Newtonian Shear Viscosities. . . . . . . 114

7.3.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . 114

7.3.2. Flow Curves . . . . . . . . . . . . . . . . . . . . . . . 115

7.3.3. Melt Viscosities. . . . . . . . . . . . . . . . . . . . . 116

7.4. Extensional Viscosities . . . . . . . . . . . . . . . 117

7.4.1. Fundamentals . . . . . . . . . . . . . . . . . . . . . . 117

7.4.2. Melts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

7.4.3. Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . 118

8. Mechanical Properties . . . . . . . . . . . . . . . 118

8.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . 118

8.1.1. Deformation of Polymers . . . . . . . . . . . . . . 118

8.1.2. Tensile Tests . . . . . . . . . . . . . . . . . . . . . . . 119

8.1.3. Moduli and Poisson Ratios. . . . . . . . . . . . . 121

8.2. Energy Elasticity . . . . . . . . . . . . . . . . . . . 121

8.2.1. Theoretical Moduli . . . . . . . . . . . . . . . . . . 121

8.2.2. Real Moduli . . . . . . . . . . . . . . . . . . . . . . . 122

8.2.3. Temperature Dependence. . . . . . . . . . . . . . 123

8.3. Entropy Elasticity . . . . . . . . . . . . . . . . . . 124

8.4. Viscoelasticity . . . . . . . . . . . . . . . . . . . . . 124

8.4.1. Fundamentals . . . . . . . . . . . . . . . . . . . . . . 124

8.4.2. Time – Temperature Superposition. . . . . . . 125

8.5. Dynamic Behavior . . . . . . . . . . . . . . . . . . 126

8.5.1. Fundamentals . . . . . . . . . . . . . . . . . . . . . . 126

8.5.2. Molecular Interpretations . . . . . . . . . . . . . . 126

8.6. Fracture. . . . . . . . . . . . . . . . . . . . . . . . . . 128

8.6.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . 128

8.6.2. Theoretical Fracture Strength . . . . . . . . . . . 128

8.6.3. Real Fracture Strength . . . . . . . . . . . . . . . . 129

8.6.4. Impact Resistance . . . . . . . . . . . . . . . . . . . 131

8.6.5. Stress Cracking . . . . . . . . . . . . . . . . . . . . . 131

8.6.6. Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

8.7. Surface Mechanics . . . . . . . . . . . . . . . . . . 132

8.7.1. Hardness . . . . . . . . . . . . . . . . . . . . . . . . . . 132

8.7.2. Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

8.7.3. Abrasion and Wear . . . . . . . . . . . . . . . . . . 132

9. Electric Properties . . . . . . . . . . . . . . . . . . 133

9.1. Dielectric Properties . . . . . . . . . . . . . . . . 133

9.1.1. Relative Permittivity . . . . . . . . . . . . . . . . . 133

9.1.2. Dielectric Loss . . . . . . . . . . . . . . . . . . . . . 133

9.1.3. Dielectric Strength and Tracking Resistance 134

9.1.4. Electrostatic Charging . . . . . . . . . . . . . . . . 135

9.2. Electrical Conductivity . . . . . . . . . . . . . . 135

9.3. Photoconductivity . . . . . . . . . . . . . . . . . . 136

10. Optical Properties . . . . . . . . . . . . . . . . . . 137

11. Polymer Composites . . . . . . . . . . . . . . . . 138

11.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . 138

11.1.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . 138

11.1.2. Mixture Rules . . . . . . . . . . . . . . . . . . . . . . 139

11.2. Filled Polymers . . . . . . . . . . . . . . . . . . . . 141

11.2.1. Microcomposites . . . . . . . . . . . . . . . . . . . . 141

11.2.2. Molecular Composites . . . . . . . . . . . . . . . . 143

11.2.3. Macrocomposites. . . . . . . . . . . . . . . . . . . . 143

11.3. Homogeneous Blends . . . . . . . . . . . . . . . . 144

11.3.1. Thermodynamics . . . . . . . . . . . . . . . . . . . . 144

11.3.2. Plastification . . . . . . . . . . . . . . . . . . . . . . . 145

11.3.3. Rubber Blends. . . . . . . . . . . . . . . . . . . . . . 146

11.3.4. Plastic Blends . . . . . . . . . . . . . . . . . . . . . . 147

11.4. Heterogeneous Blends . . . . . . . . . . . . . . . 147

11.4.1. Compatible Polymers. . . . . . . . . . . . . . . . . 147

11.4.2. Blend Formation . . . . . . . . . . . . . . . . . . . . 147

11.4.3. Toughened Plastics . . . . . . . . . . . . . . . . . . 148

11.4.4. Thermoplastic Elastomers . . . . . . . . . . . . . 148

11.5. Expanded Plastics . . . . . . . . . . . . . . . . . . 150

12. Waste Disposal . . . . . . . . . . . . . . . . . . . . 151

References . . . . . . . . . . . . . . . . . . . . . . . . 153

1. Introduction

Plastics are commercially used materials thatare based on polymers or prepolymers. Thename plastics refers to their easy processibilityand shaping (Greek: plastein ¼ to form, toshape).

Plastics and polymers are not synonyms. Poly-mersorprepolymers are rawmaterials for plastics;they become plastics only after physical com-pounding and/or chemical hardening. The samepolymersmay be used not as plastics but as fibers,in paints, or in other applications. Other polymersmay be utilized as fibers, elastomers, thickeners,ion-exchange resins, etc., but not as plastics.

36 Plastics, General Survey Vol. 28

1.1. Polymers

1.1.1. Fundamental Terms [1–5, 8–14]

Polymers are chemical substances (chemicalcompounds) composed of polymer molecules.The term polymer refers to molecules composedof many units (Greek: poly ¼ many, meros ¼parts). Polymer molecules may thus consist ofmany atoms, usually a thousand or more, therebyhaving high molar masses (‘‘molecularweights’’). Benzene can, for example, be ‘‘poly-merized’’ from three acetylene molecules andwas originally called a polymer. What is nowcalled a polymer consists of molecules withhundreds and thousands of such units; it wastherefore termed ‘‘high polymer’’ in the olderliterature.

The term polymer carries with it the connota-tion of molecules composed of many equal‘‘mers’’,such as the ethylene units in polyethyl-ene, R0(CH2CH2)nR

00. The number n of mers in apolymer molecule is called the degree of poly-merizationX. There are, however, many polymermolecules (especially biopolymer molecules)with very different types of mers per molecule,such as protein molecules H(NH – CHR –CO)nOH with up to 16 different R substituentsin irregular sequence. A less constraining andmore general term for polymer molecule is thusmacromolecule. No sharp dividing line withrespect to the number of units per moleculeexists, however, between macromolecules andlow molar mass compounds (micromolecules).

Macromolecules constitute the simplest indi-vidual chemical constituents of a polymer. Amacromolecule may exist as an individual entity(in linear and branched polymers) or may bethought of as the primary molecule before chem-ical cross-linking.

Macromolecules exist in nature; examples arenucleic acids, proteins, polysaccharides, poly-prenes, and lignins. Some of these naturallyoccurring polymers are used by man withoutfurther chemical transformation (e.g., cellulosefor paper and cardboard). The chemical transfor-mation of natural polymerswith retention of theirchain structures leads to semisynthetic materials,for example, cellulose acetates from cellulose.Chains of other natural polymers are cross-linkedbefore commercial use. Examples are the hard-ening of casein (a protein) by formaldehyde to

galalith (plastic) or the vulcanization of cis-1,4-polyisoprene (natural rubber) to an elastomer.

Most polymers are, however, synthesizedchemically from molecules with low molarmasses, the so- called monomers. Examples arethe preparations of polyethylene from ethylene,poly(vinyl chloride) from vinyl chloride, nylon 6from e- caprolactam, or nylon 66 fromadipic acidand hexamethylenediamine. Some industrialpolymers result from the chemical conversionof other synthetic polymers, for example, poly(vinyl alcohol) from poly(vinyl acetate).

1.1.2. Nomenclature [1], [5], [15]

The nomenclature of individual polymers andplastics is as confusing as their classification ac-cording to properties. Various systems of nomen-clature are used simultaneously, often by the sameauthor. Abbreviations and acronyms abound,sometimes with different meanings for the sameletter combinations and other times without ex-planation. In addition, about 25 000 trade namesare used worldwide for plastics, fibers, and elas-tomers. Furthermore, a polymer from a certaincompany may come in many different gradesdepending on the processibility and application,sometimes up to 100 per polymer type. Some ofthese grades may even bear different trade namesfor various applications. On the other hand, thesame trade name is occasionally used for plasticsbased on very different polymer types. An exam-ple is Bexloy of Du Pont, which may be anamorphous polyamide (Bexloy C), a high-impactpolyester (Bexloy J), an ionomer (BexloyW), or athermoplastic elastomer (Bexloy V).

The following nomenclature systems arecommonly used for polymers:

Long-Known Natural Polymers Often haveTrivial Names. Examples are cellulose, thepolymeric sugar (-ose) of the plant cell; casein,the most important protein of milk and cheese(Latin: caseus ¼ cheese); nucleic acids, theacids found in the cell nucleus; catalase, a cata-lyzing enzyme.

Synthetic Polymers are Often Named afterTheir Monomers. Polymers of ethylene thuslead to polyethylene, those of styrene to polysty-rene, those of vinyl chloride to poly(vinyl chlo-

Vol. 28 Plastics, General Survey 37

ride), and those of a lactam to a polylactam. This‘‘polymonomer’’ nomenclature has the disadvan-tage that the constitution of monomeric units ofthe polymer molecules is not identical with theconstitution of the monomers themselves. Forexample, the polymerization of ethylene,CH2¼CH2, leads to�(CH2 – CH2)n�, a saturat-ed compound and thus a polyalkane, not anunsaturated ‘‘ene’’ as the name polyethylenemaysuggest. The polymerization of lactams (cyclicamides) does not give macromolecules with in-tact lactam rings in the polymer chains but givesopen- chain polyamides, etc. This polymonomerscheme is also ambiguous if a monomer can leadto more than one characteristic unit in a polymer.An example is acrolein, CH2¼CH(CHO), whichcan polymerize via the ethylenic double bond togive �[CH2 – CH(CHO)]n�, via the aldehydegroup to �[O – CH(CH¼CH2)]n, or via both togive six-membered rings in polymer chains.

For trade purposes, certain polymer namesmay denote not only homopolymers but alsocopolymers, contrary to what the ‘‘chemical’’names imply. For example, the copolymers ofethylene with up to 10% butene-1, hexene-1, oroctene-1 are known as linear low-density poly-ethylenes (LLDPEs). The commonly used chem-ical names of plastics thus often do not indicatethe true chemical structure of the monomericunits of the polymers on which they are based.

Polymers are Often Named after Character-istic Groups in Their Repeating Units. Polya-mides are thus polymers with amide groups –NHCO – in their repeating units; for example�[NHCO(CH2)5]n� ¼ polyamide 6 ¼ nylon6 ¼ poly(e- caprolactam). Other examples arepolyesters with ester groups – COO – or poly-urethanes with urethane groups – NH – CO –O – in the chains. A disadvantage is that thisnaming scheme is identical with that of organicchemistry where a polyisocyanate denotes a lowmolar mass compound with more than one iso-cyanate group per molecule [e.g., C6H3(NCO)3].Amacromolecular polyisocyanate would thus bea polymer with many intact isocyanate groupsper chain, for example, poly(vinyl isocyanate)�[CH2 – CH(NCO)]n�. The poly(isocyanate)sof polymer chemistry, on the other hand, possesspolymerized isocyanate groups as, for example,in �(NR – CO)n�. Such compounds are unfor-tunately also often called polyisocyanates.

IUPACNames. IUPAC recommends the useof constitutive names, similar to those used ininorganic and organic chemistry. The nomencla-ture of low and high molar mass inorganicmolecules follows the additivity principle; thoseof low molar mass organic molecules the substi-tution principle. The nomenclature of organicmacromolecules is a hybrid of both principles:the smallest repeating units are thought of asbiradicals according to the substitution principle;then their names are added according to theadditivity principle, put in parentheses, and pre-fixed with ‘‘poly.’’ Names of repeating units arewritten without spaces between words. The poly-mer �[O – CH2]n� from formaldehyde,H2C¼O, is thus called poly(oxymethylene). Thepolycondensation of ethylene glycol HO –CH2 – CH2 – OH with terephthalic acidHOOC – ( p-C6H4) – COOH leads to a polymer�[O – CH2CH2 – O – OC( p-C6H4)CO]n�withthe systematic name poly(oxyethyleneoxyter-ephthaloyl). The trivial names of this polymerare polyethylene terephthalate, and poly(ethyleneglycol terephthalate), poly(ethylene terephthal-ate). It is also known as ‘‘saturated polyester’’(although it is only one of the many possiblesaturated polyesters), as PET (an acronym) orPETP (an abbreviation) in the plastics literature,by the acronym PES in the fiber literature, and asPETE for recycling purposes.

IUPAC names are rarely used in the plasticsliterature. They are however important for sys-tematic searches inChemical Abstracts and otherliterature services.

1.2. Plastics

1.2.1. Fundamental Terms [16–39, 41–53]

Early plastics resembled natural resins. Thesenatural resins are organic solids that break with aconchoidal fracture in contrast to the planarsurfaces created upon the fracture of crystallinematerials or the drawn-out zones formed uponthe breaking of gums and waxes. Natural resinrefers mainly to oleoresins from tree sap but isalso used for shellac, insect exudations, andmineral hydrocarbons (! Resins, Natural).

Early plastics were thus sometimes calledsynthetic resins. The word resin is today occa-sionally used for any organic chemical com-


pound with medium to high molar mass thatserves as a raw material for plastics (for a defini-tion of the term resin according to current stan-dards, see ! Resins, Synthetic). Resin is not tobe confused with rosin, which refers to mixturesof C20 fused-ring monocarboxylic acids such aspine oil, tall oil, and kauri resin. Rosin is themaincomponent of naval stores (! Resins, Natural).

Plastics are usually divided into two groupsaccording to their hardening processes. Thosethat yield solid materials by simple cooling of apolymer melt (a physical process) and softenwhile being heated are called thermoplastics.Thermosets, on the other hand, harden throughchemical cross-linking reactions between poly-mer molecules; when heated, they do not softenbut decompose chemically (! Thermosets). Theshaping of a thermoplastic is thus a reversibleprocess: the same material can be melted andprocessed again. A thermoset cannot be remeltedand reshaped; its formation is irreversible.

Thermoplastics are normally composed offairly high molar mass molecules because manyphysical properties effectively become molarmass independent only above a certain molarmass. Examples are melting temperatures andthe moduli of elasticity. Other properties, how-ever, increase with increasing molar mass (e.g.,melt viscosities).

Thermosets are usually generated from fair-ly low molar mass polymers, called oligomers(science) or prepolymers (industry). High molarmasses are unnecessary here because chemicalreactions between prepolymer molecules lead toan interconnection of these molecules (cross-linking) and thus to a giant molecule, with100% conversion of the prepolymer. The prop-erties of these giant polymer molecules are ob-viously independent (or nearly so) of the molarmass of the primary molecules. Prepolymers arethus thermosetting materials and become truethermosets only after the hardening reaction.

Plastics are usually divided into four groups:commodity plastics (also called standard plasticsor bulk plastics), engineering plastics (some-times referred to as technical plastics or techno-plastics), high-performance plastics, and func-tional plastics (or specialty plastics). A commod-ity, engineering, or high-performance plasticmay have many different applications, whereas

a functional plastic has one very specific appli-cation. Polyethylene, a commodity plastic, mayaccording to its type or grade be used for con-tainers, as packaging film, as agriculturalmulch,etc. Poly(ethylene – co – vinyl alcohol) with ahigh content of vinyl alcohol units, on the otherhand, is a functional plastic that is used only as abarrier resin. Other functional plastics are em-ployed in optoelectronics, as resists, as piezo-electric materials, etc. Functional plastic is notsynonymous with functional polymer or func-tionalized polymer, because the latter termsrefer to polymers with functional chemicalgroups (i.e., groups with specific chemicalreactivities).

Commodity plastics aremanufactured in greatamounts, hence the terms bulk plastics or stan-dard plastics. Engineering plastics possessimproved mechanical properties compared tocommodity plastics. Such improved propertiesmay be higher moduli of elasticity, smaller coldflows, higher impact strengths, etc. Engineeringplastics are also often defined as those thermo-plastics that maintain dimensional stability andmost mechanical properties above 100 �C orbelow 0 �C. High-performance plastics, on theother hand, are engineering plastics with evenmore improved mechanical properties.

No sharp dividing lines exist between com-modity plastics and engineering plastics on theone hand or engineering plastics and high-per-formance plastics on the other; nor are theregenerally agreed upon property levels beyondwhich polymers are designated as engineering orhigh-performance plastics. The three groups ofplastics, in general, include the following:

Commodity Plastics. Poly(vinyl chloride),polyethylenes (high density, low density, verylow density), isotactic polypropylene, standardpolystyrene.

Engineering Plastics. Poly(ethylene tere-phthalate), poly(butylene terephthalate), poly-amides (aliphatic, amorphous, aromatic), poly-carbonates, polyoxymethylenes, poly(methylmethacrylate), some modified polystyrenes suchas styrene – acrylonitrile (SAN) and acryloni-trile – butadiene – styrene (ABS) copolymers,and high-impact polystyrenes (SB), as well asvarious blends such as poly(phenylene oxide) –polystyrene and polycarbonate – ABS.


High-Performance Plastics. Liquid crystal-line polymers (LCPs), polyetheretherketone(PEEK), various polysulfones, polyimides, etc.

Some thermosets are also classified as engi-neering or high-performance plastics. In general,thermosets are, however, considered a separategroup of plastics. They comprise alkyd (! Al-kyd Resins), phenolic (! Phenolic Resins), andamino resins (! Amino Resins) (melamine andurea resins), epoxides (epoxies) (! Epoxy Re-sins), unsaturated polyesters (including so-called vinyl esters) (! Polyester Resins, Unsat-urated), polyurethanes (! Polyurethanes), andallylics (! Allyl Compounds, Chap. 3.).

1.2.2. Designations [54–58]

The plastics trade and technical literature in-dulges in trivial names, abbreviations, and acro-

nyms. Acetal polymer is, for example, the namegiven to polymers with – OCH2 – as the majorrepeating unit. Polymers of methacryl esters�[CH2 – C(CH3) (COOR)]n� are known asmethacrylics (or often only acrylics), but poly-acrylonitrile �[CH2 – CH(CN)]n� is not con-sidered an ‘‘acrylic’’ in the plastics literature (thetextile literature calls it an acrylic fiber). Styre-nics comprise homopolymers of styrene as wellas copolymers of styrene with other monomers.Nylon, originally a protected trade name, is nowa generic term for polyamides, especially aliphat-ic ones.

Abbreviations often have more than onemeaning (Tables 1, 2, 3, 4): PBT may, for exam-ple, denote poly(butylene terephthalate), but it isalso used for poly( p-phenylenebenzbisthiazole).Exhaustive lists of commonly used abbreviationsof polymers and additives as recommended byvarious organizations have been compiled [58].

Table 1. Polymers by chain polymerization (addition polymerization), copolymerization, polycondensation (condensation polymerization), and

polyaddition which are characterized by abbreviations based on the poly(monomer) nomenclature

Polymers of ASTM DIN ISO IUPAC Other

Acrylesterþacrylonitrileþbutadiene ABA A/B/A

Acrylesterþacrylonitrileþstyrene ASA A/S/A A/S/A

Acrylesterþethylene EEA# E/EA EAA

Acrylic acid PAA PAS#

Acrylonitrile PAN PAN PAN

Acrylonitrileþbutadiene PBAN

Acrylonitrileþbutadieneþmethyl

methacrylateþstyrene

MABS

Acrylonitrileþbutadieneþstyrene ABS ABS ABS ABS ABS

Acrylonitrileþethylene-propylene-diene

þ styrene A/EPDM/S AES

Acrylonitrileþmethyl methacrylate AMMA A/MMA A/MMA

Acrylonitrileþstyrene SAN SAN SAN SAN PSAN

Acrylonitrileþstyreneþchlorinated polyethylene A/PE-C/S

Adipic acidþhexamethylenediamine PA 6.6 PA 66 PA 6.6 PA 6.6

Adipic acidþtetramethylene glycol PTMA

Allyldiglycol carbonate ADC

p-Aminobenzoic acid PAB

Aminotriazol PAT

11-Aminoundecanoic acid PA 11

Azelaic anhydride PAPA

Bisphenol Aþphosgene PC# PC# PC# PC#

Bitumenþethylene ECB

Butadieneþmethyl methacrylate

þ styrene MBS

Butadieneþstyrene (thermoplastic) SB S/B S/B S/B PASB

Butene-1 PB PB PB BT

Butyl acrylate PBA PBA

Butylene glycolþterephthalic acid PBT PBT PBT PTMT

Butyl methacrylate PBMA

e-Caprolactam PA 6 PA 6 PA 6 PA 6

Chlorotrifluoroethylene PCTFE PCTFE PCTFE PCTFE

Chlorotrifluoroethyleneþethylene ECTFE


Table 1 (Continued)


Cresolþformaldehyde CF CF CF CF

1,4-Cyclohexanedimethylolþterephthalic acid PCDT

Diallyl chloroendate (¼diallyl ester of

4,5,6,7,7-hexachlorobicyclo-[2,2,1]

5-heptane-2,3-dicarbonic acid)

PDAC

Diallyl fumarate PDAF

Diallyl isophthalate PDAIP

Diallyl maleate PDAM

Diallyl phthalate PDAP PDAP PDAP PDAP DAP

1,4-Dichlorobenzeneþdisodium sulfide PPS PPS

2,6-Dimethylphenolþoxygen POP PPOTM

Dodecanolactam (laurolactam) PA 12 PA 12 PA 12 PA 12

Ethyl acrylate PEA

Ethyl acrylateþethylene E/EA EEA#

Ethylene PE PE PE PE PL

Cross-linked polymer VPE XLPE

High-density polymer HDPE PE-HD PE-HD

Low-density polymer LDPE PE-LD PE-LD

Low-density polymer, linear LLDPE

Medium density polymer MDPE

Ultra-high molar mass polymer UHMW-PE

Ethyleneþmethyl acrylateþvinyl

chloride VC/E/MA VC/E/MA

Ethyleneþmethyl methacrylate EMA E/MA

Ethyleneþpropylene E/P E/P PEP

Ethyleneþpropylene (þdiene) EPDM

Ethyleneþtetrafluoroethylene ETFE E/TFE

Ethyleneþvinyl acetate EVA E/VA EVA VAE

E/VAC E/VAC

Ethyleneþvinyl acetateþvinyl chloride VC/E/VAC VC/E/VAC

Ethyleneþvinyl chloride VC/E VC/E

Ethylene glycol PEG

Ethylene glycolþmaleic anhydride UP#

Ethylene glycolþterephthalic acid (ester) PET PET PETP PETP PETE

Fast crystallizing polymer CPET

Oriented polymer OPET

Ethylene oxide PEO PEOX PEOX PEO

Formaldehyde (or trioxane) POM# POM# POM# POM#

Formaldehydeþfuran FF

Formaldehydeþmelamine MF MF MF MF

Formaldehydeþmelamineþphenol MPF MPF

Formaldehydeþphenol PF PF PF PF

Formaldehydeþurea UF UF UF UF

FurfuralþPhenol PFF

Hexafluoropropyleneþtetrafluoroethylene FEP FEP FEP

Hexamethylenediamineþsebacic acid PA 610 PA 6.10

p-Hydroxybenzoic acid POB PHB#

3-Hydroxybutyric acid PHB#

2-Hydroxyethylmethacrylate PHEMA

Isobutylene PIB PIB PIB PIB IM

Laurolactam (dodecanolactam) PA 12 PA 12 PA 12 PA 12

Linseed oil, epoxidized ELO ELO

Maleic anhydrideþ styrene SMA S/MA

Methacrylimide PMI

Methyl acrylate PMA

Methyl acrylateþvinyl chloride VC/MA VC/MA

Methyl a-chloromethacrylate PMCA

Methyl methacrylate PMMA PMMA PMMA PMMA

Methyl methacrylateþvinyl chloride VC/MMA

1,4-Methylpentene PMP PMP PMP TPX

a-Methylstyrene PMS PAMS

a-Methylstyreneþstyrene SMS S/MS S/MS

(Continued)


Tables 1, 2, 3, and 4 give the recommenda-tions for abbreviations of names of thermoplas-tics and thermosets by ASTM/ANSI (AmericanSociety for the Testing of Materials/AmericanNational Standards Institute [D 1600–86 a]),DIN (German Industrial Standards [7728]), ISO(International Standardization Organization[1043 – 1986 (e)]), IUPAC (International Unionof Pure and Applied Chemistry [Pure Appl.Chem. 59 (1987) 691]). ‘‘Other’’ means otherabbreviations used in the field but not recom-mended by ASTM, DIN, ISO, or IUPAC. Therecommended abbreviations are often neitheridentical with those of fibers of the same chemialstructures nor with those of elastomers contain-ing the same monomer units; some of these alsodeviate from those recommended for recycleableplastics. Several abbreviations have differentmeanings in either two or more of the ASTM,

DIN, ISO and IUPAC systems and/or the techni-cal literature, resp.; symbols with more than onemeaning are characterized by # in Tables 1–4.

The abbreviations are in part based on the poly(monomer) nomenclature, i.e., on the names ofthe monomers used in the manufacture of poly-mers, sometimes, however, without a prefix ‘‘P’’for ‘‘poly’’ (Table 1). The names of monomersfor copolymers are given in alphabetical orderwithout regard to their prevalence.

Other abbreviations are based on characteris-tic groups of polymers (Table 2) or indicatepolymers synthesized by chemical transforma-tion of base polymers (Table 4). Special abbre-viations apply to blends, reinforced polymers,etc. (Table 4).

Special properties of polymers are symbol-ized by up to four additional letters. These lettersare arranged after the symbol for the base poly-

Table 1 (Continued)


Octyl acrylateþvinyl chloride VC/OA VC/OA

Perfluoroalkoxyalkane PFA PFA

Phosphoric acid PPA#

Propylene PP PP PP PP

Oriented polymer OPP

Oriented biaxially BOPP

Propyleneþtetrafluoroethylene (alt.) TFE-P

Propylene oxide PPOX PPOX PPOX

Soybean oil, epoxidized ESO ESO

Styrene PS PS PS PS

Expanded (foamed) polymer EPS

High-impact polymer HIPS

Impact resistant polymer SRP IPS

Oriented polymer OPS

Tetrafluoroethylene PTFE PTFE PTFE PTFE

Tetrahydrofuran PTHF

Polymer with hydroxy endgroups PTMEG

Triallyl cyanurate PTAC

Trifluoroethylene P 3 FE

Trioxane (þcomonomers) POM# POM# POM# POM#

Vinyl acetate PVAC PVAC PVAC PVAC PVA

Vinyl acetateþvinyl chloride PVCA VC/VAC VC/VAC

N-Vinylcarbazole PVK PVK PVK

Vinyl chloride PVC PVC PVC PVC PCU, V

Polymerized in bulk M-PVC

Polymerized in emulsion E-PVC

Polymerized in suspension S-PVC

Polymer as flexible film FPVC

Polymer as oriented film OPVC

Polymer as rigid film RPVC

Vinyl chloride and vinylidene chloride VC/VDC VC/VDC

Vinyl fluoride PVF PVF PVF PVF

Vinylidene chloride PVDC PVDC PVDC PVDC

Vinylidene fluoride PVDF PVDF PVDF PVDF

Vinyl methyl ether PVME

N-Vinylpyrrolidone PVP PVP PVP


mer according to ISO and DIN; in the technicalliterature, they are, however, commonly placedin front of the base symbol, following ASTM.DIN recommends the following letters for spe-cial properties: C ¼ chlorinated; D ¼ density;E ¼ expanded, expandable; F ¼ flexible, liq-uid; H ¼ high; I ¼ impact resistant; L ¼ linear,low; M ¼ molar mass, average (mean), molecu-lar; N ¼ normal, novolac; P ¼ plasticized; R ¼raised (enhanced), resol; U ¼ ultra, plasticizer-free (unplasticized); V ¼ very; W ¼ weight(mass); X ¼ cross-linked. The technical litera-ture also uses BO ¼ biaxially oriented and O ¼oriented (usually in one direction). In the ASTMscheme, an asterisk (*) denotes a saran coatedpolymer film, two asterisks (**) a metallizedpolymer film.

Companies have long used internal classifica-tion systems, and the military has issued plasticsspecifications. An industry-wide classificationsystem for thermoplastic materials introducedby ISO is based on an alphanumeric ‘‘line call-out,’’ a special code (see below) [54], [55]. Amaterial is characterized by several data blocksthat indicate its composition and certain propertydata or ranges. These property data refer toessential criteria. Since different thermoplasticshave different applications, property data arerestricted to different ‘‘leading properties’’ foreach type of thermoplastic.

Table 2. Abbreviations for polymers named after a characteristic

polymer group

Characteristic group ASTM DIN ISO IUPAC Other

Amide PA PA PA PA

Amide, aromatic PARA

Metal coated films PA**

Saran coated films PA*

Amide – imide PAI PAI

Aryl amide PARA

Aryl sulfone PAS#

Benzimidazole PBI

Carbodiimide PCD

Carbonate, aromatic PC# PC# PC# PC#

Epoxide (epoxy) EP EP EP EP

Glass-fiber reinforced GEP

Epoxide – ester EPE

Ester, saturated SP

Ester, thermoplastic TPES

Metallized polymer film MPE

Ester, unsaturated UP# UP# UP# UP#

Glass fiber reinforced FRP

Ester – alkyd PAK

Ester – ether

(thermoplastic elastomer)

TEEE

Ester – imide PEI

Ether – block-amide PEBA PEBA

Etheretherketone PEEK

Ether – imide PEI

Ether sulfone PES PES

PESU

Imide PI PI

Isocyanurate PIR

Parabanic acid PPA#

Phenylene ether PPE PPE

Phenylene sulfone PPSU PPSU PPSU PSU

Silicone SI SI SI

Sulfone PSUL PSU

Urethane PUR PUR PUR PUR

Thermoplastic TPUR

Thermoset TSUR

Table 3. Abbreviations for polymers produced by chemical transfor-

mation of other polymers

Resulting polymer ASTM DIN ISO IUPAC Other

Carboxymethyl

cellulose

CMC CMC CMC CMC

Carboxymethyl

hydroxyethyl

cellulose

CMHEC

Casein, cross-linked

with formaldehyde

CS CS CS CS

Cellulose, as

Cellophan

C

Ditto, coated

with Saran

C*

Cellulose acetate CA CA CA CA

Cellulose

acetobutyrate

CAB CAB CAB CAB

Cellulose

acetopropionate

CAP CAP CAP CAP

Cellulose nitrate CN CN CN CN NC

Cellulose plastics,

unspecified

CE

Cellulose propionate CP CP CP CP

Cellulose triacetate CTA CTA TA

Ethyl cellulose EC EC EC EC

Hydroxyethyl

cellulose

HEC

Hydroxypropyl

cellulose

HPC

Hydroxypropyl

methyl cellulose

HPMC

Methyl cellulose MC

Polyethylene,

chlorinated

CPE PE-C PEC

Chlorosulfonated CSM CSR

Poly(ethylene-

co-vinyl alcohol)

E/VAL EVAL

EVOH

Polypropylene,

chlorinated

PPC

Polyvinyl alcohol PVAL PVAL PVAL PVAL PVOH

Polyvinyl butyral PVB PVB PVB

Polyvinyl chloride,

chlorinated

CPVC PVC-C PVCC PC#,

PeCe

Polyvinyl formal PVFM PVFM PVFM PVFM


The property data covered by this classifica-tion scheme are thus not comprehensive. Rather,various plastics types are characterized by one tothree sets of leading criteria, selected from

1. Chemical structure data such as content ofvinyl acetate (VAC) or acrylonitrile units(AN), isotacticity (IT), or density (D) as ameasure of branching

2. Molar mass data such as intrinsic viscosity(IV) or Fikentscher’s K value (FK)

3. Bulk density (BD)4. Rheological data such as melt flow rate

(MFR) (melt flow index)5. Thermal data such as Vicat temperature (VT)

or torsional stiffness temperature (TST)6. Mechanical properties such as modulus of

elasticity (E), tensile stress at 100% strain(TS), Shore hardness (SH), or impact strength(notched) (ISN)

The following leading criteria are used:

Polyethylene D, MFR

Polypropylene I, MFR

Polystyrene and acrylonitrile –

styrene copolymers

VT, MFR

Styrene – butadiene,

acrylonitrile – butadiene –

styrene, and acrylonitrile –

styrene – acrylic acid copolymers

VT, MFR, ISN

Ethylene – vinyl acetate copolymers VAC, MFR

Poly(vinyl chloride) IV, FK, BD

Poly(vinyl chloride), unplasticized VT, E, ISN

Poly(vinyl chloride), plasticized TS, SH, TST

Polyamides IV, E

Polycarbonates IV, MFR, E

Poly(methyl methacrylate) IV, VT

Poly(ethylene terephthalate) IV

The standard designation of a thermoplasticmaterial consists of a description block, a stan-dard number block, and a series of data blocks.

Designation Block. The designation blockgives the type of material (e.g., thermoplastic,molding, etc.).

Standard Number Block. The standard num-ber block consists of the number of the ISO (orDIN or other national) standard, followed by ahyphen and data block 1. This data block con-tains the abbreviation of the chemical name ofthe material [e.g., PE ¼ polyethylene, PVC ¼poly(vinyl chloride)]. This may be followed byanalytical data such as the vinyl acetate contentof ethylene – vinyl acetate copolymers (EVAC).However, these are not the exact analytical databut rather code numbers for the range (called‘‘cell’’) in which this material can substitute for asimilar one. Separated by a hyphen, supplemen-tal information on this material may be given(e.g., H ¼ homopolymer, P ¼ plasticized, U ¼unplasticized, E ¼ polymerized in emulsion).

Data Block 2 may contain up to four lettersthat give qualitative information. The first letterdenotes the intended application (e.g., B ¼ blowmolding, G ¼ general purpose, P ¼ paste resin,Y ¼ textile yarn). The following one to threeletters can code up to three essential additives orsupplemental information, for example, A ¼ an-tioxidant, D ¼ powder (dry blend), L ¼ lightand weather stabilizer, S ¼ slip agent.

Data Block 3. Quantitative informationabout the designated properties is contained indata block 3. The encoding of these data isdifferent for each plastic material and each test-ing standard. For example, the code 20 – D 050in data block 3 for a polyethylene tested accord-ing to DIN 16 776 means a material with adensity of 0.918 g/cm3 (cell 020) and a melt flowrate of 4.2 g/min (cell 050) measured at 190 �Cunder a load of 2.16 kg (D). On the other hand, a

Table 4. Abbreviations for blends, reinforced polymers, etc

Resulting polymer ASTM DIN ISO IUPAC Other

Elastomers, thermoplastic

Containing ester and

ether groups

TEEE

Olefin-based TEO

Styrene-based TES

Epoxide, glass-fiber

reinforced

GEP

Plastic, carbon-fiber

reinforced

KEK CFP

Glass-fiber reinforced GFK

Man-made fiber reinforced CFK

Metal fiber reinforced MFK

Poly(acrylonitrile-co-styrene)þchlorinated polyethylene

ACS

Sheet molding compound SMC

with high glass

fiber content

HMC


third data block 22 – 030 for a polyamide 12means a polymer with an intrinsic viscosity of210 cm3/g (cell 22) and amodulus of elasticity of280 MPa (cell 030). The definition of the cellscan be found in special cell tables.

Data Block 4 gives information about thetype and content of fillers or reinforcing materi-als; these codes are independent of the types ofpolymers. The first letter gives the type of filler,for example, C ¼ carbon or G ¼ glass. Thesecond letter indicates the shape of the filler(e.g., F ¼ fiber, S ¼ sphere). The letters arefollowed by a code for the mass content of thefiller; 15 for the range 12.5 – 17.5 wt%, 60 forthe range 57.5 – 62.5 wt%.

Data Block 5 is reserved for specificationsbased on individual agreements between sup-plier and customer. It may code additional re-quirements, restrictions, or supplementalinformation.

A thermoplastic may thus carry the designa-tion ‘‘Moldingmaterial DIN 7744-PC,XF, 55 –045, GF 30,’’ which indicates a polycarbonate(PC) with no special indication of its application(X) but with special burning characteristics (F),an intrinsic viscosity in a coded range of 55 (herefor [h] ¼ 56 cm3/g), and a melt flow rate of 5.5g/(10 min) (coded as 045), which contains 30%(30) of glass (G) fibers (F).

A designation system similar to the aboveISO – DIN system has been recommended byASTM [56], [57]. A typical ASTM designation,for example, would read ‘‘Molding materialASTM D-4000 PI 000 G 42 360’’; this materialis a polyimide (PI). Since no individual propertytable has been specified for polyimides, the celltable G of ASTM D-4000 has been used tocharacterize the properties of PI. This particularcell table identifies five different properties bydesignating cell limits to the five digits followingthe letter G. The first digit characterizes theminimum tensile strength, here ‘‘4’’, which ac-cording to cell table G means at least 85 MPa.The second digit gives the cell value for theflexural modulus (here ‘‘2’’ for 3500 MPa). Thethird digit denotes the Izod impact strength(50 J/m !‘‘3’’), and the fourth digit the heatdeflection temperature (300 �C!‘‘6’’). The fifthdigit is undetermined; the ‘‘0’’ indicates an un-specified property.

1.3. History of Plastics [59–64]

The first plastics were prepared long before theirmacromolecular nature was discovered. Decora-tive coatings based on polymers such as eggwhite or blood proteins were used in the cavepaintings of Altamira, Spain, as early as15 000 B.C. Later painting methods utilized gel-atin and the polymers resulting from naturallydrying vegetable oils. The use of these materialsresulted from the eternal desire of artists for easy-to-handle materials that give an optimal artisticeffect and have infinite stability.

These requirements were not restricted tosurface coatings, which are two dimensionallyapplied plastics. Cow horns were used in theMiddle Ages to prepare windows for lanternsand intarsia in wood. To this purpose, the hornshad to be flattened by steaming, a very difficultprocess. The flattened horns also tended to curlup after a while. An early, easy-to-process sub-stitute for natural horn was reported by theBavarian monk WOLFGANG SEIDEL (1492 –1562); it undoubtedly derived from far olderrecipes. This imitation horn was based on theprotein casein, the white material from skimmilk. Casein was extracted from skim milk withhot water, treated with warm lye, and shapedwhile being warmed; the desired shape was thenfixed by immersion in cold water. Unknowninventors later discovered that the addition ofinorganic fillers increased the mechanical stabil-ity of this early thermoplastic. The samematerialwas used later for children’s building blocks bythe German aviation pioneer OTTO LILIENTHAL

(1848 – 1896) and his brother GUSTAV. In 1885 apatent based on the same physical process wasgranted to the American EMERY EDWARD CHILDS.The properties of these plastics were improvedmarkedly by the chemical reaction of casein withformaldehyde, as described in 1897 by theGerman inventors WILHELM KRISCHE and ADOLF

SPITTELER. The resulting thermoset was calledgalalith (Greek: gala ¼ milk, lithos ¼ stone); itis still used today for haberdashery.

Another early thermoset used natural rubberas the raw material. In 1839 the AmericanCHARLES GOODYEAR discovered the cross-link-ing (vulcanization) of natural rubber to anelastomer by sulfur under the action of ‘‘whitelead’’ (basic lead carbonate) and heat. Hisbrother NELSON used larger amounts of sulfur


and in 1851 invented ebonite, a hard, blackthermoset.

The first fully synthetic thermoset was in-vented in 1906 by the Belgian-born Americanchemist LEO H. BAEKELAND, who heated variousphenols with formaldehyde under pressure andproduced insoluble hard masses. These ‘‘bake-lites’’ were recognized in 1909 as excellent elec-trical insulators and thus became one of thefoundations of the modern electrical industry.BAEKELAND was not the first to prepare phenolicresins though; they were first observed by ADOLF

VON BAEYER in 1872. BAEYER’s substances weremerely resinous materials, and BAEKELAND’s‘‘heat and pressure’’ process was necessary be-fore commercially useful materials could beproduced.

The first semisynthetic thermoplastics origi-nated from cotton. Cotton fibers consist of cellu-lose; they have been used by man since prehis-toric times. Since cotton is relatively easilygrown, many attempts have been made to im-prove its textile properties. The Englishman JOHNMERCER discovered in 1844 that the treatment ofcotton with aqueous solutions of caustic soda(sodium hydroxide) leads to fibers with increasedstrength, higher luster, and improved dyeability.The Frenchman L. FIGUIER demonstrated in 1846that cellulose paperwas strengthened in amannersimilar to cotton when it was treated with sulfuricacid. In 1853 W. E. GAINE received an Englishpatent for the same process, which delivered aparchment-like material. An English patent byTHOMAS TAYLOR described the formation of veryresistant materials from layers of paper sheets bythe combined action of zinc chloride and pres-sure. These products were called ‘‘vulcanfiber’’since they resembled the vulcanization productsof natural rubber.

Mercerized cotton, artificial parchment, andvulcanized paper result from physical transfor-mations of cellulose. If, however, cellulose ma-terials are treated not by sulfuric acid alone but bya mixture of sulfuric and nitric acids, a chemicalreaction to cellulose nitrate (nitrocellulose, guncotton) occurs. This chance discovery by theGerman CHRISTIAN FRIEDRICH SCH€oNBEIN in 1846paved the way for the invention of the firstsemisynthetic thermoplastic. In 1862 ALEXANDER

PARKES found an easy method for processingcellulose nitrate into thermoplastic masses bythe addition of castor oil, camphor, and dyes.

The manufacture of the resulting ‘‘parkesine’’was difficult, however, and production ceased in1867. The use of alcoholic solutions of camphorby DANIEL W. SPILL was equally unsuccesful. In1869 a patent was granted to the American JOHNWESLEY HYATT for the use of camphor withoutcamphor oil or alcohol. The resulting ‘‘celluloid’’is generally considered the pioneering thermo-plastic [63].

Other early, fully synthetic thermoplasticshave a far longer history, albeit not as industrialmaterials. Polymers of formaldehyde were foundby JUSTUS VON LIEBIG in 1839; yet extensivescientific investigations by HERMANN STAUDINGERin the 1920s and 1930s and major industrialdevelopment work by Du Pont were necessarybefore it became an engineering plastic in 1956.

Vinyl chloride was synthesized in 1838 byH. V. REGNAULD, who also observed the forma-tion of resins. Vinyl chloride was polymerized in1912 by KLATTE in Germany and OSTROMUISLENS-

KY in England, but not until 1931 was the firstpoly(vinyl chloride) produced commercially inGermany by I. G. Farben.

Styrene was discovered by a chemist calledNEUMAN as reported in W. NICHOLSON’s 1786Dictionary of Practical and Theoretical Chem-istry. The conversion of styrene to a solid masswas discovered by E. SIMON in 1839, who con-sidered it a styrene oxide. A. W. VON HOFMANN

and J. BLYTH showed in 1845 that the allegedstyrene oxide was an isomer of styrene; theycalled it metastyrene. It was however only in1920 that the polymeric nature of polystyrenewas recognized by H. STAUDINGER; it was firstproduced commercially by I. G. Farben (Ger-many) in 1930.

A highly branched polyethylene is found innature as the ‘‘mineral’’ elaterite. Lightlybranched synthetic polyethylene was first ob-tained in 1933 by high-pressure polymerizationof ethylene at ICI (England); its commercialproduction began in 1939. Linear polyethyleneswere first synthesized in 1953 by low-pressurepolymerization using catalysts based on transi-tion metals (Ziegler), chromium oxide (PhillipsPetroleum), and molybdenum oxide (StandardOil of Indiana). For the first time, Ziegler – Nattacatalysts also enabled the polymerization of a-olefins such as propylene to solid, stereoregularpolymers; the commercial production of isotacticpolypropylene (PP) began in Italy, the Federal


Republic of Germany, and the United States in1957. The use of these catalysts and the avail-ability of inexpensive feedstocks frompetroleumrefining led to rapid growth of the polymerindustry (Table 5).

Plastics are the leader in this growth, followedby synthetic fibers and synthetic elastomers. Theworld production of semisynthetic fibers (rayonand cellulose acetate) (! Cellulose Esters) has,however, declined, mainly because of cost andenvironmental concerns in the developed coun-tries and despite increased production of semi-synthetic fibers in the developing countries.

1.4. Economic Importance [65–69]

The rapid growth of plastics production is a resultof three factors: growth of world population,average increase in standard of living, and re-placement of older materials by plastics. Thegrowth pattern may be economy driven [deter-mined by the price of materials (substitutes);shortages (‘‘ersatz’’), or government intervention(environmental concerns)], or technology driven(determined by technological requirements, in-ternal knowhow, accidental discoveries).

The world population grew from 2.532�109

in 1950 to 5.32�109 in 1980, while the worldplastics production (approximately equal to con-sumption) climbed from 0.6 kg per capita (1950)to ca. 18.8 kg per capita (1990) (Table 6).

These numbers are approximate because sta-tistics are incomplete and may differ consider-ably from source to source. For example, 1987world plastics production is given as either37.5�106 t ([65], excluding South Africa andthe People’s Republic of China) or 55.4�106 t[66].

Great differences in plastics consumption ex-ist between various countries. In 1988, the ap-parent annual per capita consumption as calcu-lated from production plus import minus export(i.e., including stockpiling) was 128 kg in theFederal Republic of Germany; 104 kg in theUnited States of America, 95 kg in Switzerland;and 81 kg in Japan and the United Kingdom butin 1978 only 1.2 kg in Black Africa, 1.1 kg inBolivia, and 0.4 kg in India [67] and has notmuch changed since. Since world populationcontinues to grow and people in less developedcountries justifiably aspire to higher living stan-dards, theworld plastics production ismost likelyto increase further despite some environmentalconcerns in highly industrialized countries (seebelow). Although all regions will share in thisgrowth, it will be most pronounced in ‘‘other’’countries (e.g., SaudiArabia, countries inCentraland South America, Southeast Asia, and theIndian subcontinent) and, if planned economiesare replaced by free-market types, also in theformer Comecon countries.

The replacement of other materials by plasticsis more difficult to judge. Since developingcountries possess a great and unsatisfied needfor goods that have long been taken for granted inmore affluent societies, an analysis cannot bebased on world production of materials but onlyon that in highly developed countries such as theUnited States (Table 7).

Table 7 gives the apparent consumption ofselected important materials, calculated fromproduction plus import minus export i.e., includ-ing stockpiling but excluding the import – ex-port of manufactured goods such as machinery

Table 5. World production of polymers (in 106 t/a)

Type 1940 1950 1960 1970 1980 1990

Plastics 0.36 1.62 6.7 31.0 59.0 100

Fibers

Synthetic 0.005 0.069 0.70 5.0 11.5 15.7

Semisynthetic 1.1 1.6 2.6 3.4 3.3 3.2

Natural** 8.7 8.0 12.8 14.0 17.7 18*

Elastomers

Synthetic 0.043 0.54 1.94 5.9 8.7 9.1*

Natural 1.44 1.9 2.02 3.1 3.9 4.9*

*Estimated.**Textile fibers only.

Table 6. Production of plastics, world population, and consumption

per capita

Region/country Production in 106 t/a

1950 1960 1970 1980 1990

European

Community

0.3 2.3 11.5 19.7 30

United States 1.1 2.8 9.1 16.1 30

Japan 0.04 0.7 5.3 7.5 13

Eastern Europe 0.1 0.5 4.0 6.9 13

Other 0.07 0.3 1.1 8.8 14

Total 1.6 6.7 31.0 59.0 100

World population,

�10�6

2532 3062 3730 4498 5320

Per capita

consumption in kg

0.6 2.2 8.3 13.1 18.8


(metals), garments (fibers), tires (cars), news-print (paper), etc. The highest per capita con-sumption is in construction materials (nonmetal-lic minerals, lumber, partly steel and aluminum),followed by packaging materials (partly steel,aluminum, paper).

