introduction to physical polymer science

Preface to the Fourth Edition xv1.1 From Little Molecules to Big Molecules / 2 1.2 Molecular Weight and Molecular Weight Distributions / 4 1.3 Major Polymer Transitions / 8 1.4 Polymer S

INTRODUCTION TO PHYSICAL POLYMER

SCIENCE FOURTH EDITION

L.H Sperling

Lehigh UniversityBethlehem, Pennsylvania

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Library of Congress Cataloging-in-Publication Data:

Sperling, L H (Leslie Howard), 1932–

Introduction to physical polymer science / L.H Sperling.—4th ed.

10 9 8 7 6 5 4 3 2 1

undergraduate students, post-doctoral research associates, and visitingscientists who carried out research in my laboratory, and to the very manymore students across America and around the world who studied out ofearlier editions of this book Without them, this edition surely would nothave been possible I take this opportunity to wish all of them continued

good luck and good fortune in their careers

Preface to the Fourth Edition xv

1.1 From Little Molecules to Big Molecules / 2

1.2 Molecular Weight and Molecular Weight Distributions / 4

1.3 Major Polymer Transitions / 8

1.4 Polymer Synthesis and Structure / 10

1.5 Cross-Linking, Plasticizers, and Fillers / 18

1.6 The Macromolecular Hypothesis / 19

1.7 Historical Development of Industrial Polymers / 20

Appendix 1.1 Names for Polymers / 26

2.1 Examples of Configurations and Conformations / 30

2.2 Theory and Instruments / 31

2.3 Stereochemistry of Repeating Units / 36

2.4 Repeating Unit Isomerism / 42

CONTENTS

vii

2.5 Common Types of Copolymers / 45

2.6 NMR in Modern Research / 47

2.7 Multicomponent Polymers / 51

2.8 Conformational States in Polymers / 55

2.9 Analysis of Polymers during Mechanical Strain / 56

3.4 Molecular Weight Averages / 85

3.5 Determination of the Number-Average Molecular Weight / 873.6 Weight-Average Molecular Weights and Radii of Gyration / 913.7 Molecular Weights of Polymers / 103