Plastics constitute a fairly small percentage ofall consumed materials (Table 7). However, theyhave the highest growth rate (Fig. 1). The data inFigure 1 are given on a volume basis becausematerials are used by volume although they aresold by mass. Although the share of plastics interms of total materials produced (and mainlydisposed) is quite low, it causes environmental

concern because of its very visible proportion inhousehold refuse (see Chap. 12).

Since construction and packaging are majorapplications for lumber, steel, and aluminum, itcan be expected that plastics are important re-placements for these materials. Packaging andbuilding – construction are indeed the most im-portant applications of plastics (Table 8); theyalso show the highest growth rates (ca. 15% peryear).

Plastics are consumed in far lesser amounts inelectric – electronics applications, transporta-tion, toys, housewares, appliances, and furniture;the U.S. use in agriculture and paints and coat-ings has not been reported. Plastics are criticaland irreplaceable components in certain fieldssuch as the electric – electronics industry. Con-sumption patterns are similar for nations withcomparable affluence; the United States andWest German applications of plastics do notdiffer significantly when the fact is consideredthat ca. 53% of U.S. applications are not ac-counted for.

2. Molecular Structure of Polymers[1–5, 8–14]

2.1. Constitution

2.1.1. Homopolymers

A homopolymer is defined as a polymer derivedfrom one type of monomer. The term homopol-ymer thus refers to the origin of the monomers ina polymer and not to the actual constitutionalunits. The polymerization of a monomerCH2¼CHR leads to constitutional units –CH2CHR –. These units may be connected toeach other not only in head-to-tail positions butalso in head-to-head and tail-to-tailarrangements:

The proportion of head-to-head regioisomericunits increases with decreasing size of substitu-ents R and with reduced resonance stabilization

Table 7. Per capita consumption of selected materials in the United

States in 1983 (estimated population: 234�106) [68]

Materials Source

Consumption

in kg/a

Imports

in % of

consumption

Nonmetallic minerals

Sand, gravel Na 2576 0

Stone Na 3322 0

Cement MNb 287 6

Clay MNb 270 0

Gypsum Na 81 39

Metals

Raw steel Sc 421 15

Aluminum, primary Sc 15.0 6

Copper Sc 6.4 31

Lead Sc 4.8 10

Zinc Sc 3.8 39

Polymers

Wood, wood products

Lumber Na 466 22

Plywood MNb 29.6 4

Paper MNb 277 6

Other ? 35 ?

Fibers (excluding

export – import

of fabrics and garments)

Cotton Na 5.5 (50)e

Rayon, acetate MNb 3.6 66

Wool, silk Na 1.6 92

Synthetic fibers Sc 16.9 ?

Elastomers (excluding

exported rubber goods)

Natural rubber MNb 2.6 100

Synthetic rubber Sc 6.7 (12)e

Plastics (excluding

manufactured goods)

Plastics, resins Sc 71 (9)e

MNb 0.2d ?

Leather MNb 6.4 ?

aNatural product.bMN ¼ physically or chemically modified natural product.cS ¼ synthetic product.dEstimated.eNet exports.


of the growing species. Free-radical polymeriza-tion of vinyl acetate [CH2¼CH(OOCCH3)] leadsto 1 – 2%, of vinyl fluoride (CH2¼CHF) to 6 –10%, and of vinylidene fluoride (CH2¼CF2) to10 – 12% tail-to-tail connections.

Monomer molecules can also polymerize to alesser or greater extent via ‘‘wrong’’ groups. Theamount of such isomeric units depends on theconstitution of the monomer and the mode ofpolymerization. Acrolein (1), for example, poly-merizes free radically via the carbon – carbondouble bond (2) and the aldehyde group (3); itforms branched (4) or cross-linked units and even

intramolecular rings (5) from two units of (4):

Monomers may also isomerize during poly-merization, especially cationic polymerization.4,4-Dimethyl-pentene-1 (6) polymerizes at low

Figure 1. Production of important materials (in liters per year) in the United States during 1910 – 1990.All metals are on smelter basis; - - - U.S. population (numbers). Reported commercial data were converted as follows: 1 boardfoot lumber ¼ 2.36 L, 1 short ton � 907 kg, 1 lb � 0.454 kg; densities of steel (7.85 g/cm3), aluminum (2.70 g/cm3), zinc(7.13 g/cm3), and plastics (1.1 g/cm3) (average, weighted according to market shares of major plastics). Data from [69].


temperature (��130 �C) via the carbon – car-bon double bond (7), but at higher temperature(�0 �C) leads to a ‘‘phantom polymer’’ (8) withthree carbon atoms per monomeric unit:

Irregular structures may also be created bychain-transfer reactions to polymer molecules(see Chap. 3); these reactions lead to branchedpolymers.

The presence of such isomeric units can oftenbe neither proved nor disproved. Polymer struc-tures are therefore generally depicted by theirmost common constitutional repeating units;they are idealized structures.

The groups at the ends of polymer chains arelikewise not shown, in part because they are oftenunknown and in part because their structure doesnot influencemost of the polymer properties. Endgroups may be initiator or catalyst residues or

Table 8. U.S. plastics sales and applications in 1988 (in 1000 t)

Polymer Domestic

sales

Domestic applications a

A B E F H P T Y U

PE-HD 3 743 9 251 53 5 143 1 692 19 77 1 494

PE-LD 4 479 127 168 4 191 1 092 20 74 2 803

PP 3 316 67 18 21 30 92 470 170 18 2 430

PS 2 329 77 127 186 55 115 108 108 1 553

SAN 62 10 2 10 8 32

ABS 562 91 69 53 2 2 95 17 233

Other styrenics 553 553

PPO alloys 82 20 2 1 59

PVC 3 779 64 2 301 232 41 29 199 101 15 809

Other vinyls b 435 2 53 380

PMMA 316 4 110 25 177

POM 58 5 7 2 12 32

PA 253 8 36 25 69 115

PC 195 16 52 25 28 74

PETP, PBT 911 3 3 20 450 20 415

Fluoropolymers 13 13

Cellulosics 41 1 2 2 3 1 32

Thermoplastic

elastomers 225 225

UP c 623 30 132 17 9 64 371

EP 213 4 19 25 15 45 105

PF d 1 376 15 411 45 77 18 6 10 794

UF, MF d 688 121 14 10 6 3 534

PUR e 1 319 73 309 257 331 349

Alkyds 145 145

Other f 500 16 21 3 29 86 52 41 252

Total 26 216 513 4 063 923 493 633 4 212 730 682 13 979

% of accounted 4.2 33.2 7.6 4.0 5.1 34.4 6.0 5.5

% of U.S. total 100 2.0 15.5 3.5 1.9 2.4 16.0 2.8 2.6 53.3

% of FRG g 100 21.0 15.0 5.0 2.5 25.0 7.0 10.5

aA¼appliances, B¼building/construction, E¼electrical/electronic, F¼furniture, H¼household goods, P¼packaging, T¼transportation,

Y¼toys, U¼unaccounted; 1982 FRG percentages (bottom line) are given for comparison.bPoly(vinyl acetate), poly(vinyl butyral), ethylene – vinyl alcohol copolymers, etc.cWithout glass fibers.dResin in plywood assumed as 20%.eRaw materials.fCoumarones, high-performance resins, etc.gPlus paints etc. (10%) and agricultural (4.0%).


groups that are generated by transfer reactions.These groups rarely affect mechanical proper-ties; they may, however, negatively influencethe thermal or photochemical stability ofpolymers.

2.1.2. Copolymers

Copolymers are generated from more than onetype of monomer; they are called bipolymers,terpolymers, quaterpolymers, etc., according tothe number of monomer types. The copolymeri-zation of ethylene (CH2¼CH2) and propylene[CH2¼CH(CH3)] thus leads to the bipolymerpoly(ethylene- co-propylene). Polymers of buta-diene (CH2¼CH–CH¼CH2) with 1,4-units –CH2 – CH¼CH – CH2 – and 1,2-units– CH2 –CH(CH¼CH2) – are not called copolymersbecause they are generated from only one mono-mer type. Rather, they are pseudocopolymerssuch as the ones that result from partial saponifi-cation of poly(vinyl acetate), �[CH2–CH(OOCCH3)]n�, to a pseudocopolymerwith vinylacetate units and vinyl alcohol units – CH2 –CH(OH) –. The term copolymer thus does not referto the chemical structure of the resulting poly-mer, but to the monomers from which it derives.

The succession of monomeric units in copol-ymer chains is known as their sequence. Mono-mer units ‘‘a’’ and ‘‘b’’ alternate in alternatingcopolymers (Table 9), which are limiting cases ofperiodic copolymers � (abb)n �, � (aabb)n �,� (abc)n �, etc.

The sequence of monomeric units in statisti-cal copolymers is determined by the statistics ofcopolymerization (Markov statistics of zeroth,

first, etc., order). Random copolymers are specialcases of statistical copolymers: the sequencefollows Bernoulli statistics (i.e., zeroth-orderMarkov statistics).

Graded copolymers (i.e., tapered copolymers)exhibit a compositional gradient along the chain:one chain end is enriched in ‘‘a’’ units, the otherin ‘‘b’’ units.Block copolymers are extreme casesof such graded copolymers; they consist ofblocks of homosequences that are joined via theirends. Linear multiblock copolymers with shortblocks are called segment(ed) copolymers. Ingraft copolymers, ‘‘b’’ blocks are connected to‘‘a’’ chains via center monomeric units.

Copolymers poly(A- co-B) of monomers Aand B possess properties quite different fromblends of homopolymers A and B.

2.1.3. Branched Polymers

Open chains of the type R – mn – R exhibit thesimplest structures. They posses n monomeric‘‘m’’ units and two R end groups. They are alsocalled linear chains (Fig. 2, L) because of theirone-dimensional connectivity or their un-branched structures and because they were origi-nally (and wrongly) assumed to be completelyextended (stretched out). Spiropolymers and lad-der polymers (see below) are also linear poly-mers because they are not ‘‘branched’’ in themacromolecular sense.

Cyclic Polymers (ring polymers; Fig. 2, R)consist of linear polymer molecules that arejoined via their ends. They do not have endgroups and are not called macrocycles because

Table 9. Types of copolymers from monomers A, B, and C (monomeric units are characterized by lower-case letters)


that term is traditionally reserved for ‘‘big rings’’of ca. 15 – 20 chain atoms.

Branched polymers contain branch points thatconnect three or more subchains (sometimescalled subunits). The following types of branchedpolymers are distinguished:

1. Star polymers possess one branching pointfrom which three or more subchains radiate(Fig. 2, S).

2. Dendrimers (dendritic polymers) are starpolymers in which the subchains are them-selves starlike branched (Fig. 2, D). They arealso called cascade polymers (because of thecascade-like sequence of branching points),isotropically branched polymers, or iso-branched polymers (since each generation ofnewly added monomer molecules is ‘‘isotro-pically’’ arranged around the central core), ormuch more poetically, starburst polymers.

3. Comb polymers have ‘‘long’’ side chains,whose chemical structures usually differ fromthose of the main chains (Fig. 2, C). The termgraft copolymer refers to comb polymers intowhich branches have been introduced by sub-sequent grafting onto a primary chain. Combpolymers whose side chains exhibit liquidcrystalline (LC) behavior are called LC side-chain polymers.

4. Randomly branched polymers have a randomdistribution of branching points (Fig. 2, B);the subchains may be further branched(Christmas tree branching) or not. Short-chain and long- chain branching are distin-

guished. Short- chain branches are often gen-erated by intramolecular transfer reactions,for example, the butyl side chain of polyeth-ylene is formed during free-radical polymeri-zation of ethylene:

Long- Chain Branches are usually generatedby intermolecular transfer reactions. In the po-lymerization of vinyl acetate, side- chain radicalsformed by transfer reactions may initiate thepolymerization of additional vinyl acetate mono-mers.

Such side- chain radicals are also formed byradical transfer from certain initiator radicals.

Figure 2. Schematic representation of linear and branched marcomoleculesL ¼ Linear (unbranched) chain in almost extended state; R ¼ ring molecule; S ¼ starlike molecule with three subchains,C ¼ comblike molecule with four branching points of functionality 3; B ¼ randomly branched chain with subsequentbranching; D ¼ dendrimer with three-functional branch points and three generations of subchains


Side chains introduced by the inherent struc-ture of a (co)monomer are not called branches inpolymer science. Neither linear poly(vinyl ace-tate) nor the low- crystallinity, low-density poly-mers formed by copolymerization of ethylenewith small amounts of a-olefins (butene-1, hex-ene-1, octene-1) are considered branched; thelatter are known as linear low-densitypolyethylenes.

2.1.4. Ordered Chain Assemblies

Two or more chains may also be joined at morethan two points by chemical bonds in an orderedway. The chains are thought to be fully extendedfor classification purposes; a distinction is madeamong one-, two-, and three-dimensional assem-blies or, according to IUPAC, among catena(Fig. 3 –1), phyllo (Fig. 3 –2) and tecto (Fig. 3–3) compounds.Linear polymers are catena polymers in this

nomenclature since the fully extended chainsextend in only one direction (Fig. 3 –1). Spiropolymers possess two chains with connectingatoms shared by both of them (Fig. 3-S).

Ladder polymers consist of two chains joinedby bonds in regular intervals (Fig. 3-L); they are

also called double-strand polymers. Such ladderpolymers are generated by first forming a linearchain with pendant side groups that are subse-quently polymerized. An example is the poly-merization of 1,3-butadiene to 1,2-polybutadienewith subsequent cyclization to cyclopolybuta-diene

Ladder polymers may also be synthesized bytwo-step polycondensation or polyaddition reac-tions; in general, however, only fairly shortladderlike units are formed in this way (seebelow). One-step ladder syntheses are very rare.Polymerization of the silicon analogue of cu-bane, (C6H5)8Si8O12, does not lead to a ladderpolymer of type L in Figure 3 but to a pearl-string-like polymer P (Fig. 3-P). Many silicatesare ladder polymers or double-ladder polymers.

Phyllo polymers are also called layer or par-quet polymers (Fig. 3). Graphite and the silicatesmontmorillonite, bentonite, and mica are well-known examples. Cell walls of bacteria consist of

Figure 3. Schematic representation of some ordered chain assemblies1 ¼ Catena polymer in all-trans conformation; S ¼ Spiro polymer; P ¼ Pearl-stringlike polymer; L ¼ Ladder polymer;2 ¼ Phyllo polymer; 3 ¼ Tecto polymer


bag-shaped polymers (i.e., layer polymers).Diamond and quartz are examples of tecto poly-mers (Fig. 3).

2.1.5. Unordered Networks

Multifunctional oligomer and polymer mole-cules can be interconnected via chain groups orend groups to cross-linked polymers (networks).The cross-linking points must be at least trifunc-tional; that is, the cross-linkable groups must beat least bifunctional. The cross-linking bridgesbetween chains can be short or long; the distri-bution of cross-linking points, at random or inclusters. Both chemical and physical bonds canbe employed for cross-linking; chemically andphysically cross-linked polymers are thusdistinguished.

Chemical Networks. The structure of chem-ical networks depends on the relative amount ofcross-linking sites and the state of the reactantsduring the cross-linking reaction. The networkstructure is to a first approximation independentof the chemical structure of the cross-linkingsites. The relative amount of cross-linking sitesdetermines the cross-link density. Light cross-linking does not change the mobility of chainsegments between cross-links, and the resultingnetworks behave as elastomers if the chain seg-ments are above the glass transition temperature.Networks with strong cross-linking or chainsegments below the glass transition temperatureare employed for thermosets.

Networks are fairly homogeneous with re-spect to the distribution of cross-links if they areprepared by polymerization in bulk or fromhomogeneous solutions and if the correspondinglinear chains are soluble in their own monomersor in the applied solvent (Fig. 4, HN). Inhomo-geneous networks are formed if phase separationoccurs during polymerization; for example, if thelow molar mass polymers generated early areinsoluble in the applied solvent or the remainingmonomer. The resulting macroreticular net-works exhibit cavities (Fig. 4, MN).

In principle, two chemically different net-works poly (a) and poly (b) can coexist indepen-dently of each other in interpenetrating networks(IPNs). In reality, these networks are not molec-ularly interdispersed; rather, each network forms

interconnected domains with higher cross-linkdensities. Semi-interpenetrating networks con-sist of cross-linked poly (a) in uncross-linkedpoly (b).

Chemical cross-links are in most cases irre-versible. These cross-linked polymers do notdissolve in solvents. With an increase in temper-ature, subchains decompose rather than revert tothe original monomers. Chemically reversiblecross-linked networks are being investigated be-cause they would be of value in the recycling ofthermosets.

Physical Networks. Physically cross-linkedpolymers, on the other hand, are in most casesreversibly cross-linked. Examples are microdo-mains in block copolymers, ion clusters in iono-mers, or even crystallites in partly crystallizedpolymers. Physically cross-linked polymers of-ten dissolve in suitable solvents.

Entanglements (Fig. 4, E) behave under strainas physical cross-links because the two chainscannot diffuse away rapidly enough; the chainsdisentangle, however, if sufficient time isallowed. Catenanes (Fig. 4, C) and rotaxanes(Fig. 4, R) have irreversible physical cross-links.Catenanes consist of two intertwined rings. Suchstructures are well known for deoxyribonucleic

Figure 4. Schematic representation of cross-linked polymersA) Physical cross-links; B) Chemical networksC ¼ catenane; E ¼ entanglement; HN ¼ homogeneous net-work; IPN ¼ interpenetrating network; MN ¼ macroreticu-lar network; R ¼ rotaxaneReprinted with permission by H€uthig and Wepf Publ., Basel[5]


acids; they have also been observed for somesynthetic polymers. Rotaxanes are rings onchains that are sealed on both ends by branchedor cross-linked structures in such a way that thering cannot slip out. Such structures are sus-pected to exist in some cross-linked polydi-methylsiloxanes.

2.2. Molar Masses and Molar MassDistributions

Molar masses of polymers can be varied over awide range; they may extend from several hun-dreds to several millions, albeit not for everypolymer type. The molar mass ranges used in-dustrially depend on the limitations of the avail-able polymerization procedures, the restrictionsimposed by processing methods, and the desiredproperties of the plastics.

Presently available polymerization methodsall employ statistical approaches to initiationand propagation of growing chains, as well as totermination and transfer, where applicable. Theresulting polymer molecules thus show a distri-bution of molar masses; they are not molecu-larly uniform, and the experimentally deter-mined molar masses represent averages. Syn-thetic copolymers are, in addition, nonhomoge-neous with respect to the distribution ofdifferent types of monomer units; they arepolydisperse with respect to both constitutionand molar mass.

In contrast, biopolymers are synthesized viamatrix polymerization. Many (if not all) biopo-lymers are monodisperse in their biological en-vironments: each macromolecule of a polymerhas the same constitution and the same molarmass. Examples are nucleic acids and enzymes.Upon isolation from living cells and furtherprocessing, some degradation may occur. Indus-trially employed celluloses thus exhibit molarmass distributions.

The recently discovered starburst dendrimersare synthetic polymers that are molecularlyuniform. Their molecular homogeneity ap-proaches that of isotopic distributions in atomsand molecules. It is caused by a self-limitationof molecular growth due to surface crowdingafter a certain number of growth generationsteps [70].

2.2.1. Molar Mass Average

Many polymer properties depend on the type andrange ofmolar mass distributions. In many cases,molar mass averages are determined instead, inpart because it is experimentally easier and inpart because a number is simpler to grasp than afunction.

The averages employed in polymer scienceare usually arithmetic averages. The polymermolecules of size i (degree of polymerizationXi, molar massMi) are counted according to theirstatistical weight gi, which may be their molefraction xi�ni/Sini, their mass fraction wi �mi/Simi ¼ xiMi/M�n, or their z-fraction defined asZi � zi/Sizi ¼ wiMi/M�w ¼ xiM

2i/(M�nMw). The

number-, mass-, and z-average molar masses aredefined as

Mn � SixiMi ¼ Siwi

Siðwi=MiÞ ð1Þ

Mw � SiwiMi ¼ SixiM2i

SixiMið2Þ

Mz � SiZiMi ¼ SiwiM2i

SiwiMi¼ SixiM

3i

SixiM2i

ð3Þ

Each of these three average moments is essen-tially a singlemoment of the distribution ofmolarmasses present. There are, however, molar massaverages which are composed of more than onemoment, for example, molar masses from sedi-mentation and diffusion coefficients for certaintypes of molecular shapes and solventinteractions.

2.2.2. Determination of Molar Mass

Many methods exist for the determination ofmolar masses. Most important for the number-average molar mass is osmometry, which mea-sures the osmotic pressure P of polymer solu-tions at various polymer concentrations c againstthe solvent. Solution and solvent are separated bya semipermeable membrane that is permeable tothe solvent but not to the polymer molecules.

Older osmometers determined osmotic pres-sure in true thermodynamic equilibrium, whichwas reached only after days and weeks becauselarge volumes of solvent had to be movedthrough the membrane. Modern osmometers


compensate for the increase in pressure differ-ence between solution and solvent caused by theflow of solvent into the solution chamber via aservomechanism by a change of solvent pressure;equilibrium pressures are established after 10 –30 min. Reduced osmotic pressures, P/c, deter-mined at various concentrations, are extrapolatedto zero concentration to give the number-averagemolar mass according to the van’t Hoff equation,�Mn ¼ RT/[limc!0 (P/c)]. Number-average mo-lar masses may be determined by osmometry inthe range of 104 g/mol (lower limit of semiper-meability of membranes) to ca. 106 g/mol (upperlimit of sensitivity).

Mass-averageMolarMasses are determinedmainly via static light scattering of dust-freedilute solutions. Modern instruments measurethe so- called Rayleigh ratio Ro ¼ K � c � �Mw, app,at very low angles relative to the incident lightbeam, where K is an optical constant andMw, app

an apparent mass average molar mass which iscalculated from Ro, c, and K. Values of K � c/Ro

are measured at various polymer concentrationsand extrapolated to zero concentration. The lim-iting value limc!0 (K � c/Ro) delivers the inversemass-average molar mass, 1/ �Mw. Molar massesfrom several hundred to severalmillion grams permole can be determined by light scattering, theupper limit beinggivenby experimental problemssuch as multiple scattering. If measurements areperformed over a wide range of scattering angles,important additional information about the radiiof gyration of the molecules can be gained fromthe angular dependence of the Rayleigh ratio.

The viscometric method is fast and simple andtherefore the most often applied method. Fromsolvent viscosity ho and viscosities h of dilutesolutions of various concentrations c (measuredat low shear rates), reduced viscosities (i.e.,viscosity numbers) are calculated via hred ¼(h – ho)/(ho � c). The reduced viscosities are ex-trapolated to zero concentration to give the in-trinsic viscosity (limiting viscosity number) [h](DIN recommends the symbol Jo). This quantityhas the physical unit of a specific volume sincethe concentration c is measured as mass pervolume. The recommended units are millilitersper gram (cubic centimeters per gram), but datain 100 mL/g are still found in the literature; in theolder literature, [h] was given as Zh in liters pergram.

Intrinsic viscosities measure the volume oc-cupied by 1 g polymer at c ! 0, that is, thespecific volumes (inverse densities) of isolatedpolymer molecules. Since molecular densityvaries with size for most molecule shapes, in-trinsic viscosities can be used to measure molarmasses for a homologous series of polymermolecules.

The viscosity increment hi of unsolvated,compact spheres is, according to EINSTEIN:

hi ¼ ðh�hoÞ=ho ¼ ð5=2Þf ¼ ð5=2ÞðNAVHc=MÞ ð4Þ

where NA is the Avogadro number, f the vol-ume fraction, VH ¼ rH/m the hydrodynamicvolume, rH the density, and m the mass of asphere. Hard spheres from the same materialhave the same density. Since m�M and hi/c�[h], intrinsic viscosities of spheres are inde-pendent of their molar masses (i.e.,[h] ¼ K �M 0).

The hydrodynamic densities of other particleshapes such as rods and coils change, however,with the molar mass

½h� ¼ K�Ma ð5Þ

The exponent a ¼ 2 for rigid rods of infinitelength. Theory and experiment indicate a valueof a ¼ 1/2 for random coils in the unperturbedstate (see below); this is a limiting case for veryflexible chains in theta solvents. A theta solvent isa solvent being at a temperature at which apolymer adopts the theta state, i.e., where coilmolecules are in their unperturbed state with aGaussian distribution of segments (no excludedvolumes). A theta solvent is a thermodynamical-ly bad solvent. Theory predicts a ¼ 0.764 fornondraining coils of high molar mass in thermo-dynamically good solvents (Fig. 5). Experimen-tally, values of 0.5<a<0.764 are often found forflexible chains (such as most thermoplastics insolution) because their molar masses are not highenough for the assumptions of the theory to befulfilled.

Wormlike molecules may adopt values of0<a<2 because they resemble spheres and el-lipsoids at low molar masses, rigid rods at medi-um ones, and random coils at very high molarmasses. This behavior is found for stiffmoleculessuch as the double helices of deoxyribonucleicacids in aqueous solutions or certain poly(a-


amino acids) in helicogenic solvents (seeChap. 5).

Viscometry delivers a peculiar molar massaverage, such as can be derived fromequation (5):

Mh ¼ ð½h�=KÞ1=a ¼ ðK�1�Siwi½h�iÞ1=a¼ ðSiwiM

ai Þ1=a

ð6Þ

Numerical values of viscosity-average molarmasses �Mh lie between number and massaverages for 0<a<1 and become identical withmass averages if a ¼ 1.

2.2.3. Molar Mass Distributions

The types and characteristic parameters of molarmass distributions of polymers are determinedthermodynamically or kinetically by the synthe-sis conditions and, to a smaller extent, by theprocessing of plastics. The molar mass distribu-tions are mathematically described by distribu-tion functions, which may be discontinuous (dis-crete) or continuous and differential or integral(cumulative) (Fig. 6). In these functions, poly-mer molecules of size i (molar massMi,degree ofpolymerization Xi) are considered according totheir statistical weights, which may be molefractions xi, mass fractions wi, etc.

All molar mass distributions are discrete be-cause successive polymer molecules of a homol-ogous series differ from each other by a degree ofpolymerization of 1 and the molar mass Mu ofone monomeric unit. The discrete distributionfunctions can normally be replaced by continu-ous ones since so many different degrees ofpolymerization exist and the difference in molarmasses between molecules with Mi and Miþ1 issmall compared to the average molar mass.

The various types of distribution functions areusually named after their discoverers. TheSchulz – Zimm distribution function derivesfrom processes in which reactive chains addother monomer or polymer molecules untilthe chains are deactivated. Such deactivation

Figure 5. Molar mass dependence of intrinsic viscosities offlexible, coillike molecules: polystyrene in the theta solventcyclohexane at 34.5 �C (.) and in the thermodynamicallygood solvent benzene at 25 �C (o)The slopes at high molar masses adopt the theoretical valuesof 0.764 (good solvent) and 0.500 (theta solvent)

Figure 6. Distributions of mole fractions x of degrees of polymerization XLeft: discontinuous (discrete); right: continuous; top: differential; bottom: integral (cumulative)Reprinted with permission by H€uthig and Wepf Publ., Basel [5]


processes may be chain termination reactions(chain polymerization, polyelimination) or thedecrease of reactivity by lowering of temperature(polycondensation, polyaddition). The massfraction of polymer molecules with degree ofpolymerization Xi is given by

wi ¼ ðk=XnÞk�Xki �expð�kXi=XnÞGðkþ1Þ ð7Þ

where k is the degree of coupling of chains (e.g.,k ¼ 2 for recombination of two growing chainsto one dead chain and k ¼ 1 if two growingchains react by disproportionation to two deadchains) and g (k ¼ 1) the gamma function of(k ¼ 1). This function is called Schulz – FloryorFlory distribution for the special case of k ¼ 1(polycondensation, radical chain polymerizationwith termination by disproportionation). Equa-tion (34 reduces for k ¼ 1 and high degrees ofpolymerization to

wi ¼ ð1=XnÞ2�Xi�½1�ð1=XnÞ�xi ð8ÞThe various average degrees of polymerizationare connected via

Xn=k ¼ Xw=ðkþ1Þ ¼ Xz=ðkþ2Þ ð9Þ

Poisson distributions are formed if a constantnumber of chains starts to grow simultaneouslyand if monomer molecules are added to thechains at random and independent of previousadditions. The mass fraction of molecules ofdegree of polymerization Xi is given by

wi ¼ Xi�ðXn�1ÞXi�1�½expð1�XnÞ�ðXi�1Þ!ðXnÞ ð10Þ

and the interrelationship between the variousaverages by

Xw=Xn ¼ 1þð1=XnÞ�ð1=XnÞ2 ð11Þ

The ratio of mass to number average approaches1 at infinitely high molar masses. The Poissondistribution is thus a very narrow distribution, incontrast to the Schulz – Zimm distributionwhere the ratio X�w/X�n equals 2 for k ¼ 1 and3/2 for k ¼ 2.

The Schulz – Zimm distribution is a specialcase of the Kubin distribution, an empirical,generalized exponential distribution (GEX dis-tribution) with three empirical, adjustable para-

meters g , e, and b:

wi ¼ g �bðeþ1Þ=g �Xei �expð�bXg

i ÞG½ðeþ1Þ=g� ð12Þ

This expression converts to the Schulz – Zimmdistribution if g ¼ 1, e ¼ k, and b ¼ k/X�n. TheKubin distribution also includes the Tung distri-bution (e ¼ g – 1) and the logarithmic normaldistribution (g ¼ 0; e ¼ ¥), both of which fre-quently describe molar mass distributions ofpolymers from Ziegler – Natta polymerizations.The Kubin distribution is a very adaptable distri-bution because it contains a ‘‘stretched exponen-tial’’ (i.e., a variable X with an exponent g in theexponential term).

Some of these distribution functions are com-pared in Figure 7. Note that only the logarithmicnormal distribution shows a maximum in thedistribution of mole fractions and that none of

Figure 7. Continuous differential distributions of degrees ofpolymerization X for a) the logarithmic normal distribution(LN); b) the Schulz – Flory distribution (SF); and c) the Tungdistribution (Tung), shown as distributions of mole fractions(top) and corresponding mass fractions (bottom) for a poly-mer with X�n ¼ 10 000 and X�w ¼ 20 000The Poisson distribution is so narrow that it is practicallyidentical with the vertical line for X�n ¼ 10 000.Reprinted with permission by H€uthig and Wepf Publ., Basel[5]


the maxima in the distributions of the massfractions correspond to simple molar massaverages.

2.2.4. Determination of Molar MassDistributions

Molar mass distributions can be determined bypreparative fractionation of polymers from solu-tions since the various species of a polymer-homologous series exhibit small differences insolubility. Fractionation occurs upon change oftemperature or addition of a nonsolvent. Themolar masses of the resulting fractions are deter-mined in separate experiments. Fractionationsare inexpensive but time consuming.

The method of choice for the fast determina-tion of molar mass distribution is size exclusionchromatography (SEC). Dilute polymer solu-tions are placed on the top of a column filledwith a porous carrier. Lowmolar mass moleculescan enter the pores, but high molar mass mole-cules cannot. Medium-sized molecules enterwith difficulty and remain for shorter times thanlowmolar mass molecules. Higher molar massesare thus eluted first, and elution curves are ob-served that give the concentration of eluted mo-lecules as a function of the eluted volumeVe. Themaximum of the elution curve is called theretention volume.

The retention volumes depend on the SECsystem (carrier, solvent, temperature) and thepolymer being investigated. The carrier mayconsist of rigid porous materials (e.g., porousglass beads) or swollen, cross-linked polymers(e.g., cross-linked polystyrenes or dextrans). Inthe latter case, the method is called gel perme-ation chromatography (synthetic polymers) orgel filtration (biopolymers).

Retention volumes are constant below andabove certain molar masses of the polymers(Fig. 8). The volume Vo at lower molar massesgives the total volume available for the flow ofsolvent; the volume Vi at upper molar massesindicates the interstitial volume between carrierparticles. Polymer molecules can thus be sepa-rated only in the rangeVi<Ve<Vo, whereVe is theelution volume.

Elution volumes depend to a first approxima-tion on the logarithms of molar masses (Fig. 8).A function Ve ¼ K � ln M is thus often used to

determine unknown molar masses with the helpof a constant K derived from calibrations withnarrow-distribution polystyrene standards. Thisprocedure does not give absolute molar massesbecause polystyrenes and test polymers with thesame molar masses possess different chromato-graphically effective volumes. A frequently used‘‘universal’’ calibration method thus employs afunction Ve ¼ f (log [h] �M) since [h] measuresthe specific hydrodynamic volume of the solutemolecules and [h] �M has the physical unit of amolar volume.

2.3. Configurations

Polymers with symmetric repeating units, suchas – CH2 – CH2 – (– CH2– CH2–), – CH2 –CF2–, and –NH–CO – (CH2)5 –, do not possessconfigurational isomers. Such isomers do exist,however, for polymer molecules with nonsym-metric repeating units, such as – CH(CH3) –(polymethylmethylene), – CH(CH3) – CH2 –(polypropylene), and – NH – CO – CH(CH3) –(polyalanine). Polypropylene, for example, hastwo configurational repeating units 9 and 10withtwo different monomeric units each:

Figure 8. Molar mass dependence of elution volumes Ve

a) Coil-like linear polystyrenes PS with two different SECcolumns from cross-linked polystyrenes; b) Various spheroi-dal proteins PR with cross-linked dextranVo ¼ Total volume; Vi ¼ Interstitial volume


The configurational units 9a and 9b are en-antiomeric; they belong to the same constitution-al unit – CH(CH3) – CH2 –. The configuration-al units 9a and 10a, on the other hand, are basedon two different constitutional units. Severalconfigurational units may be joined to give stericrepeating units; the three simplest steric repeat-ing units for polypropylene are

The repetition of these units leads to polymerchains that are called isotactic (IT), syndiotactic(ST), and heterotactic (HT). A heterotactic unitht in a polymer chain consists of three monomer-ic units (the first or last three of HT), but therepetition of such ht-triads does not lead to acompletely heterotactic polymer HT because itwould consist of alternating heterotactic andsyndiotactic triads. Whether 9a or 10a is usedas the simplest configurational repeating unit isimmaterial since infinitely long polypropylenechains of 9a differ from those of 10a only by theorientation of these units.

The term tacticity thus refers to the relativearrangements of configurational units in a chain.Relative configurations are classified by startingat one end of the polymer chain and consideringthe configuration around a central atom relativeto the preceding one. This classification is differ-ent from that of the absolute configuration oforganic chemistry where the configuration ofeach central atom is determined relative to theligand with the lowest seniority.

The ligands R of isotactic polymer moleculesare always ‘‘on the same side’’ if these moleculesare shown in Fischer projections or in other stereoformulas with hypothetical cis conformations ofthe chains. In stereo formulas based on transconformations, ligands are only on the same sidefor isotactic molecules consisting of two chainatoms per monomeric unit (Fig. 9), that is�(CHR – CH2)�.

Real polymer chains of the types �CHR�,�CHR – CH2�, �X – CHR – CH2�, etc.,

contain configurational mistakes; they are nei-ther 100% isotactic nor 100% syndiotactic. Thetacticity of such chains is expressed by the frac-tion XJ of their isotactic or syndiotactic diads,triads, etc. A diad consists of two monomericunits, a triad, of three; etc. Each monomeric unitof a polymer chain belongs to two tactic diads,three tactic triads, four tactic tetrads, and so on.Figure 9 thus shows five diads, four triads, threetetrads, . . . , etc., for� CHR �. The sum of themole fractions of all J-ads of given J must equal 1(xi þ xs � 1, xii þ xis þ xsi þ xss � 1, etc.),where i¼isotactic diad, s¼syndiotactic diad,ii¼isotactic triad of two isotactic diads, etc. Themole fraction of isotactic diads is given by themole fraction of isotactic triads plus 1/2 ofthe mole fraction of the sum of the two hetero-tactic triads, that is, xi ¼ xii þ (1/2) (xis þ xsi),etc. The number-average sequence length ofisotactic sequences is thus given by (X�I)n ¼ 2xi/(xis þ xsi).

The presence and/or fraction of tactic J-adscan be investigated by a number of experimentalmethods. 2 D-NMR spectroscopy allows abso-lute determination of the types of J-ads and theiramounts up to pentads, whereas conventionalhigh-resolution NMR spectroscopy requiresprior knowledge of the J-ad type by X-raycrystallography or other methods. Infraredspectroscopy detects only diads, whereas crys-tallinity, solubility, glass and melt tempera-tures, and chemical reactions may or may notindicate the presence of shorter or longer tacticsequences.

Figure 9. Isotactic (it) and syndiotactic (st) polymers withmonomeric units – CHR –, – CHR – CH2 –, and – CHR –CH2–X– in trans conformationsReprinted with permission by H€uthig and Wepf Publ., Basel[5]


Highly isotactic polymers can be produced byZiegler – Natta polymerization of a-olefins(e.g., it-polypropylene or it-polybutylene-1).Special Ziegler – Natta catalysts lead to st-poly-propylene and st-polystyrene; these syndiotacticpolymers have no commercial use thus far.Highly syndiotactic polymers are also generatedby most very low-temperature free-radical poly-merizations of vinyl and acryl monomers. Con-ventional vinyl and acryl polymers are, however,synthesized at ambient temperature or above,and consist, at best, of slightly syndiotactic poly-mers; in general, they are considered atacticpolymers.

Polymers with different geometric isomerismare also tactic. Depending on the configuration ofthe chain segments relative to the double bondsin the chain cis-tactic (ct) and trans-tactic (tt)structures are distinguished. The ct structure of1,4-polyprenes[� (CH2 – CR¼CH – CH2)n�]from the polymerization of 1,3-dienesCH2¼CR – CH¼CH2 via both double bondscorresponds to an E isomer; the tt structure, toa Z isomer. If the polymerization proceeds viaone double bond only, 1,2-polydienes are formedthat may be isotactic, syndiotactic, atactic, etc.

2.4. Conformations

2.4.1. Microconformations

Rotations of atoms or groups of atoms aroundsingle bonds create spatial arrangements calledconformations (organic chemistry) or microcon-formations (macromolecular chemistry). The se-quence of these microconformations determinesthe shape of the macromolecule – the macro-conformation (in statistical mechanics, theconfiguration).

In principle, an infinite number of conforma-tions is possible around each single bond. Inpractice, certain positions are energetically pre-ferred; only these are called (micro)conforma-tions. In two joined tetrahedrons, such as ethane

(H3C – CH3), two extremes of energetically dif-ferent positions are possible: the staggered posi-tion corresponds to a minimum of energy and theeclipsed position to a maximum of energy ifrepulsive forces are prevalent (Fig. 10). On rota-tion by 360� around the C – C axis, three ener-getically equivalent eclipsed and three energeti-cally equivalent staggered positions may beoccupied since the three H atoms bound to thesame C atom (‘‘bonded atoms’’) are equivalent.Small molecules, such as ethane, can be consid-ered as definite species in conformations withenergy minima; they are called conformers, ro-tamers, or rotational isomers.

The number of types of conformers increasesif the three bonded atoms are not equivalent, forexample, in butane (CH3 – CH2 – CH2 – CH3)(one CH3 group and two H atoms bonded to eachcarbon atom participating in the central C – Cbond). In polymer chains, one of the bondedatoms is never equivalent because it is part ofthe chain; in polyethylene (� CH2 – CH2 �),the bonded atoms are two H atoms and the chain.There are two energetically different eclipsedpositions (cis and anti) and two energeticallydifferent staggered ones (trans and gauche).Each gauche and each anti position can occurin two spatially different positions that are ener-getically equivalent (plus andminus) if two of the

Figure 10. Microconformations of ethaneA) Eclipsed position (cis or synperiplanar); B) Staggeredposition (trans or antiperiplanar)Reprinted with permission by H€uthig and Wepf Publ., Basel[5]


three bonded atoms are equivalent. These(micro)conformers have different names in mac-romolecular and in organic chemistry (Fig. 11).

All eclipsed positions are sterically hinderedin polymer chains and therefore only trans andgauche positions must be considered. The con-formational energy is the energy difference be-tween the energies of the trans and gaucheconformations. An activation energy (potentialenergy) is necessary to overcome the rotationalbarrier between trans and gauche conformations.This rotational barrier increases with decreasinglength of the central bond and with increasingnumber and increasing size of bonded atoms. Itsvalue is, for example, 12.1 kJ/(mol bond) for theC – C bonds in polyethylene chains �(CH2 –CH2)n� but only 2.1 kJ/mol for the CH2 – CObonds in polyester chains with units �CH2 –CO – O – CH2�. Since these bond energies caneasily be overcome by thermal energy, (hin-dered) rotations are possible around the chainbonds and the molecules may adopt many chainconformations (Section 2.4.3). Isolated aliphaticpolyester chains �OOC(CH2)x� (with x>3) arethus more flexible than carbon chains; suchpolymers are used as polymeric plasticizers.

Two different types of flexibility are distin-guished. A chain molecule is said to be staticallyflexible if it possesses many accessible confor-mational minima. Dynamic flexibilities are char-acterized by low barriers between conformation-al minima.

2.4.2. Conformations in Ideal PolymerCrystals

A regular sequence of microconformations leadsto regular macroconformations of polymer

chains. The chains are linearly extended; theend-to-end distance is commonly called the con-tour length rcont of the chain (this term originallyreferred to the contour of the chain along theindividual chain bonds). Chains in all-trans mi-croconformations are said to be fully extended,for example, the chain in Figure 3-1.

Polyethylene crystallizes ideally in an all-trans conformation because the shortest distancebetween nonbonded hydrogen atoms (0.254 nm)is greater than the sum of the van der Waals radiiof H atoms (0.24 nm). The size of substituentsR in isotactic poly(a-olefins) (�(CH2 – CHR)n�), however, forces the microconformationaround each second chain bond to adopt agauche position (see Fig. 11). All gauche con-formations must be alike for steric reasons; con-formational diads GþG� and G�Gþ are for-bidden (Fig. 11). The chain thus adopts eithera . . . TGþTGþTGþ . . . or a TG�TG�TG� . . .macroconformation; that is, it becomes helical.The number of monomeric units per completeturn is determined mainly by the size ofthe immediate substituents. it-Polypropylene� (CH2 – CH(CH3))n � has three propyleneunits per one turn (31 helix, Fig. 12 A), it-poly(4-methylpentene-1) (P4MP) � (CH2 –CH(CH2CH(CH3)2))n � has seven units pertwo turns (72 helix ¼ 3.5 helix, Fig. 12 B), andpoly(3-methylbutene-1) (P3MB) has four unitsper one turn (41 helix, Fig. 12 C). The confor-mational angles are not necessarily the idealones of 0� for trans and 120� for gauche asfound for it-polypropylene; they are rather�13�/110� for P4MP and �24�/96� for P3MB.Conformational positions with deviations upto 30� from the ideal conformational anglesare still named after the ideal microconfor-mations.

Figure 11. Chain conformations and their names and symbols in macromolecular (M) and organic (O) chemistry. Chain atoms;* substituents; T ¼ trans, A ¼ anti; G ¼ gauche; C ¼ cis; ap ¼ antiperiplanar; ac ¼ anticlinal; sc¼syncl-inal; sp ¼ synperiplanar


The R substituents of syndiotactic vinyl poly-mers [�(CH2 – CHR)n�] are farther apart thanthose of their isotactic counterparts (see Fig. 9).In general, trans conformations thus have thelowest energy in those st-polymers where onlyrepulsive forces operate. Attractive forces, suchas intramolecular hydrogen bonds betweenneighboring OH groups in poly(vinyl alcohol)(�[CH2 – CH(OH)]n�, PVAL), lead to differentconformational sequences: isotactic PVAL ex-ists in all-trans conformations, whereas syndio-tactic PVAL forms helices.

Chain atoms with free electron pairs lead togauche effects. The chains of crystallized poly-oxymethylene [�(O – CH2)n�] exist in all-gauche conformation (95 helix). Polyoxyethylene[�(O – CH2 – CH2)n�] and polyglycine[�(NH – CO – CH2)n�], on the other hand, pos-sess the conformational sequence TTG. The re-sulting 72 helices of polyglycine are stabilized byintramolecular hydrogen bonds between the first,fourth, seventh, etc., peptide bonds of a chain.

Polypeptides [�(NH – CO – CHR)n�] arebased on chiral monomeric units. An L-polymermay thus form two different helices: a right-handed and a left-handed one. These helices arediastereomers with different energy contents. Ingeneral, one ‘‘handedness’’ is preferred over theother in polymers with chiral base units. Poly

(L-a-amino acids) generally form right-handedhelices, whereas poly([S]-a-olefins) and mostpolysaccharides from D-sugars exist as left-hand-ed ones.

2.4.3. Conformations inPolymer Solutions

Helices can survive melting and dissolution pro-cesses only if the helical structure is stabilized byintramolecular attractive forces. Examples arethe hydrogen bonds in helices of poly a-aminoacids or hydrogen bonds plus base stacking indouble helices of deoxyribonucleic acids. Theseforces may be so strong that the moleculesdecompose rather than melt on heating. A deli-cate balance between intramolecular bondingand solvation of substituents is necessary topreserve helical structures in solution; examplesare poly(a-amino acids) in helicogenic solvents.

Helices that are generated in crystals by pack-ing of chains whose microconformations origi-nate from repulsive forces do not survive themelting process intact. Each macromolecule canform many macroconformers that equilibraterapidly. Only very short helical sequences invery low concentrations may thus exist in melts.

Two extreme cases must be considered for thedissolution of polymers. Only weak interactions(or none at all) exist between monomeric units ofapolar polymers and apolar solvent molecules.Conformational changes are thus entropy driven;the sequence of microconformations is irregular,and the polymer molecule adopts the macrocon-formation of a coil.

In apolar enantiomeric polymers in apolarsolvents, long conformational sequences are con-served, although fast conformational transforma-tions from left- to right-handed helices and viceversa may occur in enantiomeric polymers. Onaverage, few microconformations are convertedinto other ones. These helical sequences may bestabilized by association processes.

Polar solvents, on the other hand, interactstrongly with polar polymers; these solventscause strong changes in microconformations.Since the ligands around each chain bond canadopt various microconformations and these mi-croconformations can change rapidly, a givenmacromoleculemay exist in time inmanymacro-conformations, similar to those of simple apolarpolymers in apolar solvents:

Figure 12. Helix types of poly(a-olefins) � CH2–CHR�A) 31 Helix; B) 72 Helix; C), D) Different types of 41 helicesReprinted with permission by Societa Italiana di Fisica,Bologna, from [71]


A polymethylene [�(CH2)n�] with degree ofpolymerization n ¼ 20 001 possesses 20 000chain bonds, each of which can adopt threemicroconformations: trans, gauche (plus), andgauche (minus). According to statistics, suchchain can exist in 3n ¼ 320 000�109542 differentmacroconformations. Conversely, a collection ofchainsmayhavemanymacroconformationsatanygiven time. None of these macroconformationsadopts a simple geometric shape, not even instan-taneously. Rather, the chains form rapidly chang-ing coil structures that can be made visible byelectron microscopy as two-dimensional projec-tionsof the three-dimensionalcoil shapeforchainsof sufficiently long chain diameter (Fig. 13).

2.4.4. Unperturbed Coils

The instantaneous shapes of coils cannot bedetermined by presently known methods. Theirradius of gyration can be measured, however, bylight scattering, small-angle X-ray scattering,and small-angle neutron scattering. The end-to-end distances of coiled linear chains can bemodeled for various types of chains and calcu-lated for individual chains via the rotationalisomeric state method.