Appendix 3.1 Calibration and Application of Light-Scattering

Instrumentation for the Case Where P(q) = 1 / 142

4 Concentrated Solutions, Phase Separation Behavior,

4.1 Phase Separation and Fractionation / 145

4.2 Regions of the Polymer–Solvent Phase Diagram / 150

4.3 Polymer–Polymer Phase Separation / 153

4.4 Diffusion and Permeability in Polymers / 172

4.5 Latexes and Suspensions / 184

4.6 Multicomponent and Multiphase Materials / 186

References / 186

General Reading / 190

Study Problems / 190

Appendix 4.1 Scaling Law Theories and Applications / 192

5.1 The Amorphous Polymer State / 198

5.2 Experimental Evidence Regarding Amorphous Polymers / 1995.3 Conformation of the Polymer Chain / 211

Engineering / 237

6.1 General Considerations / 239

6.2 Methods of Determining Crystal Structure / 245

6.3 The Unit Cell of Crystalline Polymers / 248

6.4 Structure of Crystalline Polymers / 256

6.5 Crystallization from the Melt / 260

6.11 The Hierarchical Structure of Polymeric Materials / 311

6.12 How Do You Know It’s a Polymer? / 312

References / 314

General Reading / 320

Study Problems / 320

CONTENTS ix

7 Polymers in the Liquid Crystalline State 325

7.1 Definition of a Liquid Crystal / 325

7.2 Rod-Shaped Chemical Structures / 326

7.3 Liquid Crystalline Mesophases / 326

7.4 Liquid Crystal Classification / 331

7.5 Thermodynamics and Phase Diagrams / 338

7.6 Mesophase Identification in Thermotropic Polymers / 341

7.7 Fiber Formation / 342

7.8 Comparison of Major Polymer Types / 344

7.9 Basic Requirements for Liquid Crystal Formation / 345

References / 346

General Reading / 347

Study Problems / 348

8.1 Simple Mechanical Relationships / 350

8.2 Five Regions of Viscoelastic Behavior / 355

8.3 Methods of Measuring Transitions in Polymers / 366

8.4 Other Transitions and Relaxations / 375

8.5 Time and Frequency Effects on Relaxation Processes / 3778.6 Theories of the Glass Transition / 381

8.7 Effect of Molecular Weight on T g / 397

8.8 Effect of Copolymerization on T g / 399

8.9 Effect of Crystallinity on T g / 404

8.10 Dependence of T gon Chemical Structure / 408

8.11 Effect of Pressure on T g / 410

8.12 Damping and Dynamic Mechanical Behavior / 412

8.13 Definitions of Elastomers, Plastics, Adhesives, and Fibers / 415References / 415

General Reading / 420

Study Problems / 420

Appendix 8.1 Molecular Motion near the Glass Transition / 423

9 Cross-linked Polymers and Rubber Elasticity 427

9.1 Cross-links and Networks / 427

9.2 Historical Development of Rubber / 430

9.3 Rubber Network Structure / 432

9.4 Rubber Elasticity Concepts / 434

9.5 Thermodynamic Equation of State / 437

9.6 Equation of State for Gases / 439

9.7 Statistical Thermodynamics of Rubber Elasticity / 442

9.8 The “Carnot Cycle” for Elastomers / 450

9.9 Continuum Theories of Rubber Elasticity / 453

9.10 Some Refinements to Rubber Elasticity / 459

9.11 Internal Energy Effects / 469

9.12 The Flory–Rehner Equation / 472

9.13 Gelation Phenomena in Polymers / 473

9.14 Gels and Gelation / 478

9.15 Effects of Strain on the Melting Temperature / 479

9.16 Elastomers in Current Use / 480

9.17 Summary of Rubber Elasticity Behavior / 488

10.1 Stress Relaxation and Creep / 507

10.2 Relaxation and Retardation Times / 515

10.3 The Time–Temperature Superposition Principle / 529

10.4 Polymer Melt Viscosity / 533

11.1 An Energy Balance for Deformation and Fracture / 557

11.2 Deformation and Fracture in Polymers / 560

11.3 Crack Growth / 585

11.4 Cyclic Deformations / 588

CONTENTS xi

11.5 Molecular Aspects of Fracture and Healing in Polymers / 59311.6 Friction and Wear in Polymers / 601

11.7 Mechanical Behavior of Biomedical Polymers / 603

12.2 Thermodynamics of Surfaces and Interfaces / 615

12.3 Instrumental Methods of Characterization / 619

12.4 Conformation of Polymer Chains in a Polymer Blend

Interphase / 644

12.5 The Dilute Solution–Solid Interface / 646

12.6 Instrumental Methods for Analyzing Polymer

Appendix 12.1 Estimation of Fractal Dimensions / 686

13.1 Classification Schemes for Multicomponent Polymeric

Materials / 688

13.2 Miscible and Immiscible Polymer Pairs / 692

13.3 The Glass Transition Behavior of Multicomponent PolymerMaterials / 693

13.4 The Modulus of Multicomponent Polymeric Materials / 69813.5 The Morphology of Multiphase Polymeric Materials / 70613.6 Phase Diagrams in Polymer Blends (Broad Definition) / 71013.7 Morphology of Composite Materials / 721

13.8 Nanotechnology-Based Materials / 723

13.9 Montmorillonite Clays / 728

13.10 Fracture Behavior of Multiphase Polymeric Materials / 73613.11 Processing and Applications of Polymer Blends and Composites/ 741