The simplest model is that of a freely jointedchain (no fixed bond angles) that assumes infi-nitely thin segments without interactions. Themean square end-to-end distance, hr2ooi, of such acoil is given by the number N of its unspecifiedsegments with segment lengths b:

hr2ooi ¼ N�b2 ð13Þ

Real chains posses fixed bond angles t betweenchain atoms and finite torsion (or dihedral) an-gles q (q ¼ 0� for trans conformations). Themean square end-to-end distance for such a chainin the unperturbed state (zero net polymer –polymer and polymer – solvent interactions) isgiven by

hr2oi ¼ N�b2� 1�cost1þcost

� �� 1þcosq1�cosq

� �ð14Þ

hr2oi ¼ N�b2� 1�cost1þcost

� ��s2 ð15Þ

The factors is called the hindrance parameter orsteric factor. Often the hindrance parameter andthe bond angle are combined to give the charac-teristic ratio CN:

CN ¼ hr2oi=ðN2�b2Þ¼ ð1�costÞ�ð1þcostÞ�1�s2 ð16Þ

The characteristic ratio becomes approximatelyconstant for chains with more than 100 atoms. Achain can also be characterized by its Kuhnlength LK, which can be calculated from itsunperturbed mean square end-to-end distance,its degree of polymerization, and the effectivelength beff of monomeric units (i.e., length ofunits in chain direction projected on a plane;rcont ¼ X � beff ¼ NK � LK)hr2oi ¼ NK�L2K ð17Þ

End-to-end distances can rarely be measureddirectly. They are however related to the experi-mentally accessible radii of gyration s via

hs2oi ¼ hr2oi=6 ð18Þ

This relationship applies to all chains with ran-dom flight statistics (e.g., unperturbed chains andfreely jointed chains). It is not valid for perturbedchains (Section 2.4.5).

Coil densities are very low (cf. Fig. 13). Thevolume fraction of monomeric units is, for ex-ample, only 0.012 at the center of gyration for apolyethylene chain with a molar mass of1.19�106 g/mol; 99.8% of the space of thesepolyethylene coils is occupied by solvent mole-

Figure 13. Electron micrograph of the double helix mole-cules of deoxyribonucleic acid chains showing two-dimen-sional random coilsReprinted with permission by Academic Press, London, from[72]


cules (in very dilute solutions) or by units of otherpolymer chains (in melts).

A chain in a melt cannot distinguish betweenits own segments and segments of other chains.Because the interactions between the segments ofvarious chains are also the same, such chainsadopt their unperturbed dimensions, which hasbeen confirmed by small-angle neutron scatter-ing. Most of the coil volume is filled by segmentsof other chains to avoid empty space. Chains ofsufficient length may thus become entangled,which manifests itself in properties such as dif-fusion and melt viscosity.

2.4.5. Perturbed Coils

Coils adopt their unperturbed dimensions inmelts or in certain solvents at certain tempera-tures (so- called theta solvents). In such thetasolvents, polymer – solvent and polymer –polymer interactions cancel each other and thechain behaves as if it is infinitely thin. In thermo-dynamically good solvents, polymer – solventinteractions dominate and the coil is swollen.The volume requirements of such coils must thuslead to interpenetrations by other coils even atvery low concentrations. Because segments arenot infinitely thin, however, a part of the totalspace is excluded for segments of other chains(and also for other segments of the same chain).

2.4.6. Wormlike Chains

Real polymer chains are not totally flexible.Their finite thickness and the partially hinderedrotation around chain bonds prevent them fromadopting all possible positions in space. Suchchains can be described by the model of thewormlike chain (Kratky – Porod model).

The characteristic parameter of this model isthe persistence length a. This parameter is de-fined as the average of the projection of the end-to-end-distance of an infinitely long and infinite-ly thin chain in the direction of the first segment.It can be calculated from the radius of gyrationand the conventional contour length via

hs2oi ¼ a2fðy=3Þ�1þð2�yÞ�ð2=y2Þ½1�expð�yÞ�g ð19Þwhere y ¼ rcont/a. For flexible chains, it is relatedto the unperturbed radius of gyration via

hr2oi=6 ¼ hs2oi ¼ a�rcont=3 ¼ a�NK�LK=3 ð20ÞFor infinitely stiff chains,

hs2oi ¼ a2�y2=12 ¼ ðrcontÞ2=12 ð21Þthat is an infinitely stiff chain behaves like aninfinitely thin rod. Wormlike chains thus de-scribe the whole transition from rodlike mole-cules (small y) to random coils (large y). Themodel is strictly valid for infinitely thin chains,but the error produced by this assumption isnegligible if the persistence length is much great-er than the chain diameter.

3. Polymer Manufacture

3.1. Raw Materials

The raw materials for most industrially usedplastics are synthetic polymers and prepolymers;only a few are derived from naturally occurringpolymers or monomers. The overwhelmingmajority of polymers for plastics are organicmaterials; very few are semiorganics (i.e., inor-ganic polymer chains with organic substituents).Raw materials for polymers include wood, coal,petroleum, natural gas, and certain natural oils.

3.1.1. Wood

Wood (! Wood) is a naturally occurring com-posite of oriented cellulose fibers in a continuousmatrix of cross-linked lignin; it is plasticized bywater and ‘‘foamed’’ by air (vacuoles). The watercontent varies from 40 – 60% for green wood to10 – 20% for air-dried wood. Solids include cel-lulose (42%); hemicelluloses (28 – 38%); lignin(19 – 28%); and proteins, resins, andwaxes (2 –3%), depending on the type and age of the plant.Most of the wood is used directly as fuel or forconstruction purposes, but one-sixth is convertedinto wood pulp or cellulose pulp for the manufac-ture of paper, cardboard, or rayon. A very smallamount of wood is filled with monomers that aresubsequently polymerized to give polymer wood.


Cellulose pulp is chemically transformed intocellulose derivatives (! Cellulose;! CelluloseEsters; ! Cellulose Ethers):

1. 2,5-Acetate with 2,5 acetate groups,R¼OOC–CH3, per glucose residue (fibers,cigarette filters)

2. Cellulose triacetate with three acetate groupsper glucose residue (fibers)

3. Cellulose acetobutyrate with R ¼ 29 – 6 mol%acetyl and 17 – 48 mol%butyryl groups (athermoplastic for tubes, packaging)

4. Cellulose nitrate (R ¼ NO2; various degreesof substitution; gun cotton, films, lacquers,celluloid)

5. Cellulose ethers with R ¼ CH3, C2H5,CH2CH2OR

1, or CH2 – CHOR2– CH3, whereR1 may be CH2CH2OR

1 or CH2CH2OH andR2 ¼ CH2–CHOR

2–CH3 or CH2 – CHOH–CH3 (thickeners, binders, suspension agents,injection molding materials, etc.)

Huge amounts of lignin sulfonates (! Lig-nin, Chap. 5.) are generated during wood pulpproduction, most of which are burned. Smallamounts are used for street pavement, as bindersfor foundry sand, or as drilling agents, and evensmaller amounts as raw materials for organicintermediates (! Lignin, Chap. 7.). Degradationproducts of lignin have been utilized for thesynthesis of ion-exchange resins and otherpolymers.

3.1.2. Coal

Coals (! Coal) are polymerized and partlycross-linked hydrocarbons with average compo-sitions between C75H140O56N2S (peat) andC240H90O4NS (anthracite). They were the prima-ry raw materials for acetylene-based monomersduring the first half of this century but have sincebeen replaced inmost countries by oil and naturalgas as monomer sources.

Coals deliver coke and coal tar. A number ofaliphatic monomers are produced from coke viaacetylene, such as chloroprene, various vinylmonomers, acrylonitrile, and hexamethylenedia-mine. Coal tar delivers aromatics such as ben-zene, xylene, phenol, and phthalic anhydride,which lead subsequently to polystyrene, phenolicresins, and glyptal resins, to name a few.

3.1.3. Natural Gas

Natural gas (! Natural Gas) is a gas with a highproportion of aliphatic hydrocarbons. Europeangas is rich in methane, whereas American andSaudi Arabian gases are relatively rich in higherhydrocarbons. Natural gas is processed to syn-thesis gas, ethylene, and acetylene. These gasesare used to produce a variety of monomers forpolymers.

3.1.4. Petroleum

Petroleum (crude oil) (! Oil Refining) is themain feedstock for monomers. It consists of95 – 98% hydrocarbons and 2 – 5% oxygen,nitrogen, and sulfur compounds. The hydrocar-bons are largely aliphatic, partly naphthenic, andto a small extent aromatic, depending on thesource. Petroleum distillation leads to saturatedhydrocarbons (gas, naphtha, gasoline, kerosene,diesel fuel, heating oil, etc.). For monomer pro-duction, these hydrocarbons are subsequentlycracked to mixtures of olefins that are fraction-ated by distillation. The resulting compounds areused as such or are converted further into thedesired monomers.

The polymer industry is a major petrochemi-cal customer: about 60% of the cracking andsubsequent products of naphtha are used to pro-duce polymers (ca. 50% for plastics – elasto-mers, ca. 10% for fibers). However, the finalyields of polymers and converted plastics, re-spectively, are fairly small: 1000 kg of petro-leum delivers only 30 kg of polyethylene andsubsequently 16 kg of polyethylene film, in ad-dition to 360 kg of useful byproducts [liquid gas,gasoline, propylene, etc.].

3.1.5. Other Natural Raw Materials

Vegetable oils are a relatively large source of rawmaterials. They consist of mixtures of fatty acidtriglycerides and are usually subdivided intodrying oils with high linolenic and linoleic acidcontent, semidrying oils with high linoleic andoleic acid content, and nondrying oils with higholeic acid content (! Fats and Fatty Oils). Someoils are used directly for paints; others are chemi-cally converted into monomers.


Castor Oil is converted into methyl ricinole-ate, which is thermally cracked into methyl un-decenate and heptanal. Methyl undecenate is theraw material for 11-aminoundecanoic acid,which is subsequently polycondensed to formpolyamide 11. Alkali scission of castor oil orricinoleic acid produces sebacic acid, amonomerused to prepare polyamide (PA) 610.

Soybean Oil is converted by a series ofchemical reactions into the methyl ester of theC10 amino acid H2N(CH2)9COOCH3, which isthe monomer for PA 10. The plant Crambeabyssinica contains about 55% of erucic acid,which leads to the C13 amino acid and subse-quently to PA 13 (�[NH(CH2)12CO]n�).

Corn husks and other agricultural waste arerich in pentosans, which can be converted intotetrahydrofuran and further into polytetrahydro-furan [HO(CH2CH2CH2CH2O)nH], which servesas a soft block in certain polyurethanes.

The supply of raw materials from vegetablesources is relatively small. It is also fairlyuncertain because quality and quantity maydepend on weather conditions or be influencedby political turmoil. Most monomers for thepolymer industry are thus obtained from fossilfeedstocks.

3.2. Polymer Syntheses: Overview

3.2.1. Classifications

Polymersmay be synthesized frommonomers bypolymerization or from other polymers by chem-ical transformations. The nomenclature and clas-sification of these reactions have grown andchanged with the times; they are not very sys-tematic and are sometimes confusing.

All reactions of small molecules to macro-molecules are called polymerizations. Polymer-izations are classified according to the

1. Origin of polymers (biopolymerizations,synthetic polymerizations)

2. Chemical structure of monomers (vinylpolymerizations, diene polymerizations,ring-opening polymerizations, etc.)

3. Chemical structure of resulting polymers(linear, branching, cross-linking, isomeriz-ing, ring-forming, etc., polymerizations)

4. Relative composition of monomers andmonomer units (addition polymerization,condensation polymerization, etc.)

5. Formation of low molar mass byproducts(polycondensation vs. polyaddition, etc.)

6. Type of polymerization initiation (thermal,catalytic, photochemical, enzymatic, etc.)

7. Type of propagating species (free radical,anionic, cationic, etc.)

8. Type of mechanism (equilibrium, addition,insertion, living, stepwise, etc.)

9. Reaction media (bulk, solution, emulsion,suspension, crystal, mesophase, etc.)

10. State of matter (gaseous, homogeneous, het-erogeneous, etc.)

The most common classification is accord-ing to (4) the relative chemical composition ofmonomer vs. monomeric unit and (5) the typeof molecules that may react with the growingpolymer chain. The resulting four typesof polymerization can be depicted schemati-cally as

where M denotes monomer; Pn, Pm, Pnþm, Pnþ,denote polymers and L leaving molecules (e.g.,water in polyesterifications of diacids anddiols).

The names of three of these four types havebeen used with different meanings by differentresearchers over the past 70 years. The followingdiscussion thus centers around the present no-menclature recommendations by IUPAC.

Chain Polymerization. Polymer chains growby repeated addition ofmonomermoleculesM topolymer molecules Pi, consisting of imonomericunits m, an initiator end group R, and an ‘‘activecenter *,’’ without the formation of leaving mo-lecules:

RðmnÞm þM!Rðmnþ1Þm ð23Þ

An example is the polymerization of vinylmonomers (CH2¼CHR) by chain carriers Y*,which may be free radicals Y�, anions Y�, orcations Yþ :


Y��CH2 ��CHR þCH2 ¼ CHR!Y��CH2 ��CHR��CH2 ��CHR ð24Þ

A living polymerization is a chain polymeri-zation consisting only of fast initiating reactions(Y*þCH2¼CHR ! Y – CH2 – CHR*) andpropagation reactions [Y –(CH2 – CHR)n* þCH2¼CHR ! Y –(CH2 – CHR)n þ 1*] with-out termination of the growing chains and with-out side reactions. In such reactions, the degree ofpolymerization is directly proportional to theconversion u of monomer molecules or p offunctional groups, respectively (Fig. 14, curveCP – L). An example is the polymerization ofstyrene CH2¼CH(C6H5) by the butyl anionC4H

�9 from lithiumbutyl (butyllithium) LiC4H9.

The variation of the degree of polymerizationwith monomer conversion is quite different forradical polymerizations such as the polymeriza-tion of styrene by benzoyloxy radicalsC6H5COO

� from the thermal decomposition ofdibenzoyl peroxide, C6H5COO –OOCC6H5.Radicals are here formed successively and not‘‘at once’’ as are the butyl anions in living poly-merizations. Growing chains are terminated byreaction with other radicals. Many side reactionsmay occur because of the high and fairly indis-criminate reactivity of radicals. Depending onreaction conditions, the degree of polymerization

may remain constant (primarily at low conver-sions) or increase withmonomer conversion (so-called gel effect) (Fig. 14, curve CP – FR).

Chain polymerizations have generally beencalled addition polymerizations in the literature.Addition polymerization is not to be confusedwith polyaddition (see below).

Condensative Chain Polymerization. This isthe name recommended by IUPAC for a poly-merization by repeated addition of monomermolecules with elimination of low molar massmolecules L; this polymerization has thus alsobeen called polyelimination [5]:

RðmnÞm þM!Rðmnþ1Þm þL ð25Þ

Biological polymerizations to polysacchar-ides seem to proceed exclusively through poly-eliminations. Cellulose of cotton, for example, isformed by polymerization of guanosine diphos-phate D-glucose attached to a lipid matrix. Thereaction proceeds via insertion of the glucosemoiety into the chain with elimination of guano-sine diphosphate.

Synthetic polymers are rarely formed by poly-elimination. Examples are the polymerizations ofa-amino acid N- carboxyanhydrides (Leuchs an-hydrides) and the ‘‘oxidative polymerization’’ of2,6-dimethylphenol to polyphenylene oxide(PPO, PPE):

Polycondensations. In polycondensation,polymer growth proceeds by reaction betweenmolecules of all degrees of polymerization (notjust between a polymer molecule and amonomermolecule as in chain polymerization and poly-elimination), with the formation of moleculeshaving low molar mass. Many polymers withhetero atoms in the chains are generated bypolycondensation. An example is the polycon-densation of 11-aminoundecanoic acid to poly-amide 11:

nH2NðCH2Þ10COOH!H½NHðCH2Þ10CO�nOHþðn�1ÞH2O

ð27Þ

Figure 14. Change of number-average degree of polymeri-zation X�n with the extent of reaction of functional monomergroups p for living chain polymerizations CP-L and livingpolyeliminations PE-L (with initial monomer – initiator ratio100 : 1 mol/mol), free-radical chain polymerizations CP-FRwith gel effect (schematic for high initiator concentrations),and equilibrium polycondensations PC and polyadditions PA(numerically exact)


In these reactions, dimers (n ¼ 2) are formedfirst, which may then react with monomers toform trimers (n ¼ 3) orwith other dimers to formtetramers (n ¼ 4), etc. The reaction is thus sta-tistical with respect to the size of themolecules towhich the functional groups are attached. Thedegree of polymerization of the polymer is anumber average X�n over all degrees of polymer-izations of the polymer molecules.

All amino groups have the same chance toreact if their reactivity is independent of mole-cule size. The reaction of amino groups attachedto molecules with higher molar mass adds, how-ever, considerably more to the increase of thedegree of polymerization than the reaction oflower molar mass molecules: the degree of po-lymerization snowballs with increasing extent ofreaction of functional groups (Fig. 14, curve PC).

The term polycondensation was used in thepast as a synonym for condensation polymeriza-tion. The latter term included both the currentconcepts of polycondensation and polyelimina-tion (condensative chain polymerization).

Polyaddition. This is a polymerization byreaction among molecules of all degrees of po-lymerization butwithout the formation of leavingmolecules. The number-average degree of poly-merization of the resulting polymers varies withthe extent of reaction of functional groups in thesame way as it does in polycondensation. Anexample of polyaddition is the polymerization ofa diisocyanate with a diol to form a polyurethane:

nOCN��R��NCOþnHO��R0 ��OH!

OCNðR��NH��CO��O��R0OÞnH

ð28Þ

These polymerizations have also been called‘‘polyadduct formations.’’ Polyaddition is not tobe confused with addition polymerization, theterm used in the literature for chain polymeriza-tion and occasionally also for polyaddition.

3.2.2. Functionality

Polymerizable monomers must be at least bifunc-tional under reaction conditions so that they canconnect to the growing chains on one hand andgenerate new coupling sites on the other. Ethyleneand other monomers with ethylenic double bondsare such bifunctional monomers under all poly-

merization conditions (e.g., see Eq. 24). Divinylcompounds, such as the divinylbenzenesCH2¼CH – C6H4 – CH¼CH2,arethustetrafunc-tional compounds in free-radical polymerizations,leading first to branched and later to cross-linkedpolymers. The second vinyl group of a divinyl-benzene possesses, however, a different reactivityafter polymerization of the first one. The tworeactivities may differ so strongly in certain ionicpolymerizations of divinylbenzenes that linearpolymers, and not cross-linked ones, result (e.g.,in the cationic polymerization of 1,4-divinylben-zene by acetyl perchlorate in dichloromethane).

The isocyanate group – N¼C¼O is a mono-functional group under the conditions of poly-addition reactions (Eq. 28). It may, however,undergo a chain polymerization to polyisocya-nates via the N¼C double bond

nR��N ¼ C ¼ O! � ðNR��COÞn � ð29Þand it thus reacts as a bifunctional group underthese conditions. It may even behave as a half-functional group because urethane groupsformed according to Equation (28) may reactfurther to allophanate groups by the addition ofisocyanate groups

The functionality f of polymer molecules isgiven by the functionality fo of the monomermolecules and the number X of mers if nointramolecular rings are formed between func-tional groups.

f ¼ 2ðfo�1ÞþðX�2Þðfo�2Þ¼ 2þXðfo�2Þ ð31Þ

A monomer with functionality fo ¼ 3 thus givesa dimer (X ¼ 2) with a functionality f ¼ 4 and a100-mer (X ¼ 100) with a functionality f ¼ 102.Since the molecule needs to be bifunctional onlyfor the formation of linearmolecules, the ‘‘extra’’functionalities lead to interconnections betweenvarious molecules (branching) and thus finally tocross-linked, ‘‘infinitely large’’ molecules.

3.2.3. Cyclopolymerizations

Polymerizations of multifunctional moleculesmay proceednot only intermolecularly to produce


branched and cross-linked molecules but alsointra/intermolecularly with the formation of ringsin chains. These polymerizations are called cy-clopolymerizations. They occur especially withmonomers having carbon – carbon double bondsin the 1,5- or 1,6-position. An example is acrylicanhydride (11), CH2¼CH –CO – O – OC –CH¼CH2, which polymerizes free-radically evenat high monomer concentrations to soluble poly-mers with 90 – 100% six-membered (12) andfive-membered (13) ring structures, and only0 – 10% ‘‘linear’’ monomeric units 14 (R sym-bolizes a polymer chain and * an active chainend):

3.3. Chain Polymerizations andPolyeliminations

Chain polymerization and polyelimination (con-densative chain polymerization) agree in theirpolymerization kinetics, molar mass distribu-tions, etc., if similar polymerization mechanismsare compared. They differ in the formation of lowmolar mass byproducts and thus in the design ofindustrial polymerization reactors.

3.3.1. Thermodynamics

Polymerizations occur only if their molar stan-dard Gibbs energies DGo

p are negative. Since theGibbs energy

DGop ¼ DHo

p�T�DSop ¼ �RT�ln K ð32Þ

is determined by both the polymerization enthal-pyDHo

p and the polymerization entropy DSop, fourdifferent cases are possible:

Case 1. Both enthalpy and entropy are neg-ative; the entropy term �T �DSop becomes morepositivewith increasing temperature. At a certain

temperature, the enthalpy and entropy termsbalance each other; no polymerization to highmolar mass molecules is possible above thisceiling temperature. Oligomers may be formedat the ceiling temperature, however, since poly-merization equilibria consist of a series of con-secutive equilibria between monomer and grow-ing chains of different degrees of polymerization.

Case 1 is themost common case. It is found formonomers with polymerizable double and triplebonds, such as C¼C, C¼O, C¼S, or C¼N. Thepolymerization entropies of such monomers arepractically determined only by the loss of trans-lational entropy; they are thus almost indepen-dent of the chemical structure of the monomers.The polymerization enthalpy of a-olefinsCH2¼CHR is influenced little by resonance sta-bilization and is practically independent of thesize of the substituent R. Steric hindrance, how-ever, strongly decreases the polymerization en-thalpy of 1,1-disubstituted compoundsCH2¼CRR0. Styrene and a-methylstyrene, havepractically the same polymerization entropies(� 105 J K�1 mol�1) but very different poly-merization enthalpies (� 71 vs.�35 kJ/mol, re-spectively) for the polymerization of liquidmonomers to condensed polymers. The ceilingtemperatures in bulk are 303 �C (styrene) and60 �C (a-methylstyrene), (i.e., the latter cannotbe homopolymerized to high molar mass com-pounds above 60 �C).

s-Bonds are opened and formed again in ring-opening polymerization of cyclic monomers.Differences of bond energies in monomers andpolymers are thus practically zero, and the poly-merization enthalpy is determined by delocali-zation and strain energies. Polymerizationenthalpies are very negative for ring-openingpolymerization of three-membered rings, in-crease to about zero for five- or six-memberedrings, drop again to negative values, and returnalmost to zero for very large rings. The polymer-ization entropies of very small rings are verynegative due to the release of rotational entropyupon polymerization. They become less negativewith increasing ring size.

Case 2. The polymerization enthalpy is neg-ative (or zero) and the polymerization entropypositive. Polymerization is possible at all tem-peratures in this rare case, the polymerization ofcyclooctamethyltetrasiloxane being an example.


Case 3. The polymerization enthalpy is pos-itive (or zero) and the polymerization entropy isnegative. No polymerization is possible at anytemperature. This case seems to apply to thepolymerization of acetone.

Case 4. Both polymerization enthalpy andpolymerization entropy are positive. A floortemperature exists below which no polymeriza-tion is possible. This rare case is fulfilled for thepolymerization of tightly packed cyclic mono-mers such as cyclooctasulfur or oxacycloheptane(oxepane) since the number of rotatory degreesof freedom increases strongly upon polymeriza-tion to open chains.

Polymerization enthalpies and entropies areinfluenced by the state of monomers and poly-mers (gaseous, liquid, crystalline, etc.); the phys-ical interaction between reactants themselves orreactants and solvents; and pressure. Especiallyimportant for industrial polymerizations is thefact that most (but not all, see above) chainpolymerizations are exothermic. The heatof polymerization can be considerable: adiabaticpolymerization of gaseous ethylene to crystallinepolyethylene would result in a temperature in-crease of 1800 K for complete monomer conver-sion. Polymerization reactors must be designedin such a way that the heat of polymerization canbe removed rapidly because, otherwise, inhomo-

geneous charges may result or the reactor mayeven explode.

3.3.2. Free-Radical Polymerizations

Free-radical polymerizations are initiated andpropagated by free radicals. Such polymeriza-tions are relatively insensitive to impurities in thereaction mixture and fairly easy to control. Theyare thus the methods of choice for the industrialproduction of plastics if the monomers can besubjected to free-radical polymerizations. This istrue for ethylene and many ethylene derivatives:most commodity plastics are thus obtained fromfree-radical polymerizations (Table 10).

Other industrial polymers formed by free-radical homopolymerizations include poly(vinylacetate) (for coatings and adhesives), poly(acrylester) (for adhesives), polyacrylamide (for thick-eners), polyacrylonitrile (for fibers), polychlor-oprene (for elastomers), poly(acryl acid) (forthickeners), and poly(N-vinylpyrrolidone) (forvarious applications).

Polymerizations may be carried out in the gasphase, bulk, suspension, emulsion, solution, orunder precipitation. Most monomers are bifunc-tional; they lead to linear or slightly branchedpolymers and thus to thermoplastics. The onlythermosets obtained from free-radical homopo-

Table 10. Plastics by free-radical chain polymerizations*

Monomers Polymerization in Monomeric units

Gas phase Bulk Suspension Emulsion Solution Precipitation

Living polymerization

p-Xylylene þ – CH2 – (p-C6H4) – CH2 –

Irreversible polymerization to

linear or slightly branched polymers

Ethylene þ þ (þ) (þ) (þ) – CH2 – CH2 –

Styrene þ þ (þ) (þ) – CH2 – CH(C6H5) –

p-Methylstyrene þ þ – CH2 – CH( p-CH3C6H4) –

Vinyl acetate (þ) (þ) þ (þ) – CH2 – CH(OOCCH3) –

Vinyl chloride þ (þ) (þ) þ (þ) – CH2 – CHCl –

Vinyl fluoride þ – CH2 – CHF –

Vinylidene fluoride þ þ – CH2 – CF2 –

Trifluorochloroethylene þ – CF2 – CFCl–

Tetrafluoroethylene þ – CF2 – CF2 –

Methyl methacrylate þ þ þ þ – CH2 – C(CH3) (COOCH3) –

Cross-linking polymerization

Diallyl phthalate þ see Equation (32)

*þ ¼ major processes; (þ) ¼ minor processes. Other industrial polymers by free radical homopolymerizations include poly(vinyl acetate)

(for coatings and adhesives), poly(acryl ester) (for adhesives), polyacrylamide (for thickeners), polyacrylonitrile (for fibers),

polychloroprene (for elastomers), poly(acrylic acid) (for thickeners), and poly(N-vinyl pyrrolidone) (for various applications).


lymerizations are diallyl and triallyl compoundsthat cross-link under polymerization conditions:

where R may be COO(CH2)2O(CH2)2OOC[diethylene glycol bis(allyl carbonate], o-C6H4(COO)2 (diallyl phthalate), or m-C6H4(COO)2 (diallyl isophthalate). Other allylcompounds are used as cross-linking comono-mers (diallyl fumarate, diallyl maleate, triallylcyanurate).

Most free-radical polymerizations follow thekinetics of true chain reactions. In initiating (start)reactions (Eq. 35), radicals R. formed from thedecomposition (Eq. 34) of initiator molecules Ireact with monomer molecules M. The resulting‘‘monomerradicals’’R – M. addfurthermonomermolecules in the propagation reaction (Eq. 36)until the growing polymer radicals R��M. areterminated by recombination (Eq. 37) or dispro-portionation (Eq. 38) with other polymer radicalsor by addition of initiator radicals (Eq. 39):

I!2 R. ð34Þ

R.þM!R��M

. ð35Þ

R��M.þM!R��M��M

.; etc:!R��Mn�1 ��M

.

ð36ÞR��Mn�1 ��M

.þ.M��Mm�1 ��R!R��Mnþm ��R

ð37Þ

R��Mn�1 ��M.þ.

M��Mm�1 ��R!R��Mn�2 ��M ¼ MþX��Mm ��R

ð38Þ

R��Mn�1 ��M.þR

.!R��Mn ��R ð39Þ

In Equation (38), X is an atom or a group thatis transferred from the ultimate monomeric unitof one polymer radical to another polymer radi-cal, for example, the H atom in the reaction

� CH2 ��C.HRþ.

CHR��CH2 � ! � CH2 ��CH2R

þCHR ¼ CH2 �

These reactions are kinetically classified astermination reactions and not as transfers be-

cause they lead to dead chains. The term ‘‘trans-fer’’ is rather reserved for chemical transfers thatgenerate new propagating radicals, such as

� CH2 ��C.HRþAX! � CH2 ��CHRXþA

. ð40Þ

Initiation. Free-radical polymerizationscan be initiated thermally by thermal initiators,by redox initiators, by photoinitiators, orelectrolytically.

Thermal Initiation is utilized in the polymer-ization of p- cyclophane to poly(p-xylylene):

Propagation proceeds by addition of biradi-cals of various sizes (i.e., by polyaddition and notby chain polymerization). The resulting polymeris cross-linked since radicals also attack methy-lene groups, which generates more than tworadical sites per reactant and thus cross-linkingsites. The reaction is utilized for the formation ofthin coatings.

Styrene is the only monomer that is polymer-ized commercially by thermal initiation throughmonoradicals. The primaryDiels – Alder adductof two styrene molecules reacts with anotherstyrene molecule to give two different starterradicals:

Only relatively small amounts of styrene are,however, polymerized commercially by thismethod. Most styrene polymerizations, likemany other commercial free-radical polymeriza-


tions, are started by radicals from thermal initia-tors. These thermal initiators dissociate homoly-tically into two radicals at elevated temperature,usually 60 – 80 �C. For the bulk polymerizationof styrene, high-temperature initiators such as1,2-dimethyl-1,2-diethyl-1,1-diphenyl-ethane orvinylsilane triacetate are preferred. For styrenepolymerization in suspension, dibenzoyl peroxide(BPO) (C6H5CO – O – O – OCC6H5) and tert-butyl perbenzoate [C6H5CO – O – O – C(CH3)3 ] are used.

Many other bulk polymerizations employ dii-sopropyl peroxydicarbonate (IPP), which de-composes according to

ðCH3Þ2CHO��COO��OOC��OCHðCH3Þ2!2ðCH3Þ2CHO��COO

. ð41Þ

Water-soluble initiators such as dipotassiumpersulfate (K2S2O8) and certain redox initiatorsare used in emulsion polymerizations. Redoxinitiators generate radicals by reaction of a re-ducing agent with an oxidizing agent (e.g., Fe2þ

þ H2O2). These systems need far less activationenergy for the formation of radicals, and poly-merization can thus be initiated at lowtemperature.

Photochemical Initiations are utilized forthe production of lithographic plates (! Imag-ing Technology, 3. Imaging in Graphic Arts) andfor hardening lacquers but not in themanufactureof plastics. Electrolytic polymerizations find ap-plications in the coating of metal sheets byplastics.

Only initiator radicals are formed at the earlystages of free-radical polymerizations. Theseradicals are successively converted into mono-mer radicals by addition of initiator radicals tomonomermolecules and into polymer radicals byfurther addition of monomers. At the same time,some polymer radicals are removed by termina-tion reactions. Finally, a steady state is estab-lished in which as many radicals are formed asare removed by termination. This state of con-stant total radical concentration (ca. 10�8 mol/L)is in general observed within seconds at mono-mer conversions of 10�2 – 10�4%.

Propagation. Monomer molecules are usu-ally added head-to-tail to growing polymerradicals:

� CH2 ��CHR.þCH2 ¼ CHR!

� CH2 ��CHR��CH2 ��CHR. ð42Þ

but tail-to-tail additions do occur (see Section2.1).

Free-radical polymerizations lead in generalto atactic or predominantly syndiotactic poly-mers. The syndiotacticity increases with decreas-ing polymerization temperature.

Termination. Termination reactions byrecombination, disproportionation, and (athigher initiator concentrations) addition of ini-tiator radicals, cannot be avoided. Since initiatorradicals and thus also polymer radicals areformed successively and are deactivated at ran-dom by different termination reactions, distri-butions of molar masses are formed. The widthof these distributions is given by the relativeproportion of the different types of terminationreactions.

Chain Transfer. The transfers of radicals tomonomers, solvents, and initiators terminatepolymer chains and generate others (Eq. 40).The ratios of rate constants ktr of transfer to rateconstants kp of propagation are called transferconstants, Ctr ¼ ktr/kp; at 60 �C they possessvalues between ca. 2�10�6 for the transfer ofpolystyryl radicals to benzene and 5700 for thetransfer of poly(vinyl acetate) radicals to carbontetrabromide.

Chain transfers often lead to new radicals thathave approximately the same reactivity as thedisappearing ones. In this case, the rate of poly-merization is not decreased by chain transfer, butthe degree of polymerization is lowered. Certaintransfer agents with high transfer constants (suchas thiols) are thus often employed to regulatemolar mass.

Retardation occurs if the new radical ismoresluggish in adding monomers than the transfer-ring polymer radical; inhibition, if a new chaindoes not start at all. Chain transfers to polymerslead to branched polymers; most radically poly-merized polymers are thus slightly branched.

The chain transfer to nonionic allylmonomersgenerates resonance-stabilized allyl radicals.The addition of monomer molecules to theseradicals produces radicals


that are more stabilized by resonance than theirprecursors and thus do not start a polymer chain.The polymerization of noncharged monoallylmonomers thus leads to oligomers with degreesof polymerization of ca. 10 – 20.

Polymerization Kinetics. Initiator radicalsare generated by initiator decomposition(Eq. 34) with a rate of 2 f � kd � [I] where f is theradical yield (i.e., the fraction of radicals thatstart the polymerization). Initiator radicals dis-appear in the start reaction with a rate of kst[I

.][M]. In the steady state, the rate of the startreaction equals the rate of the termination reac-tion(s), thus Rst ¼ Rt, and for terminationsthrough deactivation by other polymer radicals,

d½P�=dt ¼ Rst�Rt ¼ 2 f �kd�½I��kt½P�2 ¼ 0 ð44Þ

Since monomer is practically consumed only bythe propagation reaction with a rate of Rp ¼ � d[M]/dt ¼ kp[P

.] [M], the propagation rate at di-minishing initiator consumption is obtained fromEquation (44)

Rp ¼ �d½M�=dt ¼ kpð2 f �kd=ktÞ1=2�½I�1=2o ½M� ð45Þ

The polymerization rate is directly proportionalto the monomer concentration; bulk polymeriza-tion is thus always faster than solution polymeri-zation. The monomer concentration decreaseswith increasing monomer conversion as does therate Rp.

A ‘‘self-acceleration’’ of the polymerizationand a concomitant increase in the degree ofpolymerization are observed at higher monomerconversion, especially in bulk and in concentrat-ed solutions. This gel effect or Trommsdorff –Norrish effect is caused by a changing diffusioncontrol of the termination by mutual reaction oftwo polymer radicals (i.e., a decrease of termi-nation reactions), which in turn comes from anincreasing entanglement of polymer chains. Be-cause neither the rate of the initiator decomposi-tion nor the rate of monomer addition is affected

by increasing entanglements, both overall poly-merization rates and molar masses increase. Thegel effect broadens molar mass distributions.

Cross-Linking Polymerizations. Free-rad-ical chain polymerizations are employed com-mercially in the manufacture of diallyl thermo-sets and in styrene – divinylbenzene copolymer-izations for polymer beads. Primary macromo-lecules produced at very low monomerconversions are almost linear and carry pendantpolymerizable groups. The likelihood of an at-tack at these groups increases with increasingmass average molar mass. Branched moleculesare formed that convert to cross-linked polymersat the gel point. Monomer conversion at the gelpoint cannot at present be predicted theoreticallyfor such free-radical polymerizations.

Process Engineering. Free-radical poly-merizations may be performed in the gas phase,in bulk, solution, emulsion, suspension, or underprecipitation (Table 10). Each method has ad-vantages and disadvantages.

Bulk Polymerizations. Industrial bulk poly-merizations are performed in liquid monomers,occasionally with the addition of 5 – 15 vol%solvent as a polymerization aid. The process leadsto very pure products. However, much heat isgenerated per unit volume and, in addition, by thegel effect. Local overheating may cause multi-modal molar mass distributions, branching, poly-mer degradation, discoloring, or explosion. Bulkpolymerizations are thus often terminated at 40 –60%monomer conversion.The remainingmono-mer is distilled and recovered. Alternatively,polymerizations may be performed in two steps:first in large batch reactors, then in thin layers.Residual monomer is usually removed by steam.

Suspension Polymerization is a ‘‘water-cooled’’ bulk polymerization. Water-insolublemonomers are suspended as small droplets of0.001 – 1- cm diameter with the help of suspend-ing agents. The polymerization is initiated by oil-soluble initiators. The droplets are converted bypolymerization into pearls, and the process is alsocalled pearl polymerization. Suspension poly-merization allows easy control of the reactionand delivers the polymer as easy-to-handlebeads. A disadvantage is the cost of water


removal and cleaning, along with the sometimesdeleterious effects of incorporated suspensionagents.

Emulsion Polymerization. In emulsion poly-merizations, water-insoluble monomers are sol-ubilized in water by micelles of surfactant mo-lecules (4 – 10-nm diameter); the monomers arealso suspended in a few droplets (ca. 1000-nmdiameter). Water-soluble initiators decomposeinto radicals that travel through the water to themicelles where polymerization begins. Diffusionof monomer from the droplets to the micellesreplenishes themonomer that has been used up byreaction in themicelles. Themicelles finally growinto latex particles of 500 – 5000-nm diameter.Since the reaction volume is very small in mi-celles (and in growing latex particles), termina-tion reactions are rare and polymerization pro-ceeds in a quasi-living manner, leading to muchhigher molar masses than bulk polymerization. Interms of reaction control, emulsion polymeriza-tions have advantages similar to suspension poly-merizations. In addition, they offer higher poly-merization rates by redox initiators and highermolar masses (which can be regulated by transferagents). The resulting latex can furthermore beused directly for paints, adhesives, and coatings.

Gas-Phase Polymerization. Gas-phase poly-merizations can be initiated photochemically.Each growing particle contains only one radicaland the polymerization is thus quasi-living. Thepolymerization rate is determined by the rate ofmonomer adsorption in the precipitating particlesand later by monomer diffusion to the occludedpolymer radicals. The resulting polymers are veryclean.

Solution Polymerization. Solution polymer-izations decrease polymerization rates by mono-mer dilution and allow easy removal of the heat ofpolymerization. Solvents are however costly toremove, and the process is used only if the result-ing polymer solutions can be used directly or ifmonomers and polymers decompose in melts.

3.3.3. Anionic Polymerizations

Anionic polymerizations are initiated by bases orLewis bases such as alkali metals, alkoxides,

amines, phosphines, Grignard compounds, andsodium naphthalene, very often in solution. Theinitiators dissociate ‘‘instantaneously’’ intothe initiating species. These dissociations andthe subsequent start reactions need little activa-tion energy; anionic polymerizations thus oftenproceed with high speed even at �100 �C.

The initiating species and the growing macro-ions are rarely completely dissociated into anionsand counterions. They are rather in equi-libriumwith various types of ion pairs (nondissociatedspecies contact ion pair solvent-separated ionpair free ions; plus associates of these species).The type and amount of initiating species strong-ly affect the polymerization rates and the tacticityof polymers.

The initiating species are present in theireffective concentrations at the beginning of po-lymerization; they are not formed one after an-other as in free-radical polymerization. Termi-nation reactions are fairly rare; anionic polymer-izations are often ‘‘living.’’ Very low initiatorconcentrations are required for living polymer-izations to highmolar masses (see Section 3.2.1);however, high monomer – initiator ratios aredifficult to control and may lead to low polymer-ization rates. In general, polymers from livingpolymerizations have very narrow molar massdistributions of the Poisson type if diffusioneffects are avoided during the mixing of mono-mer and initiator solutions.

Very few anionic polymerizations are there-fore employed for the production of thermoplas-tics, most notably those of formaldehyde, e- cap-rolactam (also for reaction injection molding),and laurolactam (Table 11). Anionic polymeriza-tions are however the method of choice for thesyntheses of block copolymers (e.g., thermoplas-tic elastomers of the styrene – butadiene – sty-rene type).

3.3.4. Cationic Polymerizations

Three groups of monomers can be polymerizedcationically: olefin derivatives CH2¼CHR withelectron-rich substituents, monomers with dou-ble bonds containing heteroatoms or hetero-groups Z (e.g., CH2¼Z), and rings with heteroa-toms. Initiators are Brønsted acids (perchloricacid, trichloroacetic acid, trifluoromethanesulfo-nic acid, etc.); Lewis acids (AlCl3, TiCl4, etc.)


with ‘‘coinitiators’’ such as water; and carbeniumsalts (acetyl perchlorate, tropylium hexachlor-oantimonate, etc.). The propagating macroca-tions are thermodynamically and kinetically un-stable. They attempt to stabilize themselves byaddition of nucleophilic species, which leads tovery fast polymerization on one hand and to ahost of transfer and termination reactions on theother. Very few monomers are thus polymerizedcationically on an industrial scale (Table 12).

3.3.5. Ziegler – Natta Polymerizations

Ziegler – Natta polymerizations are chain poly-merizations that are initiated and propagated byZiegler catalysts, a vast group of coordination

compounds from transition-metal compoundsand metal alkyls. These polymerizations are alsocalled coordination polymerizations or anionic –coordination polymerizations, although coordi-nation of a monomer to an initiator need not leadto a Ziegler – Natta type of polymerization andno anions are involved at all.

Typical Ziegler catalysts for industrial poly-merizations are shown in Table 13. The so- calledthird-generation catalysts for ethylene polymer-izations are composed of TiCl3 þ AlR3 þMgCl2; their high catalyst yield of more than50 000 g of polyethylene produced per 1 g ofTiCl3 makes removal of catalyst residues fromthe polymer unnecessary.

Various complexes between transition-metalcompounds and metal alkyls are known to beformed, but which of these are polymerizationactive and to what extent are rarely known. Inany case, the transition-metal atoms of thesecomplexes are bound to the growing chains;Ziegler catalysts are thus not catalysts butinitiators.

Propagation proceeds via insertion of themonomer molecule between the already existingchain and the bound transition metal Mt:

The isospecific polymerization of propenewith TiCl4 – AlR3 is ana-insertion; the syndios-

Table 11. Industrial anionic homopolymerizations

Monomer Repeating unit Application

Butadiene �CH2– CH¼CH – CH2� elastomer

(1,4-cis)

Isoprene �CH2– C(CH3)¼CH – CH2� elastomer

(1,4-cis)

Methyl

cyanoacrylate

�CH2C(CN) (COOCH3)� adhesive

Formaldehyde �O – CH2� engineering

plastics

Ethylene oxide �O – CH2– CH2� thickener

Glycolide �O – CO – CH2� surgical threads

e-Caprolactone �O – CO – (CH2)5� polymer

plasticizer

e-Caprolactam �NH – CO – (CH2)5� fiber,

thermoplastic

Lauryllactam �NH – CO – (CH2)11� fiber, film

Hexamethyl-

cyclotrisiloxane

�O – Si(CH3)2� elastomer

Table 12. Industrial cationic polymerizations

Monomer Application**

Name Structure*

Isobutene CH2¼C(CH3)2 elastomers, adhesives,

VI improvers

Vinyl ethers CH2¼CHOR adhesives, textile aids,

plasticizers

Formaldehyde CH2¼O engineering plastic

Ethyleneimine c-(NHCH2CH2) paper additive,

flocculant

Tetrahydrofuran c-[O(CH2)4] soft segment for

polyurethanes or polyether –

ester elastomers

*c¼cyclo.**VI¼viscosity index.

Table 13. Important industrial polymerizations with transition-metal

catalysts

Monomer Initiator Application

Ethylene TiCl3 – AlR3; Cr – silica thermoplastic

Propene TiCl3 – R2AlCl thermoplastic

Ethyleneþpropeneþnonconjugated diene

VOCl3 – R2AlCl elastomer

Butadiene TiI4 – AlR3;

R3Al2Cl3 – Co(OOCR0)2elastomer

Isoprene TiCl3 – AlR3 elastomer

Butene-1 TiCl3 – Et2AlCl thermoplastic

4-Methylpentene-1 ? thermoplastic


pecific polymerization of the same monomer isvery probably a b-insertion. The ability of Zieg-ler catalysts to regulate the stereocontrol of suchpolymerizations to a very high degree makesZiegler – Natta polymerizations extremely use-ful industrially. Propene, for example, poly-merizes free-radically or cationically to highlybranched, atactic, lowmolar mass polymers thatdo not crystallize and have low glass transitiontemperatures. They can be used only for hotmeltadhesives. Ziegler – Natta polymerizations(Table 13) lead, however, to stereoregular poly-mers with high melting temperatures; isotacticpolypropylenes find extensive use asthermoplastics.

Similar catalysts are used in metathesis poly-merizations. Metatheses are exchange and dis-proportionation reactions of double bonds, main-ly carbon – carbon double bonds in olefins andcycloolefins. A low molar mass example is themetathesis of pentene-2 to butene-2, pentene-2,and hexene-3 (in the ratio 1 : 2 : 1) by the cata-lyst system WCl6 – C2H5AlCl2 – C2H5OH.Industrially, cyclooctene, norbornene, and dicy-clopentadiene are polymerized by metathesispolymerization. Cyclooctene gives polyoctena-mer � CH¼CH–(CH2)6 �; both the cis and thetrans isomers are elastomers (! Rubber, 6. Syn-thesis by Radical and Other Mechanisms, Chap.4.). Norbornene polymerizes to a thermoplasticpolymer

that is plasticized with mineral oil to give anelastomer (! Rubber, 6. Synthesis by Radicaland Other Mechanisms, Chap. 3.). Dicyclopen-tadiene is considered as a monomer for reactioninjection molding (RIM) processes.

Group transfer polymerizations are also in-sertion polymerizations because a monomermolecule is inserted into the bond between theactive center and the remaining polymer chain.Depending on the monomer, these polymeriza-tions may proceed by either a- or b-insertionsand with the help of nucleophilic or electrophiliccatalysts. Only a small-scale polymerization ofalkyl methacrylates to low molar mass polymersby silylketene acetals and nucleophilic catalysts([(CH3)3SiF2]

�, [HF2]�, CN�, etc.) is utilized

industrially at present:

3.3.6. Copolymerizations

Copolymerizations are joint polymerizations oftwo or more monomers; they were also calledinterpolymerizations in the older literature. In thesimplest case, both active chain ends �a* and�b* react irreversibly with the two monomers Aand B:

� a þA! � a�a;RaA ¼ kaA½a�½A�

� a þB! � a�b;RaB ¼ kaB½a�½B�

� b þA! � b�a;RbA ¼ kbA½b�½A�

� b þB! � b�b;RbB ¼ kbB½b�½B� ð46Þ

Four rates Rij and four rate constants kij are tobe considered in this terminal model, whichcorresponds to Markov first-order statistics. Athigh molar masses, monomers are consumedonly by the four propagation reactions. Therelative monomer conversion is given by

�d½A�=dt�d½B�=dt ¼

RaAþRbA

RbBþRaB¼ kbAþkaAð½a�=½b�Þ

kbBþkaBð½a�=½b�Þ� �

� ½A�½B� ¼d½A�d½B�ð47Þ

The ratios of rate constants of homopropaga-tions and cross-propagations are called copoly-merization parameters

rA � kaA=kaB; rB � kbB=kbA ð48ÞFive different cases can be distinguished for

each copolymerization parameter:

r ¼ 0 The rate constant of homopropagation iszero; the active center adds only theother monomer.

r < 1 The other monomer is addedpreferentially.

r ¼ 1 Both monomers are added in the sameamounts.

r > 1 The ownmonomer is added preferential-ly but not exclusively.


r ¼ ¥ No copolymerization, only homopoly-merization.

Depending on the relative numerical value ofthe two copolymerization parameters, five dif-ferent types of copolymerization can be distin-guished (Table 14).

In general, one of the monomers is consumedpreferentially during copolymerization (rA„rB).This drift of copolymer composition can beavoided if the more reactive monomer is fed intothe reactor according to its consumption. A con-version-independent polymer composition alsoresults if copolymerization is performed underazeotropic conditions, which are defined by

d½A�=d½B� � ½A�=½B� ð49Þ

i.e., the relative rate of monomer consumptionequals the ratio of monomer concentrations atany time: The monomer and the polymer com-positions do not drift with the progress ofpolymerization.

This equation is a special case of the Lewis –Mayo equation, which describes the instanta-neous composition of the copolymer as a func-tion of the ratio of instantaneous monomer con-centrations:

d½A�d½B� ¼

1þrAð½A�=½B�Þ1þrBð½B�=½A�Þ ¼

xaxb

ð50Þ

All types of copolymerization can in principleoccur with the same monomer pair if variousinitiators are used. All copolymerizations ofstyrene and methyl methacrylate shown in Fig-ure 15 are, for example, statistical. The free-radical-initiated copolymerization is, however,azeotropic, and the cationic and anionic ones arenonazeotropic. Initiation by Et3Al2Cl3 and tracesof oxygen leads to almost alternating copoly-mers, whereas cationic polymerization generateslong styrene sequences and anionic polymeriza-tion produces long methyl methacrylate ones.The sequence length determines many polymerproperties, most notably glass and meltingtemperatures.

Table 14. Types of copolymerization of monomers A and B

Types Copolymerization parameters

Azeotropic Nonazeotropic

rA rB rA rB rArB

Alternating 0 0 0 > 0 0

Statistical < 1 < 1 < 1/rB > 1 < 1

Ideal 1 1 1/rB 1/rA 1

Block forming > 1 > 1 > 1/rB < 1 > 1

Blend forming ¥ ¥ ¥ <¥ ¥

Figure 15. Instantaneous mole fraction xs of styrene units in the polymer formed as a function of the instantaneous molefraction xs of styrene in the copolymerization of styrene with methyl methacrylate initiated by (o) cations; (.) free radicals; (�)Et3Al2Cl3; (�) AnionsSolid lines: calculated with copolymerization parameters shown to the right; dotted line: theory for alternatingcopolymerizations.


Ionic copolymerizations very often lead tolong block sequences, whereas free-radical co-polymerizations tend in general to produce morerandom copolymers. Free-radical copolymeriza-tions are thus the method of choice for industrialpurposes if allowed by monomer structures(Table 15).

3.4. Polycondensations andPolyadditions

3.4.1. Bifunctional Polycondensations

Polycondensations and polyadditions are gener-ally divided into bifunctional reactions (twofunctional groups per reactant) and multifunc-tional ones (three or more functional groups permonomer molecule). Bifunctional reactions leadto linear macromolecules; multifunctional ones,to branched and finally cross-linked polymers.

Bifunctional reactions are further subdividedinto AB reactions (e.g., that of H2N –R –COOH)and AA/BB reactions (e.g., H2N –R –NH2 þHOOC–R0 –COOH).

All reactants, from monomer to high poly-mer, may react to form macromolecules inbifunctional polycondensations and polyaddi-tions. Only monomers are present at the begin-ning of the reaction; later, oligomers are present.If the reactivity of the functional groups isindependent of molecule size, then the greaternumber of smaller molecules leads first to lowmolar mass polymers and only at high conver-sions to chemical compounds with high molarmasses (see Fig. 14). In equilibrium, the num-ber-average degree of polymerization of poly-mers from AB and stoichiometric AA – BBreactions is dictated by the extent of functionalgroup reaction p:

Xn ¼ 1=ð1�pÞ ð51Þ

Table 15. Industrial copolymerizations

Monomers Polymerization Application

Free radical, linear (or slightly branched)

Ethyleneþ10% vinyl acetate bulk shrink films

Ethyleneþ10 – 35% vinyl acetate bulk thermoplastics

Ethyleneþ35 – 40% vinyl acetate under precipitation a films

Ethyleneþ>60% vinyl acetate emulsion elastomers

Ethyleneþ<10% methacrylic acid bulk extrusion coating

Ethyleneþtrifluorochloroethylene thermoplastics

Butadieneþstyrene emulsion multipurpose elastomers

Butadieneþ37% acrylonitrile emulsion oil-resistant elastomers

Vinyl chlorideþ3 – 20% vinyl acetate solution b paints

Vinyl chlorideþ15% vinyl acetate solution b Hi-fi records

Vinyl chlorideþ3 – 10% propene bulk thermoplastics

Acryl estersþ5 – 15% acrylonitrile oil-resistant elastomers

Acrylonitrileþ4% different monomers under precipitation c fibers with improved dyeability

Acrylonitrileþstyrene thermoplastics

Acrylonitrileþbutadieneþstyrene thermoplastics

Tetrafluoroethyleneþpropene emulsion thermoplastics

Methacrylic acidþmethacrylonitrile hard foams (after cyclization)

Free radical, cross-linking

Glycol methacrylateþ2 – 4% glycol dimethacrylate contact lenses

Unsaturated polyestersþstyrene or methyl methacrylate bulk glass-fiber-reinforced thermosets

Anionic

Styreneþbutadiene solution elastomers

Cationic

Isobuteneþ2% isoprene solution butyl rubber

Trioxaneþethylene oxide solution thermoplastics

Ethylene oxideþpropylene oxide solution thickener, detergents

Ziegler – Natta polymerization

Propylene oxideþnonconjugated dienes solution elastomers

Ethyleneþpropeneþnonconjugated dienes elastomers

a In tert-butanol.b In acetone, 1,4-dioxane or hexane.c In water.


At 50% conversion (p ¼ 0.5), the number-aver-age degree of polymerization of reactants is only2 (this includes monomer molecules), and thenumber-average degree of polymerization ofpolymers (2 < Xi < ¥) is only 3. Industrialpolycondensations rarely deliver number-aver-age degrees of polymerization greater than100 – 200 (i.e., p ¼ 0.99 – 0.995 in equilibri-um). The endgroups of these equilibrium poly-mersmay condense further during processing by,e.g., extrusion or injection molding. The accom-panying strong increase in viscosity is undesir-able and these endgroups are therefore blockedagainst further polycondensation by ‘‘sealing’’them with monofunctional reagents.

Equilibria are established not only by retro-reactions (reversal of polycondensations andpolyadditions) but also by catalyzed exchangereactions between chain segments. In these transreactions, number-average molar masses remainconstant, but mass-average molar masses in-crease if the initial ratio of mass to number-average molar mass was smaller than dictatedby equilibrium conditions. An example is thetransesterification of poly(ethylene terephtha-late):

Higher degrees of polymerization at lowerextents of reaction can be obtained by irrevers-ible ‘‘activated reactions’’ and especially by het-erogeneous reactions of fast reacting monomers.An example is the Schotten – Baumann reactionof diamines in water with diacid dichlorides inchloroform, for example. A polyamide film isformed at the interface of the two solutions.Functional groups of this polymer are buried inthe interior of the film; they cannot react witheach other. Exchange reactions and retroreac-tions are also absent. Only surface groups canreact; the resulting irreversible reaction leads tohigh molar masses. Industrially, this reaction isutilized for one of the two industrial syntheses ofpolycarbonates, i.e., from the sodium salt ofbisphenol A and phosgene (Table 16).

Most industrial polycondensations are of theAA – BB type (Table 16); they can be describedby

nA�V�AþnB�W�B!A�ðV�WÞn�Bþð2n�1ÞABð52Þ

where A– and B– are leaving groups, AB repre-sents leaving molecules, –V– and –W– are mo-nomeric units, and –V–W– are repeating units.

Industrial AB polycondensations are fairlyrare. Examples are the formation of polyamide11 (nylon 11) (Eq. 27), the polycondensation ofcarbodiimides

O ¼ C ¼ N��R��N ¼ C ¼ O!� R��N ¼ C ¼ N � þCO2

ð53Þ

and the synthesis of certain polysulfones

C6H5Oðp-C6H4ÞSO2Cl!� ðp-C6H4Þ ��O��ðp-C6H4Þ ��SO2 � þHCl

ð54Þ

3.4.2. Multifunctional Polycondensations

Multifunctional polycondensations are condensa-tion reactions with the participation of monomers

having higher functionality ( fo>2). At low con-versions, branched molecules are formed with in-creasingly higher numberof functional endgroupsper molecule (i.e., increased functionality f ) :

f ¼ 2ðfo�1ÞþðX�2Þðfo�2Þ ¼ 2þXðfo�2Þ ð55Þ

Only one such group is however needed to linktwo molecules; the probability of such a linkagethus increases dramaticallywith increasingdegreeof polymerization X. At a certain degree of con-version of functional groups, molecules are linkedthroughout the volume of the reactor. The viscos-ity increases strongly, and themass-averagemolarmass of the cross-linked polymer approachesinfinity at this ‘‘gel point.’’ Not all reactants arelinked at the gel point; some are still soluble up to


high conversions. The number-average degrees ofpolymerization of reactants are thus fairly low atthe gel point, usually in the range 10<X�n<50.

Knowledge of the gel point is technically veryimportant. Polymers cannot, or can only withdifficulty, be processed beyond the gel point andmust thus be shaped before or during the cross-linking reaction. The gel point can be calculatedfrom the functionality and relative amounts ofreactive groups if intramolecular cyclizations areassumed absent. In practice, such cyclizations areoften present and cross-linking occurs at higherextents of reaction than calculated. The theoreti-cal calculations thus provide a safety margin.

Chemical cross-linking reactions are utilizedfor thermosets, certain leathers, and the prepara-tion of elastomers from rubber. Thermosettingpolycondensation reactions allow the hardeningof phenol, amino, and alkyd resins. In the reactionof phenol(s) with formaldehyde, methylene, for-mal, and ether bridges are formed between theortho and para positions of the phenols; thehardening of novolacs with hexamethylenetetra-mine (urotropin) also leads to imine structures(! Phenolic Resins). Amino plastics result fromthe reaction of urea or melamine with formalde-hyde (! Amino Resins), and alkyd resins frommultifunctional alcohols with bifunctional organ-ic acids or their anhydrides (! Alkyd Resins).

Cross-linking also occurs inadvertently duringcyclopolycondensations. In such reactions, ringsare formed during the polycondensation. An ex-ample is the formation of polyimides from pyro-mellitic acid dianhydride with aromatic diamines.

Step I is a polyaddition to a polyamic acid.Step II may occur as shown but also by intermo-lecular reaction. To prevent such cross-linkingreactions, step I is performed at 10 – 15% solidscontent and conversion is limited to 50%. Poly-imide films are formed from the cross-linking ofpolyamic films. Polybenzimidazoles and ladderpolymers are similarly obtained through suchcyclopolycondensations.

Table 16. Industrially important linear AA – BB polycondensations following Equation (52)

Polymer Chemical structure Remarks

A V W B

Poly(ethylene H O(CH2)iO CO – p-Ph – CO OH i¼2 (ethylene) or

terephthalate) H O(CH2)iO CO – p-Ph – CO OCH3 4 (butene)

Unsaturated polyesters H O(CH2)2O CO – CH¼CH – CO O1/2 from maleic anhydride

(isomerizes mainly to

fumaric acid residues)

Polycarbonate H O – p-Ph – C(CH3)2 –

p-Ph – O

CO OC6H5

Na O – p-Ph – C(CH3)2 –

p-Ph – O

CO Cl

Polyarylates Na O – Ar – O CO – Ar – CO Cl different Ar

Poly(phenylene sulfide) Na S p-Ph Cl

Polysulfides Na S R Cl different R

Polysulfones K O – p-Ph – O SO2 – p-Ph – O –

p-Ph – SO2

Cl different V and W units

Polyamides H NH(CH2)iNH CO(CH2)jCO OH PA 66 (i¼6; j¼4) PA 610

(i¼6; j¼8) PA 46 (i¼4; j¼4)

Polyetheretherketone K O – p-Ph –

CO – p-Ph – O

p-Ph – CO – p-Ph F

Ar¼aromatic residue,

p-Ph¼para-substituted phenylene group,

R¼organic residue.


3.4.3. Polyaddition

No leaving molecules have to be removed duringpolyadditions, an important advantage for pro-cess engineering. Practically all industrially im-portant polyadditions are thus performed withthermosetting resins. Polyurethanes are formedfrom diisocyanates (or triisocyanates) and poly-ols (see Eq. 28 for diols). Polyurethane forma-tion may be so rapid that cross-linking andshaping can be performed in one step throughreaction injection molding with short cycletimes. Epoxides (epoxy resins) contain two ormore epoxy groups per prepolymermolecule andare cured with either difunctional or multifunc-tional amines or with anhydrides of organicacids.

3.5. Polymer Reactions

3.5.1. Polymer Transformations

Several polymers are chemically transformedinto industrially useful polymers by polymera-nalogous reactions of their substituents (Table17).

These reactions per group are chemicallyidentical to their lowmolarmass analogues. Theydiffer in the effect of side reactions, which do notlead to removable byproducts as in micromole-cules but to ‘‘wrong’’ structures in the polymer

chain. In most cases, such structures decrease thedesired polymer properties. Polymer transforma-tions that are prone to side reactions are thusgenerally avoided. This is one reason why onlyfive types of polymer-analogous reactions areutilized commercially: transesterification –saponification, chlorination – sulfochlorination,etherification, hydrogenation, and cyclization.

The reaction of poly(vinyl alcohol) withbutyraldehyde leads to acetals. For statisticalreasons, however, not all hydroxyl groups canbe transformed:

The resulting poly(vinyl butyral) is used as anintermediate layer in safety glass and for washprimers.

Heating of methacrylic acid – methacryloni-trile copolymers with ammonia produces poly-methacrylimide structures that are hard foams:

Table 17. Industrial polymer transformations (for ring formations see text)

Base units in primary polymer Reagent Conversion, % Base units in final polymer Application

CH2CH(OOCCH3) ROH 98 CH2 – CHOH thickener

CH2CH2CH2CH(OOCCH3) CH3OH 99 CH2 – CHOH/CH2 – CH2 engineering plastics

Cellulose – NHCOCH3 H2O ? Cellulose NH2 paper additive

Cellulose OH CH3COOH 83 – 100 Cellulose OOCCH3 fibers, films

Cellulose OH HNO3 67 – 97 Cellulose – ONO2 plastics, fibers

Cellulose ONa oxirane 53 – 87 Cellulose – OCH2CHRCH3 thickener

Cellulose OH oxirane 100 – 400 a Cellulose – OCH2CH(OR0)CH3 thickener

CH2 – CH2 Cl2 25 – 40 b CH2 – CHCl elastomer

>40 b CH2 – CHCl/CHCl – CHCl impact improver for PVC

CH2 – CHCl Cl2 64 b CH2 – CHCl/CHCl – CHCl adhesives, paints

CH2 – CH2 Cl2/SO2 <42 b; <2 c coatings

CH2CH¼CHCH2/CH2 – CHCN H2 ? (CH2)4/CH2 – CHCN elastomer

CH2 – CH(C6H5) SO3 low CH2 – CH(C6H4SO3H) ion exchangers

N¼PCl2 RONa ? N¼P(OR)2 elastomer

aFurther reaction of primary reaction products may lead to more than one monomeric unit of reagent per hydroxyl group of cellulose.bChlorine content in %.cEther groups per glucose unit.


3.5.2. Block and Graft Formations

Reactive chain ends can either initiate the poly-merization of other monomers or couple withother preformed macromolecules to give blockpolymers:

AnþmB!AnBm

ð56ÞAn

þBm!AnBm ð57Þ

Both methods are used industrially with avariety of strategies for the synthesis of diblockpolymers AnBm as compatibilizing agents forpolymer blends, triblock polymers AnBmAn asthermoplastic elastomers, and various multi-block polymers for different purposes, especiallyfor thermoplastic elastomers. Anionic livingpolymerizations are used for the syntheses ofpoly(styrene – block-butadiene – block-styrene)and poly(styrene – block-isoprene – block-sty-rene). Polycondensations serve for the prepara-tion of multi[{poly(butylene terephthalate)} –block-poly{(polytetrahydrofuran) – terephthal-ate}], and various polyesteramide and polyether-amide segmented block polymers.

Graft copolymers result from the grafting ofmonomers on chemically different polymerchains. Grafts of isobutene – isoprene on poly-ethylenes, vinyl chloride on poly(ethylene-stat-vinyl acetate), ethylene – propylene on poly(vi-nyl chloride), or styrene – acrylonitrile on satu-rated acryl rubber also yield thermoplasticelastomers.

3.5.3. Cross-Linking Reactions

Cross-linking of preformed polymers is used forvulcanizing unsaturated rubbers with sulfur, vul-canizing saturated rubbers with peroxides, hard-ening unsaturated polyester chains with styreneor methyl methacrylate via copolymerization, ortanning collagen with certain reagents to leather.

3.5.4. Degradation Reactions

Degradation of polymers is undesirable for theirapplication and often desirable for their disposalafter use. The term degradation includes thedecrease in degree of polymerization with pres-ervation of the chemical structure of monomeric

units (depolymerization), the unwanted chemicaltransformation of some monomeric units withpreservation of the degree of polymerization(decomposition), and a combination of both. Theterms degradation, depolymerization, and de-composition are sometimes used with the samemeaning as in this article, but other times withbroader ormore restrictedmeanings; no acceptedusage exists.

Depolymerizations involve chain scissions.They are retroreactions (i.e., the reverse of chainpolymerizations, polyeliminations, polyconden-sations, or polyadditions). Chain scissions maybe at random as in retropolycondensations andretropolyadditions ormay be unzipping reactionsas in retro- chain polymerizations andretropolyeliminations.

Unzipping can occur only with activatedchains above their ceiling temperatures, that is,with living polymers, chain ends comprisingcertain functional groups, or radical ends gener-ated by a prior chain scission.

Unzipping at higher temperature results in gas-eousmonomers that lead to voids in molded parts.This can be prevented or reduced by shorter se-quence lengths of the unzippable polymer blocks.This strategy is utilized, for example, in the for-mation of acetal copolymers by copolymerizationof trioxane (gives unzippable oxymethylene se-quences�OCH2�)with ethylene oxide (oxyethy-lene sequences �OCH2CH2� do not unzip).

Decomposition can be caused by heat, light,oxygen, water, or other environmental agents aswell as mechanical forces such as extensionalflow, ultrasound, or a combination of these. Itmay lead to undesirable changes of mechanical,electrical, or optical properties. Unstabilizedpoly(vinyl chloride) �(CH2CHCl)n� discolorson decomposition because HCl is eliminated andcolored polyene sequences �(CH¼CH)i� areformed. The polymer ultimately becomes brittle.

Decomposition is the primary degradationprocess in the pyrolysis of polymers, which maybe desirable (rocket fuels, waste disposal) or not(fires), and often produces toxic fumes or smokeat lower flame temperatures. The risk of pyrolysisis enhanced for polymers with branching points,electron-accepting groups, long methylenesequences, and all groups capable of formingfive- or six-membered rings. Thermostability is


enhanced by aromatic rings, ladder structures,fluorineasa substituent, and lowhydrogencontent.

4. Plastics Manufacture

4.1. Homogenization andCompounding

Polymerization reactors do not deliver polymersthat can be used directly as raw materials forplastics. Polymer melts must be filtered; melts,powders, beads, pellets, and granulates must bedegassed; and all particulates must be dried orconditioned to environmental surroundings.Beads from suspension polymerization arewashed and polymer solutions concentrated.

Batchwise polymerizations often lead toslightly different products, which are mixed(blended) to guarantee customers polymer gradesaccording to specifications (microhomogeniza-tion). Granulates and pellets are sometimes sim-ilarly blended by macrohomogenization.

Compounding is the mixing of polymers andadditives. This process can be performed either byadding single additives one at a time, by usingadditive systems, or by employingmaster batches.Additive systems are carefully adjusted mixturesof additives that are formulated to avoid mutuallysynergistic or antagonistic effects.Master batchesare concentrates of additives in polymers; theyfacilitate thedosageof small amountsof additives.

The properties of compounds depend verymuch on the compounding process. Only hetero-geneous compounds resultwhen poly(vinyl chlo-ride) is mixed with additives in regular mixers;these compounds cannot be processed directly toend-use products. High-performance mixers de-liver free-flowing powders; these ‘‘dry blends’’can be extruded and injection molded. Com-pounding is often carried out by specializedcompanies (compounders).

4.2. Additives [5], [73] (! Plastics,

Additives)

4.2.1. Overview

Polymers are rarely used directly as materials.They do not fulfill per se all technological re-

quirements and become commercially usefulonly after they have been mixed with certainadditives. These additives average ca. 23%of thetotal weight of plastics (Table 18) but may rangefor individual plastics from 0% (packaging filmsfor food) to 90% (barium ferrite-filled ethylene –vinyl acetate copolymers for magnetizable seal-ing strips). Their economic value approximatesthat of plastics because some additives commandprices that are a hundred times those of theplastics themselves.

Polymer additives are to be distinguishedfrom polymer auxiliaries; the former are addedto polymers after the polymerization process,whereas the latter are used for the manufactureof polymers (e.g., polymerization catalysts,emulsifiers, initiators). The free-radical initiatorsused for the hardening of unsaturated polyestersare sometimes considered additives (added to thesolution of unsaturated polyester molecules inmonomers such as styrene) and sometimes aux-iliaries (promoting the thermosetting reaction).

Additives are usually subdivided according totheir application into process additives and func-

Table 18.Annual U.S. consumption of polymer additives for plastics,

1980 (plastics production: 16 076 000 t/a)

Additive Consumption in t/a

Process additives

Processing stabilizers

Heat stabilizers (PVC) 43 000

Antioxidants 18 000

Processing aids

Lubricants, slip agents, etc. 50 000

Polymeric processing aids <1 000

Mold-release agents <1 000

Nucleating agents <1 000

Radical initiators for thermosets 15 000

Functional additives

Stabilizing additives

Antioxidants see above

Metal deactivators <1 000

Light stabilizers 2 400

Flame retardants 220 000

Biostabilizers <1 000

Modifiers

Colorants 150 000

Fillers and reinforcing agents

Mineral-based 1730 000

Glass 462 000

Natural organic 133 000

Synthetic organic 2 000

Plasticizers 1 000 000

Blowing agents (without gases) 7 000

Impact modifiers <5 000

Antistatic agents 2 000

Total 3 844 400


tional additives. Process additives aid the proces-sing of plastics by either stabilizing the chemicalcomposition of polymers (processing stabilizers)or facilitating the processing itself (processingaids). Functional additives stabilize the chemicalcomposition against attacks by environmentalagents (stabilizing additives) or improve certainend-use properties (modifiers). Additives mayalso be classified according to their primarymodeof action (chemical or physical). Some additivesact in more than one way: a filler or colorant mayalso be a nucleating agent for crystallization, apigment may enhance discoloration, etc.

4.2.2. Chemofunctional Additives

Polymers can be attacked by oxygen and ozoneduring processing and use. The attack generatesradicals that cause chain reactions to produceeven more radicals. Ultimately, changed chemi-cal compositions, degradation, or cross-linkingresult. Oxidation is reduced if the accessibility ofthe oxidizable groups is limited or if radicalformation is prevented. Oxygen diffusion intothe polymer is slowed by certain coatings that actasmechanical barriers or by additives that diffuseinto surface layers and are preferentially oxidizedthere.

Antioxidants (! Antioxidants) prevent rad-ical formation, at least during processing and forthe targeted lifetime of the plastic. They aresubdivided into deinitiators and chain ter-minators.

Deinitiators prevent the formation of radi-cals (therefore: preventive antioxidants) and arealways used in combination with chain termina-tors (therefore also called secondary antioxi-dants). They are further subdivided into peroxidedeactivators, metal deactivators, and UV absor-bers. Peroxide deactivators (tertiary amines, ter-tiary phosphines, sulfides) convert hydroperox-ides into harmless compounds before they canform radicals. Metal deactivators are chelatingagents that form inactive complexes with cata-lytically active metal species (mainly from Zieg-ler – Natta polymerizations).

Chain Terminators, such as hindered phe-nols, amines, and anellated hydrocarbons, react

with already formed radicals and terminate thekinetic chain (chain-breaking or primary antiox-idants). A combination of deinitiators and chainterminators often leads to synergistic effects.Antagonistic effects are also known (e.g., withcarbon black as filler).

Light-induced degradation reactions can beprevented by the reduction of light absorption orby the addition of UV absorbers and quenchers.Less light is absorbed by the plastic if the surfacesare reflective or if certain pigments are added(e.g., carbon black). Ultraviolet absorbers eitherconvert the incident light into harmless infraredradiation or are transformed into other chemicalcompounds. Quenchers deactivate excited statesand themselves become excited.

Heat Stabilizers prevent chemical transfor-mations of plastics at higher temperature; theirmain application is for the stabilization of poly(vinyl chloride) against HCl elimination duringprocessing.

Flame Retardants either prevent oxygen ac-cess to burning plastics by formation of nonburn-ing gases or by ‘‘poisoning’’ radicals generatedby the burning. Some plastics are selfextinguish-ing because either CO2 (polycarbonates) or watervapor and a protecting carbon layer are formed(vulcanized fiber: a ZnCl2-treated cellulose) dur-ing burning. Chlorine and bromine compoundsgenerate radicals during burning; these radicalscombine with radicals from the degradation ofplastics and stop the kinetic chain. Phosphoruscompounds are oxidized during the burning tononvolatile phosphor oxides, which either form aprotective layer or are converted by water intophosphorus acids that catalyze the elimination ofwater.

The flammability of plastics is often charac-terized by the limiting oxygen index (LOI). TheLOI value indicates the limiting value of thevolume fraction of oxygen in an oxygen – nitro-gen mixture that just allows the polymer to burnafter ignition with a flame. Materials withLOI>0.225 are called flame retardant; thosewithLOI>0.27, self-extinguishing. Low LOI values(high flammabilities) are exhibited by polyoxy-methylenes (0.14), polyolefins (0.17 – 0.18),saturated polyesters (0.20), and cellulose(0.20). High LOI values are exhibited by poly(vinyl chloride) (0.32), polybenzimidazole


(0.48), and polytetrafluoroethylene (0.95). How-ever, LOI values are not absolute measures of theflammability or combustibility of plastics be-cause these properties also depend on flametemperatures, heat capacities, heat conductivi-ties, melting temperatures, and melt viscosities.The hazard of burning plastics is also determinedby smoke formation and the toxicity of theevolving gases.

4.2.3. Processing Aids

Processing aids facilitate the processing of plas-tics by enhancing either transport rates to theprocessing machines, flow behavior in thesemachines, achievement of final properties duringprocessing, or removal of shaped articles fromthe machines or from each other.

Easy-flow grades of powdered polystyrenes,for example, often contain 3 – 4% mineral oil,which forms a low-viscosity film on the surfaceof the particles and thus reduces friction in polarpolymers; amphiphilic compounds such as metalstearates or fatty acid amides are used for thispurpose. Such external lubricants also reduce thefriction between polymer particles and the wallsof the processing machine and the friction ofpolymermelts at suchwalls; they also prevent thecleavage of particles to smaller flow units. Ex-ternal lubricants are always incompatible withpolymers and are thus found predominantly atpolymer surfaces. They are related to releaseagents, which facilitate the separation of shapedarticles from the tools (molds), and slip agents,which prevent the sticking together of shapedarticles. Slip agents are thus sometimes alsocalled lubricants.

Internal lubricants improve the flow behaviorand homogeneity of polymer melts; they alsoreduce the Barus effect (see Section 7.3.2) andthemelt fracture. Internal lubricants probably actby desegregating larger units (aggregates), whichwere probably formed during polymerization andare still present shortly after the melting of thepolymer to a macroscopically homogeneous ma-terial. Typical internal lubricants are amphipolarcompounds, e.g., modified esters of long- chainfatty acids.

Nucleating agents promote the crystallizationof crystallizable polymers by generating manynuclei for crystallites. They prevent the forma-

tion of larger spherulites and thus improve themechanical properties of plastics.

4.2.4. Extending and Reinforcing Fillers

Fillers are solid inorganic or organic materials.Some fillers are added mainly to improve theeconomics of expensive polymers; they are ex-tenders. Extenders are usually particulate mate-rials of corpuscular nature, such as chalk andglass spheres (aspect ratio ca. 1). Other fillersare reinforcing agents (‘‘active fillers’’); theyimprove certain mechanical properties. Rein-forcing agents possess aspect ratios higher than1; they may be short fibers, platelets (e.g., kao-lin, talc, mica) (! Reinforced Plastics), or longfibers (continuous filaments). Active fillers aresometimes subdivided into property enhancers(aspect ratio < 100) and true reinforcing fillers(aspect ratio > 100). No sharp dividing lineexists between fillers and reinforcing agents,nor can the term ‘‘reinforcement’’ be unambig-uously defined (e.g., it may denote an increase inbreaking or impact strength or a decrease ofbrittleness).

A variety of fillers are used for plastics(Table 19).

Glass-fiber-reinforced polymers often carrythe abbreviation GRP (or FRP); those reinforcedby synthetic organic fibers, CRP. Syntactic plas-tics are polymers reinforced with hollow glassspheres. The amounts of fillers added vary wide-ly: in general, industry standards are about30 wt% for thermoplastics and 60 wt% forthermosets.

Fillers act very differently in polymers. Somefillers form chemical bonds with polymers; anexample is carbon black, which acts as a chemi-cal cross-linker in elastomers. Other fillers canadsorb polymers on their surfaces: that is, physi-cal bonds are introduced between fillers andpolymers. On impact, adsorbed chain segmentsmay take up energy and slip from the surface,which increases impact strength. Still other fillersact as nucleating agents in crystallizable poly-mers. Fillers furthermore constitute impenetrablewalls to polymer coils. They restrict the numberof conformational positions of chain segmentsnear the filler surface; chains become less flexi-ble, and tensile strengths and moduli of elasticityincrease.


4.2.5. Plasticizers (! Plasticizers)

Plasticizers are added to polymers to improvetheir flexibility, processibility, or foamability.About 500 different types of plasticizers aremarketed. They are generally low molar massliquids; polymer plasticizers are used in muchsmaller amounts. Of all plasticizers for thermo-plastics, 80 – 85% are used for poly(vinyl chlo-ride); themost important plasticizer is di-2-ethyl-hexyl phthalate (‘‘dioctyl phthalate,’’ DOP). Themain plasticizer for elastomers is mineral oil;tires contain up to 40%. Polymer plasticizers aremainly aliphatic polyesters and polyethers. Theformer are prepared by polycondensation; theythus possess fairly broad molar mass distribu-tions and also containmonomeric and oligomericmolecules. Since their number-average molarmass is low (ca. 4000 g/mol), they are calledoligomer plasticizers. Plasticization can also beachieved by copolymerization of the parentmonomer with certain other monomers; this ef-fect is called internal plasticization, in analogy toexternal plasticization by added high and lowmolar mass plasticizers.

External plasticizers are subdivided into pri-mary and secondary ones. Primary plasticizersinteract directly with chains by way of solvation.Secondary plasticizers are merely extenders; they

can be used only in combination with a primaryplasticizer. A certain plasticizer may thus be aprimary or a secondary one, depending on thechemical constitution of thepolymer.Mineral oilsare, for example, primary plasticizers for poly-dienes but extenders for poly(vinyl chloride).

4.2.6. Colorants

Colorants are subdivided into dyes (soluble inpolymer matrix) and pigments (insoluble). Tex-tile fibers are dyed mainly with dyes. Pigmentsare preferred for plastics because they have ahigher lightfastness and are more stable againstmigration than dyes. Colorants for plastics aredominated by titanium dioxide (60 – 65%) andcarbon black (20%); only 2% are dyes.

Pigment particles generally possess diametersof 0.3 – 0.8 mm, which allows the pigmentationof films and fibers of > 20-mm thickness. Verythin films and fibers are colored exclusively byorganic pigments because these can be ground tomuch smaller diameters than inorganic ones. Thehiding power of pigments increases with increas-ing difference between refractive indices of pig-ment and polymer.

Pigments need not have a special affinity forpolymers. They must be wettable by the polymer

Table 19. Fillers for thermoplastics (T), thermosets (D), and elastomers (E). For definition of other acronyms see Tables 1–4

Filler Application in Concentration in % Improved property

Inorganic fillers

Chalk PE, PVC, PPS, PB, UP < 33 in PVC price, gloss

Potassium titanate PA 40 dimensional stability

Heavy spar PVC, PUR < 25 density

Talc PUR, UP, PVC, EP, PE, PS, PP white pigment, impact strength,

plasticizer uptake

Mica PUR, UP < 25 dimensional stability, stiffness, hardness

Kaolin UP, vinyls < 60 demolding

Glass spheres T, D < 40 modulus of elasticity, shrinkage,

compressive strength, surface properties

Glass fibers T, D < 40 fracture strength, impact strength

Fumed silica T, D < 3 tear strength, viscosity (increase)

Quartz PE, PMMA, EP < 45 heat stability, fracture

Sand EP, UP, PF < 60 shrinkage (decrease)

Al, Zn, Cu, Ni, etc. PA, POM, PP < 100 conductivity (heat and electricity)

MgO UP < 70 stiffness, hardness

ZnO PP, PUR, UP, EP < 70 UV stability, heat conductivity

Organic fillers

Carbon black PVC, HDPE, PUR, PI, PE, E < 60 UV stability, pigmentation, cross-linking

Graphite EP, MF, PB, PI, PPS,

UP, PMMA, PTFE

< 50 stiffness, creep

Wood flour PF, MF, UF, UP < 5 shrinkage (decrease), impact strength

Starch PVAL, PE < 7 biological degradation


melt, however, which can be achieved by treatingthem with surfactants. The aggregation of pig-ments is mainly the result of air inclusions; it canbe removed by the application of vacuum. Pig-ments can be metered into plastics via masterbatches (in plastics), color concentrates (in plas-ticizers), or electric charging of the surface ofpolymer particles in granulate mixers. Up to1 wt% of pigment can be mixed in by the lastmethod.

4.2.7. Blowing Agents

Foamed plastics (plastic foams, cellular plastics,expanded plastics) are blends of polymers withgases (! Foamed Plastics). They may be rigid(glass transition or melting temperature higherthan use temperature) or flexible; their cell struc-ture can be open or closed. The gases may be air,nitrogen, carbon dioxide, fluorinated hydrocar-bons, etc.

Plastic foams can be produced by mechanicalmeans (whipping, stirring), physical methods(shock volatilization of liquids, washing-out ofsolids), or chemical foaming either by internalfoaming during the polymerization or by externalfoaming with chemical blowing agents. Chemi-cal blowing agents are chemical compounds thatdecompose at elevated temperature with releaseof gases. The most widely used agent for naturalrubber is N,N0-azobisisobutyronitrile (CH3)2C(CN) –N¼N–C(CN)(CH3)2 (AIBN); for plasti-cized PVC, N,N0-dinitroso dimethyl tereph-thalamide CH3–N(NO) –CO– ( p-C6H4) –CO –N(NO) –CH3 (NTA); and for other plastics, 1,1

0-azobisformamide H2N –CO–N¼N–CO–NH2

(ABFA). Blowing agents are used in amountsof ca. 0.1% to eliminate sinks in injection mold-ing; 0.2 – 0.8% for injection-molded structuralfoams; 0.3% for extended profiles; 1 – 15% forvinyl plastisol foaming; and 5 – 15% for com-pression-molded foam products.

4.3. Processing

Manydifferent types of processes exist to convertmonomers, prepolymers, or polymers into plas-tics. In general, four procedures can be distin-guished for processing raw materials into shapedplastics:

1. From monomers to polymers by direct poly-merization with simultaneous shaping

2. From monomers by oligomerization to pre-polymers, followed by simultaneous poly-merization and shaping

3. From monomers by polymerization to poly-mers, followed by separate shaping

4. From monomers by polymerization to poly-mers, shaping to semifinished product, andfinally to the end product

In all four cases, end productsmust sometimes beaftertreated (degated, polished, etc.).

Procedure 1 has only one process step andshould be the most economical. It is widely usedfor wire coatings. However, technological pro-blems are often encountered for shaped articlesbecause the process involves the conversion of alow-viscosity liquid into a high-viscosity body.Since very high polymerization rates are requiredfor this process to achieve high cycle times(phase sequences) in molding (i.e., number ofarticles produced per unit time), very few mono-mers, types of polymerization, and shapingmethods are suitable. The method is utilizedindustrially in the RIM process, mainly forthe polyaddition of diisocyanates with polyols.The anionic polymerization of lactams and theDiels – Alder polymerization of dicyclopenta-dienes and related compounds are also (in prin-ciple) suitable for RIM.

Procedure 2 is typical for thermosets. Oli-gomerizations are conducted to conversionsshortly before the gel point. Additives are added,and the final processing step consists of a simul-taneous cross-linking polymerization and shap-ing. Typical processing methods include mold-ing, compression molding, cavity compressionmolding (hot pressing), injection – compressionmolding, injection molding, and extrusion.

Procedure 3 is generally chosen for thermo-plastics. Polymers from the polymerization pro-cess are isolated before shaping and stored (e.g.,as granulate) for a shorter or longer period oftime. The stored polymers must be dried beforefurther processing; otherwise, steam producedat higher processing temperatures may lead tovoids and cavities in shaped articles. Aftercompounding, the plastic raw material must be


weighed out accurately for each cycle in dis-continuous processing procedures. The fillingfactor (¼ raw material density/bulk density)must be known.

The choice of a processing technique is influ-enced technically by the rheological properties ofthe material and the form or shape of the desiredarticle. The cost of processing machines and thecycle time are economically important. Com-modity articles are produced by casting, centrif-ugal casting, hot pressing, injection – compres-sion molding, coating, spraying, roll milling,extrusion, injection molding, cold forming, pressforming, stretch forming, blowing, extrusionblowing, sintering, fluidized-bed sintering, flamespraying, or hot blast sprinkling, and specialtyarticles by molding.

Procedure 4 is the method of choice fordifficult-to-manufacture articles. Proceduressuch as welding, stamping, cutting, forging, saw-ing, boring, turning,milling (in themetalworkingsense), sintering, and baking are employed forboth thermoplastics and thermosets. The surfacesof plastics are sometimes treated further fortechnical (surface hardness, friction) or aestheticreasons (gloss, color) by polishing, painting,metallizing, coating, etc.

5. Supermolecular Structures(! Plastics, Properties and Testing)

Polymer properties are influenced not only by thechemical structure (constitution, molar mass,configuration, microconformation) but also bythe physical structure of polymers. These struc-tures may range from totally irregular arrange-ments of chain segments over shorter or longerparallelizations of chains, to voids and otherdefects in otherwise highly organized assembliesof polymer molecules. Two possible ideal struc-tures exist in the solid state: perfect crystals andtotally amorphous polymers. Polymer moleculesare perfectly ordered in ideal crystals. Theyconvert at the thermodynamic melting tempera-ture into melts, which ideally are totally disor-dered. Amorphous polymers can be viewed asfrozen-in polymer melts. They are polymerglasses that convert tomelts at the glass transitiontemperature.

5.1. Noncrystalline States

5.1.1. Structure

Isolated polymer coils possess approximately aGaussian distribution of chain segments; theirsegment density decreases with increasing chainlength. However, the macroscopic densities ofpolymer melts do not change with chain lengthsif end group effects on small molar mass mole-cules are neglected. Coils must therefore overlapconsiderably in polymer melts. At the glasstransition temperature, cooperative segmentalmovements freeze in, and the physical structureof the melt is conserved. Small-angle neutronscattering studies have shown that the radii ofgyration of amorphous polymers are indeed es-sentially identical for their melts, glasses, andsolutions in theta solvents.

The absence of long-range order in melts andamorphous polymers does not exclude the pres-ence of short-range order in these states. Becauseof the persistence of polymer chains, a paralle-lization of short segments seems probable, as isfound, for example, for alkanes according to X-ray investigation. This local order does not ex-ceed 1 nm in each direction.

The packing of chain segments cannot beperfect. Amorphous polymers thus possess ‘‘freevolumes’’, which are regions of approximatelyatomic diameters. The volume fraction of thisfree volume is ca. 2.5% at the glass transitiontemperature and is independent of polymer con-stitution. Polymer segments in melts can movemore freely than in the glassy state; the densitiesof melts are thus higher than the densities ofglasses at the same temperature.

5.1.2. Orientation

Polymer segments, polymermolecules, and crys-talline domains may be oriented along the ma-chine direction by drawing or other mechanicalprocesses. The orientation of chain segmentsneed not necessarily lead to crystallization, how-ever. An example is injection-molded polysty-rene, which shows optical birefringence due tothe orientation of segments but no X-raycrystallinity.

The degree of orientation of segments orcrystallites can bemeasured bywide-angleX-ray


or small-angle light scattering, infrared dichro-ism, optical birefringence, polarized fluores-cence, and ultrasound velocity. The orientationis usually characterized for each of the threedirections a, b, and c by a Hermans orientationfactor fi, where b is the angle between the drawdirection and the principal axis of the segments:

fi ¼ ð1=2Þð3hcos2bi�1Þ ð58ÞThe orientation factor becomes 1 for a completeorientation of that axis in the draw direction(b ¼ 0�), �1/2 for a complete orientation per-pendicular to the draw direction (b ¼ 90�), and 0for a random orientation.

Since methods to determine orientation fac-tors are often expensive, time consuming, ordifficult to perform, the easy-to- calculate drawratio (length after drawing/length before draw-ing) is often used to characterize orientation. Thedraw ratio is, however, not a goodmeasure of thedegree of orientation because it depends on thehistory of the specimen. Drawing may also leadto viscous flow of the polymer without anyorientation of segments and crystallites.

5.2. Polymer Crystals [74]

5.2.1. Introduction

Spheres and other geometrically simple entitiescan be arranged in crystal lattices irrespective ofwhether they are atoms, small molecules, largemolecules such as enzyme, or latex particles. Thecenters of gravity of these entities occupy latticesites that are regularly spaced in three dimen-sions. Lattices are called superlattices if thedistances between lattice points significantlyexceed atomic dimensions. The existence ofthree-dimensional order on the atomic level iscalled crystallinity.

Chain molecules can also be arranged incrystal lattices. The whole chain may becompletely parallel to other chains as in the caseof truly extended chain crystals; the microcon-formation of the chain can be all trans or helical(Fig. 16), and the chains may have a directionalsense as in polyamide 6 or an inversion center asin polyamide 66 (Fig. 17). In other cases, onlysections of the chains may be parallel to eachother, either sections of a single chain as in foldedchain crystals or those of neighboring chains as in

Figure 16. Schematic representation of crystalline polymersas extended chain crystals with chains in all-trans (T) orhelical conformation (H), (L) lamellae of chains intercon-nected by tie molecules, and (F) fringed micelles. No bondangles are shown for H, L, and F

Figure 17. Pleated-sheet structures of polyamides 6 (anticli-nal) and 66 (isoclinal)


fringed micelles. These ordered segments formcrystalline regions in otherwise less ordered(though not necessarily completely disordered)polymers.

Crystalline regions may be assembled intogreater entities, which themselves may be moreor less ordered. The types and degrees of order –disorder depend on external conditions such astemperature, pressure, cooling and heating rates,and presence of solvents. A variety of morphol-ogies may thus exist for any crystallizable poly-mer [73], for example, spherical, platelet-like,fibrillar, and sheaflike structures of a polyamide 6(Fig. 18).

5.2.2. Crystal Structures

The unit cell describes the smallest, regularlyrepeating structure of a parallelepiped that gen-erates a crystal by parallel displacements in threedirections. The parallelepipeds are characterizedby three lattice constants (distances between

lattice points in three directions) and three latticeangles (Table 20).

Lattice constants reflect the microconforma-tions of chains in crystal lattices. The c-directionis normally assigned to the chain direction; avalue of c ¼ 0.254 nm thus gives the distancebetween repeating units – CH2 – CH2 – in all-trans conformation (bond distance 0.154 nm,bond angle 112�). The c-values in carbon chainsthat are nonmultiples of 0.254 indicate the pres-ence of non-all-trans conformations (e.g., helicalstructures in it-polypropylene and it-polybuty-lene-1). The a and b values reflect physical bonds(such as van der Waals or hydrogen bonds) thatare longer than the chemical bonds in the c-direction. The anisotropy of bond lengths in thethree spatial directions prevents the existence ofcubic lattices for chain molecules. The other sixlattice types are however found [hexagonal, te-tragonal, trigonal, (ortho)rhombic, monoclinic,triclinic].

Most polymers form polymorphs (i.e., poly-mers of the same constitution and configuration

Figure 18. Electron micrographs of different morphologies of a polyamide 6a) From a 260 �C solution in glycerol quenched into 20 �Cglycerol; b) Same solution fast cooled (40 K/min); c) Same solutionslowly cooled (1 – 2 K/min); d) Slow evaporation of formic acid solution at room temperature [75]


can possess various energetically different crys-tal modifications). Polymorphismmay be causedby different microconformations of polymerchains (e.g., polybutylene-1) or by differentpacking of chains with identical chain conforma-tions (e.g., it-polypropylene). Such differencescan be generated by small changes in processingconditions (e.g., different crystallization tem-peratures) or by stretching.

Copolymers can furthermore show isomor-phism if different monomeric units can replaceeach other without change of lattice structure.Isomorphism of chains is also possible if the twocorresponding homopolymers have analogouscrystal modifications, similar lattice constants,and the same helix types. An example is amixture of the g-modification of it-polypropyl-ene and the modification I of it-polybutylene-1(Table 20). This phenomenon is sometimes alsocalled allomerism. One company calls its crys-talline copolymers from two or more olefinicmonomers polyallomers because the monomericunits are isomorphic.

5.2.3. Crystallinity

Perfect crystal lattices should give sharp X-rayreflections and sharpmelting points. Polymers donot exhibit these features, even if they show acrystallike appearance in electron micrographs.In addition, X-ray patterns of polymers frequent-ly exhibit continuous, diffuse scattering. Thesefindings can be interpreted by either a one-phasemodel (voids in crystals) or a two-phase model

(coexistence of completely crystalline andcompletely amorphous regions). Crystallinity isdefined as the presence of three-dimensionalorder on the level of atomic dimensions.

In reality, segments are ordered to variousdegrees. Since most experimental methods aresensitive to different types and degrees of order,various ‘‘degrees of crystallinities’’ are founddepending on the experiment. The degree ofcrystallinity is the fractional amount of crystal-linity. Stretched poly(ethylene terephthalate)has, for example, a degree of crystallinity of59% by IR spectroscopy, 20% by density deter-mination, and 2% by X-ray diffraction.

5.2.4. Morphology

Earlier experimental findings were interpreted interms of the two-phase model of partially crys-talline polymers: the coexistence of crystallinereflexes and amorphous halos in X-ray diagrams,the independence of X-ray short periodicities onmolar masses, the disappearance of X-ray longperiodicities with increasing molar masses, low-er macroscopic densities than predicted by X-raydensities of unit cells, broad melting ranges,optical birefringence of oriented polymers, andheterogeneity of partially crystalline polymersagainst chemical reactions.