14.2 Thermoset Polymer Materials / 762

14.3 Polymer and Polymer Blend Aspects of Bread Doughs / 76514.4 Natural Product Polymers / 769

14.5 Dendritic Polymers and Other Novel Polymeric

Structures / 773

14.6 Polymers in Supercritical Fluids / 779

14.7 Electrical Behavior of Polymers / 782

14.8 Polymers for Nonlinear Optics / 786

14.9 Light-Emitting Polymers and Electroactive Materials / 78914.10 Optical Tweezers in Biopolymer Research / 794

14.11 The 3-D Structure and Function of Biopolymers / 795

14.12 Fire Retardancy in Polymers / 807

14.13 Polymer Solution-Induced Drag Reduction / 811

14.14 Modern Engineering Plastics / 814

14.15 Major Advances in Polymer Science and Engineering / 815References / 817

General Reading / 822

Study Problems / 823

CONTENTS xiii

PREFACE TO THE FOURTH EDITION

“So, what’s new in polymer science?” “Much more than most people realize!”Yes, polymer science and engineering is marching on as it did in the 20thcentury, but the emphasis is on new materials and applications

Two of the most important advances are in the fields of nanocompositesand biopolymers The nanocomposites are of two basic types, carbon nan-otubes and montmorillonite clay exfoliated platelets The biopolymer aspectscan be traced to such Nobel Prize winning research as Watson and Crick’s discovery of the double helix structure of DNA and an understanding of howproteins work in muscles

Computers are playing increasingly important roles in physical polymerscience Polymer chain structures may be made to undergo Monte Carlo sim-ulations to gain new insight as to how polymers crystallize, for example.Polymer science was born of the need to understand how rubber and plas-tics work This speaks of the practicality of the subject from the beginning.Today, polymers form the basis of clothing, automobile parts, etc Yet, in fact,today we are seeing a shift from theory to new applications, to such topics aselectronics and fire resistance

All of these topics are covered in this fourth edition There are, as the readermight imagine, many other topics demanding consideration Alas, my goal was

to create a readable introductory textbook, and not an encyclopedia!

I want to take this opportunity to thank the many students who helped inproofreading the manuscript for this book Many thanks must also be given

to the Department of Chemical Engineering and the Department of terials Science and Engineering, as well as the newly renamed Center forAdvanced Materials and Nanotechnology, and the Center for Polymer Scienceand Engineering at Lehigh University Special thanks are due to Prof.Raymond Pearson, who made valuable suggestions for this edition Specialthanks are also due to Ms Gail Kriebel, Ms Bess King, and the staff at the

Ma-E W Fairchild-Martindale Library, who helped with literature searching, andprovided me with a carrel right in the middle of the stacks

xv

To all of the students, faculty, and industrial scientists and engineers whoread this textbook, good luck in your careers and lives!

February 2005

xvi PREFACE TO THE FOURTH EDITION

PREFACE TO THE

FIRST EDITION

Research in polymer science continues to mushroom, producing a plethora ofnew elastomers, plastics, adhesives, coatings, and fibers All of this new infor-mation is gradually being codified and unified with important new theoriesabut the interrelationships among polymer structure, physical properties, anduseful behavior.Thus the ideas of thermodynamics, kinetics, and polymer chainstructure work together to strengthen the field of polymer science

Following suit, the teaching of polymer science in colleges and universitiesaround the world has continued to evolve Where once a single introductorycourse was taught, now several different courses may be offered The polymerscience and engineering courses at Lehigh University include physical polymerscience, organic polymer science, and polymer laboratory for interestedseniors and first-year graduate students, and graduate courses in emulsionpolymerization, polymer blends and composites, and engineering behavior ofpolymers There is also a broad-based introductory course at the senior levelfor students of chemical engineering and chemistry The students may earndegrees in chemistry, chemical engineering, metallurgy and materials engi-neering, or polymer science and engineering, the courses being both inter-disciplinary and cross-listed