In 1957, however, three different groupsfound that rhombic platelets are obtained if verydilute solutions of polyethylene are cooled. Sim-ilar platelets of 5 – 20-nm thickness are nowknown from many other crystallizable polymers

Table 20. Crystal structure of some polymers

Lattice constants Angles of unit cell

Polymer Nu a b c a b g Helix Crystal

nm nm nm � � � type system

PE I a 2 0.742 0.495 0.254 90 90 90 21 R

II a 2 0.809 0.479 0.253 90 90 107.9 21 M

PP, st 8 1.450 0.560 0.74 90 90 90 21 R

it a a 12 0.665 2.09 0.495 90 99.6 90 31 M

it b a 3 0.638 0.638 0.633 90 90 120 31 VI

it g a 12 0.647 2.140 6.50 89 100 99 31 T

PB, it I a 18 1.769 1.769 0.650 90 90 90 31 VI

II a 44 1.485 1.485 2.060 90 90 90 113 IV

III a 8 1.238 0.892 0.745 90 90 90 41 R

aNu¼Number of monomeric units per unit cell.bCrystal modification.cR¼(ortho)rhombic; M¼monoclinic; VI¼hexagonal; T¼triclinic; IV¼tetragonal.


(e.g., see Fig. 18). Electron diffraction showedsharp reflections typical of single crystals andchain directions perpendicular to the surface ofthe platelets. Since the contour lengths of thechains are greater than the thicknesses of theplatelets, chains must be folded back as shownin Fig. 16 – L.

Crystallization from polyethylene melts sim-ilarly shows stacked single crystals. These lamel-lae are 75 – 80% X-ray crystalline. After oxida-tion of the surface, a 100% crystalline materialremains. The folds or the interface betweenlamellae must thus be ‘‘amorphous.’’ Variousmodels have been suggested for the surfacelayers: loose folds with adjacent reentry of thechains, a switchboard-like structure, adsorbedchains not involved in chain folding, loose orentangled cilia (tangling chain ends), and crystalbridges composed of tie molecules (Fig. 19).Electron microscopy has shown that crystalbridges exist in crystallized mixtures of high andlow molar mass polyethylenes. Such interlamel-lar connections are responsible for some remark-

able properties of partially crystalline polymers(see below). Highly crystalline polymers result iftie molecules and surface layers are removed(e.g., by grinding); these fairly low molar massmaterials are called microcrystalline polymers.

Crystallization of melts sometimes deliversspherical, polycrystalline entities (Fig. 20). Thesespherulites exhibit radial symmetry. They consistof lamellaewith tangential chain axes (Fig. 21A);radial chain axes seem to be unknown (Fig. 21B).The formation of spherulites can be controlled bythe crystallization temperature, the cooling rate,and the addition of nucleating agents.

Spherulites lead to opaque plastics if theirdiameters are greater than one-half the wave-length of incident light and their densities andrefractive indices are different for crystalline andnoncrystalline regions. The numbers and sizes ofsuch spherulites are important for the fracturebehavior of polymers.

Spherulites develop in a viscous environmentif crystallization nuclei are present and if equalcrystallization rates prevail in all three directions.

Figure 19. Models for the fine structure of lamellae of single crystalsA)Chains between two adjacent lamellae: F ¼ sharp folds, L ¼ loose loops, A ¼ adsorbed chain, C ¼ cilium, E ¼ entangledcilium, B ¼ crystal bridge or tie segment; B) Structures of lamellae: R¼Regular lamellae with sharp folds, adjacent chainreentry, void from chain ends (below) and dislocation (above); L ¼ lamellae with loose loops and adjacent reentry;S ¼ switchboard model; d ¼ crystallographic long period; Lc¼thickness of lamella; La ¼ thickness of ‘‘amorphous’’ surfacelayer (d ¼ Lc þ La)Reprinted with permission by H€uthig and Wepf Publ., Basel [5]


Different crystallization rates exist in stronglystirred dilute solutions. Polymer chains then tryto orient themselves along the flow gradients andcrystallize in an extended (nonfolded) conforma-tion. The resulting fibrils are organized in bun-dles with chains parallel to the fibril axes. These

bundles act as nuclei – substrate for the epitaxialgrowth of the remaining chains. Since the shearrate is strongly reduced between bundles, crys-tallization leads to lamellae with folded chainswhose axes are parallel to the fibril axes(Fig. 22). The resulting extended- chain struc-tures are responsible for the remarkable proper-ties of some ultraoriented polymers.

5.3. Mesophases

5.3.1. Introduction

Mesomorphic chemical compounds exhibit mi-croscopic structures (mesophases) that are inter-

Figure 20. Spherulites of it-polypropylene under the phasecontrast microscope (A) and the polarization microscope(B) 76

Figure 21. Schematic representation of spherulite structuresA) Tangential chain axes; B) Radial chain axes (hypothetical)Reprinted with permission by H€uthig and Wepf Publ., Basel[5]

Figure 22. Shish kebab structures of linear polyethylenecrystallized from rapidly stirred 5% solutions in toluene [71]A) Electron micrograph; B) Schematic draw\ing of chainarrangements


mediate between crystals with long-range three-dimensional order and liquids without long-range order (Greek:mesos ¼ middle,morphe ¼shape, form). Three types of mesophases aredistinguished: liquid crystals, plastic crystals,and condis crystals. Since liquid crystals werediscovered first and are furthermore the mostcommon of the three classes, the termmesophaseis often used as a synonym for liquid crystal.

Liquid Crystals (LCs) (! Liquid Crystals)possess a certain ordered structure like crystals,but they flow like liquids. Thermotropic liquidcrystals exhibit this phenomenon in the pure stateabove a certain solid – mesophase transitiontemperature, where the solid may be a crystal ora glass. Lyotropic liquid crystals exhibit meso-phase behavior in certain solvents above criticalconcentrations. Liquid crystalline behavior ispresent in both cases if the molecules contain‘‘mesogens’’, that are short rodlike sections thatcomprise the whole molecule as in low molarmass LCs, or segments thereof as in polymerliquid crystals (LCPs). Mesogens are anisotro-pic; they are oriented with respect to their meso-gen axes but not with respect to their positions.

Plastic Crystals exhibit order of positionsbut disorder of orientations of molecules. Theyare found for certain spherical low molar massmolecules packed in cubic lattices (i.e., they areisotropic). The absence of strong attractive forcesbetween molecules and the presence of slipplanes lead to easy deformabilities of plasticcrystals, sometimes even under their ownweight.No polymers are known that form plasticcrystals.

Condis Crystals are conformationally disor-dered crystals containing several conformationalisomers in more or less ideal crystalline positionswith respect to position and orientation of seg-ments (conformational isomorphs). An exampleis the hexagonal high-pressure phase of polyeth-ylene extended- chain crystals. It is often difficultto determine whether polymer crystals are nor-mal or condis crystals.

On cooling, thermotropic liquid crystals ei-ther crystallize or solidify to ‘‘mesomorphicglasses’’ with retention of their liquid crystalstructures. These glasses do not carry specialnames, but since ‘‘liquid crystalline glass’’ and

similar names are oxymorons, the terms ‘‘LCglass,’’ ‘‘PC glass,’’ and ‘‘CD glass’’ have beensuggested for the three classes of mesomorphicmaterials. The LCPs are used mainly as LCglasses not as liquid crystals per se, except inprocessing.

Condensed matter can thus exist in several ofthe five possible classes of pure phases:completely ordered crystal oC, mesomorphicglass mG, amorphous glass aG, ordered meso-phase oM, and isotropic melt (liquid) iL. Seventypes of biphasic materials exist: oC þ mG, oCþ aG, oC þ oM, oC þ iL, mG þ aG, mG þiL, oM þ iL, and three types of triphasic materi-als: oCþmGþaG, oC þ mGþiL, oC þ oM þiL. Since each class can be subdivided further,many physical structures (and thus properties)are possible for the same polymer.

Mesophasic polymers are characterized bydomains of microscopic size (see below). ‘‘Mi-crodomains’’ of similar size are also exhibited bycertain block copolymers and, in much smallersizes, by ionomers.

5.3.2. Types of Liquid Crystals

Liquid crystals and LC glasses are generated byrod- or disclike mesogens, which either comprisethe whole molecule (as in low molar mass LCs)or sections of it (LCPs). Examples are

where X ¼ O, OOC, COO, etc.; Y ¼ COO,p-C6H4, CH¼CH, N¼N, etc.; R ¼ CO(CH2)nCH3, etc.; and phenylene residues maybe replaced by 1,4- cyclohexane rings. Thelengths of polymer mesogens are often compa-rable to those of repeating units; they seem to beidentical with respect to persistence lengths.

Rodlike mesogens are also called calamitic(Greek: calamos ¼ reed) and disclike ones dis-cotic. Calamitic liquid crystals are further sub-divided into smectic, nematic, and cholestericmesophases. Smectic LCs show fan-shapedstructures under the polarization microscope;they feel like soaps (Greek: smegma ¼ soap).


Nematic LCs form threadlike schlieren (Greek:nema ¼ thread). Cholesteric LCs exhibit beau-tiful reflective colors,whichwere first discoveredwith cholesterol.

The birefringence of LCs originates from theanisotropy of mesogens, which are more or lessaligned in microscopic domains with diametersin the micrometer range. These alignments leadto different refractive indices parallel and perpen-dicular to the direction of polarization of incidentlight. The domains themselves are arranged ran-domly. The presence of birefringence however isnot proof for the existence of mesogens; it mayalso result from higher-melting crystallites inpartially molten polymers or from crystallitesin partially molten polymers or from crystallitesin gels or concentrated solutions.

Liquid crystals are turbid because their do-mains are anisotropic structures whose dimen-sions are greater than the wavelength of incidentlight. At a certain ‘‘clearing temperature,’’ thesedomains melt to a transparent (isotropic) liquid.

The soaplike character of smectic LCs is dueto two-dimensional, layerlike arrangements ofmesogens (Fig. 23). At present, twelve differentsmectic types are known: four with the averagedirection of the long axes perpendicular to layerplanes and seven with tilted axes. Examples aretype S-A with mesogens perpendicular to thelayer planes; type S-B, the same but with perfecthexagonal packing of mesogens; type S-C, withmesogen axes at an angle to the planes, etc.

Nematic Mesophases (Fig. 23, N) are one-dimensionally ordered. The principal axes ofmesogens are more or less parallel to each other;the centers of mass are however distributed atrandom.

Cholesteric Mesophases (Fig. 23, N – C)are observed only with chiral mesogens. Theyconsist of layers of nematically ordered meso-

gens. These layers have a sense of rotation rela-tive to each other due to the presence of chiralitycenters in mesogens. Cholesteric mesophases arethus screwlike nematics.

Discotic Mesophases may exist in many dif-ferent structures. The disclike mesogens are ran-domly arranged in nematic-discotic types(Fig. 23, N – D) but stacked like coins in colum-nar-discotic ones (Fig. 23, C – D).

5.3.3. Mesogens

Mesogens of polymers can be contained in mainchains (MC-LCPs) or in side chains (SC-LCPs).Thermotropic MC-LCP glasses are used as engi-neering plastics; lyotropic MC-LCP glasses, forfibers. Thermotropic SC-LCPs are not used com-mercially at present but may find use in opticalrecording devices.

Mesogens usually constitute the whole mole-cule in low molar mass LC molecules. In macro-molecules, this is true only for dissolved helicesup to certain molar masses. Such helicogenicmacromolecules are rigid rods at small molarmasses but become coillike at very high degreesof polymerization (cf. the behavior of short andvery long garden hoses). This behavior is dem-onstrated by the molar mass dependence of theirintrinsic viscosities, which are measures of themolecule volume per unit mass (Fig. 24). Rod-like molecules are characterized by their axialratio (aspect ratio) L (length/diameter).

All other polymer chains form either flexibleor semiflexible coils in dilute solution or in theirisotropic melts (see examples in Fig. 25). Semi-flexible (wormlike) chains SF allow rotationsaround some of their chain bonds. The rodlikecharacter of their segments is however preservedin melts or concentrated solutions if the chainaxes remain linear or if the segment linearity can

Figure 23. Schematic representation of mesogens in different types of mesophasesS ¼ smectic (types A andC); N ¼ nematic; N–C ¼ nematic cholesteric; C–D ¼ columnar discotic; N–D ¼ nematic discoticReprinted with permission by H€uthig and Wepf Publ., Basel [5]


be restored by a crankshaft motion. Conjugatedbond structures are helpful but not necessarilyrequired for mesogens since, for example, 1,4-phenylene rings may be replaced by 1,4- cyclo-hexylene units.

Linear chain axes are present in poly( p-phe-nylene) (PPP) or poly( p-phenylene benzoxa-zole) (PBO). Crankshaft motions around thechain axes are possible in the conjugated chainsof poly(p-phenylene vinylene) (PPV), the par-tially conjugated chains of poly( p-hydroxyben-zoic acid) (PHB), and even in the nonconjugatedpoly( p-phenylene alkylenes) as long as evennumbers of methylene groups are present be-tween phenylene rings as in poly( p-phenyleneethylene). Semiflexible molecules are character-ized by their persistence lengths a or their Kuhnlengths LK ¼ 2 a.

Rodlike molecules and semiflexible mole-cules with long persistence lengths form manyphysical bonds between parallel chains. The totalenergy of such assemblies is so high that indi-vidual intramolecular chemical bonds rather thanall of the physical bonds are broken upon heat-ing: these molecules decompose instead of pro-ducing thermotropic mesophases. They mayhowever form lyotropic mesophases in suitablesolvents. An example is poly( p-phenylenebisbenzoxazole).

The ‘‘stiffness’’ of the chain segments can beremoved or reduced by several means (Fig. 26).

Figure 24. Molar mass dependence of intrinsic viscosities ofwormlike chains(*) Helices of poly(g-benzyl-L-glutamate) (PLBG) in N,N-dimethylformamide at 25 �C; (.) double helices of deoxyr-ibonucleic acids in dilute aqueous NaCl solutions at 20 �C.The twopolymers are comparable because the helix diametersare similar (1.5 nm for PLBG, 2.0 nm for DNA). Numbersindicate exponents a in Equation (5)Reprintedwith permission byH€uthig andWepf Publ., Basel [5]

Figure 25. Examples of rodlike (R), wormlike or semiflexible (SF), and flexible (F) molecules and segments. See text forfurther explanation.Reprinted with permission by H€uthig and Wepf Publ., Basel [5]


Bulky substituents prevent the parallelization ofchains; they ‘‘frustrate’’ crystallization. Nonlin-ear chain elements (such as ortho and metasubstituents) work in the same way. Flexiblechain segments reduce the persistence lengthsof the chains.

5.3.4. Lyotropic Liquid CrystallinePolymers

Molecule axes of low molar mass rodlike mole-cules are disordered in isotropic melts, whereasmesogen axes are more or less parallel to eachother in nematic and smectic mesophases. Veryshort rods resemble spheroids. They can arrangethemselves in various stable ways, but the paral-lel ordering need not be much more stable thanother arrangements. Therefore, a critical axialratio exists above which the simple geometricanisotropy is sufficient to stabilize a mesophase.

This critical axial ratio has been calculatedwith the lattice theory of polymer solutions asLcrit�6.42. A geometric stabilization by repul-sion is insufficient for L<Lcrit and the mesogensmust exert additional orientation-dependent at-tractive forces.

In solution, repulsive forces between meso-gens can act only at sufficiently high mesogenconcentrations. At a critical volume fraction fp,phase separation occurs into a polymer-rich me-sophase and a dilute isotropic phase. The depen-dence of fp on L can be described to a firstapproximation by [77]

fp � 8ð1�2L�1Þ=L ð59Þ

The axial ratio L is the molar mass-dependenttrue axial ratio of rodlike molecules (i.e., helices)and the molar mass-independent Kuhn length ofsemiflexiblemolecules. Equation (59) is remark-ably well fulfilled for both helical and semiflexi-ble molecules (Fig. 27). An exception is thetobacco mosaic virus, probably because of addi-tional charge effects that are not considered bythe theory.

Lyotropic mesophases are formed by the he-lices of tobacco mosaic virus (c>2%) and deox-yribonucleic acids (c>6%) in dilute aqueous saltsolutions as well as by poly(a-amino acids) inhelicogenic solvents, e.g., poly(g-methyl L-glu-tamate) in dichloromethane – ethyl acetate

Figure 26. Flexibilization of rigid chain segments by frustrated crystallization (FC), nonlinear chains (NL), or flexible chainelements (FL); M ¼ mesogen-forming monomeric units; B ¼ stiffness-breaking unitsReprinted with permission by H€uthig and Wepf Publ., Basel [5]

Figure 27. Critical volume fractionsfp for phase separations

of isotropic solution ! nematic mesophase as function of L[i.e., the axial ratio of helical (rigid) molecules (circles) andtheKuhn length of semiflexiblemolecules (triangles, square)]*Tobacco mosaic virus; solid line: prediction ofEquation (59)Reprinted with permission by H€uthig and Wepf Publ., Basel[5]


(12 : 5) (c>15%). Hydroxypropyl cellulose(HPC) forms a cholesteric mesophase at roomtemperature in water at wHPC>0.41.

On shearing, mesophase domains becomeoriented with respect to the mesogen axes(Fig. 28). This alignment becomes frozen-in onrapid quenching of thermotropic LCs or by pre-cipitation of lyotropic ones into baths (half-lifesof orientation between a few seconds and a fewhundredths seconds). The resulting LC glassespossess good orientations of mesogen axes in theshear direction (e.g., fiber direction), high tensilestrengths, and low extensibilities.

A number of LC fibers are produced commer-cially.Poly( p-phenyleneterephthalamide) (PPB –T) was originally spun from concentrated sulfuricacid solutions, whereas chlorinated N-methyl pyr-rolidine is now used:

A similar copolyamide is also on the market

Even better LC fibers are produced from poly( p-phenylene-2,6-benzoxazoles) and poly( p-phenylene-2,6-benzthiazoles) (PBT), which arespun from poly(phosphoric acid) solutions, atpresent on a bench scale. Both ‘‘cis’’ (shown)and ‘‘trans’’ (X and N exchanged at one ring)structures are known:

5.3.5. Thermotropic Liquid CrystalPolymers

Non-Newtonian shear viscosities of liquid crystalpolymers drop drastically with increasing shearrates due to the orientation of mesogen axes uponshearing.Lessenergyis thusneededforprocessingthermotropic LCPs than isotropic thermoplastics.The high orientation times permit a freezing-in ofthe mesogen orientation in injection molding, forexample. Because of the higher than usual moduliof elasticity and tensile strengths, such LCPs arealso called self-reinforcing polymers.

The first self-reinforcing polymer was thecopolyester X7 G with 60 mol% p-hydroxyben-zoyl and 40 mol% terephthaloyl glycol units. Itis no longer produced because the less expensiveglass-fiber-reinforced saturated polyesters pos-sess similar properties. Xydar and Vectra are,however, industrially produced:

Polymeric side- chain LCs can serve for thethermooptical storage of information. A guidedlaser beam increases the temperature locally,whereupon phase transformations occur. Thechange of order can then be frozen-in on coolingbelow the glass transition temperature. The res-olution is ca. 0.3 mm.

5.3.6. Block Copolymers

Block copolymers consist of two and moreblocks of constitutionally or configurationally

Figure 28. Alignment of mesogen axes upon shearingA) Mesophase domains in liquid crystalline state at rest; B)During shearing or as LC glass with ‘‘frozen in sheared state’’


different monomeric units (e.g., An – Bm, An –Bm – An). In most cases these blocks are thermo-dynamically or kinetically immiscible becausetheir homopolymers An, Bm, etc., are not misci-ble. The demixing of block copolymers cannotproceed, however, to macroscopic phase separa-tions because the blocks are chemically coupled.Similar blocks of different block copolymer mo-lecules can thus only aggregate and form do-mains in a matrix of the other blocks. Thisphenomenon is called microphase separation.

Three different applications of block copoly-mers are known: polymeric detergents, thermo-plastic elastomers, and compatibilizers forblends. Polymeric detergents consist of hydro-philic and hydrophobic blocks. Examples are themultiblock copolymers from watersoluble ethyl-ene oxide blocks [– (OCH2CH2)n –] and water-insoluble propylene oxide blocks – [OCH2CH(CH3)]n –. The hydrophobic blocks associate inwater, which produces high viscosities.

A similar action is exerted by compatibilizersfor nonmiscible blends of An and Bm polymers.These polymers are Ap – Bq diblock copoly-mers: the Ap block resides in the An phases andthe Bq block in the Bm ones. Compatibilizers thusanchor the two types of phases (Fig. 29).

Thermoplastic Elastomers consist of tri- ormultiblock copolymers. Triblock copolymersSn – Bm – Sn possess a soft center polybutadieneblock – Bm – (glass transition temperature be-low use temperature) and two hard end polysty-rene blocks Sn – (glass transition temperatureabove use temperature). Below certain m/n ra-tios, styrene blocks form sphericalmicrodomains

in a continuousmatrix of butadiene blocks. Thesespherical domains thus act as cross-linking unitsin an elastomer (Fig. 29, S). The hard domains‘‘melt’’ above their glass transition temperatures,and the block copolymers can then be processedlike thermoplastics.

The morphology of diblock copolymers isgoverned mainly by the relative spatial require-ments of the blocks. Both blocks, if independent,would form unperturbed random coils. If theunperturbed volumes of both blocks are of equalsize, all An blocks would line up in one layer andall Bm blocks in another because the blocks are(1) coupled to each other and (2) incompatible.TheAn layer faces another An layer, where theAn

blocks are coupled toBm blocks, etc. (Fig. 29, L).The diblock polymers thus form lamellae with athickness of two coil diameters. Similar struc-tures result for triblock polymers Ar – Bm – Ar,where r ¼ n/2.

If the volume of the An blocks is much lowerthan the volume of the Bm blocks, then the An

blocks can no longer be packed into layers with-out violating the demand for tightest packing ordeviating from the shape of unperturbed coils.Both possibilities are energetically unfavorable,and the smaller An blocks thus cluster togetherand form spherical domains in a continuousmatrix of the larger Bm blocks. If the An blocksare somewhat larger (but not big enough to formlamellae), then cylinders would result (Fig. 30).

A great number of thermoplastic elastomersof both the triblock and the multiblock type isknown [67]. Their chemical structures rangefrom (styrene)n – (butadiene)m – (styrene)n tri-block copolymers to polyether – urethane multi-

Figure 29. Arrangement of An blocks (with A units .) and Bm blocks (with B units*) in diblock (C, L) and triblock copoly-mers (S)C: compatibilizers at an interface - - -; S: spherical An domains in continuous matrix Bm; L: lamellae of An and Bm


block polymers, ethylene – propylene copoly-mer – polyolefin blends, polyether – esters, andgraft copolymers of butyl rubber onpolyethylenes.

5.3.7. Ionomers

Ionomers are copolymers from primarily hydro-phobic monomers with small amounts of ioniccomonomers. The ionic groups may be in themain chain or in substituents. Four different typesof ionomers are produced commercially.

Surlyn, EEA, and Nafion are synthesized bydirect copolymerization of the corresponding

monomers. Thionic results from the postpoly-merization sulfonation (< 5%) of the diene units(usually 5-ethylidene-2-norbornene) of the pri-mary ethylene – propylene – diene (EPDM)rubber. Both EEA and Nafion are used as acids,whereas Surlyn and Thionic are obtained byaftertreatment that leads to sodium or zinc salts.

The introduction of ionic groups into hydro-phobic polymers leads to ion associations andsubsequently to microphase separations. The ionassociation is controlled by the coordinationnumber of the ions; that is, sodium ions withvalence 1 and coordination number 6 are as good

cross-linkers as zinc ions with valence 2. Cross-linking by ions does not occur via ion pairs but

Figure 30. Morphology of styrene – butadiene diblock copolymers as a function of the mass fraction of the styrene units.White: polystyrene blocks (PS); black: polybutadiene blocks (BR). The block length distribution may be (m) molecularlyhomogeneous (theory), (n) narrow, or (b) broadS ¼ Spherical domains, C ¼ cylinders (rods), L ¼ lamellae (layers). Upper row: predictions of Meier theory; rows 2 – 5:schematic after experimental results of many authorsReprinted with permission by H€uthig and Wepf Publ., Basel [5]


via clusters and domains of many ions. Theseionic bonds dissociate at higher temperature, andthe ionomers can then be processed like thermo-plastics. At lower temperature, they behaveeither as thermoplastic elastomers (TG of poly-mer segments lower than use temperature) or as‘‘reversible’’ thermosets (TG of segments higherthan use temperature).

5.4. Gels

Chemically lightly cross-linked polymers swellupon addition of solvent to form gels. The maxi-mum degree of swelling results from the attemptof segments located between cross-linking sitesto attain their energetically most favored coildimensions which in turn is counteracted by theelastic retraction due to cross-links. Physicallycross-linked polymers behave in the same way ifthe physical cross-links (crystallites, ion clusters,etc.) survive the dissolution process.

The latter phenomenon is utilized in poly(vinyl chloride) pastes. The strong dipole – di-pole interactions between C–Cl bonds leads toassociations of chain segments, which at roomtemperature resist dissolution by plasticizerssuch as phthalates, adipates, sebacates, or ci-trates. Heating of PVC with these plasticizersand subsequent cooling leads to gelation byformation of a lightly physically cross-linkednetwork. Plasticized PVC thus behaves like anelastomeric material. The physical cross-linksdissociate at higher temperature, and the result-ing PVC paste can be processed with extruders orroll mills.

5.5. Polymer Surfaces

5.5.1. Structure

Outer layers of solid or liquid polymers do notexhibit – against air, water, metal surfaces, etc. –the same average composition as the interiors ofthese polymers. Groups or segments with thelowest Gibbs interfacial energy will reside pref-erentially at the surface or interface. Surfacestructures may also be altered by chemical attackduring processing or on prolonged use (e.g., byoxidation) or by physical processes such astranscrystallization.

This behavior can be studied by a wide varietyof new spectroscopic methods, for example, theconcentration of immediate surface groups byFourier transform infrared spectroscopy (FT-IR);the composition of the upper 0.3 – 0.5-nm layerby ion scattering spectroscopy (ISS, LEIS); of theupper 1 – 10 nm by photoelectron spectroscopy[UPS, PE (S)], electron spectroscopy for chemi-cal analysis (ESCA, XPES, XPS, IEE), andAuger spectroscopy (AES).

These methods have shown that poly-(2-vi-nylpyridine) and poly(4-vinylpyridine) havemuch more hydrophobic surfaces than theirchemical structure indicates: CH2 andCHgroupsface the surface; pyridine residues (C5H4N), theinterior. Imide – carbonyl residues of polyi-mides, on the other hand, are preferentially foundat the surface and aromatic rings in the interior.The surface is enriched by siloxane residues inpolycarbonate – polydimethylsiloxane block co-polymers but by styrene units in polystyrene –poly(ethylene oxide) block copolymers. Sincethe surface energy depends on the contact (air,water, metals, etc.) and also on kinetic effects(thermal history, solvents, etc.), one and the samepolymer may possess various surface composi-tions and thus also surface properties.

5.5.2. Interfacial Tension

Interfacial tension is the force that acts at theinterface between two phases; it is called surfacetension for the interface condensed phase – gasphase.

Surface tensions g lv of liquid polymers againstair decrease with the two-third power of themolar mass according to

g lv ¼ g¥lvþKe�M�2=3 ð60Þ

They do not vary markedly with temperature.Typical values (at 150 �C) range from 13.6 mN/m (polydimethylsiloxane), 22.1 mN/m (it-poly-propylene), 28.1 mN/m (polyethylene), and33.0 mN/m poly(ethylene oxide). At present, nocorrelation of these surface tensions with chemi-cal constitution is possible because the surfacestructures of liquid polymers are unknown.

Interfacial tensions between two liquid poly-mers are always lower than surface tensions.They are low for two apolar polymers but higher


if one polymer or both of them are polar. Forexample, the interfacial tension of polyethyl-ene – it-polypropylene is only 1.1 mN/m, butthat of polyethylene – poly(ethylene oxide) is9.5 mN/m and poly(ethylene oxide) – polydi-methylsiloxane 9.8 mN/m.

The interfacial tensions between solid poly-mer and air are generally unknown. They do notdiffer markedly, however, from the critical sur-face tensions determined by the Zisman method.In this method, the liquid – air surface tensionsof various liquids are plotted against the cosine ofcontact angles q of these liquids against air andextrapolated to cos q ! 0. The resulting ‘‘criti-cal’’ surface tensions of polymers are alwayslower than the surface tension of water: polyte-trafluoroethylene, 18.5; polyethylene, 33; poly(vinyl alcohol), 37; polyamide 66, 46; and urea –formaldehyde resins, 61 mN/m. Fluorinatedpolymers have especially low critical surfacetensions. They are not wetted by water(72 mN/m) or oils and fats (20 – 30 mN/m) andare therefore used as surface coatings to preventsticking.

5.5.3. Adsorption

Macromolecules possess many adsorbablegroups and segments. The type of adsorptiondepends on the adsorption energy per segment(group), the concentration of adsorbable macro-molecules, and the duration of the experiment.

‘‘Adsorption equilibria’’ are established inminutes to hours at smooth surfaces but maytake days to attain at rough surfaces or powders.The adsorption time increases with the concen-tration and molar mass of the polymer.

Polymer coils tend to overlap even in fairlydilute solutions: the adsorbed polymer layers arealmost alwaysmultilayers, except for the adsorp-tion of oligomers (X<10 – 100) or from verydilute solutions (volume fractions <10�4 –10�3). At higher concentrations or molar masses,adsorbed amounts and structures of polymerlayers are mainly kinetically controlled. Reorga-nization may occur with time: for example, theadsorption of polar polymers at polar surfacescan change from an initial loose loop structure toa more compact, flat covering. The layer of poly(ethylene oxide) adsorbed on chromium surfacesis only ca. 2 nm thick and so tightly packed that

the refractive index of the adsorbed layer isidentical with that of the crystalline polymer.The thickness of the surface layer of polystyreneof M ¼ 176 000 g/mol adsorbed from a 5 mg/mL solution in the thermodynamically bad sol-vent cyclohexane is however about 27 nm (i.e.,identical with the end-to-end distance in theunperturbed state). The physical structures ofadsorbed polymers obviously play an important,yet widely unknown, role in many technologicalapplications of polymers.

6. Thermal Properties

6.1. Molecular Motion

6.1.1. Thermal Expansion

Isotropic bodies expand upon heating equally inall three spatial directions because of the increas-ing thermal motions of atoms, groups, and mo-lecules. The expansion is characterized by thecubic expansion coefficient b ¼ V �1 (q V /q T )p, which is usually converted by b ¼ 3 ainto the linear expansion coefficient a ¼ L �1

(qL /q T )p. Such isotropic materials are, forexample, diamond (a ¼ 1.06�10�6 K�1), iron(12�10�6 K�1), water (70�10�6 K�1), and car-bon disulfide (380�10�6 K�1) (all data at25 �C). All of these materials exhibit the sametypes of bonds in the three directions: all covalentbonds between carbon atoms in diamond, allmetallic bonds between iron atoms, all hydrogenbonds between water molecules, and all disper-sion forces between CS2 molecules.

Polymer chains are however anisotropic: theintramolecular bonds along the chain are chemi-cal (almost always covalent); the intermolecularbonds perpendicular to the chain, physical (dis-persion forces, dipole – dipole interactions). Onthermal expansion of polymer crystals, chainscontract because of the increasing amplitude ofthe lateral motions. The thermal expansion coef-ficient in the chain direction is thus zero tonegative, whereas the overall expansion coeffi-cient is positive. The linear thermal expansioncoefficients of polymers are thus averages overthe three spatial directions; they lie betweenthose of metals and liquids. Typical values area ¼ 60�10�6 K�1 (polyamide 6) and 80�10�6

K�1 [poly(vinyl chloride)].


Significant problems may thus arise due todifferent expansion coefficients for polymer –metal composites upon thermal stress. Anotherproblem is the low dimensional stability of poly-mers on temperature change. This problem maybe aggravated by a concomitant change of thewater content of polymers or by recrystallizationphenomena, both of which can lead to warping.

6.1.2. Heat Capacity

The molar heat capacity can be 3 R per atomaccording to the law of equal distribution ofenergy. In reality, degrees of freedom are alwaysfrozen in and the molar heat capacity is lowered.Empirically, a value of ca. 1 R has been found forsolid polymers at room temperature. Poly(2,6-dimethylphenylene oxide) [(C8H8O)n] at 25

�Chas a specific heat capacity of 1.22 J K�1 g�1

and a molar heat capacity (per monomeric unit)of 146.4 J K�1 mol�1. The molar heat capacity(per mole of atoms) is thus 146.4 J K�1 mol�1/17 ¼ 8.61 J K�1 mol�1 (i.e., approximately1 R ¼ 8.314 J K�1 mol�1).

Below the glass transition temperature TG,heat capacities are not influenced by the degreeof crystallinity of the polymer. At TG, a stepwiseincrease is observed. The heat capacity passesthrough a maximum a few degrees below themacroscopic melting temperature; that is, thetrue melting temperature is given by the upperend of the melting range where the largest andmost perfect crystals melt.

6.1.3. Heat Conductivity

Conventional polymers are electrical insulators.Heat is thus not transported by electrons but byelastic waves (phonones in the corpuscular mod-el). The free path length of phonones is defined asthe distance at which the intensity of elasticwaves has decreased to 1/e. This free path lengthis about 0.7 nm for glasses, amorphous poly-mers, and liquids; it is practically independentof temperature. The slight decrease of heat con-ductivities (thermal conductivities) of amor-phous plastics and elastomers below their glasstransition temperatures must thus be caused bythe decrease of heat capacities with decreasingtemperature. For crystalline polymers, a strong

decrease of heat capacities is observed at theirmelting points because packing densities declinedrastically at these temperatures.

6.2. Thermal Transitions andRelaxations

6.2.1. Overview

Thermal transitions and relaxations are charac-terized by large changes of physical properties atthe corresponding temperatures. In a true thermaltransition, chemical compounds are in equilibri-um on both sides of the transition temperature.An example is the melting transition.

Thermal Relaxations, on the other hand, arekinetic effects. They depend on the frequency ofthe experimental method and thus on the timescale. Typical thermal relaxations are caused bythe onset of translations and rotations of charges,dipoles, and chemical groups (i.e., by atomicmotions).

Some experimental methods work at frequen-cies that such relaxations appear to be thermaltransitions. The best-known example is the glasstransition temperature at which hard, glassypolymers convert to soft, rubbery materials andvice versa. Inmany cases, a thermal effect cannotbe unambiguously classified as either transitionor relaxation.

Thermal transitions and relaxations can bedetected and determined by many different ex-perimental methods. The most commonly ap-plied methods for the determination of thermaltransitions are differential thermoanalysis (mea-sures temperature differences between specimenand standard on heating or cooling with constantrate), differential scanning calorimetry (does thesame for enthalpy differences), thermomechani-cal analysis (deformation of specimen underload), dynamical – mechanical analysis (eitherfree or forced vibration of specimen), and tor-sional braid analysis (specimen on vibratingsupport). Figure 31 shows a typical thermogram.

Many methods are available for the study ofmolecular motions and thus thermal relaxations.These methods work with frequencies n whichcorrespond to correlation times tc of 10

�12 s <1/n<106 s (11.5 d). Typical methods includequasi-elastic neutron scattering (10�12<tc/


s<10�8), NMR spin-lattice relaxation (10�12

< tc/s<10�5), dielectric relaxation (10�10 <tc/s<10�5), and photon correlation spectroscopy(10�4<tc/s<102). Thermal relaxations further-more manifest themselves in sudden changes ofmechanical properties, such as rebound elasticity(tc/s�10�5), penetrometry (tc/s�102), mechani-cal loss (103<tc/s<107), and thermal expansion(tc/s�104). Slow methods (high tc) are called

‘‘static’’ methods; fast ones, ‘‘dynamic.’’ Transi-tion – relaxation phenomena are also detected byseveral empirical, standardized methods thatmeasure the resistance of specimens against flowunder various loads (Vicat temperature, heat dis-tortion temperature, Martens temperature, etc.).

Various characteristic signals are observed at afixed temperature for a given frequency (see insertin Fig. 32). They often cannot be correlated with

Figure 31. Idealized thermogram of a partially crystalline polymer with solid – solid transition Tss, glass transitiontemperature TG, liquid – liquid transition Tll, maximum crystallization temperature Tcryst, melting temperature TM, maximumtemperature Treact of a chemical transformation, and maximum temperature Tdecomp of chemical degradationReprinted with permission by H€uthig and Wepf Publ., Basel [5]

Figure 32. Dependence of inverse relaxation temperature 1/T on the logarithm of reduced frequency n/T for various relaxationprocesses of a low-density polyethyleneInsert shows the mechanical relaxation spectrum at n ¼ 1000 Hz.Reprinted with permission by H€uthig and Wepf Publ., Basel [5]


molecular processes and are commonly indicatedwith descending temperature by letters in thesequence of the Greek alphabet, starting with themelting temperature (crystalline polymers, sub-script c) or glass transition temperature (amor-phous polymers, subscript a).

The various methods work at different fre-quencies and thus give different relaxation tem-peratures for the same molecular process. Thefrequency dependence of relaxation tempera-tures can be described by the Eyring equationfor rate processes:

n ¼ ðkBT=2phÞ exp ð�DH„=RTÞ exp ðDS„=RÞ ð61Þwhere kB is the Boltzmann constant, h the Planckconstant, DH „ the activation enthalpy, and DS „

the activation entropy. Transformation of Equa-tion (61) leads to

1

T¼ R

DH„ �DS„

Rþln

kB2ph

� ��ln

nT

� �ð62Þ

In a (1/T ) ¼ f [ln(n/T )] plot, lines for variousprocesses intersect at the melting temperature(TM ¼ 131 �C in Fig. 32). Such common inter-sects seem to be general for nonhelical polymers.

6.2.2. Crystallization

The crystallization of coillike polymers fromdilute solutions leads to platelets (Fig. 18) in

which folded polymer chains are arranged withtheir stems perpendicular to the fold surface(Fig. 19). From concentrated solutions and meltsat rest, lamellae are organized into spherulites(Fig. 21), which may be transformed to rowstructures by shearing or drawing (Fig. 33).

Crystallization can be subdivided into twoelementary processes: primary nucleation andcrystal growth (secondary nucleation). Both pro-cesses determine the crystallization rates, whichdepend strongly on both temperature and polymerstructure. At 30 K below the melt temperature,the linear crystallization rate may, for example,range between 5000 mm/min for polyethyleneand 0.01 mm/min for poly(vinyl chloride). Sym-metrically structured polymers usually crystallizerapidly; polymers with bulky groups or low tacti-cities, only slowly. Quenching of poly(ethyleneterephthalate) melts leads, for example, to amor-phous polymers, whereas quenching of polyeth-ylene melts never gives amorphous polymers,even if liquid nitrogen is used.

Primary Nucleation may be homogeneous(spontaneous, sporadic, thermal) or heteroge-neous (simultaneous, athermal). Homogeneousnuclei are formed from segments of the crystal-lizing polymer molecules; they are very rare.Heterogeneous nuclei result from extraneousmaterials such as additives, dust particles, con-tainer walls, or specially added nucleation

Figure 33. A) Formation of spherulites from lamellae on crystallization of melts at rest; B) Transformation of spherulites intorow structures by shearing or drawing in l direction.Reprinted with permission by H€uthig and Wepf Publ., Basel [5]


agents. Such nuclei must have minimum sizes of2 – 10 nm. Their concentrations can range fromca. 1 nucleus per cubic centimeter (polyoxyethy-lene) to ca. 1012 nuclei per cubic centimeter(polyethylene).

Above the melting temperature, fragments ofcrystallites may survive for certain time periods.These fragments act as athermal primary nucle-ation agents on subsequent cooling. They areresponsible for the ‘‘memory effect’’ (i.e., thereappearance of spherulites at the same locationsafter and before the melting), which occurs be-cause of low diffusion rates at very high meltviscosities.

Growth of primary nuclei occurs by a second-ary nucleation process. The growth rate is lowjust below the melting temperature because sec-ondary nuclei are formed and dissolved rapidly.About 50 K below the glass transition tempera-ture, on the other hand, motions of moleculesegments are practically zero and the crystalgrowth rate is therefore low as well. Crystalliza-tion rates must thus exhibit a maximum betweenthemelting and glass transition temperatures; themaximum crystallization rates are usually at(0.80 – 0.87) TM (in kelvin).

In addition, the entire crystallization processcan be subdivided into a primary and a secondaryphase. The primary phase comprise the conver-sion of the total volume to a solid. At the end ofthis phase, the volume may be filled (e.g., withspherulites), but not all polymer segments be-tween spherulites or between the lamellae of thespherulites may have crystallized. The polymerhas not attained its maximal crystallinity (thecrystallizability). Crystallization may thus con-tinue during the second phase. In this aftercrys-tallization, lamellae may thicken, lattices be-come more perfect, etc.

Primary crystallization can be characterizedby the Avrami equation:

f=f¥ ¼ 1�expð�z�tnÞ ð63Þwhere f ¼ fraction of crystallized volume, f¥fraction of maximal attainable crystallinity for agiven entity (e.g., spherulite), and z and n areconstants that depend on both the nature of thenucleation process (homogeneous, heteroge-neous) and the type of growing entity (rod, disk,sphere, sheaflet, etc.). The exponents n rangebetween 1 and 7; empirically, they may assumefractional values.

6.2.3. Melting

Melting is defined as the thermal transition of acrystal to an isotropic melt. The melting temper-ature TM (fusion temperature) is defined as thetemperature at which crystallites are in equilib-rium with the melt. Melting starts at the cornersand edges of crystal surfaces; in contrast tocrystallization, no nuclei are needed.

Segments of about 60 – 100 chain atomsparticipate in the melting process. During heat-ing, segments are redistributed continuously be-tween crystalline and noncrystalline regions; amelting range exists and no sharpmelting point isobserved. The melting temperature is defined asthe upper end of the melting range because thebiggest and most perfect crystals melt there.Published melting temperatures often refer tothe maxima of DT ¼ f (T) curves, however. Ob-served melting temperatures are in general lowerthan the thermodynamic melting temperatures ofperfect crystals but may be occasionally higherbecause of overheating effects.

Melting temperatures increase with molarmass and become practically constant at molarmasses of ca. 50 000 – 150 000 g/mol. Themeltcan be considered as a dilute solution of endgroups in monomeric units, and the reduction ofthe melting temperature with decreasing molarmass (i.e., increasing concentration of endgroups) can be described by the thermodynamiclaw for the lowering of freezing temperatures:

1

TM¼ 1

T0M

þ 2R

DHmM;u

!� 1

Xnð64Þ

where DHmM;u is the molar melt enthalpy per

monomeric unit, X�n the number-average degreeof polymerization, and TM and To

M are the ther-modynamic melting temperatures at finite andinfinite molar masses. Similar depression of themelting point is caused by addition of low molarmass solvents and amorphous polymers or bystatistical copolymerization; in all these cases,the term 2/ �Xn must be replaced by

ðVmu =

Vm1 Þ½ð1�f2Þ�cð1�f2Þ2� ðsolventÞ ð65Þ

ðVmu =

VmA Þ�cð1�f2Þ2� ðamorphous polymerÞ ð66Þ

½�ln xu�cð1�f2Þ2� ðstatistical copolymerÞ ð67Þ


where *V m is the partialmolar volume of solvent1, amorphous polymer A, or monomeric units uof copolymer; xu the mole fraction of units u; f2the volume fraction of crystallizable polymer 2;and c an interaction parameter.

Melting temperatures TM ¼ DHmM=DSmM are

determined by the changes in molar meltingenthalpies DHm

M and molar melting entropiesDSmM. The melting entropy results from confor-mational changes and volume changes uponmelting. The melting entropy theoretically addsR � ln 3 ¼ 9.12 J K�1 mol�1 for the formationof three conformers with equal energy and 7.41 JK�1 mol�1 for one trans and two gauche confor-mers in the case of polymethylene � (CH2)n �.The entropy change due to the volume changeshould add another 10.9 J K�1 mol�1 so that thetheoretical melt entropy of polymethyleneshould be ca. 18.3 – 20.0 J K�1 mol�1. Experi-mentally, only 9.9 J K�1 mol�1 is observed,which points toward either the existence of localorder in melts or a high segment mobility belowthe melting temperature. The latter was foundexperimentally by broad-line NMR for cis-1,4-polyisoprene (DSmM ¼ 4:8 J K�1 mol�1).

MeltingEnthalpies are usually between1 and5 kJ per mole of chain atom. Low values are to beexpected for polymers with high chain mobilitiesbelow the melting temperature (cis-1,4-polyiso-prene, aliphatic polyesters and polyethers). Highvalues are found for polymers with strong inter-actions between chains and tight packing of chainsin crystals (polyoxymethylene, it-polystyrene).Some of these strong interactions may survive themelting process; for example, most of the hydro-gen bonds of polyamides are still detected by IRspectroscopy above the melting temperature.

Thus the primary factors for high meltingtemperatures are not intermolecular interactions(e.g., cohesive energies) but reduced flexibilitiesof chains. Low melting temperatures are foundfor polymers with low rotational barriers (ester,oxygen, sulfide groups in chains), high meltingtemperatures for tightly packedhelices [polyox-ymethylene, it-poly(3-methylbutene)] and forladder and ladderlike polymers [poly( p-pheny-lene), polybenzimidazole, etc.]. Such factors areresponsible for the variation of melting tempera-tures with the number of methylene units inaliphatic polymer chains of the type �X–(CH2)n� (Fig. 34).

6.2.4. Liquid Crystal Transitions

Thermal transitions of thermotropic LC poly-mers from their crystals to smectic (Tcs) or ne-matic phases (Tcn), from smectic to nematicmesophases (Tsn), and from nematic phases toisotropic melts (Tni, clearing temperature) arethermodynamic first-order transitions. They ex-hibit steplike changes in volume, enthalpy, andentropy, just like themelting of three-dimension-al crystals to isotropic melts. Thermodynamical-ly stable phases can exist only between meltingand clearing temperatures (Tcs,Tcn<Tni); they arecalled enantiotropic phases.

Mesophases form dispersions in supercooledisotropicmelts if clearing temperatures are lowerthan melting temperatures (Tcs, Tcn>Tni). Suchphases are thermodynamically unstable com-pared to the crystalline; they are calledmonotropic.

Mesophases may be supercooled below TMTcs to smectic liquids sL* and below Tsn tonematic liquids nL* if crystallization can besuppressed. At even lower temperatures Tgn andTgs, these supercooled liquids may yield aniso-tropic glasses nG and sG, respectively. Some ofthese transition temperatures cannot bemeasureddirectly, but their existence can be deduced fromextrapolations of transition temperatures of co-

Figure 34. Melting temperatures of (*, �, �) aliphaticpolymers � [X-(CH2)n]� and (.) isotactic poly(a-olefins)� {CH2–CH[(CH2)nH]}� as function of the length n ofmethylene sequencesa) X ¼ NHCO (polyamides); b) X ¼ O (polyoxides);c) X ¼ COO(CH2)3OOC (aliphatic polyesters of trimethy-lene glycol)– � – � – � theoretical melting temperature of polyethylene


polymers to 100% of the pure mesogenic com-pound (virtual transition temperatures).

The transition temperatures Ttrans (i.e., Tcs,Tgs, Tsn, Tcn, Tgn, Tni) depend on the degree ofpolymerization X in the same way the meltingtemperature does: 1/Ttrans ¼ f (1/X). The transi-tion enthalpy DHni is always lower than thetransition enthalpies DHgs and DHsn because then ! i transition is from order to disorder, where-as the g ! s and s ! n transitions are fromorder to less order. Transition entropies of me-sophases are lower than melt entropies; theyusually have values of ca. 0.5 – 1.5 J K�1

mol�1, with DSsn<DSni.

6.2.5. Glass Transitions

Glass transitions are phenomenologically char-acterized by a change from a ‘‘hard,’’ noncrys-talline, glasslike material to a rubbery to highlyviscous ‘‘melt.’’ The viscosities at glass transi-tions are ca. 1012 Pa � s, independent of chemicalstructures. Glass transitions were thus thought tobe ‘‘isoviscous’’ phenomena. Today, glass tran-sitions are considered to occur at that physicalstate where all materials exhibit the same ‘‘freevolume.’’

Various free-volume fractions are discussedin the literature. The empirical Boyer – Simharule relates a free-volume fraction fexp to thecubic expansion coefficients b of liquid (L) andamorphous, glasslike (G) polymers and theirglass transition temperatures TG (see Table 21):

fexp � ðbL�bGÞ�TG � 0:11 0:02 ð68Þ

The Williams – Landel – Ferry (WLF) ap-proach relates a free-volume fraction fWLF to theprobability of segment movements. Empirically,values of fWLF�0.0250.01 were found; thesevalues can be calculated, for example, fromK¼fWLF/(bL�bG) and K 0¼log e/fWLF of thesemiempirical WLF equation (Eq. 69) where�log at¼D(log t ) is a shift factor

T ¼ TGþ K�log atK 0�log at

¼ TGþ 51:6�log at17:4�log at

ð69Þ

TheWilliams – Landel – Ferry equation appliesto all relaxation processes; its use is restricted totemperatures in the rangeTG< T < (TGþ100 K).

The WLF equation allows calculation of thestatic glass transition from the various dynamicglass transition temperatures if the deformationtimes (inverse effective frequencies) of themeth-ods are known. The glass transition temperaturesof poly(methyl methacrylate) (PMMA) are givenas 105 �C (thermal expansion, ‘‘static’’), 120 �C(penetrometry), and 160 �C (rebound elasticity).The same polymer may thus exhibit very differ-ent mechanical properties if subjected to differ-ent stresses; at 140 �C, PMMA behaves as eithera glass (rebound elasticity) or an elastomer(penetrometry).

The glass transition temperature indicates theonset of cooperative movements of chain seg-ments of 25 – 50 chain atoms, which can bededuced from the ratio of molar activation ener-gies and melt energies. These cooperative move-ments very probably involve trans – gauchetransitions that proceed cooperatively alonggreater distances since only small changes ofchain axes are involved according to deuteriumNMR. The participation of segments of 25 – 50chain atoms is also indicated by cross-linkingexperiments: as long as the average segmentlength Nseg between two cross-linking points isless than 25 – 50 chain atoms, no change of glasstransition temperatures is observed. AtNseg<25 – 50, TG increases with the inversemolar mass of the segments.

Since both glass transition and melt tempera-tures depend on segmental motions, close rela-tionship between these two temperatures can beexpected. The empirical Beaman – Boyer rulestates that TG�(2/3)TM, which holds reasonablywell for many polymers except for chains suchas polyethylene and polyoxyethylene for whichTG/Tm�1/2.

A vast literature exists about effects of con-stitution on TG. Cyclic macromolecules possess

Table 21. Glass transition temperatures and free-volume fractions of

polymers (for explanation of symbols, see text)

Polymer TG�C fexp fWLF ffluc

Polyethylene � 80 0.098 0.025

Polyisobutylene � 73 0.079 0.026 0.0017

Poly(butyl 20 0.13 0.026 0.0010

methacrylate)

Poly(vinyl acetate) 27 0.128 0.028 0.0023

Polystyrene 100 0.133 0.025 0.0035

Poly(methyl 105 0.118 0.025 0.0015

methacrylate)


no end groups, and thus no free-volume effectsfrom these. Small rings are furthermore strained(less possible microconformations). The greaterthe molar mass, the more microconformationscan be adopted, the greater is the chain flexibilityand the lower is TG. The same is true for segmentflexibilities of star-branched polymers and longside chains in comblike molecules (side- chain‘‘crystallization’’).

Linear relationships are found between thelogarithms of glass transition temperatures TGand the logarithms of cross-sectional areas A ofeither carbon, carbon – oxygen, or carbon –ni-trogen chains (another measure of segment flex-ibilities). The three lines intersect atA¼0.17 nm2

and TG¼141 K, which should be the lowest glasstransition temperature possible. The lowest ex-perimentally found glass transition temperature(150 K) is that of polydimethylsiloxane,� (O –Si(CH3)2)n �.

Glass transitions can be decreased (or in-creased) by copolymerization with suitablemonomers (internal plasticization) and by addi-tion of external plasticizers (see Section 4.2.5).

6.2.6. Other Transitions and Relaxations

Experimentally, a number of other transition –relaxation temperatures are observed, mostly ofunknown origin. Amorphous polymers exhibitweak ‘‘liquid – liquid’’ transitions at ca. Tll�1.2TG. Below the critical molar mass for entangle-ments, transition temperatures Tll equal flowtemperatures TF at which polymers start to flowunder their own weight. At higher molar masses,TF>Tll.

Another transition temperature TU�1.2 TMseems to exist for crystalline polymers. Thistransition has been interpreted as the dissolutionof smectic structures.

Few b-relaxations have been correlated withmolecular phenomena. An example is the fre-quency-dependent boat – chair transition of cy-clohexane rings, which occurs at e.g., � 125 �C(10�4 Hz) and þ 80 �C (105 Hz).

6.2.7. Technical Methods

The technical testing on thermal transitions andrelaxations of plastics is usually performed with

simple methods under standardized conditionsand always under load. Martens numbers mea-sure temperatures at which the specimen hasexperienced a certain bend, Vicat softening tem-peratures give the temperatures for a certainpenetration of a rod into the plastics, and theheat distortion temperatures (heat deflectiontemperatures) indicate the temperatures for acertain bending with a three-point method. Thetemperatures from these three methods do notonly depend on transitions or relaxations but alsoon the elasticity of the specimen; Vicat and heatdistortion temperatures are in addition affectedby the surface hardness. The resulting softeningtemperatures are neither identical with glasstransition nor with melting temperatures; theyare often also not a good measure of the continu-ous service temperature of a plastic.

6.3. Transport

6.3.1. Self-Diffusion

Brownian movements cause molecules and theirsegments to interchange positions in fluid phases.If all entities are of the same type, such inter-changes lead to a ‘‘self-diffusion’’, which in-volves no net transport of polymers. Self-diffu-sions can be measured by pulsed field-gradientspin-echo NMR (segments) and radioactive tra-cers (molecules).

Coiled molecules behave in their melts asunperturbed coils with low coil densities, whichare filled with segments of other coils. Self-diffusion of a segment must therefore occur byinterchanging position with a segment of anothermolecule.

Self-diffusion coefficients decrease with thesquares of molar masses (Fig. 35). According toreptation theory, this functionality is caused bytemporary (but fairly long-lived) entanglementsof polymer chains. Such entanglements cause thesudden change of molar mass dependences ofmelt viscosities above a critical molar mass Mc

(Fig. 35).The resulting topological restraints make the

polymer chain move through the maze of othersegments like a reptile through brush. Accordingto the Doi – Edwards theory, the test chain re-ptates in a tube of ca. 5-nm diameter, which isformed by other segments (Fig. 36). The theory


predicts the experimentally found functionD2¼f (M �2) albeit only forM>Mc. Experimen-tally, the same function is also observed forM<Mc, probably because end groups cause suc-cessively greater free-volume fractions, whichare assumed by the reptation theory to be molarmass independent.

The same dependence of self-diffusion coef-ficients of test chains on the squares of theirmolarmasses is theoretically predicted and experimen-tally found for test chains in higher molar massmatrices of the same constitution and configura-

tion (Mtest << Mmatrix); the molar mass of thematrix exerts no influence. If however Mtest Mmatrix, then a function Dtest¼f [(Mtest)

�1/2 �(Mmatrix)

�1] is predicted and observed.

6.3.2. Permeation

The transport of extraneous material throughpolymers is called permeation. The resulting netflow of mass is caused by differences in chemicalpotentials, that is, concentration differences (atconstant temperature) or thermal gradients (atconstant concentration). Permeation may be de-sirable as in the dyeing of textiles or the con-trolled transdermal delivery of pharmaceuticals,or undesirable as in the loss of carbon dioxidefrom plastic bottles for carbonated soft drinks orin migration of plasticizers.

Permeation of chemical compounds throughamorphous polymers below their glass transitiontemperatures or through crystalline polymersbelow their melting temperatures can occur ei-ther by flow through pores or by moleculartransport. Pores have diameters much greaterthan the diameters of permeating substances(diameter of spheres, cross section of coillikechains); the interactions of permeants and pore

Figure 35. Segmental self-diffusion coefficientsD2 (*) and Newtonian melt viscosities h of alkanes and narrow-distributionpolyethylenes (.) as function of the relative molecular mass Mr at 175

�CReprinted with permission by H€uthig and Wepf Publ., Basel [5]

Figure 36. Reptation of a test chain (black) through thesegments of a matrix (white). The ‘‘walls’’ of the tube areindicated by dotted lines.Reprinted with permission by H€uthig and Wepf Publ., Basel[5]


walls are negligible. Molecular transport, on theother hand, depends on such interactions be-tween permeant andmatrix (i.e., on the solubilityof the former in the latter). Both types of trans-port can be distinguished by their temperaturedependence: permeation coefficients of gasesdecrease with temperature at pore membranes;they increase with temperature at solubilitymembranes.

The counteraction of the two types of perme-ation can be utilized in lamination. Oxygenpermeates through pores in aluminum films butby molecular transport through polyethylenefilms. At 1 bar, permeation rates decrease from5�10�5 cm3/s for 0.025-mm-thick aluminumfilms to 5�10�13 cm3/s for the same films lami-nated with 0.025-mm-thick PE films.

The permeation coefficient P is given bythe product of the diffusion coefficient D andthe solubility coefficient S of the permeant in thematrix and, in the steady state, by the expressionto the right of the second equality sign:

P ¼ D�S ¼ Q�LA�Dp�t ð70Þ

where Q ¼ permeated amount, L ¼ thicknessof film (membrane, etc.), A ¼ area, Dp ¼ pres-sure difference, and t ¼ time. The literatureoften uses different ‘‘practical units’’ for thevarious quantities of Equation (70), for exam-ple,Q in cm3, L in mm, A in m2, Dp in atm, and tin 24 h; P is then given in (cm3 �mm)/(24 h m2

atm). If like units are used, then the unit ofP is ofcourse length2 � time�1 � pressure�1 and the unitof S is pressure�1. Permeation coefficients P*of liquids are usually measured without a pres-sure differential; their unit is cm2/s and the unitof S is 1.

PermeationCoefficients ofGases in polymersvary widely; for example, oxygen permeates 10million times faster through polydimethylsilox-ane than through polyacrylonitrile (Table 22).Gases in general, have lower permeation coeffi-cients in thermoplastics than in elastomers be-cause segmental movements of the former arefrozen-in below the glass transition temperature.Bulky substituents, orientation of polymer seg-ments, crystalline domains, and added fillers allincrease the pathway for a gas molecule througha polymer matrix; these tortuosity factors de-crease permeation coefficients.

The permeation of nondissolving liquidsthrough a polymer is proportional to tn. Theexponent n depends on the ratio of the relaxationtime of the polymer – solvent system to thediffusion time of the solvent (i.e., on the Deborahnumber DB).

Three different regimes are normally consid-ered. In the regime denoted as Case I, the mobil-ity of the permeant is much smaller than therelaxation of the polymer segments (DB<0.1).The movement of the permeant causes ‘‘instan-taneous’’ conformational changes of the polymersegments. Both permeant and polymer behave asviscous liquids: the system can be described byFickian diffusion laws (i.e., n¼1/2).

In the Case II regime, the mobility of thepermeant is much higher than the relaxation ofthe polymer segments (DB>10). The physicalstructure of the polymer does not change duringthe permeation; the polymer appears to the per-meant as an elastic body. Case II is characterizedby a sharp demarcation line between the glassyinner polymer core and the swollen zone advanc-ing with constant speed. The permeating amountis directly proportional to time (i.e., n¼1).

Relaxation and permeation become compara-ble for 0.1<DB<10. This third regime is usuallycalled anomalous diffusion or viscoelastic diffu-sion (1/2<n<1).

Table 22. Permeation coefficients of gases (P) and water vapor (P*)

through polymers at 30 �C a: P¼1�10�14 cm2 s�1 Pa�1 corresponds

to P *¼1�10�9 cm2/s at normal pressure (p¼1�105 Pa)

Polymer 1014Pcm2s�1Pa�1

109Pcm2s�1

O2 CO2 H2O

Polydimethylsiloxane 25 000 85 000 40

cis-1,4-Polyisoprene 2 000 10 000 0.3

Butyl rubber 100 500 0.1

Polystyrene

Regular 200 1 000 1

Biaxially oriented 0.1 100 0.5

Poly(ethylene terephthalate)

Regular 4 20 0.2

Biaxially oriented 0.2 1 0.2

Poly(vinylidene chloride) 0.05 0.15 0.02

Cellulose 0.03 0.1 10

Polyacrylonitrile 0.002 0.02 0.02

Required for bottles

Cola 1 0.5 0.14

Beer 0.05 0.5 0.14

aLiterature values vary widely because polymers are often not

identical with respect to crystallinity, orientation, water

absorption, etc.


7. Rheological Properties

7.1. Introduction

Materials exhibit two limiting types of behavioragainst deformation. Typicial liquids such aswater flow under their own weight and are irre-versibly deformed (viscous behavior). Typicalsolids such as iron resist deformation; they returnfrom small deformations to their former statesafter removal of loads (elastic behavior). Poly-mers commonly combine both types of behavior:they are viscoelastic materials. Their melts ex-hibit viscous behavior at small deformations andelastic properties at larger ones. Polymer solidsrespond elastically at small deformations butbegin to flow at larger ones.

Polymer melts and solutions have extremelyhigh viscosities which may, in addition, be de-pendent on deformation rates and duration ofthe experiment. Air has, for example, a viscosityof 10�5 Pa � s; water, 10�3 Pa � s; and glycerol,1 Pa � s, whereas polymer melts exhibit viscosi-ties of ca. 102–108 Pa � s.

Three types of viscosity are usuallydistinguished:

1. Shear viscosity describes the rate of shearflow as function of the applied stress.

2. Extensional viscosity measures the rate ofextensional (elongational) flow as function oftensile stress.

3. Bulk viscosity relates the rate of deformationof volume to the applied hydrostatic pressure.

Shear Viscosities are the most often studiedrheological properties of polymers; they are ofgreat importance for the processing of plastics byextrusion or injection molding, for example.Much less is known about extensional viscosities(important for blow forming and fiber spinning)and practically nothing about the bulk viscositiesof polymers.

7.2. Shear Viscosities at Rest

7.2.1. Fundamentals

Nine different shear stresses may be assigned to athree-dimensional body: one parallel to each ofthe three spatial directions (s11, s22, s33) and six

perpendicular to these (s12, s13, etc.). A body isby definition sheared in the 2 – 1 direction. Theratio of shearing force K to contact area is calledthe shear(ing) stresss21¼K/A; it produces a shearstrain g . The ratioG¼s21/g is the shear modulus.Between layers of distance y moving parallel toeach other with different rates v, a shear gradientg_¼d v/d y thus exists. The ratio of shear stress toshear rate is the (dynamic) viscosity (Newton’slaw);

h ¼ s21=g_ ð71Þits inverse 1/h is called fluidity.

Viscosities are independent of shear rates forNewtonian liquids (h¼ho); these viscosities arealso called zero-shear viscosities, viscosities atrest, or stationary viscosities. For Newtonianliquids, the shear modulus Go is independent ofthe extent of deformation. ho and Go are truematerial constants, whereas h and G depend onshear rates and sometimes also on shearing time.

Shear stresses and shear gradients (and thusviscosities) can be measured with a variety ofinstruments that usually belong to one of threegroups: capillary, rotatory, and cone – plateviscometers. A number of industrially used in-struments provide viscometric indicators (butneither shear stress, shear gradient, nor viscosi-ty); this group includes H€oppler viscometers,Cochius tubes, Ford beakers, and instrumentsthat measure melt flow indices orMooney values(Mooney viscosities).

Thermoplastics are usually characterized bytheir melt flow indices MFIT/F. The melt flowindex measures the mass of polymer extruded in10 min by a standard load F from a standardplastometer at temperature T. It is a measure ofthe (usually non-Newtonian) fluidity. The higherthe melt flow indices, the lower are the molarmasses of polymers of the same constitution.

The Mooney ‘‘viscosity’’ is really a measureof elasticity; it is used mainly for elastomers butalso for polymermelts. A polymer is deformed ina standardized cone – plate viscometer at con-stant rotational speed and constant temperatureT; after t minutes, the force to recover is read.

7.2.2. Molar Mass Dependence

Newtonian viscosities exhibit two differentregimes for their (mass-average) molar mass


dependencies ho¼K �M a: a weaker dependency(a¼1/2 – 1) for lowmolar masses and a strongerone (a�3.4) at higher molar masses (Fig. 35).The transition from one to the other is thought tobe caused by the onset of molecular entangle-ments that cause the molecules to behave asphysically cross-linked networks.

The number of entanglements can be assumedto be constant at low shear rates. The elasticity ofsuch a network is described by its shear modulusG (unit of pressure). Because shear viscositieshave the unit pressure � time, ho¼Go � t. The re-ptation model identifies the time t as the timerequired for a chain to leave the tube. This time isproportional to the third power of the number ofsegments per molecule (i.e., the viscosity shouldbe proportional to the third power of the molarmass). The deviation between the theoreticallypredicted a¼3 and the experimental value ofa¼3.4 is thought to be due to ‘‘breathing’’ of thetube. Breathing pushes nonentangled chain loopsback into the surrounding matrix; chain endscause additional relaxations and the tube lengthdecreases.

7.2.3. Concentrated Solutions

Newtonian viscosities of concentrated solutionsincrease with both solute concentrations c andmolar masses M or, since [h]¼K �M a, withintrinsic viscosity [h] as well. The concentrationc measures the mass of polymer per unit volumeof solution; the intrinsic viscosity, the volume ofpolymermolecules per unitmass of polymer. Theproduct c � [h] is thus a measure of the volumefraction of polymer molecules that would beoccupied by isolated polymer coils. At higherconcentrations, coils start to overlap and the totaloccupied volume is smaller than the one de-manded by isolated coils (i.e. c � [h]>1).

At low values of c � [h], hi (the ‘‘specificviscosity’’) and c � [h] are proportional (Fig. 37),where hi¼(h/h1)�1, h is the viscosity of thepolymer solution at rest, and h1 the viscosity ofthe solvent. At higher c � [h] values,hi �(c � [h])qor, since [h]�M a,hi �cq �M aq. Because at veryhigh concentrations hi�h/h1 and h approachesthe Newtonian melt viscosity ho �M 3.4 for highmolar masses, a � q¼3.4 is obtained. In thetasolvents and melts, coils are unperturbed (a ¼1/2) and q¼6.8 (Fig. 37). In good solvents, a

0.764 and q¼4.55. These relationships are inde-pendent of the chemical nature of polymers andsolvents.

7.3. Non-Newtonian Shear Viscosities

7.3.1. Overview

The shear stresss21 is directly proportional to theshear gradient g_ for Newtonian liquids; theserelationships and thus the viscosities h are more-over, independent of the duration of the experi-ments. Non-Newtonian viscosities (apparent vis-cosities), on the other hand, vary with shear rateand sometimes even with time.

Various dependencies of (apparent) viscosityon shear rate are found for time-independent non-Newtonian liquids (Fig. 38). Plastic bodies(Bingham bodies) exhibit a yield value y, i.e.,shear stresses have finite values so at g_! 0.Above so, such bodies may behave in a Newto-nian (ideal Bingham bodies) or non-Newtonian(pseudoplastic Bingham bodies) manner. Thisbehavior seems to be due to the disappearanceof aggregates. An example for a Bingham body istomato ketchup.

In dilatant liquids, the shear stress increase ismore than linearly proportional to shear rate;viscosities increase with shear rate (shear thick-ening). This behavior occurs frequently in poly-mer dispersions.

Figure 37. Relative viscosity increment (‘‘specific viscosi-ty’’) as function of c � [h] for (*) polystyrenes in trans-decalin (theta solvent) or toluene (good solvent G) at 25 �C;(.) cis-1,4-polyisoprene in toluene at 34 �C; and (D) hyalur-onates in water at 25 �CReprinted with permission by H€uthig and Wepf Publ., Basel[5]


A decrease of apparent viscosity with shearrate is most common for polymer melts. Becausesuch behavior resembles that of pseudoplasticBingham bodies, it is called pseudoplasticity inthe English literature (‘‘structural viscosity’’ inGerman), although such ‘‘pseudoplastic’’ mate-rials do not possess a yield value. Pseudoplasticbehavior eases polymer processing from meltsand reduces the energy required (e.g., lowerpressures can be applied in injection molding).It is usually accompanied by an orientation ofchain segments that is most pronounced in theprocessing of liquid crystalline polymers withrigid mesogens and the ultradrawing of flexiblepolymers.

Dilatant and pseudoplastic liquids are charac-terized by ‘‘instantaneous’’ adoption of shearrates on application of shear stresses (i.e., bytime-independent apparent viscosities). Thixo-tropic materials exhibit a decrease of apparentviscosity with time at constant shear rate; exam-ples are dispersions of bentonite and other plate-let-like silicates. Rheopectic or antithixotropicmaterials show an increase of apparent viscositywith time at constant shear rate. The flow behav-ior may be further complicated by wall effects.Certain dispersions and gels exude liquid onapplication of a shear stress. The liquid acts as

an external lubricant and a pluglike flow results(e.g., tooth pastes). An additional complicationmay result from the onset of turbulence, whichusually occurs at much lower Reynolds numbersin non-Newtonian than in Newtonian liquids.

7.3.2. Flow Curves

A plot of log g_¼f (s21) or vice versa is usuallycalled a flow curve. A generalized flow curvemay contain an initial Newtonian region, fol-lowed by pseudoplasticity and a second Newto-nian regime. Since experiments are difficult toconduct at high shear rates, many rheologistsdoubt the existence of true second Newtonianregions. Dilatancy may or may not be present.Finally, turbulence sets in and melt fractureoccurs (Fig. 39).

Several empirical laws have been suggestedfor the description of flow curves, all of whichusually apply only to limited ranges of shearrates. Examples include

_g ¼ a�ðs21Þm Ostwald�de Waele ð72Þ_g ¼ b�sinhðs21=dÞ Prandtl�Eyring ð73Þ

_g ¼ f �s21þg�ðs21Þ3 Rabinowitsch�Weissenberg ð74Þ

Figure 38. A) Shear stress s21 and B) shear viscosity h as a function of shear rate g_ for Newtonian (N), dilatant (D), andpseudoplastic (P) liquids and for ideal (iB) and pseudoplastic (pB) Bingham bodies (y¼yield)Reprinted with permission by H€uthig and Wepf Publ., Basel [5]


where a, b, d, f, g, andm are empirical constants.The exponent m is known as the ‘‘flow expo-nent’’; it takes a value of 1 (Newtonian liquid)and < 1 (pseudoplasticity). No constitutiveequations are known that cover the entire rangeof rheological phenomena.

7.3.3. Melt Viscosities

Polymers below the critical molar massesMc forentanglements show extended Newtonianranges. For M>Mc, non-Newtonian behaviorappears at lower shear rates as molar mass in-creases (lowermelt flow index) (Fig. 40). At highshear rates, a constant exponent q is approachedfor the function h¼f (g_q). The non-Newtonianviscosities are no longer proportional to themass-average molar masses; the broader themolar mass distribution, the more the numberaverage seems to be the correct correspondingquantity.

The decrease of apparent viscosity with shearrate is very important for plastics processing.Viscosities describe a frictional behavior: thehigher the viscosity, the higher is the internalfriction of the melt and the greater is the propor-tion of energy provided that is converted intoheat. Strong non-Newtonian behavior thus savesenergy. Polymer melts are therefore processed atthe highest possible shear rates. The upper range

is given by the processing method (calendering,extrusion, etc.), and the polymer properties (ther-mal degradation, melt fracture, etc.).

Surface roughnesses of barrel walls, diameterchanges, etc., create additional rate componentsin extrusion that are dampened by the viscosity ofthe liquid. These disturbances become strongerwith increasing flow rate and can no longer bedampened at high shear rate. Finally, turbulencesets in. In entangled polymer melts, additionalelastic vibrations occur due to the presence ofphysical cross-links. The resulting elastic turbu-lences lead to rough surfaces of the extrudate,which are subsequently frozen-in upon exit fromthe orifice. The polymer surface appears ‘‘frac-tured’’; ‘‘melt fracture’’ thus does not refer to abreakage of the extrudate strand.

Molecular coils are deformed if their melt ispressed through an orifice (Fig. 41). ForM>Mc,segments can no longer slip from each other at

Figure 39. Generalized flow curve with first Newtonianregion (N), pseudoplasticity (pp), second Newtonian region(N2), dilatancy (d), and onset of turbulence (t)- - - Schematic representations of various viscosity ‘‘laws’’:a) Prandtl – Eyring; b) Rabinowitsch – Weissenberg; c) Ost-wald – de WaeleReprinted with permission by H€uthig and Wepf Publ.,Basel [5]

Figure 40. Dependence of melt viscosities of polyethyleneswith different melt flow indices (MFI, inversely proportionalto molar mass) on shear rates (mf¼onset of melt fracture forthe highest molar mass polyethylene)The ranges of the various processing regimes overlap:P¼compression molding, C¼ calendering, E¼extrusion,I¼injection molding. Shear rates refer to those at orificesand are much lower in the mold (tool, die).Reprinted with permission by BASF AG, Ludwigshafen [78]

Figure 41. Parison swell upon extrusion (Barus effect)Reprinted with permission by H€uthig and Wepf Publ., Basel[5]


high stresses and short times because of entan-glements; a ‘‘normal’’ stress builds up perpen-dicular to the stress direction. At the die exit, thisstress is relieved and the coil returns to thethermodynamically more favorable shape of anunperturbed coil. The melt expands perpendicu-lar to the flow direction. This phenomenon isknown as Barus effect or memory effect (melts),theWeissenberg effect (solutions), parison swell(extrusion), swelling (blow molding), etc. It isespecially pronounced for high molar mass tailsin polymers with M>Mc because of the 3.4power dependence of h on �Mw.

Negative Barus effects are known for solu-tions of rodlike molecules or LCPs with rodlikemesogens (diameter of strand smaller than diam-eter of orifice). If suchmolecules crystallize afterexiting from the die, the strand contracts perpen-dicular to the extrusion direction and the stranddiameter becomes smaller than the diameter ofthe orifice.

The effect of normal stress can be determinedby the Bagley equation. A force Ff¼p R 2 p isexerted on a liquid during the flow through acapillary with radius R and length L under apressure p. It is counteracted by a frictional forceFr¼2 p RL s21. In steady state, Ff¼Fr; thus p¼2 s21(L/R)¼2 h � _g � (L/R) since s21¼h � _g . In theBagley diagram, pressure p is accordingly plot-ted at constant shear rate against die geometryL/R (Fig. 42). For non-Newtonian liquids, a re-lationship

p ¼ poþK�ðL=RÞ ð75Þis found. The intercept po atL/R ! 0 is identifiedwith the pressure loss caused by the elasticallystored energy of the flowing melt and the forma-tion of a steady-state flow profile at both ends ofthe capillary (die). The higher L/R is, the highermust the applied pressure be. Die lengths shouldthus be as short as possible.

7.4. Extensional Viscosities

7.4.1. Fundamentals

Polymer liquids can be elongated considerablywithout being broken. This extensibility allowsfiber spinning from melts and solutions, blowmolding of hollow bodies, vacuum forming ofparts, etc.

The extensional viscosity he (elongationalviscosity) is given by the ratio of tensile stresss11 in draw direction 11 to the elongational rate e_

he ¼ s11= _e ð76Þ

The type of deformation must always be indicat-ed for extensional viscosities, contrary to shearviscosities. The three principal deformation ratescan be defined in such a way that _e11� _e22� _e33.The ratio m¼ _e22/ _e11 characterizes the specialtype of elongational flow: theory gives m¼� 1/2 for uniaxial elongation, m¼1 for equal-biaxial, and m¼0 for planar (pure shear). Uniax-ial elongational viscosities are important for fiberspinning; they are the only ones used to charac-terize fluids. Biaxial elongational viscosities playan important role in blow and vacuum forming;very little is known about them.

The elongation in Equation (76) is the truestrain e0¼ln (L/Lo) (Hencky strain) and not thenominal strain e¼(L�Lo)/Lo (Cauchy strain, en-gineering strain). The rate of elongation is thus_e¼d e/dt¼d ln L/dt¼L�1 (dL/dt).

Extensional viscosities are very difficult tomeasure. Elastomers andmelts of entangled poly-mer coils canbe stretchedbetween rotating rollers.Extensional viscosities of solutions can be deter-mined if two liquid jets streaming toward eachother are redirected by rollers or siphoned off.

Figure 42. Bagley diagram for a high-impact polystyrene at189 �C and different shear ratesThe intercept at L/R ! 0 is the pressure correction; theintercept at p ! 0, the Bagley correction.a) g_¼4000 s�1 ;b) g_¼1000 s�1 ; c) g_¼100 s�1 ; d) g_¼ 10 s�1

Reprinted with permission by BASF AG, Ludwigshafen [78]


7.4.2. Melts

Extensional and shear viscosities depend verydifferently on deformation rates. At low rates,extensional viscosities are independent of the rateof extension (Fig. 43). The uniaxial extensionalviscosity at rest (historically called ‘‘Troutonviscosity’’) is three times the Newton viscosity[(he)o¼3 (hs)o], whereas the biaxial extensionalviscosity at rest is six times its shear counterpart.

Above a critical deformation rate, shear thin-ning is observed for the shearing and extension ofmelts of linear coil molecules. At the same rate,melts of branched coil molecules become dilat-ant on extension. The apparent extensional vis-cosities then pass through a maximum and de-crease with further increase of extension rates.The maximum of the extensional viscosity in-creases with broader molar mass distribution andincreased long chain branching, which indicatesthe strong influence of entanglements on exten-sional viscosities.

7.4.3. Solutions

Rodlike Molecules and Segments are in-creasingly oriented in the extensional directionwith increasing elongational rates. The molecu-lar axes are no longer distributed at random, andthe solution becomes anisotropic and thus bi-refringent. A limiting value is asymptoticallyreached if all molecular axes are completelyaligned in the flow direction.

Flexible Molecules in solution are onlyslightly deformed and oriented at comparableextension rates because elastic (entropic) forcescause the chains to return to the thermodynami-cally favored coil shape. At high critical exten-sion rates, these retraction forces can be over-come and the chain axes become oriented in theflow direction. Only an incremental increase ofextension rates is needed to orient the chainscompletely. Molecules are stressed more andmore above the critical extension rates until theyfinally break. This fracture occurs primarily inthe middle of the molecule so that degradationproducts possess 1/2, 1/4, 1/8, etc., of the initialmolar mass. Such degradation occurs under verylow deformation rates for rigid macromolecules,for example, during pipetting of dilute solutionsof high molar mass deoxyribonucleic acids.

These degradations by extensional flow arenot caused by turbulence because they happen atlower Reynolds numbers than those of puresolvents. Chain degradations by turbulence dooccur on shearing of very dilute solutions offlexible coil molecules (e.g., 10�4 g/mL aqueoussolutions of polyoxyethylenes). The degradationreduces the frictional resistance of liquids up to75%. This ‘‘Toms effect’’ by added smallamounts of such polymers eases the flow of crudeoil through pipelines and increases the distanceand height to which water can be directed at fires.

8. Mechanical Properties

8.1. Introduction

8.1.1. Deformation of Polymers

Mechanical properties of a polymer include thedeformationofbulkpolymersor their surfaces, theresistance to such deformation, and the fractureunder static or dynamic loads. Deformations maybe reversible or irreversible; they can be caused bydrawing, shearing, compression, bending, andtorsion, as well as by combinations of these.

Reversible deformations are due to the pres-ence of elasticity. Irreversible deformations arealso called inelastic; they are further subdividedinto deformation by viscous flow, plasticity,phase transformations, craze formation, crack-ing, viscoelasticity, creep, etc. An inelastic de-formation of metals by viscoelasticity is known

Figure 43. Shear viscosity hs as function of shear rate q_¼g_,and extensional viscosity he as function of the uniaxialextensional rate q_¼e_ of a polyethylene at 150 �CReprinted with permission by Steinkopff Verlag, Darmstadt[79]


as anelasticity; in polymer physics, anelasticitydenotes a reversible elasticity with retardation,which does not lead to energy dissipation. De-formation of the upper layers of a polymer bodyis characterized by its ‘‘hardness,’’ which influ-ences friction and abrasion.

The term elasticity may refer to either energyor entropy elasticity. These elasticities differ intheir molecular mechanisms and the resultingphenomenological behavior. In energy-elasticbodies (steel, plastics, and elastomers at lowstrains), torsion and bond angles are changedand bond distances are enlarged on deformation,whereas the macroconformations of chains, forexample, remain basically the same. A deforma-tion of entropy-elastic bodies (elastomers at highstrains), on the other hand, leads to entropicallyunfavorable positions of chain segments which,however, cannot slip irreversibly from each otherbecause of their cross-linking (‘‘rubber elastici-ty’’). The deformation thus changes the macro-conformation (molecular picture), decreases en-tropy (thermodynamics), and creates normalstresses (mechanics).

These molecular changes are reflected in theproperties of energy- and entropy-elasticmaterials:

Energy- Entropy-

elastic elastic

Elastic moduli large small

Reversible deformation small large

Temperature change on

deformation cooling warming

Length change on heating expansion contraction

The deformation behavior of plastics dependson the molar mass of their constituting polymersand on the testing temperature: That is, whetherthe molar mass is greater than the one needed forthe establishment of entanglements betweenchains (M>Ment) and whether the testing tem-perature is lower than the glass transition tem-perature of the polymers (T<TG). All mechanicaldeformations recover for M>Ment and T<TGsince chain entanglements cannot reorganizebelow the glass transition temperature (memoryeffect). Yielded plastics and crazed plastics re-cover on (not too long) heating above the glasstransition temperature. These plastics thus do notshow true plastic flow.

8.1.2. Tensile Tests

Mechanical properties of polymers aremost com-monly evaluated by tensile tests in which a speci-men is drawn with constant speed. The tensilestress s11 is recorded as a function of time t, drawratio (strain ratio) l¼L/Lo, or tensile strain (elon-gation) e¼(L-�Lo)/Lo¼l�1. If a specimen isextended to L¼2.5 Lo of the original length Lo,then it is said to have been drawn by 150%.

The tensile stress of elastomers increasescontinuously with increasing tensile strain untilthe polymer finally ruptures at sR and eR(Fig. 44). Typical thermoplastics (and most fi-bers) follow Hooke’s law

s11 ¼ ðF=AoÞ�e ¼ E�e ð77Þfor small strains (up to point I), where Ao is theoriginal cross section of the specimen, F is theforce, and E is the tensile modulus (Young’smodulus). Point I is thus called the proportionalitylimit or elastic limit; it is defined for a remainingstrain of 0.1% after removal of the stress.

The maximum of the stress – strain curve iscalled the upper yield (point II), and the subse-quent minimum is the lower yield (point III). Theratio of upper yield stress sS to tensile modulus Eis practically constant for all polymers; the nu-merical value of sS/E�0.025 suggests that vander Waals bonds are broken and molecule seg-ments begin to move more freely.

Brittle polymers break at the upper yield.Tough polymers continue to extend and the stresseither remains constant (see below) or decreases.The latter phenomenon is called stress softening.It is typical for polymers with neck formation(telescope effect) and is nominal since it disap-pears if the stress is given relative to the actualcross section instead of the initial one.

The region between points III a – II – III isknown as the ductile region; its area describes theabsorbed energy and thus the toughness of thespecimen. The subsequent increase of stress withstrain is called stress hardening. At point IV, theultimate strength (tensile strength, tenacity atbreak) sB and ultimate elongation (elongationat break) eB occur.

Stress – strain curvesmay differ considerablyfor plastics. Polymers with high Young’s moduli(steep initial slopes) are called hard polymers;those with low moduli, soft; this hardness shouldnot be confused with surface hardness. Typical


hard polymers are phenolics [phenol – formal-dehyde (PF)], polyacetals [polyoxymethylene(POM)], polycarbonates (PC), and poly(ethyleneterephthalates) (Fig. 45). Polymers are further

characterized by their stress – strain behaviorbetween upper yield and failure. Polymers with-out yield cannot absorb energy and thus breakeasily; they are hard-brittle polymers (e.g., PF).

Figure 44. Stress – strain curves of an elastomer (a) and a partially crystalline thermoplastic (b) (schematic) (for furtherexplanation, see text)The necking effect shown below is characteristic for conventional thermoplastics; it is not found for elastomers and hard-elasticthermoplastics.Reprinted with permission by H€uthig and Wepf Publ., Basel [5]

Figure 45. Stress – strain curves of polymers at room temperature (see text for explanation)


Polycarbonates, on the other hand, show anextended ductile region and a fairly high fracturestrain; they are called hard-tough. Polyethyleneis similar with respect to ductile behavior andstrain hardening; the modulus is however muchlower, and PE is considered soft-tough.

The stress – strain behavior described aboveis typical for tensile experiments. Tensile stres-ses lead to strong deformations in neck zones andcause microscopic voids at which fracture ori-ginates. Atactic polystyrene (PS) is such a hard-brittle polymer under tension T. No voids can beformed, however, under compression C, and PSappears as a hard-toughmaterial (Fig. 45, insert).Rubber modification of PS leads to high-impactpolystyrene (HIPS), which behaves quite differ-ently from PS under tension (see Section 8.6.4).

No yield value is found if drawn polymers arefurther subjected to tensile tests. In biaxiallystretched poly(ethylene terephthalate) (PETP-str) some chain segments are already oriented,whereas other remain in their original positions.Biaxially stretched films are thus under stress,which is utilized in shrink films. Such films areused for the packaging of goods. On heatingsemicrystalline polymers above the glass transi-tion temperature and below the melting temper-ature, chain segments become more mobile.Molecules attempt to attain their unperturbeddimensions and the films shrink, covering thegoods tightly.

8.1.3. Moduli and Poisson Ratios

Elasticities can be described by three elasticmoduli: tensile modulus or Young’s modulusE, shear modulus G, and bulk modulus or com-pressive modulus K. Their values are inverselyproportional to the corresponding compliancesfor static deformations (but not for dynamicones):

Moduli Compliances

E¼s11/e D¼1/E

G¼s21/g J ¼1/G

K¼p/(�DV/Vo) B¼1/K

The three simple moduli are related to eachother for small deformations of simple isotropicbodies:

E ¼ 2G�ð1þmÞ ¼ 3K�ð1�2mÞ ð78Þwhere m¼(D d/do)/(D L/Lo) is the Poisson ratio(Poisson number), d is the diameter, and L is thelength of the specimen. Poisson ratios can onlyadopt values 0<m<1/2 for isotropic bodies butmay assume m>1/2 for anisotropic ones. Equa-tion (78) is invalid for anisotropic bodies andviscoelastic materials; E/3<G<E/2 and 0<K<E/3, are however, still valid for these materials.

Common polymers behave with respect to m,E, G, and K more like liquids than like metals(Table 23). Ultradrawn and self-reinforcingpolymers may however exhibit tensile modulithat exceed those of steel (see below).

8.2. Energy Elasticity

8.2.1. Theoretical Moduli

The tensile moduli of common polymers are farlower than the theoretical moduli deduced fromtheir chemical and physical structures (Table 24).Such theoretical moduli can be calculated frombond lengths, valence angles, and force constantsfor the deformation of these quantities. The

Table 23. Poisson ratios and elastic constants of various materials

Material m E/GPa G/GPa K/GPa

Water 0.50 � 0 � 0 � 2

Gelatin (80% water) 0.50 0.002

Natural rubber 0.495 0.0009 0.0003 � 2

Polyethylene, LD 0.49 0.20 0.070 3.3

Polystyrene 0.38 3.4 1.2 5.0

Granite 0.30 30 12 25

Steel 0.28 211 80 160

Glass 0.23 60 25 37

Quartz 0.07 101 47 39

Aluminum oxide

fibers 0 2000 1000 667

Table 24. Modulus of elasticity

Polymer E k /GPa E?/GPa

Theory Lattice Tensile Lattice

Polyethylene 340 325 < 1 3.4

Polypropylene, it 50 42 < 3 2.9

Polyoxymethylene

Orthorhombic 220 189 < 2 7.8

Trigonal 48 54 2

Poly(p-phenylene

terephthalamide)

182 200 132 10

Poly(4-methylpentene) 6.7 1 2.9


theoretical moduli agree well with the micro-scopic lattice constants, which are determinedexperimentally by X-ray diffraction (change ofBragg reflexes), Raman spectroscopy, or inelas-tic neutron scattering under load. The longitudi-nal theoretical moduli E k are far greater than thetransverse moduli E? because the former arecontrolled by covalent bonds and the latter byvan der Waals forces.

The larger the cross-section of the singlepolymer chain, the larger is the force distributedto fewer chains per unit area and the smaller arethe moduli (Fig. 46). Chains in the all-transconformation always exhibit higher theoreticalmoduli than do helical chains since the elonga-tion of the former changes bond angles, whereasthe extension of the latter involves only lower-energy torsion angles.

Polyethylene has the highest theoretical mod-ulus of all one-dimensional chains (E k¼340GPa), about one-third that of diamond (E k1160 GPa)with its ‘‘naked’’ carbon chains. Poly-propylene has the highest theoretical modulus ofhelical chains (E k¼50 GPa).

Moduli approaching these theoretical valueshave been realized by ultradrawing of mats ofpolyethylene single crystals, giving polymerswith E k¼240 GPa. Industrially, high-moduluspolyethylene fibers are manufactured by gel spin-ning of ultra-high molecular polyethylene (E k¼97 GPa=90 N/tex, 1 tex¼1 g per 1000 m).

8.2.2. Real Moduli

Themuch lower tensilemoduli of conventionallyprocessed polymers result from their disorderedphysical structures. In amorphous polymers,chain segments are oriented at random. Even inpartially crystallized polymers, amorphouslayers exist and chain axes (stems of lamellae)are distributed at random. The moduli of flexiblepolymers can be increased somewhat by proces-sing under external force fields, for example, bypartial orientation of chain segments during fiberspinning (Table 25, columnL). Extrusion of solidpolymers is a particularly effective method: thelongitudinal modulus of polyoxymethylene in-creased to 24 GPa from 2 GPa on hydrostaticextrusion.

Rodlikemesogens of liquid semiflexible poly-mers align in mesophase domains. The domainsorient themselves in shear fields; the orientationscan be frozen-in to LCP glasses. Such self-or-

Figure 46. Longitudinal lattice moduli Ek as function ofcross-sectional area Am of polymer chains in all-trans (21) orhelical conformations (95, 83, 31, 41) of their main chainsReprinted with permission by H€uthig and Wepf Publ., Basel[5]

Table 25. Moduli and fracture strengths of conventional polymers as isotropic molding masses (I) or in draw direction of fibers (L) and of

thermotropic (TT) and lyotropic (LT) glasses longitudinal (L) and transverse (T) to draw direction compared to isotropic polymers (I)

Polymer E/GPa sB/MPa

L T I L T I

PE-LD ? ? 0.15 ? ? 23

PA 6.6 13 ? 2.5 1000 ? 74

PETP 19 ? 0.13 1400 ? 54

TT X 7 G a 54 1.4 2.2 151 10 63

TT Vectra b 11 2.6 5.0 144 54 97

LT Kevlar c 138 7 ? 2800 ? ?

LT PPBT d 120 17 62 1500 680 700

aX 7 G¼poly(p-hydroxybenzoate-co-ethylene terephthalate).bVectra¼poly(p-hydroxybenzoate-co-2-hydroxy-6-naphthalate).cKevlar 49¼poly(p-phenylene terephthalamide).dPPBT¼30% poly(p-phenylene benzbisthiazole) in poly(2,5-benzimidazole).


ienting polymers possess much higher moduli inthe longitudinal direction than conventionallyprocessed flexible polymers (Table 24). Theirtransverse moduli are also higher because ofintermolecular dipole – dipole interactions.

8.2.3. Temperature Dependence

Young’s moduli change characteristically withtemperature for the various classes of polymers(Fig. 47). Five characteristic ranges can be dis-tinguished: glassy (GL), leatherlike (LE), rub-bery (RE), viscoelastic (RF), and viscous (VF).

Amorphous Polymers. Moduli (0.1 –1 GPa) are practically independent of tempera-ture below the glass transition temperature TGbutdrop to 105–106 Pa atT¼TG; the polymer appearsleathery around TG and rubbery above the glasstransition temperature. The rubbery region ismaintained for entangled (high molar mass)polymers but is nonexistent for lowmolarmasses(M<Mc). Moduli decrease on further tempera-ture increase until the polymers behave likeviscous liquids (E�103 Pa).

Elastomers. At use temperatures, thesepolymers are above their TG’s and thus behavelike cross-linked thermoplastics above the TG’sof the latter. The decrease in modulus at TG islimited by (and a measure of) the degree ofcross-linking. At higher temperatures, elasto-mers decompose and the moduli decreasedrastically.

Crystalline Polymers have only a weakleathery region around TG since their amorphi-city is slight and their crystallites act as physicalcross-linkers. The modulus at the beginning ofthe rubbery plateau is a measure of the degree ofcrystallinity. The moduli decrease slowly duringthe rubbery ‘‘plateau’’ because more and morecrystallites are molten. The remaining crystal-lites practically disappear at the melt tempera-ture: the moduli drop drastically and the poly-mers behave like viscous liquids.

Thermosets. Thermosets are highly cross-linked polymers. They have high Young’s mod-uli below TG, usually one decade higher thanthermoplastics. A very weak glass transition isaccompanied by a somewhat leathery behavior.

Figure 47. Temperature dependence of Young’s moduli for conventional polymersat-PS¼Amorphous (atactic) polystyrene (M>Mc); at-PS-X¼Its slightly cross-linked product; it-PS¼Partially crystalline(isotactic) polystyrene; PF¼Hardened phenol – formaldehyde resin; GL¼glasslike; LE¼leatherlike; RE¼rubber (entangled);RF¼viscoelastic; VF¼viscous flowReprinted with permission by H€uthig and Wepf Publ., Basel [5]


The subsequent rubbery region is not verymarked because the cross-linking density is high.

8.3. Entropy Elasticity

Elastomers show pronounced entropy elastici-ties. They exhibit simultaneously some charac-teristics of solids, liquids, and gases. Like solids,they display Hookean behavior at not too highdeformations (i.e., they show no permanent de-formation after removal of the load). Moduli andexpansion coefficients, on the other hand, resem-ble those of liquids. Like compressed gases,stresses increase with increasing temperature forelastomers at T>TG.

The elastic behavior can be modeled withvarious theories. In the simplest case, disloca-tions of network junctions are assumed to beaffine to the macroscopic deformation of thenetwork. The tensile stress s11 varies with theelongation l¼L/Lo according to

s11 ¼ RT�½Mc��ðVo=VÞ�1=3ðl�l�2Þ ð79ÞIt depends on the volumes before (Vo) and after(V) deformation and on the molar concentration[Mc] of network junctions. True Young’s modulican be obtained from the limiting value of s11/(l�l�2) at l ! 1, for example, for volume-constant deformations (Vo/V¼1):

RT �½Mc� ¼ liml!1½s11=ðl�l�2Þ�¼ s11=½3ðl�1Þ� ¼ s11=ð3eÞ ¼ Eo

ð80Þ

The Young’s modulus is thus directly propor-tional to the molar concentration of networkjunctions (cross-linking sites), independent ofthe nature of the latter. On shearing, elastomersbehave like Hookean bodies because

RT�½Mc� ¼ s21=g ¼ G ð81ÞThey are, however, non-Hookean for elongationsbecause Eo„s11/e (Eq. 80).