The physical polymer science course is usually the first course a interested student would take at Lehigh, and as such there are no special pre-requisites except upper-class or graduate standing in the areas mentionedabove This book was written for such a course

polymer-The present book emphasizes the role of molecular conformation and figuration in determining the physical behavior of polymers Two relativelynew ideas are integrated into the text Small-angle neutron scattering is doingfor polymers in the 1980s what NMR did in the 1970s, by providing an entirelynew perspective of molecular structure Polymer blend science now offersthermodynamics as well as unique morphologies

con-Chapter 1 covers most of the important aspects of the rest of the text in aqualitative way Thus the student can see where the text will lead him or her,having a glimpse of the whole Chapter 2 describes the configuration of

xvii

polymer chains, and Chapter 3 describes their molecular weight Chapter 4shows the interactions between solvent molecules and polymer molecules.Chapters 5–7 cover important aspects of the bulk state, both amorphous andcrystalline, the glass transition phenomenon, and rubber elasticity These threechapters offer the greatest depth Chapter 8 describes creep and stress relax-ation, and Chapter 9 covers the mechanical behavior of polymers, emphasiz-ing failure, fracture, and fatigure.

Several of the chapters offer classroom demonstrations, particularly Chapters 6 and 7 Each of these demonstrations can be carried out inside a50-minute class and are easily managed by the students themselves In fact, all

of these demonstrations have been tested by generations of Lehigh students,and they are often presented to the class with a bit of showmanship Eachchapter is also accompanied by a problem set

The author thanks the armies of students who studied from this book inmanuscript form during its preparation and repeatedly offer suggestions rel-ative to clarity, organization, and grammar Many researchers from around theworld contributed important figures Dr J A Manson gave much helpfuladvice and served as a Who’s Who in highlighting people, ideas, and history.The Department of Chemical Engineering, the Materials Research Center,and the Vice-President for Research’s Office at Lehigh each contributed sig-nificant assistance in the development of this book The Lehigh UniversityLibrary provided one of their carrels during much of the actual writing In par-ticular, the author thanks Sharon Siegler and Victoria Dow and the staff atMart Library for patient literature searching and photocopying The authoralso thanks Andrea Weiss, who carefully photographed many of the figures inthis book

Secretaries Jone Susski, Catherine Hildenberger, and Jeanne Loosbrockeach contributed their skills Lastly, the person who learned the most from thewriting of this book was

November 1985

xviii PREFACE TO THE THIRD EDITION

SYMBOL DEFINITION SECTION English Alphabet

A A2= second virial coefficient 3.3.2

A1= first virial coefficient 3.5.3.3

A3= third virial coefficient 3.5.3.3

A4= fourth virial coefficient 3.5.3.3

A (with various subscripts) = area under a Bragg 6.5.4diffraction line

C1¢, C2¢ = WLF constants 10.4.1

C p , C v= capacitance of polymer and vacuum 14.7.1

SYMBOLS AND DEFINITIONS

xix

SYMBOL DEFINITION SECTION

4.4.2,5.4.2.1

Eact= energy of activation 2.8, 8.6.1.2

E1, E2, etc = spring moduli 10.1.2.1

Group molar attraction constant 3.2.3

DG M= change in free energy on mixing 3.2

G N0= steady-state rubbery shear modulus 5.4.2.1Radial growth rate of crystal 6.6.2.2