8.4. Viscoelasticity (! Plastics,

Properties and Testing)

8.4.1. Fundamentals

Most polymers do not revert ‘‘instantaneously’’to their initial states after the removal of loads;they are neither ideal energy elastic (Section 8.2)nor ideal entropy elastic (Section 8.3). Theseprocesses take certain times, (i.e., time-indepen-dent elastic and time-dependent viscous proper-ties work together to produce a viscoelasticbehavior). If stress, strain, and strain rate can becombined linearly, then the process is said tobe linear elastic. In addition, some polymers maybe irreversibly deformed.

The two ideal cases of response to deforma-tions can be well described by mechanical mod-els: a spring for a Hookean body (instantaneousresponse) and a dashpot for a Newtonian liquid(linear time dependence of response) (Fig. 48).TheMaxwell element combines spring and dash-

Figure 48. Time dependence of deformations according to various models. Loads are added at # and removed at "Reprinted with permission by H€uthig and Wepf Publ., Basel [5]


pot in a series; the Voigt – Kelvin element, in aparallel manner.

The Maxwell element describes a relaxation(i.e., the decrease of stress at constant deforma-tion; Table 26). Linear combination of elasticdeformation rates dge/dt¼(1/G) (ds/dt) and vis-cous deformation rates dgh/dt¼s/h yields, afterintegration of the resulting expression and index-ing the time for this particular behavior for dg/dt¼0,

s ¼ s0�expð�G�te=hÞ ¼ so�expð�te=tÞ ð82Þ

The relaxation time t¼h/G indicates the timeafter which the stress has fallen to the e�1thfraction of its initial value. The ratio t/te of therelaxation time t to the time scale te of theexperiment is called the Deborah number(DB¼t/te); it is 0 for liquids, ¥ for ideal-elasticsolids, and approximately 1 for polymers neartheir glass transition temperatures.

Retardation is defined as the increase ofdeformation with time at constant stress. It ischaracterized by a ‘‘creep’’ of the material. Sincethis phenomenon was first observed on seeming-ly solid polymers at room temperature, it is alsocalled ‘‘cold flow.’’ In principle, retardation phe-nomena can be described by a Maxwell element.Because of mathematical difficulties in the solu-tion of the equations, a special model is prefered(Voigt – Kelvin element) (Fig. 48),which yieldsfor the deformation g r at constant stress so afterindexation for retardations r

g r ¼ ðso=GrÞ�½1�expð�Gr�tr=hÞ� ð83Þwhere Gr is the retardation modulus, also oftencalled the relaxation modulus. The retardationtime tr indicates the time at which the deforma-tion has reached (1�1/e)¼0.632 of the finaldeformation so/Gr. Retardation times and relax-

ation times are of the same magnitude, but notequal because they rely on different models.

The term ‘‘viscoelasticity’’ is sometimes usedto describe the reversible deformation accordingto Equation (83). However, it is often applied tothe total deformation, which is composed of thecontributions by Equation (83), a Hookean bodywith ge¼so/Go, and aNewtonian liquid [gh¼(so/ho) � t]:g tot ¼ fð1�GoÞþðt=hoÞþð1=GrÞ�½1�expð�t=tÞ�g�so

¼ geþghþg rð84Þ

The three deformation terms ge (elastic), gh(viscous), and g r (viscoelastic) are often notexplicitly evaluated. The time-dependent vis-cous and viscoelastic parts are rather combinedinto a new parameter gc¼g �t n (Findlay law). Theresulting function for the creep curve allows anextrapolation to long-time behavior from short-time experiments:

g tot ¼ geþgc ¼ geþg �tn ð85Þ

8.4.2. Time – Temperature Superposition

Deformations, shear moduli, and shear com-pliances are time and temperature dependent(Fig. 49). The moduli vary about one decade forsix decades in time at constant temperature, andup to one decade for each 10 K at constantfrequency. Since no single experimental methodcan cover the 15 – 20 decades of frequency thatare required for good characterization of a poly-mer, time – temperature data from various tech-niques are usually combined with the help of theBoltzmann superposition principle.

This principle states that the deformation (orrecovery) caused by an additional load (or re-moval thereof) is independent of previous loadsor their removal. The G¼f (t, T) curves can becombined if (1) the relaxation time spectrum istemperature independent and (2) the thermalactivation is the same over the entire time andtemperature range (no transition or relaxationtemperatures). A reference temperature is chosenclose to the static glass transition temperature(115 vs. 105 �C in Fig. 49) and the G values areshifted horizontally with the help of a shift factorfrom the WLF equation (Eq. 69).

Table 26. Simple mechanical models for the deformation of polymers

Model Function Behavior a

Initial Final

Newtonian liquid s ¼h � g_ L L

Voigt – Kelvin element s ¼G � gþh � g_ L S

Maxwell element sþ(h/G) �s_¼h � g_ S L

Hookean body s ¼G � g S S

Jeffrey’s body sþ(h/G) �s_¼G � gþh � g_ S S

*S¼solid-like behavior; L¼liquid-like.


8.5. Dynamic Behavior

8.5.1. Fundamentals

Dynamic – mechanicalmethods expose the spec-imen to periodic stresses. The polymer either isput under torsion once and then oscillates freely(torsionpendulum)or is subjected continuously toforced oscillations (e.g., Rheovibron). In addition,ultrasound, dielectric, and NMR methods can beused to study the dynamic properties of polymers.

In the simplest case, the applied stress issinusoidal with a frequency w (st¼so � sin w � t).The deformation of ideal-elastic bodies followsthe stress instantaneously (g t¼go � sin w � t) butthat of viscoelastic polymers experiences a delay(g t¼go � sin (w � t�q). The stress vector is as-sumed to be a sum of two components: onecomponent is in phase with the deformation(s0¼so � cos q); the other is not (s00¼so � sin q).

Each of these two components possesses amodulus. The real modulus (shear storage mod-ulus)G0measures the stiffness and shape stabilityof the specimen:

G0 ¼ s

0=go ¼ ðso=goÞ�cosq ¼ G�cosq ð86Þ

whereas the imaginary modulus (shear loss mod-ulus) G00 describes the loss of usable mechanicalenergy by dissipation into heat:

G00 ¼ s

00=go ¼ G�sinq ð87Þ

The same quantities can also be derived if com-plex variables are introduced

G ¼ G0þi�G00 ¼ ½ðG0 Þ2þðG00 Þ2��1=2 ð88Þ

The loss factor d is the ratio of imaginary to realmodulus. It is the same for shear and Young’smoduli but not for compression moduli

D ¼ tanq ¼ G00=G

0 ¼ E00=E

0< K

00=K

0 ð89Þ

8.5.2. Molecular Interpretations

The shear storage moduli of low molar masspolymer melts with narrow molar mass distribu-tions increase continually with increasing fre-quency (Fig. 50). At high normalized frequen-cies aTw, all storage moduli asymptotically

Figure 49. Time dependence of the shear modulus frommeasurements of the stress relaxation of a poly(methyl methacrylate)( �Mv¼3 600 000 g/mol) at various temperatures (left) and the resulting time – temperature superpositions for a referencetemperature of 115 �C (right) (circles represent equivalent positions)Reprinted with permission by H€uthig and Wepf Publ., Basel [5]


approach a limiting line, regardless of molarmass. This part of the relaxation spectrum thusoriginates from themobility of chain segments; itis called the transition range.

High molar mass polymers show a corre-sponding frequency dependence of loss moduliat very low frequencies (called end range),followed by a plateau at higher frequencies(plateau modulus Go

N), and finally the transitionrange. The end ranges of these spectra aremolar mass dependent; this behavior mustcome from long-range conformational changes.Since the transition range characterizes viscousbehavior, and the end range viscoelastic behav-ior, the plateau range must reflect rubberybehavior (see Fig. 47 for the temperaturedependence).

The rubbery behavior of polymer melts canbe described by the theories of entropy elastic-ity according to which the shear modulus ofchemically cross-linked polymers depends onthe molar concentration of network junctions.The plateau modulus Go

N of melts thus indi-cates the concentration of temporary junctions(entanglements). The molar mass Me of seg-ments between such junctions of polymerswith volume fractions fp in solution (fp¼1 for

melts) and polymer melt densities rp is givenby

Me ¼ RT �rp�fp=GoN ð90Þ

These dynamic entanglement molar masses Me

are a factor 2.00.2 lower than the correspondingmolarmassesMc from rest viscosities (Table 27).

The plateau is not well developed ormay evenbe absent for polymers with broad molar massdistributions; a complicated dependence of shearcompliances on higher molar mass averages hasbeen predicted by reptation theory.

Figure 50. Frequency dependence of the shear storagemodulusG0 for narrow-distribution polystyrenemelts of differentmolarmasses M. A shift factor aT was used to convert to 160 �C data measured at various temperaturesa) M¼581 000 g/mol; b) M¼351 000 g/mol; c) M¼215 000 g/mol; d) M¼113 000 g/mol; e) M¼46 900 g/mol;f) M¼14 800 g/mol; g) M¼8900 g/molReprinted with permission by H€uthig and Wepf Publ., Basel [5] after data of [80]

Table 27. Critical molar masses for entanglement from shear moduli

(Me) and rest viscosities (Mc)

Polymer T Mc Me Mc�C g/mol g/mol Me

Polyethylene 190 3 800 1 790 2.1

Polypropylene, it 190 7 000

Polyisobutylene 25 15 200 8 800 1.7

Polydimethylsiloxane 25 24 500 10 500 2.4

Poly(vinyl acetate), at 57 24 500 12 000 2.0

Poly(a-methylstyrene), at 100 28 000 13 500 2.1

Polystyrene, at 190 35 000 18 100 1.9


8.6. Fracture

8.6.1. Overview

Polymers break very differently depending ontheir chemical and physical structure; environ-ment (humidity, solvents, temperature); and thetype, duration, and frequency of deformation.Some polymers break immediately; others areunchanged even after months. The fracture sur-face can be smooth or splintery; the elongation atfracture, less than 1% or greater than 1000%.

Two fracture modes can be distinguished:brittle and tough (ductile). Brittle polymers frac-ture perpendicularly to the stress direction, toughpolymers longitudinally (Fig. 51). A polymer isdefined as brittle if its elongation at break is lessthan 20%.

Brittle Fractures are rare for ideal solidssincemany bondsmust be severed simultaneous-ly. Real polymers however contain many smallimperfect regions that act as ‘‘nuclei’’ for theformation of microcracks. Brittle polymers usu-ally possess ‘‘natural’’ microvoids, which mayalso appear in drawn amorphous polymers orthrough separation of crystal lamellae in hard-tough polymers.

Tough Failures (ductile fractures) are causedby viscous flow (‘‘plastic flow’’). This processmay involve the slipping of chain segments pasteach other (amorphous polymers) or the move-ment of crystalline domains (partly crystallinepolymers). Polymer chains may also de-entangleat long times and under small stresses. The sameprocesses and additional ones may occur onfailure of composites (Fig. 51).

Polymers are subjected to very different stressconditions in typical applications; they thus ex-perience different failure modes. Test methodstry to simulate complex real-life situations bystandardized procedures. They include long-termexperiments such as static deformations underconstant load by tension, compression, or bend-ing; short-term methods such as tensile testsunder various speeds or impact tests with un-notched or notched specimens; dynamic testingwith variation of the number of loadings – un-loadings, impacts, vibrations, etc.

8.6.2. Theoretical Fracture Strength

The fracture of brittle polymers generates freeradicals. Since the probabilities of such homo-lyses depend on bond strengths, which also de-termine tensile moduli, relationships must existbetween the theoretical moduli and the theoreti-cal fracture strengths of polymers.

Bonds are severed if atoms are separated fromeach other by certain distances Lb greater thantheir equilibrium distances Lo. The necessarytheoretical strength so

k is given by [5].

sok ¼

Eok�ðLb�LoÞ

pLo¼ K�Eo

k ð91Þ

Polymer main- chain bonds break at approxi-mately the same relative distance (Lb�1.3 Lo)because bond lengths and strengths are not toodifferent for bonds such as C�C, C�O, andC�N.Thus,K�0.095 and the theoretical fracturestrength so

k should be ca. one-tenth of thetheoretical tensile modulus E o

k in the chaindirection, regardless of the chemical nature of

Figure 51. Failure modes of polymers (matrix M), fibers (F), and fiber-reinforced polymer composites (C) by brittle failure(br), plastic flow (pl), shear band formation (sb), shearing (s), kink formation (k), bending (b), longitudinal splicing (sp),formation of kink bands (kb), and step formation by compression (cp)Reprinted with permission by H€uthig and Wepf Publ., Basel [5]


the polymer. Polyethylene with a theoreticalmodulus of 340 GPa (Table 24) should thus havea theoretical fracture strength of ca. 32 GPa [i.e.,much higher than the theoretical strength of steel(ca. 20 GPa)]. Industrially manufactured ultra-drawn polyethylene fibers have higher experi-mental fracture strengths than steel(2.9 GPa¼2.7 N/tex vs. 2.5 GPa).

The theoretical fracture strength – tensilemodulus relationship of Equation (91) has beenrealized for certain ultradrawn polyethylenes inwhich both the predicted proportionality con-stant K¼0.095 and the first power of E werefound (Fig. 52). The type of same relationshipis also observed formolecular composites of poly( p-phenylene-2,6-bisbenzthiazole) (PPBT) withrodlike mesogens in coillike polybenzimide(ABPBI), albeit with a lower proportionalityconstant. In other ultradrawing experiments, apower dependence s¼K0 �En was found,however.

8.6.3. Real Fracture Strength

The lower than theoretical fracture strengths ofmost polymers (see Tables 24 and 25) are causedby many factors. Theoretical fracture strengthsrelate to infinitely long, completely aligned, im-mobile polymer chains. End groups and chainfolds act as disturbances: fracture strengths ofconventional polymers increase with increasingmolar mass and become practically constantabove a ‘‘critical’’ molar mass.

At the lattermolarmass range, chain segmentsof amorphous polymers are distributed at ran-dom. A brittle fracture across such polymers willcreate two new surfaces with a total surfaceenergy of 2 g lv. The theoretical fracture strengthfor brittle, energy-elastic bodies

soa ¼ ðE�g lv=LoÞ1=2 ð92Þ

now depends on the product of modulus andsurface energy (Ingles theory). The Ingles theoryworks well for silicate glasses.

The experimentally found fracture strengthssb of plastics are however much lower than thestrengths predicted by Equation (92). The ratiossoa /sexp of molded (unoriented) plastics decrease

Figure 52. Tensile strength at break as function of tensile modulus: (.) experimentally ultradrawn ultra-high-moduluspolyethylenes; (*) industrially manufactured ultradrawn polyethylene (Dyneema); (�) theory for perfectly aligned polyeth-ylene; (¤) heterogeneous molecular composites of ABPBI fibers or PBT fibers or films in ABPBI matrix; (¤) homogeneousmolecular composites of PBT fibers or PBT fibers for films in ABPBI. Solid line corresponds to sB¼0.095 �E k


with increasing elongation eb at break (Fig. 53),whereas those of drawn fibers (partially orientedchain segments) increase.

The reason for the lower than expected frac-ture strengths of amorphous polymers is thepresence of microvoids, which act on drawingas nuclei for cracks. According to the Griffiththeory, a crack can grow only if the energyrequired for the fracture of chemical bonds isjust surpassed by the stored elastic energy. Thistheory predicts a dependence of the fracturestrength on crack length L:

sB ¼ ½ð2E�g lvÞ=ðp�LÞ�1=2 ð93Þ

This functionality is indeed observed for artifi-cially introduced long cracks. The predictedfracture strengths are however much lower thanthose found by experiment. Furthermore, devia-tions from Equation (93) occur at small cracklengths because the fracture behavior of plasticsis not dominated by the cleavage of chemicalbonds but by other types of energy absorption(crazing; shear flow).

On drawing, stresses are imposed on micro-voids. The polymer reaches its upper yield stressat sufficiently high stress concentrations at the tipof such a void and relieves the stress by stress

softening (Fig. 44). The induced cooperativemovements of chain segments cause long-rangechanges of macroconformations. In partiallycrystalline polymers, these changes can occuronly in amorphous domains; spherulitic poly-mers break accordingly either between spheru-lites or in the radial spherulite direction.

The cooperative movements of segments leadto either shear or normal stress yielding. Onshearing, the whole specimen yields either ho-mogeneously or heterogeneously (localized). Inthe latter case, shear bands are formed at anglesof 38 – 45� to the stress direction (Fig. 51).Chain segments are arranged at angles betweenshear bands and stress directions.

All polymers with upper yield values formcrazes upon stress softening (Fig. 54), regardlessof whether they are amorphous, crystalline, line-ar, or cross-linked. Crazes can be up to 100 mmlong and 10 mmwide; their long axes are parallelto the stress direction. They are not voids sincetheir interior is filled with amorphous microfi-brils of 0.6 – 30 nm diameter; these microfibrilsare oriented in the stress direction (i.e., perpen-dicular to the craze long axes). On further defor-mation, microvoids are formed.

The formation of crazes is the primary mech-anism for the dissipation of stress energy. It is

Figure 53. Ratio soa /sexp of theoretical [Eq. (92)] and experimental fracture strengths as function of elongation at break eb for

(*) nonoriented (molded plastics) and (.) oriented (fibers) polymersHe¼hemp, Co¼cotton, Wo¼wool (for other abbreviations see Tables 1–4)


utilized in the rubber reinforcement of polysty-rene. Rubber-modified polypropylene, on theother hand, deforms mainly by shear flow.

8.6.4. Impact Resistance

Impact strength is the resistance of a material toimpact. It is one of the many quantities used tocharacterize the strength of a material under (theusually complex) use conditions; all test methodsare thus standardized.Most testmethodsmeasurethe energy required to break a notched or un-notched specimen (Izod, Charpy, high-speedtensile). Impact speeds range from 10�5–10�1

m/s in conventional tensile tests to 20 – 240 m/sfor high-speed tensiles; elongation speeds areusually from 10�3 to 104 s�1.

Impact strengths depend on experimental con-ditions. The smaller the radius of the notch, thehigher is the stress concentration at the tip and thelower is the impact strength. At very low tem-perature, all polymers are brittle. The mobility ofchain segments increases with increasing tem-perature, allowing stresses to be relieved byshear-band or craze formation: impact strengthsincrease with temperature, especially near theglass transition temperature. Polymers with ad-ditional transition temperatures below the glasstransition temperatures are for the same reasonalmost always more impact resistant than poly-mers without such transitions. Nonentangledpolymers exhibit very low impact strengths be-cause no crazes can be formed. The impactbehavior of polymers can be improved consider-

ably by modification with rubber (see Section11.4.3).

8.6.5. Stress Cracking

Stress cracking (stress corrosion, stress crazing)is the formation of crazes under the physicalaction of chemicals, especially surfactants.Stress corrosion starts at polymer surfaces andproceeds into the interior until the polymerfinally cracks. The appearance and the extentof stress cracking depend on the polymer –reagent interaction and the magnitude of thestress.

Effects are weak in nonwetting liquids butstrong in polymer – liquid systems with solubil-ity parameters of polymers and liquids matchingeach other and evenmore dramatic under tensionin the presence of surfactants. Stress crackingdecreases with increasing molar mass of thepolymer since entanglements allow stresses torelax elastically. Cross-linked polymers are lessprone to stress cracking for the same reason.Stress cracking is also reduced if polymer plas-ticizers are present in plastics because theseadditives increase themobility of chain segmentsand thus the ability to relieve stresses. The sameaction is responsible for the fact that no stresscorrosions are observed above glass transitiontemperatures.

8.6.6. Fatigue

Materials may be damaged not only ‘‘instan-taneously’’ (i.e., on impact) but also by static orperiodic loads after certain times or number ofloadings. This fatigue is characterized by thefatigue limit (endurance) at which the plasticsare not damaged even after infinite time and thefatigue strength, which indicates the load atwhich damage sets in after a certain time.

Plastics may be subjected to static loads forcertain times t, after which their fracturestrengths sB are measured by tensile tests. Thelogarithms of strength of amorphous polymersusually decrease linearly with logarithms of timedue to viscous flow (Fig. 55). Partially crystal-line polymers show a bend in these lines aftercertain times, which indicates a change fromtough fracture (short times) to brittle fracture

Figure 54. Crazes in a polystyrene drawn to 25% [81]


(long times), probably caused by recrystalliza-tion phenomena.

8.7. Surface Mechanics

8.7.1. Hardness

The hardness of a material is its resistance topenetration by another body. Hardness is a verycomplex quantity; it depends on Young’s modu-lus, yield stress, and stress hardening. A generaldefinition of hardness, applicable to all materials,does not exist; neither does a universally appli-cable testing method. The various technical testmethods thus emphasize one or another factorthat contributes to the hardness of a specific classof materials.

The hardness of hard plastics is normallycharacterized by various Rockwell (ISO, ASTM)or ball indentation hardnesses (DIN, ISO). Thesemethodsmeasure the indentation of a polymer bya steel sphere under load and thus the compres-sion set and the recoverable deformation. Theplastic deformations of polymers increase withtime (creep), whereas those of metals are timeindependent. Because of the short duration of thehardness test polymers exhibit relatively highRockwell hardnesses.

The hardness of soft plastics is characterizedby their durometer (ASTM) or various Shorehardnesses (ISO, DIN). These methods measurethe resistance to penetration by a truncated cone

(static methods). Hardness properties of metalsand hard plastics are evaluated by another Shorehardness that uses the rebound of a small steelsphere (dynamic method).

Allmethodsmeasure the hardness of surfaces,not of the interior of the specimen. The surfacemay, for example, be plasticized by the humidityof the air. Crystallizable polymers may havelower surface hardnesses than interior hard-nesses (if the plastic had been injected into acold mold) or the reverse may be true (if tran-scrystallization occurred).

8.7.2. Friction

Friction, the resistance against the relativemove-ment of two bodies contacting each other ismeasured by the friction coefficient m¼R/L(i.e., the ratio of friction R to total load L).Friction depends in a complex and not under-stood way on both the surface roughness of thespecimen and its mechanical properties.

The rolling of hard bodies on soft materials isdeterminedalmost exclusively by thedeformationof the soft base (i.e., its viscoelastic properties).Elastomers thus have fairly high friction coeffi-cients of 0.5<m<3.0, depending on the contactingbody and its type of movement (rolling, sliding).

The sliding of hard bodies on other hardbodies occurs on the tops of the microscopicsurfaces: the true contact area is much smallerthan the geometric one. The applied load thusacts on very small effective areas. Local stressesare high and the tops are leveled. Large adhesionforces exist between chemical groups of theresulting effective contact areas of both bodies,which must be overcome by breaking the bondsor by shearing one of the materials. The adhesivefriction R¼Aw �sb is given by the effective con-tact surface Aw and the shear strength sb. Softmaterials possess high effective surfaces (largeAw) and are easily sheared (small sb), whereasthe opposite is true for hard materials. Plastics,metals, and ceramics therefore often exhibit verysimilar friction coefficients (Table 28).

8.7.3. Abrasion and Wear

Abrasion is the loss of material from surfaces byfriction. It is thus affected by both friction prop-

Figure 55. Time dependence of tensile fracture strengthsafter static loading during time t. UP-GF¼Glass-fiber-rein-forced unsaturated polyester; SAN¼Styrene – acrylonitrilecopolymer (impact polystyrene); PS¼Polystyrene;PE¼PolyethyleneReprinted with permission by BASF AG, Ludwigshafen [78]


erties and hardnesses of the specimens. Theabrasion coefficient K is given by the appliedforce F, the linear speed v of the contacting body,the total time t, and the volume loss DV of theabraded material: K¼DV/(F � v � t).

Abrasion coefficients vary widely withpolymer type and state (resting, mobile)(Table 29).

The best resistance against abrasion is shownby polyureas, followed by polyamides and poly-acetals. It can be enhanced greatly by addition ofcertain fillers (e.g., short fibers).

9. Electric Properties

Matter is subdivided according to its specificelectrical conductivity s into insulators (s ¼10�14–10�22 S/cm), semiconductors (102 –10�9 S/cm), conductors (> 103 S/cm), andsuperconductors (� 1020 S/cm). Most plasticsare insulators (Section 9.1), but certain poly-mers are intrinsic semiconductors and somemay even be conductors after doping(Section 9.2).

9.1. Dielectric Properties

9.1.1. Relative Permittivity

Groups within a molecule and entire moleculesof an insulator are polarized by applied electricfields. Polarization is usually measured by theratio of capacitances of a condensor in vacuo andin the specimen (i.e., the relative permittivity erof the specimen; formerly called the dielectricconstant). Relative permittivities are low forapolar polymers [polytetrafluoroethylene(PTFE); PE], higher for polymers with polariz-able groups (PS, PC), and still higher for polarmaterials [dry polyamide (PA)] (Table 30).

The relative permittivity thus increases withincreasing water content of plastics (er¼81 forwater). It also increaseswith increased segmentalmobility (er¼13.0 for cis-1,4-polyisoprene); rub-ber-modified plastics have higher relative per-mittivities than conventional plastics. Expandedplastics and elastomers are composites with air(er¼1.00058) and subsequently have low relativepermittivities of ca. 1 – 2. Fillers increase therelative permittivities to values up to 170 (filledthermoplastics) and up to 18 000 (filledelastomers).

9.1.2. Dielectric Loss

Dipoles try to follow the direction of an electricfield if an alternating current is applied. Therequired adjustment times correspond to the ori-entation times of groups and molecules. Thefaster the alternation, the longer the orientationlags behind the field and the greater is the elec-trical energy consumed. Available output poweris decreased because electric power is lost byconversion into thermal energy.

The ratio of power loss Nv to total poweroutput Nb is called the dielectric dissipationfactor or loss tangent tan d, which can also beexpressed as the ratio of imaginary relative per-mittivity (e00) to real relative permittivity (e0):

Nv=Nb ¼ tand ¼ sind=cosd ¼ e00=e

0 ð94Þ

Sometimes power factors sin d are given insteadof loss tangents tan d.

Polymers with high loss factors e � tan d canbe heated and thus welded by high-frequency

Table 28. Friction coefficients of various sliding bodies

Plastic Friction coefficient of

Plastic Plastic Steel

on on on

plastic steel plastic

Poly(methyl methacrylate) 0.8 0.5 0.45

Polystyrene 0.5 0.3 0.35

Polyethylene, high density 0.1 0.15 0.20

Polyethylene, low density 0.3 0.80

Polytetrafluoroethylene 0.04 0.04 0.10

Table 29. Abrasion coefficients K for moving plastics against resting

materials

Resting material 1010 K Moving polymer 1010 K

MPa�1 MPa�1

Polycarbonate A 200 000 polyamide 66 11 000

Polyamide 66 250 polycarbonate A 9 800

Polyamide 66 220 polyamide 66 510

Polyamide 66 10 polyacetal 12

Polyacetal 11 polyamide 66 15

Steel polyamide 66 8 600

Steel polyamide 66

with 30% glass fibers

1


fields; PVC is an example. Polymers with lowloss factors [PE, PS, polyisobutylene (PIB)], onthe other hand, are excellent insulators for high-frequency conductors.

Real and imaginary relative permittivitiesdepend on the frequencies v of the alternatingcurrent (Fig. 56). The function e0¼f (v) corre-sponds to a dispersion and the function e00¼f (v)to an absorption of energy. Transitions and re-laxations consume energy and therefore inflec-tion points (e0- curves) and maxima (e00- curves)are found at appropriate temperatures andfrequencies.

9.1.3. Dielectric Strength and TrackingResistance

The imaginary part of the relative permittivity iscaused by the dissociation of polar groups thatmay be either inherent to the polymer or intro-duced by extraneous impurities. These polargroupsmust be of ionic nature since the electricalconductivities of conventional plastics arestrongly temperature dependent (electronic con-ductivities are far less temperature dependent).

Heat is caused to develop by the imaginarypart of the relative permittivity. The low thermalconductivities of plastics do not allow this heat todissipate, and the temperature increases. Ionicconductivities are thus increased until a break-down (arcthrough) finally occurs. The resistanceagainst such a breakdown is measured by theelectric strengths S of a plastic (‘‘dielectricstrength’’) (Table 30).

A breakdown can also occur through trackingon the surface of a plastic. The tracking resis-tance is difficult to measure because surfaceresistivities are 2 – 3 decades lower than vol-ume resistivities (Table 30). The tracking resis-tance is thus measured by standardized meth-ods, such as the maximal voltage that does notcause tracking if 50 drops of an aqueous0.1 wt% NH4Cl solution are applied betweentwo platinum electrodes that are under an alter-nating current and 4 mm apart on the specimensurface. A polymer has a good tracking resis-tance if it forms volatile products and no carbonupon degradation (volatile monomer by depo-lymerization of PMMA, volatile oligomers bydegradation of PE or PA). Poly(N-vinyl carba-zole) does not form volatile products and thus

Table 30. Electrical properties of plastics

Polymer Dwa rvc

W � cmrsd

WSf

% erb tan de kV�1mm�1 Ug/V

PTFE 0 2.15 1018 0.0001 40 > 600

PE 0.05 2.3 1017 1013 0.0007 70 600

PS 0.1 2.5 1018 1015 0.0002 140 500

SAN 3 0.0070 100

ABS 3.2 1015 1013 0.02 15 600

PVC < 1.8h < 3.7h 1015 1013 0.015 < 50 < 600

PA 6

Dry 0 3.7 1015 0.03 < 150 600

Conditioned 9.5 7 1012 0.3 80 600

CA 4.7 5.8 1013 0.03 35

UP 3.4 1013 1012 0.01 50 500

PUR 4 1013 0.05 30

PF 8 1014 0.05 12

With inorganic fillers 1010 < 0.5 14 < 150

Without inorganic fillers 109 < 0.5 10 125

UF 6 1011 0.1 10

aDw¼water absorption (at 50% relative humidity.ber¼relative permittivity (‘‘dielectric constant’’).crv¼volume resistivity (inverse specific electrical conductivity).drS¼surface resistivity (inverse surface conductivity).e tan d¼dissipation factor (loss tangent, at 1 MHz).f S¼dielectric strength.gU¼tracking resistance (method KC).hDepends on impurities from polymerization (e.g., emulsifier residues).


has a poor tracking resistance although it is agood insulator.

9.1.4. Electrostatic Charging

Static electricity originates from an excess or adeficiency of electrons on isolated or ungroundedsurfaces. It can be created by rubbing two sur-faces against each other (triboelectric charging)or by contact of a surface with ionized air. Matteris charged electrostatically if specific conductivi-ties are lower than ca. 10�8 S/cm and relativehumidities lower than ca. 70%. All conventionalplastics can thus be electrostatically charged (Ta-ble 30). Charge densitiesmay vary between, e. g.,8.2 C/g for polychlorotrifluoroethylene (PCTFE)and � 13.9 C/g for phenolic resins, and chargesmay vary between 3000 V/cm (POM vs. PA 6)and � 1700 V/cm (ABS vs. PA 6).

Static charging can be reduced by incorpo-ration of conducting fillers into the plastics, suchas carbon black or metal powders (internal anti-statics). External antistatics reduce surface resis-tivities by increasing the polarity of the surfacevia application of humidity-absorbing additivesor by reducing friction through lubricants orcoating with PTFE.

9.2. Electrical Conductivity(! Polymers, Electrically Conducting)

Electrical conductivities in metals are caused byN/V¼1021–1022 (quasi) free electrons per cubiccentimeterwith electric charges e�1.6� 10�19 Cand mobilities m¼10 – 106 cm2 V�1 s�1. Ac-cording to

s ¼ ðN=VÞ�m�e ð95Þ

specific electrical conductivities of metals aretherefore between ca. 630 000 (Ag) and 10 400(Hg) S/cm. Graphite exhibits s¼104 S/cm inplane direction and 1 S/cm perpendicular to it.Semiconductors possess carrier mobilities simi-lar to metals but at far lower carrier concen-trations.

Charge transfer occurs fairly easily in metalsand semimetals because atoms are tightly packed.Chain atoms of polymer molecules are also closein the chain direction because of covalent bonds.Only van der Waals and/or dipole forces actbetween chains, however, resulting in large inter-molecular atomic distances and very difficultcharge transfers. All electrons are furthermorelocalized in covalent polymer chains. Conven-tional polymers are thus insulators.

Figure 56. Frequency dependence of real (eþ) and imaginary relative permittivities (e00) of a poly(vinyl chloride) at varioustemperaturesUpper: b-dispersion; lower: g-dispersion.Reprinted with permission by H€uthig and Wepf Publ., Basel [5]


Polymers with conjugated chains [e.g., trans-polyacetylene�(CH¼CH)n�] are, for these rea-sons, merely semiconductors and insulators evenif the chains are planar. These low conductivitiescan be increased substantially, however, if thepolymers are doped with substances such as I2,AsF5, BF3, etc.: doping with AsF5 increases thespecific electrical conductivity of trans-polyace-tylene from 10�9 to 1200 S/cm and of poly(p-phenylene) from 10�15 to 500 S/cm. Such dopedpolymers can be processed like thermoplastics toany shape desired, which together with their lightweight makes them attractive for manyapplications.

The action of these dopants is quite differentfrom those of small amounts of dopants ininorganic semiconductors. The doping of inor-ganic semiconductors such as GaP, InSb, or Gegenerates quasi-free electrons (n- carriers) ordefect electrons (p- carriers), whereas the dop-ing of suitable organic polymers leads to oxida-tion (p-doping) or reduction (n-doping) reac-tions. Sizable effects in organics are thusachieved only if large amounts of dopants areused, often up to 1 : 1 molar ratios of dopants torepeating units.

Doped polymers exhibit neither Curie para-magnetism (localized charge carriers) nor Pauliparamagnetism (electrons delocalized over theentire system). Thus the electrical conductivityof such systems is assumed to be due to solitonsor polarons.

Double and single bonds alternate in trans-polyacetylene. Since these bonds are exchange-able, two low-energy states A and B with equalenergy must exist. A soliton is a kind of topolog-ical kink that separates the A state from the Bstate with opposite bond alternation. Polaronsare similar kinks between aromatic and quinoidstructures:

The kink is small (about 14 chain atoms intrans-polyacetylene) and thus very mobile. Two

types of solitons and polarons exist. Neutralsolitons and polarons possess radicals that areproduced as defects during isomerization of thepolymers. Charged solitons and polarons arecreated by doping, either as carbonium ions oras carbanions.

Solitons can move only along the chain; thereis no tunnel effect between chains. Because ofthis anisotropic behavior, doped polymers (andconducting low molar mass organic molecules)are called low-dimensional conductors, syntheticmetals, or organic metals.

The most important condition for the exis-tence of electrical conductivity in organicpolymers seems to be the ability to form over-lapping orbitals. The planar structure of trans-polyacetylene promotes the overlapping of itsp and p orbitals. In poly(p-phenylene sulfide)(PPS) �[S – ( p-C6H4)]n�, p and d orbitals ofsulfur atoms probably overlap with the psystems of phenylene groups; PPS – AsF5shows an electrical conductivity of 10 S/cm,although the chain is not planar and thephenylene residues are arranged at angles of45 �C to the planar zigzag chain of the sulfuratoms.

Electrically conducting polymers are present-ly used in small batteries, for example, a complexof poly(2-vinylpyridine)/I2 as cathode in Li/I2batteries for pacemakers (s¼10�3 S/cm). Otherpossible applications of electrically conductingpolymers are in solar cells, electrolysis mem-branes, microwave shielding, and integratedcircuits.

9.3. Photoconductivity

Light generates radical ions and thus photocon-ductivities in certain systems. This effect is usedin xerography to generate pictures of objects(e.g., copies of documents). The early photocon-ducting material As2Se3 has since been replacedby poly(N-vinylcarbazole), which absorbs UVlight and forms an exciton, which is ionized by anelectric field. The polymer is nonconducting invisible light; upon sensibilization by certainelectron donors, charge-transfer complexes areformed, however. Another photoconductingsystem consists of polycarbonate A andtriphenylamine.


10. Optical Properties

Many optical properties of plastics depend ontheir refractive index n, for example, reflection,gloss, transparency, and hiding power. Refrac-tive indices are in turn determined by the polar-izabilities Q according to the Lorenz – Lorentzrelationship

ðn2�1Þ=ðn2�2Þ ¼ ð4=3ÞpQ ¼ ð4=3ÞpðN=VÞ�a ð96Þ

where N/V is the number concentration ofmolecules with polarization a. The polariza-tion is a function of the dipole moments of allgroups in a molecule (i.e., the mobility and thenumber of electrons per molecule). Contribu-tions to the refractive index are thus muchhigher for carbon atoms than for hydrogenatoms. Since the contributions of the latter canbe neglected and since carbon atoms dominatethe structures of polymers, all polymers pos-sess approximately the same refractive index of1.5 (e.g., PMMA 1.492, PP-it 1.53, PS 1.59).Deviations from this rule exist for stronglypolarizable polymers (PTFE 1.37), polymerswith bulky conjugated substituents (PVK 1.69),or polymers with a high content of noncarbonatoms (PDMS 1.40). According to the molecu-lar structure of all known polymers, their re-fractive indices should be between ca. 1.33 and1.73.

Molecules are more tightly packed in crystal-line polymers than in amorphous ones. Refrac-tive indices thus increase with increasing crys-tallinity. Because crystalline polymers are al-ways anisotropic, different polarizabilities andrefractive indices are exhibited in the chain di-rection and perpendicular to it.

A part of the light falling on a homogeneous,transparent body is reflected. Reflectivity is de-fined as the ratio of the intensities of reflected andincident light R¼Ir/Io, which according toFresnel’s law depends on the angles of incidencea and refraction b:

R ¼ IrI0

¼ 1

2

sin2ða�bÞsin2ðaþbÞþ

tan2ða�bÞtan2ðaþbÞ

� �ð97Þ

The reflectivity is low at small incident angles(R¼0.040 for n¼1.5 at 10�) and rises sharply athigher ones (R¼0.388 for n¼1.5 at 80�).

Gloss is the ratio of the reflection of thespecimen to that of a standard, for example, abody with nD¼1.567 in the paint industry. Themaximum theoretical gloss Ro is given by Equa-tion (97). It increases with increasing refractiveindex of the specimen and with increasing angleof incidence (Fig. 57). Themaximum theoreticalgloss is almost never achieved because of surfaceroughnesses.

The maximum transparencies ti¼1�Ro canbe calculated from Ro¼(n�1)2/(nþ1)2 byFresnel’s law for a!0 and b!0. They can havevalues between 98.0% (n¼1.33) and 92.8%(n¼1.73) for polymers, (i.e., between 2 and7.2% of the indicent light is maximally reflectedat the polymer – air interface). These ideal trans-parencies are rarely achieved for polymers be-cause a small portion of the light is alwaysabsorbed and/or scattered. Poly(methyl methac-rylate), one of the most transparent plastics,never exceeds a transparency of ca. 93% be-tween wavelengths of 430 and 1100 nm (theory96.1%). Transparencies decrease above wave-lengths of ca. 1150 nm and (rapidly) below380 nm. All polymers except halogenated poly-ethylenes absorb infrared radiation.

A distinction is usually made between trans-parent and translucent polymers. Transparentpolymers have transparencies> 90%; they lookclear even at greater thicknesses. Translucentpolymers (ti<0.90) appear clear only as thinfilms. They are also called contact clear because

Figure 57. Maximum theoretical gloss as a function of therefractive index of specimen for various angles of incidenceaand a standard with nD¼1.567Reprinted with permission by H€uthig and Wepf Publ., Basel[5]


films look clear in contact with packaged goodsbut turbid when viewed alone.

An additional loss of clarity is caused by lightscattering. Electromagnetic waves lose part oftheir energy by scattering in inhomogeneoussystems. The loss of contrast by forward scatter-ing is called haze. The combined loss by forwardand backward scattering makes a specimenmilky. A body appears opaque if local fluctua-tions of refractive indices or orientations ofanisotropic volume elements are present. Thedifferent volume elements must also be largerthan the wavelength of incident light. The clarityof a material can thus be increased considerablyif the size of the different volume elements (e.g.,microdomains) is decreased. Diminished differ-ences in refractive indices improve the clarity toonly a small extent. Lamellar structures areoptically less heterogeneous than spherulites ofapproximately the same diameter. Under certainconditions, clear polyethylene films can be pro-duced by quenching and orientation, althoughcrystalline lamellaewith dimensions greater thanthe wavelength of light are present in these films.

11. Polymer Composites(! Composite Materials)

11.1. Introduction

11.1.1. Overview

The term composite has various meanings. Ingeneral, it denotes a complex material in whichtwo or more distinct substances combine toproduce some properties not present in any indi-vidual component. In biomaterials, it means anytwo joined materials (e.g., polymer- coated tita-nium parts). In engineering, composites are morenarrowly defined as physical admixtures of vari-ous materials that are present as distinct phases.The term ‘‘phase’’ is used here in the descriptivesense, not in the thermodynamic one. The engi-neering term ‘‘composite’’ thus includes onlyheterogeneous composites. Heterocompositescan be further subdivided into microcomposites(dispersed phase in the micrometer to millimeterrange) and macrocomposites. Typical nonpoly-mer heteromicrocomposites are metal alloys; atypical heteromacrocomposite is steel-reinforcedconcrete.

Polymer composites are defined as compositesin which at least one component is of a polymericnature. In accordance with the general definitionof a composite and in contrast to the engineeringuse of the word, the term ‘‘polymer composite’’ isoften used to cover not only heterogeneous mix-tures of a polymer and anothermaterial (minerals,fibers, other plastics, elastomers, etc.), but alsohomogeneous (singlephase) materials of twopolymers (homogeneous polymer blends). Suchpolymer composites are a subgroup of ‘‘multi-component polymer systems’’,which also includecopolymers (two or more types of monomericunits chemically bound together).

Polymer composites occur naturally (wood,bamboo, lobster shells, bone, muscle tissue, etc.)or are manufactured synthetically. Syntheticpolymer composites can also be subdivided intosingle-phase (homogeneous) and multiphase(heterogeneous) composites. Further subdivi-sions may be according to the secondcomponent’s size (microcomposites, macrocom-posites), chemical nature (air, low molar massplasticizer, elastomer, plastic, mineral), geome-try (particulate, fiber, platelet, fabric), andmacroconformation (if polymeric: coil, rod), etc.(see Fig. 58). Most of these subclasses havedifferent technical names depending on whetherthe glass transition temperature of the continuousphase is above (plastics) or below (rubbers) theuse temperature. The same name is often given tovarious subtypes.

Amixture of two (ormore) different polymersis often called a blend when both polymers areeither above (rubber) or below (plastics) theirglass transition temperatures. Blends are distin-guished from composites of two polymers suchas polymer – fiber-reinforced or rubber-tough-ened plastics. The term blend is sometimes re-stricted to mean only ‘‘incompatible polymermixtures’’, whereas compatible polymer mix-tures are called polymer alloys. The latter termis, however, occasionallymore narrowly used formixtures of two crystallizable polymers.

The term miscibility refers to admixtures onthe molecular level (nanometer range), that istrue thermodynamic solubility. It is sometimesused more loosely for any polymer mixture thatexhibits only one glass transition temperature.Compatibility denotes the ability of admixturesto be blended to heterogeneous microcompositesthat do not separate into macroscopic phases.


11.1.2. Mixture Rules

The composition dependence of properties Q ofcomposites can often be described by mixturerules. The generalized simple mixing law relatesQ to the fractions fA¼1�fB of components A andB with properties QA and QB:

Qn ¼ QnA�fAþQn

B�fB ð98Þ

The generalized simple mixing law is usuallyapplicable to single-phase composites without

specific interactions of its components and totwo-phase systems with regularly dispersed dis-crete phases of ‘‘infinite’’ dimensions. It includesthree special cases that are known by differentnames in different fields (Table 31) and areillustrated in Figure 59.

The rule of mixtures (n¼1) applies, for exam-ple, to variousmoduli if both components behaveelastically. An example is Young’s modulusparallel to the fiber direction for epoxide resinsreinforcedwith long glass fibers (see below). The

Figure 58. Classification of polymer composites of a base polymer (matrix polymer) with other materials (plasticizer, plastic,air, long fiber, layered materials). Some of these materials have their molecules in different shapes (coils, rods) or have variousouter shapes (particulates, short fibers, platelets). Adopted from [1].


same composites follow the inverse rule of mix-tures (n¼�1) if the modulus is measured per-pendicular to the fiber direction and no slippageoccurs. The logarithmic mixture rule

logQ ¼ fA�logQAþfB�logQB ð99Þis obtained from Equation (98) for n¼0 aftersome mathematical manipulation. The onlyknown case concerns the permeation of oxygenthrough ABS resins. The proper fraction fi inEquations (98) and (99) is always the volumefraction. If weight fractions are used instead,deviations from the curves shown in Figure 59occur, which may be confused with either devia-tions from additivity or specific interactions.

True deviations from the upper bound S andlower bound I (Fig. 59) may be caused by irregu-larities in phase distributions (discrete phases) orphase continuities (continuous phases), phase

alignments (anisotropic phases), bonding (adhe-sion), or nonuniform stresses. The resulting func-tions always lie between the upper and the lowerbound if specific interactions are absent. Manyempirical, semiempirical, and theoretical expres-sions have been proposed for such composites. Awidelyusedfunction is theHalpin – Tsai equation

Q ¼ QB� 1þK1K2fA1�K2fA

;K2 ¼ QA�QB

QAþK1QBð100Þ

whereK1 is an adjustable constant. The Halpin –Tsai equation gives the lower bound for K1!0and the upper bound forK1 !¥. Particulate fillersoften have K1�0, and fiber-reinforced plasticsK1�2 L/d, where 2 L/d is the aspect ratio of thefiber.

Specific interactions between components canbe considered by an additional interaction term.This term is differently defined, for example:

Table 31. Names of simple mixing rules

Field Property exponent in generalized mixing law

n¼1 n¼0 n¼� 1

Mathematics arithmetic mean harmonic mean geometric mean

Chemical engineering rule of mixtures logarithmic mixture rule inverse rule of mixtures

Mechanical engineering Voigt model Reuss model

Electrical engineering parallel series

Materials science upper bound lower bound

Figure 59. Mixing laws for composites with QA¼110 and QB¼10: left: Q¼f (fA); right: log Q¼f (fA)Simple mixing laws with interaction parameterQAB¼0 (S¼simple mixing law; L¼logarithmic mixing law; I¼inverse mixing law- - - Composites with interaction parameters QAB¼140 and 15, as indicated


Q ¼ QAfAþQBfBþKifAfB;Ki ¼ 2ð2QAB�QA�QBÞ ð101Þ

where the property termQAB is taken at fA¼fB¼1/2. The valueQABmay be an interaction parameterbetween components A and B in homogeneousmixtures or the property of the interphase betweenA and B phases in heterogeneous mixtures. Theupper bound for absent interactions or interphasesis retrieved for the condition QAB¼(QAþQB)/2.The functions for QAB„(QAþQB)/2 may lie fullyor partially outside the range between upper andlower bounds (Fig. 59); that is synergistic effects(above the upper bound) or antagonistic effects(below the lower bound) may be present. Theymay also show maxima and minima, dependingon the relative magnitudes of QAB, QA, and QB.Maxima or minima that exceed the highest prop-erty value (either QA or QB) are sometimes con-sidered the true criteria for synergistic and antag-onistic effects, respectively.

11.2. Filled Polymers

11.2.1. Microcomposites

The addition of fillers (low thermal expansion) topolymers (high thermal expansion) reduces the

proportion of the latter and thus the shrinkage ofplastics on processing (Table 32).

The melt flow is also lower.Heat deflection temperatures (HDT) of

amorphous polymers are either the same asthose of unfilled plastics or no more than ca.10 K higher (Fig. 60), group a), probably be-cause of the increased viscosity of the filledplastic. The HDTs of amorphous thermoplas-tics are almost identical with glass transitiontemperatures.

Figure 60. Heat deflection temperatures HDTF of thermoplastics filled with 30 wt% short glass fibers as a function of heatdeflection temperatures HDTu of the corresponding unfilled polymers, both at 1.85 N/mm2 (ISO/R 75 A)(.) Amorphous polymers; (�, *) crystalline polymers; solid line: HDTF¼HDTu; broken lines: empiricala) Amorphous polymers; b) Apolar crystalline polymers; c) Polar crystalline polymersInsert: difference HDTF–HDTu as function of melting temperatures TM of unfilled crystalline polymers

Table 32. Effect of fillers on some properties of amorphous (A) and

crystalline (C) thermoplastics [(") weak increase, " increase, ""strong increase, (#) weak decrease, # decrease, ## strong decrease]

Property Extenders

Reinforcing

agents

A C A C

Shrinkage # # # #Heat deflection

temperature (" #) "Melt flow # # # #Young’s modulus (") (") " "Flexural modulus " " " " "Fracture strength # # " "Brittleness " " " # a " # a

*Tough plastics become more brittle and brittle plastics become

tough.


The HDTs of crystalline polymers depend ona number of factors. Unfilled or particulate-filledcrystalline polymers show HDTs that are oftenconsiderably lower than their melting tempera-ture. Upon fiber-filling, HDTs of crystallinepolymers increase strongly; they may reach va-lues near the melting temperatures. This behav-ior is thought to be due to additional polymercrystallization near, or polymer adsorption on,the fiber surface, epitaxial layers have been foundto extend from the filler up to 150 nm into thematrix. The surface layers overlap; the resultingphysical network reduces creep.

Two groups of HDTs of glass-fiber-filledcrystalline polymers can be distinguished(Fig. 60). The HDTs of group b are about 50 –60 K above those of their unfilled counterparts.This group comprises apolar polymers such aspolyethylene, polypropylene, and poly(pheny-lene sulfide); polyoxymethylene also belongs togroup b because its oxygen groups are burieddeep inside compact helical structures, which arethus apolar on their surfaces. The difference inHDTs of filled and unfilled group b polymersdoes not vary with melting temperature. Group cincludes polar crystalline polymers (polyesters,polyamides, etc.). For this group, the differencein HDTs of filled and unfilled polymers increaseswith the melting temperature of the unfilledpolymer.

Young’s moduli of thermoplastics increasewith filler content (Fig. 61). The increase is smallfor spheroidal fillers (glass spheres, chalk),stronger for platelets (kaolin, talc), and stron-gest for fibers (glass). Short fibers are usuallyadded in amounts of ca. 30 wt%, which corre-sponds to ca. 17 vol% for glass fibers ( r¼2.55g/cm3) in an average polymer ( r�1.2 g/cm3).Higher fiber content often leads to packingproblems since the maximum volume fractionof three-dimensional randomly packed rodswith L/d¼20 is already ca. 25% (glass fiberstypically have diameters d¼10 – 20 mm andlengths of ca. 0.2 mm after injection molding).Particulate fillers can be added in far greateramounts without sacrificing properties (see Ta-ble 19) because maximum packing densities ofspheres are, for example, 0.745 for the hexago-nally most dense and 0.637 for the randomlymost dense packing.

Young’s moduli E of filled materials can bedescribed by a modified mixing law

E ¼ EMfMþf EFfF ¼ EMþðf EF�EMÞ�fF ð102Þ

where f is an adjustable parameter. The data inFigure 61 can be described with f¼0.390.03(chalk), 0.660.04 (kaolin), and 1.61 (talc). Theeffect of 30 wt% of short glass fiber was testedin 14 thermoplastics, and f was found to be0.570.04. These numbers increase with thespecific area of the fillers, which are given as0.3 – 2.2 (ground limestone), 0.5 – 1 (glassfibers), 6 – 22 (kaolin), and 6 – 17 m2/g (talc)[83]. Composites obviously increase in stiffnessas the contact between filler and polymer seg-ments increases. Good adhesion is not neces-sary, sinceE ismeasured for strains approachingzero.

The adjustable parameter f of Equation (102)adopts a physical meaning for short fiber rein-forced plastics. In such composites, forces aretransferred to the hard fiber from the softmatrix if(1) the Young’s modulus of the fiber is greaterthan the Young’s modulus of the matrix(EF>EM), (2) the fiber lengthLF exceeds a certaincritical value LF, crit, and (3) the shear strength inthe matrix is smaller than the shear strengthbetween fiber and matrix (the fiber would beotherwise pulled out of the matrix unless thefiber breaks). In this case, f¼1�[LF, crit/(2 LF)].

Figure 61. Influence of the volume fraction fF of fillers onthe difference in Young’s moduli of filled thermoplastics (E)and their polymer matrices (EM)GS¼glass spheres; C¼chalk; K¼kaolin; GF¼glass fibers;(S¼short; L¼long)*¼polyethylene;�¼polypropylene;�¼polyoxymethylene;�¼poly(butylene terephthalate); .¼polyamide 6The solid line for GF-L ( k) corresponds to the simple mixinglaw. From data of [82]


Fracture strengths are, however, measured formaximum strains. The failure mode of filledthermoplastics is matrix dominated. Electronmicrographs show that at low fiber contents,planar cracks spread through the matrices anddebonded fibers are pulled out of either surface;the matrix must thus adhere well to the filler.

The tensile strengthsB at break is given by therule ofmixtures (sB¼sF fFþs0

M0 fM)wheres0M0

is the tensile stress of the matrix upon applicationof a load sB to the composite. This relationshipapplies if (1) the tensile strength sB is greaterthan the contribution sM fM of the matrix com-ponent to the total tensile strength sB (that issB>sM fM), and (2) the volume fraction fF of thefiber exceeds a certain minimum value(fF>fF, min).

Particulate Fillers usually strongly reducethe fracture strengths of composites of amor-phous thermoplastics, whereas those of crystal-line polymers are reduced less or not at all. Shortfibers generally increase the fracture strengths byfactors of 1.5 – 2 for amorphous and crystallinepolymers alike. Rigid PVC is an exception be-cause its fracture strength is reduced on fiber-filling. The moduli and strengths can be furtherenhanced if coupling agents are used, whichimproves the bonding between fiber and matrix(e.g., silanes for glass-fiber-filled polymers).

11.2.2. Molecular Composites

The problem of insufficient bonding betweenfiber and matrix can be dramatically reduced ifso- called molecular composites are used. Thesematerials are dispersions of semiflexible (rod-like) polymer molecules with mesogenic units inchemically similar polymer matrices, e.g., poly( p-phenylenebenzobisthiazoles) in polybenzi-mides (see Fig. 52). The mesogens are not trulymolecularly dissolved; rather, they form micro-domains in the matrix. The segment axes arerandomly distributed in these domains if themolecular composites are formed from polymersolutions with total polymer concentrations cbelow the critical isotrope phase – mesophaseconcentration ci/n. Microdomains show meso-phase behavior if films or fiber are formed atc>ci/n. Such microcomposites have excellentmoduli and fracture strengths (Fig. 52).

11.2.3. Macrocomposites

Polymer macrocomposites are heterogeneouscomposites of polymers and ‘‘macro’’-sized ad-ditives. Examples are polymer concrete, compo-sition board, long fiber-reinforced polymers, andplywood.

Polymer Concrete is composed of polymer[usually polyester or poly(methyl methacry-late)], aggregate (sand, ground limestone, etc.),and other additives (dyes, etc.); it does not con-tain cement. Polymer- concrete hybrids includepolymer – cement hybrids (cement is partiallyreplaced by polymers) and polymer-impregnatedconcrete (conventional concrete saturated with amonomer that is polymerized in place). Polymerconcretes have higher moduli and higher tensileand compressive strengths than ordinary con-cretes. They are not vulnerable to damage byfreeze-thaw cycles.

Composition Boards are panel products.They include particleboard, fiberboard, hardboard from flakes or shearings, etc. The fillersare mainly wood products; the resins, urea –formaldehyde (interior applications), and poly-urethanes or phenolic resins (exterior).

Long-fiber-filled polymer macrocompositesrange in structure from polymers filled with‘‘long’’ fibers 6 – 12 mm in length to fiber strandsand mats filled with polymers. The filler contentcan often reach 65 wt%. Upon application oftensile stress, local stress concentrations are trans-ferred by shear forces onto the plastic – fiberinterface and distributed over the much greaterfiber surface area. The fibers must therefore bondwell to the plastic (use of coupling agents) andmust have a certain length to avoid slipping.

Young’s moduli of long glass-fiber-rein-forced epoxide resins follow the simple mixinglaw if the tensile stress is in the fiber direction(Fig. 62). The inversemixing law is not observedas well for stresses perpendicular to the fiberdirection since some fibers bend under stress.

The simple mixing law corresponds to f¼1 inEquation (102). For long fibers, f has the mean-ing of an orientation factor. It becomes 1/6 forfibers distributed three-dimensionally at random,1/2 for 90� cross-plies measured in either fiberdirection, and 3/8 for a uniform, planar distribu-tion of fibers.


This group of macrocomposites also includesprepregs (fiber mats soaked with unsaturatedpolyester resins) and the composites generatedby filament winding (wound filaments saturatedwith epoxies or unsaturated polyesters), both ofwhich are subsequently polymerized.

11.3. Homogeneous Blends

Mixtures of polymers with other polymers arecalled polymer blends (! Polymer Blends).Such blends may be composed of two thermo-plastics (plastic blends), two elastomers (rubberblends), a plastic filled with an elastomer as thedispersed phase (rubber-modified plastics), anelastomer with a plastic as the dispersed phase(polymer-filled elastomer), or a plastic filledwitha polymer melt or a low molar mass liquid(plasticized polymers). Whether or not theseblends are truly miscible on a molecular leveldepends on the thermodynamics of the systems.

11.3.1. Thermodynamics

If two components 1 and 2 are mixed, entropy S,enthalpyH, and volumeV change. Inmany cases,volume changes can be neglected and the Gibbsenergy of mixing is given by the changes inenthalpy and entropy: DGmix ¼ DHmix�T �Smix. These changes can be calculated by theFlory – Huggins theory, which assumes that themixture can be modeled by a three-dimensionallattice on which the monomeric units (or solvent

molecules) can be placed. Each monomeric unitexperiences the same force field; the theory isthus a mean-field theory. The assumption of aconstant force field is fairly well fulfilled forpolymer blends and concentrated polymer solu-tions but not for dilute solutions.

The entropy and enthalpy of mixing are cal-culated separately. Entropies are calculated forideal solutions (zero mixing enthalpy); all envi-ronment-dependent entropy changes are thuszero (translational, vibrational, and inner rota-tional entropies do not change). Units can how-ever be arranged relative to each other in manyways; however, there is a combinatorial entropythat is also called ‘‘configurational entropy’’ instatistical mechanics.

The mixing of two components is modeled asa quasi- chemical reaction. The mixing enthalpyis thus determined by the change in interactionenergies and the number and type of nearestneighbors. Enthalpy and entropy terms are addedto give the molar Gibbs energy of mixing:

ðDGmixÞm=RT ¼ c�f1f2þf1�lnf1þðX1=X2Þ�f2�lnf2 ð103Þwhich, on differentiation with respect to themolar amounts of the components, yieldsthe chemical potentials, for example, of compo-nent 1

Dm1 ¼ RTfc�f22þlnð1�f2Þþ½1�ðX1=X2Þ��f22g ð104Þ

where c is the parameter for the interactionbetween component 1 and component 2 (usuallywith numerical values between 0 and 2), alsocalled the Flory – Huggins parameter. All threeterms in braces must be considered if a polymer 2is mixed with a solvent 1, for example, a plasti-cizer (X1�X2). If both components are polymershowever, then X1�X2 and the entire entropycontribution comes from the relatively smalllogarithmic term. Thus little combinatorial en-tropy is gained on mixing two polymers, and themiscibility is determined mainly by the mixingenthalpy, that is, by the term c f22.

Phase separation occurs if the curve(DGmix)

m ¼ f (f2) (at T¼const.) has a shape thatcan be touched at two points by a tangent. Thecompositions at these points are f20 and f200 (withf20<f200). Two phases exist for the unstable rangef20<f2<f200, which is separated from the stableranges f2<f20 and f200>f2 by the so- calledbinodal. The unstable range itself is subdivided

Figure 62. Young’s moduli of epoxy – glass-fiber compo-sites parallel ( k) and perpendicular (?) to the fiber direction.


by the spinodal into two metastable ranges andone unstable one. Spinodals are characterized byinflection points in the Gibbs energy – composi-tion functions and extremal values in the chemi-cal potential – composition functions. Maxi-mum, minimum, and inflection point becomeidentical at the critical point, which is definedby a zero value of the second derivative of thechemical potential

q2Dm1=qf22 ¼ RT �½2c�ð1�f2Þ�2� ¼ 0 ð105Þ

This critical point is characterized by a criticalvolume fraction f2;crit ¼ 1=ð1þX

1=22 Þ and a criti-

cal interaction parameter ccrit�(1/2)þ (1/X2)1/2.

The temperature dependence of c is approxi-mately

c � AþðB=TÞ ð106Þ

whereA andB are system-dependent constants;Bis positive for endothermal mixtures [i.e., c in-creases with increasing temperature and a homo-geneous solution exists above an ‘‘upper criticalsolution temperature’’ (UCST)]. Other systemsare homogeneous only below a ‘‘lower criticalsolution temperature’’ (LCST). The demixing iscorrespondingly either enthalpy (UCST) or en-tropy (LCST) induced.

The terms UCST and LCST do not indicatethe absolute position of demixing temperaturessince some systems show LCST>UCST(Fig. 63). Depending on the system, either anhourglass-type diagram or a closed miscibilitygap is shown.

11.3.2. Plastification

Plastification of a plastic is the flexibilization ofthematerial either by added plasticizers (externalplastification) or by incorporated flexibilizingcomonomer units (internal plastification).

The molecular action of plasticizers consistsof a flexibilization of chain segments, which canhave various causes. Polar plasticizers increasethe proportion of gauche conformations in polarchains, thus decreasing rotational barriers. Pri-mary plasticizers can dissolve helical structuresand crystalline regions if they are thermody-namically good solvents. Furthermore both pri-mary and secondary plasticizers are diluents;their addition increases the distance betweenpolymer segments and thus decreases the acti-vation energy needed for cooperative move-ment of segments. Solvation does not per seincrease chain flexibility, however, because

Figure 63. Phase separation temperature as function of polymer – solvent compositionA) Polystyrenes with various molar masses in acetone; B) Poly(vinyl alcohol- co-vinyl acetate) (93 : 7) in waterReprinted with permission by H€uthig and Wepf Publ., Basel [5]


solvent shells act as substituents and increasethe rotational barriers.

The molecular effect of an increase in chainflexibility by plasticization is measured as adecrease of glass transition temperatures(Fig. 64). Small molecules are better plasticizersthan bigger ones of similar chemical constitu-tion. The plasticizer efficiency decreases withincreasing thermodynamic ‘‘goodness’’ of theplasticizer for the polymer (greater interaction,i.e., bigger solvation). Good plasticizers withrespect to lowering glass transition temperaturesare thus small molecules that act as theta sol-vents. These plasticizers are however bad fortechnological applications because they bleed(transport of plasticizer to the surface of theplastic), migrate (transport of plasticizer intoanother contacting material), or are extractable(e.g., transport into packaged foods). Thesetransport phenomena can be reduced if polymerplasticizers are used. Increasing molar masseslead to decreasing thermodynamic compatibility,however (see below). Technical plasticizers aretherefore in most cases a compromise betweenthermodynamic plasticizer efficiency and kineti-cally hindered plasticizer transport.

Plastification can also be followed by thechanges of certain mechanical properties suchas lowering of fracture strength, increase ofelongation, and decrease of tensile moduli. Suchmethods sometimes show ‘‘antiplasticizations’’at low plasticizer concentrations (Fig. 65) (e.g.,increases of moduli). Glass transition tempera-tures are not increased, however. The effect thus

cannot be the result of increased segment mobil-ity. It may be due to a healing of microvoids inamorphous polymers such as polystyrene or toadditional crystallization of slightly crystallinepolymers such as poly(vinyl chloride).

11.3.3. Rubber Blends

About 75% of all elastomers are employed asblends. Heterogeneous blends of natural (rub-ber – styrene) – butadiene rubber or (cis-buta-diene rubber – styrene) – butadiene rubber areused mainy for tire treads since they reduceabrasion. Homogeneous blends are more rare.They possess only one glass transition tempera-ture which, for 50 – 50 blends, is an average ofthe glass transition temperatures of the two par-ent polymers. Heterogeneous blends exhibit twoglass transition temperatures, both practicallyidentical to those of the parent polymers.

Figure 64. Glass transition temperatures of (.) polystyreneplasticized with methyl acetate (MeAc) or poly(vinyl methylether) (PVM) and (*) copolymers of styrene with butadiene(Bu), butyl acrylate (Ba), or acryl amide (Am)

Figure 65. A) Glass transition temperature TG and B) frac-ture strength sB and elongations eB at break of a poly(vinylchloride) plasticized with tricresyl phosphate (TCP).Reprinted with permission by H€uthig and Wepf Publ.,Basel [7]


Homogeneous blends are usually formed if thedifference in solubility parameters is smaller than0.7 cal1/2 cm�3/2 (1.44 J1/2 cm�3/2).

11.3.4. Plastic Blends

Plastic blends are usually immiscible because thecombinatorial entropy of mixing is too small(high molar masses) and the enthalpy changeson mixing are often positive. Miscibility is ob-served for three types of systems:

1. Chemically similar polymers, for example,polystyrene – poly(o- chlorostyrene), show-ing both LCST and UCST

2. Systems having specific interactions betweendifferent components, for example, polysty-rene – poly(vinyl methyl ether); these sys-tems show only LCSTs

3. Systems consisting of oligomers, for exam-ple, oligo(ethylene oxide) – oligo(propyleneoxide); these systems possess only UCSTs

Homogeneous polymer blends show only sin-gle glass transition temperatures; the compositiondependence of these TG’s can be described by thesimple rule of mixtures. Two-phase systems al-ways show twoglass transition temperatures if thephase diameters are greater than ca. 3 nm. Trans-parency, on the other hand, is no indication of asingle-phase blend since opacity can be observedonly if the refractive indices of the two phases aresufficiently different and if the phase diametersare greater than ca. one-half the wavelength ofincident light. The presence of two phases in clearspecimens can often be detected with electronmicroscopy by special staining techniques.

Modified PPO, a blend of poly(2,6-dimethyl-phenylene oxide) and polystyrene, is the industri-ally leading homogeneous blend. Blends of poly(vinyl chloride) with poly(methyl methacrylate),poly(ethylene-co-vinyl acetate) or chlorinatedpolyethylenearealsosaid tobeone-phasesystems.

11.4. Heterogeneous Blends

11.4.1. Compatible Polymers

Two polymers may be thermodynamically im-miscible but still mechanically compatible.

These compatible blends are two- or multiphasesystems that show multiple glass transition tem-peratures, which do not change with composi-tion. The components do not separate, however,under mechanical stress during the expected lifeof the product. Such mechanical compatibilitiescan be improved or introduced by the addition ofdiblock polymers. One block of these diblockpolymers is compatible with one phase type ofthe heterogeneous blend and the other one withthe other type (see Section 5.3.6). The two blocksneed not necessarily be chemically identical withthe two parent polymers, that is, a compatibilityof poly (A) and poly (B) can be achieved notonly by addition of poly (A)-block-poly (B) butalso by poly (A)-block-poly (C) if the C block iseither miscible with poly (B) or can form mixedcrystals with poly (B).

11.4.2. Blend Formation

Heterogeneous polymer blends can be producedby mixing together two polymers (as melts,lattices, or in solution) or by in situ polymeriza-tion of a monomer in the presence of a dissolvedpolymer.

The energy taken up during melt mixing isused for flow processes and for the generation ofsurfaces of new microdomains. After some time,a steady state is established and the domain sizebecomes constant. No macroscopic demixingoccurs because of the low diffusion coefficientsresulting from the high viscosities.

Latex Blending consists of the mixing ofaqueous dispersions of two polymers. Far lowertemperatures and lower shear fields can be em-ployed compared to melt blending. The goodmixing of the latex particles remains after coagu-lation. The domain size is, however, restricted tothe size of the latex particles themselves; it is notaltered by subsequent melting of the coagulate.

Solution Blending involves the mixing oftwo polymer solutions. Miscible polymers canbe blended to domains of molecular size. Solu-tions of immiscible polymers demix, however, atvery low concentrations, sometimes under frac-tionation with respect to molar masses. Domainsgrow further on solvent removal by distillation orfreeze drying.


In situ polymerization involves solutions orgels of polymers in monomers, which are subse-quently polymerized. The in situ polymerizationof styrene in a styrenic polydiene solution, whichleads to rubber-toughened polystyrene (HIPS) ismost important industrially. The polymerizationof a cross-linkable monomer in a gel of a cross-linked rubber in the very same monomer resultsin interpenetrating networks.

Various blending processes produce blendswith very different properties (Fig. 66). The highnotched impact strengths of the polymerization-blended materials (line P) are caused by a stronganchoring of phases due to the formation of graftcopolymers of styrene on polybutadiene andcross-linking within the rubber domains, bothcaused by free-radical initiators. Such processesare less prevalent during melt blending (radicalformation by high shearing at elevated tempera-ture) (line M) and latex blending (low shearing atambient temperature) (line L). In situ polymeri-zation is thus themethod of choice for unsaturatedrubber (easy cross-linking and grafting by chaintransfer) andmonomer – rubber pairs with favor-able Q, e-values for copolymerizations. In allother cases, blends are formed by melt mixing.

11.4.3. Toughened Plastics

Rubber-modified plastics (toughened plastics,high-impact plastics) consist of rubber domainsdispersed in plastic matrices. The domain sizevaries with the blending process. Typical values

are ca. 0.1 mm for melt-blended poly(vinyl chlo-ride) – acryl rubber and 1 mm for polystyrene –polybutadiene. The domains are often multi-phased; small plastic domains are imbedded inthe rubber domains (Fig. 67). The morphologiesdepend strongly on the blending process. Duringstirred in situ polymerizations, phase inversionsoften occur if the amount of newly formed plasticapproaches that of the incipient rubber. Duringphase inversion, already present plastic particlesmay be embedded in the newly formed rubberdomains.

Rubber-toughened plastics are valued be-cause of their improved impact strength. Onimpact, very many crazes are formed near theequators of the rubber particles. The crazes prop-agate until they encounter an obstacle (e.g.,rubber particle or shear band) or until the stressconcentration at the tip of the craze becomes verylow. Many small crazes result, and the stress isevenly distributed if the rubber phase is cross-linked and binds well to the thermoplast phase[e.g., by in situ formed graft copolymers (HIPS)].In contrast, stress peaks concentrate at a fewdefect points in normal thermoplasts.

11.4.4. Thermoplastic Elastomers(! Thermoplastic Elastomers)

Thermoplastic elastomers (elastoplastics, ther-moplastics, plastomers) are processed like ther-

Figure 66. Impact strength with notch FB as function of themass concentrationwBR of cis-1,4-polybutadiene in its blendswith polystyrene. P¼In situ polymerization of styrene;M¼Melt blending; L¼Latex blendingReprinted with permission by Plenum, New York [84]

Figure 67. Rubber domains in high-impact polystyrene by insitu free-radical polymerization of styrenic polybutadienesolutionsReprinted with permission by Society of Plastics Engineers[85]


moplastics but applied like elastomers. Theirunique properties follow from their molecularstructures; their chains consist of ‘‘soft’’ and‘‘hard’’ segments in block, graft, or segmentedcopolymers composed ofmonomeric units A andB. The A and B segments are mutually incom-patible and form locally separated regions. Witha well-designed molecular architecture, domainsof the ‘‘hard’’ A segments (transition tempera-ture>service temperature) act as physical cross-links in the continuous matrix of the ‘‘soft’’ Bsegments (transition temperature<service tem-perature) (Section 5.3.6). Such transition tem-peratures may be glass transition temperatures inamorphous polymers or melting temperatures inpartially crystalline polymers. The A segmentsattain mobility above these transition tempera-tures and the elastoplasts become processible.

Thermoplastic elastomers comprise linear tri-block polymers of the polystyrene – block-poly-diene – block-polystyrene type; radial, star, or‘‘teleblock’’ polymers of the same monomericunits; urethane segment or block copolymerswith polyester or polyether soft segments; poly-esteramides and polyesteretheramides; graft co-polymers of butyl rubber on polyethylene, vinylchloride on poly(ethylene-co-vinyl acetate), sty-

rene – acrylonitrile on saturated acryl rubbers,and various ionomers.

Thermoplastic elastomers can also be pro-duced by ‘‘dynamic vulcanization.’’ The masti-cation of blends of conventional rubbers andcrystalline poly(a-olefins) leads to chain scis-sions. The resulting macroradicals cross-link therubber domains.

The mechanical properties of thermoplasticelastomers are determined mainly by theirmorphologies. In styrene – butadiene – styrenetriblock polymers, for example, morphologiesare governed by the spatial requirements of thevarious blocks (Section 5.3.6). With a low con-tent of hard styrene segments, small sphericalpolystyrene microdomains are formed in the softpolybutadiene matrix. These microdomains actas physical cross-linkers. The distances betweenthe domains are large, and the polymer behavesas a weakly linked elastomer with correspond-ingly high extension (Fig. 68). The domains arelarger and their distances are shorter at 28%styrene units and the polymer strengthens(stiffens). The stiffening becomes strongerfor rodlike styrene domains (39% S). Lame-llar morphologies (53% S) show an ‘‘unruly’’behavior initially because of reorientation of

Figure 68. Stress – strain curves and morphologies of styrene – butadiene – styrene triblock polymers with various styrenecontentsReprinted with permission by H€uthig and Wepf Publ., Basel [5]


lamellae. At even higher styrene content, thepolymer behaves as a plasticized tough thermo-plast (65% S) or almost like polystyrene itself(80% S).

11.5. Expanded Plastics (! Foamed

Plastics)

Expanded plastics (foams, foamed plastics, cel-lular plastics) are blends of plastics with air. Theyare subdivided according to their rigidity, theircell structure, and the nature of the parent plas-tics. Rigid expanded plastics are used mainly forthermal insulation, and flexible foams for damp-ing and cushioning materials.

The rigidity (‘‘hardness’’) of expanded plasticsfollows the properties of the parent polymers.Phenolic and urea resins thus yield brittle-rigidplastics; polystyrene andhard poly(vinyl chloride),tough-rigid; and polyethylenes, polyurethanes,and plasticized PVC, semirigid to flexible foams.The elastic moduli of expanded plastics decreaseapproximately proportional to their polymercontent (simple mixing law). Since, however, thestiffness of an article increaseswith the third power

of thewall thickness, the gases in expandedplasticswork as enhancers that reduce material costs andweights.

Tensile strengths of foamed plastics also fol-low the simple mixing law. Because the tensilestrengths of gases are diminishingly small, ten-sile strengths sB of foamed plastics are deter-mined by the volume fraction fp and strengthssB,p of the plastics themselves [i.e., sB�sB,p �fp ¼sB,p � (r/rp)] (Fig. 69). Compressionstrengths follow a similar simple mixing law.

The cell structure can be open, closed, ormixed. Open- celled foams are always air filled,regardless of the blowing or expanding gasesused for foam manufacture. The trapped gasesin closed- cell structures can be exchanged withthe surrounding air only by slow diffusionthrough the polymer matrix. Since thermal con-ductivities of low-density foams ( rp<0.3) obey,to a first approximation, a logarithmic mixinglaw, they are considerably affected by the ther-mal conductivities of trapped gases [(l¼93 Jm�1 h�1 K�1 (nitrogen), 56 J m�1 h�1 K�1

(CO2), 26.4 J m�1 h�1 K�1 (CCl3F)]. The gasexchange is considerably reduced in integral skinfoams (dense skin, low-density core) and insyntactic foams (plastics filled with hollow

Figure 69. Tensile strengths of expanded plastics as a function of the volume fraction of the rigid (.) or flexible (*) parentpolymers PSolid lines indicate a) Simple mixing law for sp¼20 MPa; b) Simple mixing law for sp¼10 MPa;Insert: Thermalconductivities (for lp¼700 and lair¼110 J (m�1 h�1 K�1) of rigid (.) and flexible (o) plastic foams S: Simple mixing law;L: Logarithmic mixing law; I: Inverse mixing law


spheres; spheresmay bemade of glass, ceramics,or plastics and contain either gases or a vacuum).

12. Waste Disposal (! Plastics,Recycling)

Four different, although frequently intercon-nected, aspects must be considered in the dispos-al of plastic waste: (1) technological demands,(2) economic considerations, (3) energy con-sumption, and (4) environmental concerns.

Modern technology demands certain materialproperties for certain applications that can bedelivered only by polymers and not by othermaterials such as metals or ceramics. Examplesrange from rubber tires to high-tech applicationssuch as polymer resists in electronic chip pro-duction. The desirability of polymers for tech-nology-driven demands is usually undisputed;the discussion centers rather around the desir-ability of commodity plastics, especially forpackaging purposes.

It is also not much disputed, at least amongpeople that are well-versed in technology, thatpolymeric materials are very economical com-pared to other materials in terms of productionand use. However, the ecological costs are ques-tioned: the hidden costs of the ‘‘free’’ use of air,water, and land in the production and disposal ofpolymers and the suspected high energy con-sumption in the use of polymers.

Energy consumption has been studied byconsumer agencies (e.g., NATO Science Com-mittee), industry (e.g., BASF), and government(e.g., Swiss Environmental Protection Agency).Although differences exist, newer data all agreethat the energy consumed in plastics productionagrees favorably with that of other materials(Table 33) if use (on a volume basis) rather thansale (on a weight basis) is considered.

Energy considerations must however bebased on specific applications of materials. Forexample, these considerations must take intoaccount for a certain good the current possibleuse of different materials for its manufacture, itsuse (including cleaning), possible recycling, and/or disposal by landfill or incineration (with par-tial use of heat). This is shown for the example of1000 1-L milk packages (in Table 34).

Energy data are again favorable for plastics,as are the critical amounts of air and water

employed in their production, use, and disposal(i.e., volumes to which air and water can bemaximally charged without exceeding Swissenvironmental laws). It must be mentioned inthis context that only ca. 5% of the world petro-leum production is used for the manufacture ofpolymers; the remainder is burned (as gasoline,heating oil, etc.), often with very low energyefficiency (ca. 30% in cars) and large amountsof harmful byproducts (exhaust gases).

Environmental concerns include possibleharmful effects by plastic articles, plasticsthemselves, polymers, incineration products,and byproducts of polymer and plastics manu-facture. Environmentalists estimate the amount

Table 33.Energy consumption for the production of variousmaterials

according to various sources

Material Consumption, kJ/cm3

NATO BASF SEPA*

Lumber 2.0

PE-HD 63 68

PVC 11 73 84

ABS 89 87

PET 113

PS, expanded 1.4

PUR, expanded 3.0

Paper (kraft, unbleached) 40 63

Tin plate 210

Aluminum < 460 750

Glass < 125 > 26

*Swiss Environmental Protection Agency.

Table 34. Energy consumption and critical environmental data for

1000 1-L packages of milk [86]

PE Paper

carton

Glass

bottle

Tube Bottle

Use cycle (life) 1 1 1 40

Weight per life in kg 7.0 22.0 25.0 40.0

Energy consumption in

MJ* 400 1510 1770 650

Environmental impacts

Air, 106 m3 5.9 20.5 30.9 5.4

Water, m3 3.0 17.2 154 9.3

Solids (landfill), L 2.3 9.8 8.3 6.8

Solids, (average Swiss

disposal), L** 0.35 3.0 1.3 3.3

*For average Swiss disposal: 23% landfill and 77% incineration

(55% with use of energy).**Solid waste from PE (ash from production processes), paper

(ash from production and paper), glass (with 60% recycling

assumed), aluminum and tin plate (100%, no recycling).


of plastics discarded annually into the high seasas 1�106 t. Certain plastics articles are un-doubtedly harmful to wildlife, for example,six-pack rings and old fishing nets to fish andother animals. Since man is notoriously care-less, the use of biodegradable plastics for sucharticles may be justified.

Biodegradable plastics either contain biode-gradable polymers themselves or are compoundsof conventional polymers with biodegradablepolymers such as starch. Biodegradation mayoccur via hydrolysis (starch, polyesters) or UVradiation (polymers containing carbonyl groups)or both. The degradation however is slow, takingfrom several months under laboratory conditionsto several years in landfills. Biodegraded pro-ducts may no longer be visible, but whetherbiodegradation proceeds to small molecules andwhether these molecules are harmful to livingorganisms are still not known. Harmful polymeradditivesmay be released during biodegradation.Conventional polymer molecules, on the otherhand, are not harmful to living beings, at least notto higher ones, because they can be neitherresorbed nor digested. The energy content ofplastics is of course wasted duringbiodegradation.

Biodegradable polymers thus do not seem tobe the general solution to the plastic waste prob-lem. Contrary to popular opinion, the amount ofplastics in household refuse is relatively small,ca. 7 wt% vs. ca. 50% paper, and almost con-stant over at least 25 years according to archaeo-logical studies of landfills. Weight fractions andnot volume fractions of plastics must be used forcomparison with other materials because hollowplastic containers and expanded plastics are com-pressed by the weight of the landfill (glass bottlesare not compressed). Biodegradation processesare very slow in landfills (absence of light, air,and even microorganisms); some buried paperscould be read after 25 years in a landfill.

This leaves recycling and incineration as pos-sible ways for disposing of plastics. Most indus-trial plastic waste is already recycled or inciner-ated. The problem is the collection, cleaning, andrecycling of household refuse. Only ca. 2% of allplastics consumed were recycled in the UnitedStates (Table 35) and the Federal Republic ofGermany in 1988.

Since unsorted recycled polymers representmixtures of different grades and even differentpolymers, they can be used only for low-valuearticles. For comparison: the gross discards re-covered in the United States were 25% of alu-minum, 23% of paper and paperboard, and 9%of glass.

The sorting of discarded plastics articles ismade more easy by recently introduced codeswhich are stamped on the bottom of containersor other inconspicuous places. The codes con-sist of three broken arrows, arranged in a trian-gle, and a number, sometimes also combinedwith letters and/or bar code (Fig. 70). The num-bers and letter combinations indicate the type ofplastics. The letter combinations are not alwaysidentical with the acronyms and abbreviationsrecommended by ISO, ASTM, DIN, IUPAC,etc. for the same polymers. The following num-ber and letter codes are used: 1¼PETE [for poly(ethylene terephthalate)], 2¼HDPE (for high-density polyethylene), 3¼V (for vinyl chloridepolymers), 4¼LDPE (for low-density polyeth-

Table 35. Recycling of plastics in the United States (1988)

Polymer Mass in 1000 t % Recycled

Consumed Recycled

Polyolefins 11 538 343 3.0

PVC 3 779 34 0.9

Styrenics 3 516 39 1.1

PETP (bottles) 911 54 5.9

PA 253 27 10.7

Other 6 219 < 1 < 0.01

Total 26 216 498 1.9

Figure 70. Symbols for recyclable plastics. Left: U.S. symbol with code number and code letters. All others: various symbolsused by European manufacturers.


ylene), 5¼PP (for polypropylene), 6¼PS (forpolystyrene), 7 (for all other plastics, includingmultilayered materials).

Incineration is the present method of choice inmany European communities: 77% of all house-hold refuse is incinerated in densely populatedSwitzerland and 30% inWest Germany, but only10% in the United States where 80% of therefuse is accumulating rapidly in landfills. Fur-thermore, concerns exist about the emission ofHCl from the burning of PVC, the generation ofdioxins, and the disposal of heavy-metal- con-taining ash. In the Federal Republic of Germany,only 18%of theHCl comes from the incinerationof refuse (and not more than half of it from PVC);the primary sources of HCl are power plants(1978 data). This HCl is removed by scrubbing,etc., and may be used to bind heavy metals incompost from incineration. Generation of diox-ins can be reduced significantly by high-temper-ature incinerators, which of course commandhigher investment costs.

References

1 H.-G. Elias: ‘‘Technologie,’’ Makromolek€ule, vol. 2,

H€uthig and Wepf, Basel 1992.

2 F. W. Billmeyer, Jr.: Textbook of Polymer Science, 3rd

ed., Wiley, New York 1984.

3 F. Rodriguez: Principles of Polymer Systems, 3rd ed.,

Hemisphere Publ., New York 1989.

4 G. Champetier, R. Buvet, J. N�eel, P. Sigwalt, (eds.):Chimie Macromol�eculaire, 2 vols., Hermann, Paris

1970 – 1972.

5 H.-G. Elias: ‘‘Grundlagen,’’ Makromolek€ule, 5th ed.,

vol. 1, H€uthig and Wepf, Basel 1989.

6 Macromolecules, 2nd ed., 2 vols., Plenum, New York

1984.

7 Makromolek€ule, 4th ed., H€uthig and Wepf, Basel 1981.

8 L. Mandelkern: An Introduction to Macromolecules, 2nd

ed., Springer, New York 1972, 1982.

9 J. M. G. Cowie: Polymers: Chemistry and Physics of

Modern Materials, Intext Educational Publ., New York

1974; Polymers: Chemistry and Physics of Modern

Materials, 2nd ed., Routledge, Chapman and Hall, New

York 1991.

10 F. A. Bovey, F. H. Winslow (eds.): Macromolecules,

Academic Press, New York 1979.

11 R. B. Seymour, C. E. Carraher, Jr. Polymer Chemistry,

2nd ed., Dekker, New York, 1989.

12 A. Rudin: The Elements of Polymer Science and Engi-

neering, Academic Press, New York 1982.

13 P. C. Hiemenz: Polymer Chemistry, Dekker, New York

1984.

14 P. Munk: Introduction to Macromolecular Science,

Wiley, New York 1989.

15 International Union of Pure and Applied Chemistry:

Compendium of Macromolecular Nomenclature (Purple

Book), Blackwell Sci. Publ., Oxford 1991.

16 J. Schultz: Polymer Materials Science, Prentice-Hall,

Englewood Cliffs, N.J., 1974.

17 J. A. Brydson: Plastics Materials, 3rd ed., Butterworth,

London 1975.

18 S. Rosen: Fundamental Principles of Polymeric Materi-

als for Practicing Engineers, Cahners Books, Boston

1973.

19 J. H. DuBois, F.W. John:Plastics, 5th ed., VanNostrand-

Reinhold, New York 1976.

20 W. E. Driver: Plastics Chemistry and Technology, Van

Nostrand-Reinhold, Cincinnati 1974.

21 Houben-Weyl, 5th ed., 20; Science of Synthesis, vol. 1,

2001, p. 57; Science of Synthesis, vol. 2, 2002, p. 291;

Science of Synthesis, vol. 2, 2002, p. 906.

22 G. W. Becker, D. Braun et al. (eds.): Kunststoff-Hand-

buch, 2nd ed., Hanser, M€unchen, 1983 ff. (many

vols.).

23 H.Mark, C. Overberger, G.Menges, N.M. Bikales (eds.):

Encyclopedia of Polymer Science and Engineering, 2nd

ed., 19 vols., Wiley, New York 1985 – 1990.

24 W. A. Kargin (ed.): Enciklopedia Polimerov, 3 vols.,

Sovietskaya Enciklopedia Publ., Moscow 1972.

25 G. Allen, J. C. Bevington (eds.):Comprehensive Polymer

Science, 7 vols., Pergamon, Oxford 1989.

26 Chemiefasern auf dem Weltmarkt, 7th ed., Deutsche

Rhodiaceta , Freiburg/Br., 1969, Supplement 1976 (trade

names of fibers).

27 The International Plastics Selector, Commercial Names

and Sources, Cordura Publ., San Diego 1978.

28 Parat (Fachinformationszentrum Chemie, Berlin), Index

of Polymer Trade Names, VCH, Weinheim, Germany

1987.

29 J. Brandrup, E. H. Immergut (eds.): Polymer Handbook,

3rd ed., Wiley, New York 1989.

30 O. Griffin Lewis: Physical Constants of Linear Homo-

polymers, Springer, Berlin 1968.

31 R. E. Schramm, A. F. Clark, R. P. Reeds (eds.): A

Compilation and Evaluation of Mechanical, Thermal,

and Electrical Properties of Selected Polymers, U.S.

National Bureau of Standards , Washington, D.C., 1973.

32 P. A. Schweitzer: Corrosion Resistance Tables (Metals,

Plastics, Nonmetallics, Rubbers), Dekker, New York

1976.

33 The International Plastics Selector, San Diego 1977.

34 H. Saechtling: Kunststoff-Taschenbuch, 24th ed., Hanser,

Munich 1989; International Plastics Handbook, 2nd ed.,

Hanser, M€unchen 1989.

35 Modern Plastics Encyclopedia, McGraw-Hill, New York

(annually in October as issue 10 A).

36 Encyclope die Francaise des Matieres Plastiques, Les

Publicateurs Techniques Association , Paris, annually.

37 J. E. Williams (ed.): Computer-Readable Databases,

American Library Association, Chicago 1985.


38 German Plastics Institute, Plastics Databank POLYMAT,

Darmstadt; Fachinformationszentrum Chemie, Berlin

(6000 polymers from 80 manufacturers).

39 Plastics Databank CAMPUS (¼ Computer Aided Mate-

rial Preselection by Uniform Standards), (5000 thermo-

plastics with 50 most important properties each), issued

for their company products by 17 European companies.

40 Polymer Materials Database, Fachinformationszentrum

Berlin (continuously updated).

41 E. R. Yescombe: Plastics and Rubbers: World Sources of

Information, 2nd ed., Appl. Sci. Publ., Barking 1976.

42 G. J. Patterson: Plastics Book List, Technomic Publ.,

Westport 1975.

43 P. Eyerer: Informationsf€uhrer Kunststoffe, VDI-Verlag,D€usseldorf 1976.

44 J. Schrade: Kunststoffe (Hochpolymere), Bibliographie

aus dem deutschen Sprachgebiet, Erste Folge 1911 –

1969, I. Schrade, Schweiz. AluminiumAG., Z€urich 1976,Zweite Folge, Z€urich 1980.

45 O. A. Battista, The Polymer Index, McGraw Hill, New

York 1976.

46 S. M. Kaback: ‘‘Literature of Polymers, ’’ Encycl. Polym.

Sci. Technol. 8 (1968) 273; J. T. Lee, Encycl. Polym. Sci.

Eng., 2nd ed., 9 (1987) 62.

47 W. J. Roff, J. R. Scott: Handbook of Common Polymers,

Butterworths, London 1971.

48 M. Ash, I. Ash: Encyclopedia of Plastics, Polymers and

Resins, 4 vols., Chem. Publ. Co., New York 1982 –1988.

49 M. S. M. Alger: Polymer Science Dictionary, Elsevier

Applied Sci. Publ., Barking 1989.

50 American Society for TestingMaterials, ASTMD-1600–

86 a; D-1418–67; D-4020–81.

51 German Industrial Standards DIN 7723; 7728 (1988);

16 913; 55 950; 60 001.

52 European Textile Characterization Law.

53 International Organization for Standardization, ISO 1043

– 1978, ISO 1629 – 1980.

54 Guide for the Harmonisation of Designations of Thermo-

plastic Materials, ISO/TC 61/SC 9 N 435, April 1981;

ASTM D 4000.

55 K. Wiebusch, Kunststoffe-German Plastics 72 (1982) 22,

167.

56 F. O. Swanson, Plastics Engng. (1983) Jan. 31.

57 R. H. Wehrenberg, II, Mat. Engng. (1984) Feb. 48.

58 H.-Elias et al.,PolymerNews 9 (1983) 101; 10 (1985) 169.

59 J. H. DuBois: Plastics History – U.S.A., Cahners, Boston

1971.

60 J. K. Craver, R. W. Tess (eds.): Applied Polymer Science,

Am. Chem. Soc., Washington, D.C., 1975.

61 F. M. McMillan: The Chain Straigtheners: Fruitful Inno-

vation. The Discovery of Linear and Stereoregular Poly-

mers, MacMillan, London 1981.

62 R. B. Seymour (ed.): History of Polymer Science and

Technology, Dekker, NewYork 1982 (Reprint of articles

in J. Macromol. Sci.-Chem. A 17 (1982) 1065 –1460.

63 R. Friedel: Pioneer Plastic. The Making and Selling of

Celluloid, University ofWisconsin Press,Madison, 1983.

64 W. Glenz (ed.): Kunststoffe – Ein Werkstoff macht Kar-

riere, Hanser, M€unchen 1985.

65 United Nations, Statistical Yearbooks.

66 Calculated from data in Kunststoffe 73 (1983) no. 10.

67 H.-G. Elias, F. Vohwinkel: New Commercial Polymers,

Gordon and Breach, New York 1986; Neue polymere

Werkstoffe, Hanser, M€unchen 1983.

68 H.-G. Elias, Grosse Molek€ule, Springer, Berlin 1985

Mega Molecules, Springer, Berlin 1987. Megamolekuly,

Khimiya, Leningrad 1990.

69 United States, Statistical Abstracts (annually).

70 D. Tomalia, A. M. Naylor, W. A. Goddard III, Angew.

Chem. 102 (1990) 119; Angew. Chem. Intern. Ed. 29

(1990) 138.

71 G. Natta, P. Corradini, Nuovo Cimento, Suppl. 15 (1960)

11.

72 D. Lang, H. Bujard, B. Wolff, D. Russell, J. Mol. Biol. 23

(1967) 163.

73 R.G€achter,H.M€uller (eds.):Plastics AdditivesHandbook

3rd ed., Hanser, M€unchen 1989.

74 A. E. Woodward, Atlas of Polymer Morphology, Hanser,

M€unchen 1988.

75 C. Ruscher, E. Schulz, private communication.

76 R. J. Samuels, private communication.

77 P. J. Flory, Adv. Polym. Sci. 59 (1984) 1.

78 Kunststoff-Physik im Gespr€ach, 8th ed., BASF, Ludwig-

shafen 1988.

79 H. M. Laun, H. M€unstedt, Rheol. Acta 17 (1978) 415.

80 S. Onogi, T. Matsuda, K. Kitagawa, Macromolecules 3

(1970) 109.

81 S. Wellinghoff, E. Baer, private communication.

82 G. E. Ehrenstein, R. Wurmb, Angew. Makromol. Chem.

60/61 (1977) 157.

83 T. H. Ferrigno, in S. Katz, J. V. Milewski (eds.): Hand-

book of Fillers and Reinforcements for Plastics, Van

Nonstrand, New York 1978, p. 11.

84 J. A. Manson, L. H. Sperling: Polymer Blends and Com-

posites, Plenum, New York 1976.

85 S. L. Aggarwal, R. L. Livigni, Polym. Eng. Sci. 17 (1977)

498.

86 Bundesamt f€ur Umweltschutz, Oekobilanzen von Pack-

stoffen (Schriftenreihe Umweltschutz), no. 24, Bern

1984.

Further Reading

C. A. Harper: Handbook of plastics technologies, McGraw-

Hill, New York, NY 2006.

E. Lokensgard: Industrial plastics, 5th ed., Delmar Cengage

Learning, Clifton Park NY 2009.


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