G c= critical energy of crack growth 11.1.2

G lc= critical energy of crack growth on extension 11.5.2.4

I = single mer emission intensity 2.10.3.1

xx SYMBOLS AND DEFINITIONS

SYMBOL DEFINITION SECTION

K d= distribution coefficient 3.9.2

K ¯ = constant relating end-to-end distance to 4.3.9molecular weight

K1, K2= measures of free volume 8.6.1.1

K L , K H= constants in melt viscosity 10.4.2.1

M n= number-average molecular weight 1.2.1, 3.4

M w= weight-average molecular weight 3.4

M z = z-average molecular weight 3.4

M v= viscosity-average molecular weight 3.4

M c= number-average molecular weight between 9.4cross-links

SYMBOL DEFINITION SECTION

M M e= molecular weight between entanglements 9.4

M c¢ = entanglement molecular weight 9.4, 10.4.2.3

P c= critical extent of reaction at the gel point 3.7.4

R e= hydrodynamic sphere equivalent radius 3.8.2

R = ratio of radii of gyration 9.10.6

S = mean separation distance 6.6.2.5

xxii SYMBOLS AND DEFINITIONS

SYMBOL DEFINITION SECTION

Sth= interphase surface thickness 12.3.7.2

T f= fusion or melting temperature 1.1, 6.1

T g= glass transition temperature 1.3

DT b= boiling point elevation 3.5.2

DT f= freezing point depression 3.5.2

T = Fraction of light transmitted 5.2.1

T f* = equilibrium melting temperature of crystals 6.8.5

SYMBOL DEFINITION SECTION

X Brownian motion average distance traversed 5.2.2.1

a Exponent in the Mark–Houwink–Sakurada 3.8.3

equation

a H , a D= scattering lengths 5.2.2.1End-to-end distance of a Rouse–Bueche segment 5.4.1

Statistical segment step length 12.3.7.2

xxiv SYMBOLS AND DEFINITIONS

SYMBOL DEFINITION SECTION

f f0= fractional free volume at T g 8.6.1.2

f e= energetic portion of the retractive force 9.5

f s= entropic portion of the retractive force 9.5

j

k i= rate constant of initiation 3.7.2.2

k p= rate constant of propagation 3.7.2.2

k t= rate constant of termination 3.7.2.2

Number of network chains per unit volume 1.3

n c , n p= chemical and physical cross-links 9.10.5.1

ntot= total number of effective cross-links 9.10.5.1

n(t), n•= number of chains intersecting a unit area 11.5.3

of interface at t and at infinite time

o

SYMBOL DEFINITION SECTION

Probability of Avrami crystal fronts crossing 6.6.2.1

1/p2= measure of stiffness 8.3.3

p1= probability of finding a molecule 9.6

q q1, q2= heat absorbed and released 9.8.3

9.7.1,10.2.7

r˜0 = root-mean square end-to-end distance of 3.9.7

Exponent in interface theory 11.5.3

v2= volume fraction of polymer 4.1.2,

9.10.4

v2* = critical volume concentration 7.5.1

v f= specific free volume 8.6.1.1

Axial ratio of liquid crystalline molecule 7.5.1

y

xxvi SYMBOLS AND DEFINITIONS

SYMBOL DEFINITION SECTION Greek Alphabet

a ax= mechanically induced peak frequency shift 2.9

Expansion of a polymer coil in a good solvent 3.8.2

aA/B= gas selectivity ratio 4.4.6.2Volumetric coefficient of expansion 8.3

aR= cubic expansion coefficient in the rubbery 8.6.1.1state

aG= cubic expansion coefficient in the glassy state 8.6.1.1

SYMBOL DEFINITION SECTION

a af= expansion coefficient of the free volume 8.6.1.2

bf= compressibility free volume 8.11

g Number of flexible bonds per mer 8.6.3.2

gs= surface tension (intrinsic surface energy) 11.3.1

gp= plastic deformation energy 11.3.2

g (r) = Debye correlation function 12.3.8.1

Measure of internal structure 6.6.2.2

h0= viscosity of the solvent 3.8.1

SYMBOL DEFINITION SECTION

Number of network junctions 9.10.2

mtube= tube mobility of a chain 10.4.2.4

SYMBOL DEFINITION SECTION

f Volume element in the Takayanagi model 10.1.2.3

c Flory–Huggins heat of mixing term (Sometimes 3.3.2

INTRODUCTION TO POLYMER SCIENCE

1

Polymer science was born in the great industrial laboratories of the world ofthe need to make and understand new kinds of plastics, rubber, adhesives,fibers, and coatings Only much later did polymer science come to academiclife Perhaps because of its origins, polymer science tends to be more inter-disciplinary than most sciences, combining chemistry, chemical engineering,materials, and other fields as well

Chemically, polymers are long-chain molecules of very high molecularweight, often measured in the hundreds of thousands For this reason, the term

“macromolecules” is frequently used when referring to polymeric materials.The trade literature sometimes refers to polymers as resins, an old term thatgoes back before the chemical structure of the long chains was understood.The first polymers used were natural products, especially cotton, starch, pro-teins, and wool Beginning early in the twentieth century, synthetic polymerswere made The first polymers of importance, Bakelite and nylon, showed thetremendous possibilities of the new materials However, the scientists of thatday realized that they did not understand many of the relationships betweenthe chemical structures and the physical properties that resulted The researchthat ensued forms the basis for physical polymer science

This book develops the subject of physical polymer science, describing theinterrelationships among polymer structure, morphology, and physical andmechanical behavior Key aspects include molecular weight and molecularweight distribution, and the organization of the atoms down the polymerchain Many polymers crystallize, and the size, shape, and organization of the

Introduction to Physical Polymer Science, by L.H Sperling

ISBN 0-471-70606-X Copyright © 2006 by John Wiley & Sons, Inc.

crystallites depend on how the polymer was crystallized Such effects asannealing are very important, as they have a profound influence on the finalstate of molecular organization.

Other polymers are amorphous, often because their chains are too lar to permit regular packing The onset of chain molecular motion heralds theglass transition and softening of the polymer from the glassy (plastic) state tothe rubbery state Mechanical behavior includes such basic aspects as modulus,stress relaxation, and elongation to break Each of these is relatable to thepolymer’s basic molecular structure and history

irregu-This chapter provides the student with a brief introduction to the broaderfield of polymer science Although physical polymer science does not includepolymer synthesis, some knowledge of how polymers are made is helpful inunderstanding configurational aspects, such as tacticity, which are concernedwith how the atoms are organized along the chain Similarly polymer molec-ular weights and distributions are controlled by the synthetic detail Thischapter starts at the beginning of polymer science, and it assumes no priorknowledge of the field

1.1 FROM LITTLE MOLECULES TO BIG MOLECULES

The behavior of polymers represents a continuation of the behavior of smallermolecules at the limit of very high molecular weight As a simple example,consider the normal alkane hydrocarbon series

(1.1)

These compounds have the general structure

(1.2)where the number of —CH2— groups, n, is allowed to increase up to several

thousand The progression of their state and properties is shown in Table 1.1

At room temperature, the first four members of the series are gases

n-Pentane boils at 36.1°C and is a low-viscosity liquid As the molecular weight

of the series increases, the viscosity of the members increases Although mercial gasolines contain many branched-chain materials and aromatics aswell as straight-chain alkanes, the viscosity of gasoline is markedly lower thanthat of kerosene, motor oil, and grease because of its lower average chainlength

com-These latter materials are usually mixtures of several molecular species,although they are easily separable and identifiable This point is important

H CH2 nH

C

HMethane

H

CHHEthane

HCH

H

HPropane

HCH

HCH

HH

2 CHAIN STRUCTURE AND CONFIGURATION

because most polymers are also “mixtures”; that is, they have a molecularweight distribution In high polymers, however, it becomes difficult to separateeach of the molecular species, and people talk about molecular weight averages.

Compositions of normal alkanes averaging more than about 20 to 25 carbonatoms are crystalline at room temperature These are simple solids known aswax It must be emphasized that at up to 50 carbon atoms the material is farfrom being polymeric in the ordinary sense of the term

The polymeric alkanes with no side groups that contain 1000 to 3000 carbonatoms are known as polyethylenes Polyethylene has the chemical structure

(1.3)which originates from the structure of the monomer ethylene, CH2=CH2 The

quantity n is the number of mers—or monomeric units in the chain In some

places the structure is written

(1.4)

or polymethylene (Then n¢ = 2n.) The relationship of the latter structure to

the alkane series is clearer While true alkanes have CH3— as end groups, mostpolyethylenes have initiator residues

Even at a chain length of thousands of carbons, the melting point of ethylene is still slightly molecular-weight-dependent, but most linear polyeth-

poly-ylenes have melting or fusion temperatures, T f, near 140°C The approach tothe theoretical asymptote of about 145°C at infinite molecular weight (1) isillustrated schematically in Figure 1.1

The greatest differences between polyethylene and wax lie in their ical behavior, however While wax is a brittle solid, polyethylene is a toughplastic Comparing resistance to break of a child’s birthday candle with a washbottle tip, both of about the same diameter, shows that the wash bottle tip can

mechan-be repeatedly mechan-bent whereas the candle breaks on the first deformation

CH2 n¢

CH2 CH2 n

Table 1.1 Properties of the alkane/polyethylene series

Polyethylene is a tough plastic solid because its chains are long enough toconnect individual stems together within a lamellar crystallite by chain folding(see Figure 1.2) The chains also wander between lamellae, connecting several

of them together These effects add strong covalent bond connections bothwithin the lamellae and between them On the other hand, only weak van derWaals forces hold the chains together in wax

In addition a certain portion of polyethylene is amorphous The chains inthis portion are rubbery, imparting flexibility to the entire material Wax is100% crystalline, by difference

The long chain length allows for entanglement (see Figure 1.3) The glements help hold the whole material together under stress In the melt state,chain entanglements cause the viscosity to be raised very significantly also.The long chains shown in Figure 1.3 also illustrate the coiling of polymerchains in the amorphous state One of the most powerful theories in polymerscience (2) states that the conformations of amorphous chains in space arerandom coils; that is, the directions of the chain portions are statistically determined

entan-1.2 MOLECULAR WEIGHT AND MOLECULAR

WEIGHT DISTRIBUTIONS

While the exact molecular weight required for a substance to be called apolymer is a subject of continued debate, often polymer scientists put thenumber at about 25,000 g/mol This is the minimum molecular weight requiredfor good physical and mechanical properties for many important polymers.This molecular weight is also near the onset of entanglement

1.2.1 Effect on Tensile Strength

The tensile strength of any material is defined as the stress at break duringelongation, where stress has the units of Pa, dyn/cm2, or lb/in2; see Chapter 11

4 CHAIN STRUCTURE AND CONFIGURATION

Figure 1.1 The molecular weight-melting temperature relationship for the alkane series

An asymptotic value of about 145°C is reached for very high molecular weight linear polyethylenes.

The effect of molecular weight on the tensile strength of polymers is illustrated

in Figure 1.4 At very low molecular weights the tensile stress to break, sb, isnear zero As the molecular weight increases, the tensile strength increasesrapidly, and then gradually levels off Since a major point of weakness at themolecular level involves the chain ends, which do not transmit the covalentbond strength, it is predicted that the tensile strength reaches an asymptotic

Figure 1.2 Comparison of wax and polyethylene structure and morphology.

value at infinite molecular weight A large part of the curve in Figure 1.4 can

be expressed (3,4)

(1.5)

where M n is the number-average molecular weight (see below) and A and B

are constants Newer theories by Wool (3) and others suggest that more than90% of tensile strength and other mechanical properties are attained whenthe chain reaches eight entanglements in length

1.2.2 Molecular Weight Averages

The same polymer from different sources may have different molecularweights Thus polyethylene from source A may have a molecular weight of150,000 g/mol, whereas polyethylene from source B may have a molecularweight of 400,000 g/mol (see Figure 1.5) To compound the difficulty, allcommon synthetic polymers and most natural polymers (except proteins) have

a distribution in molecular weights That is, some molecules in a given sample

about 600 backbone chain atoms.

Figure 1.4 Effect of polymer molecular weight on tensile strength

of polyethylene are larger than others The differences result directly from thekinetics of polymerization.

However, these facts led to much confusion for chemists early in the tieth century At that time chemists were able to understand and characterizesmall molecules Compounds such as hexane all have six carbon atoms If polyethylene with 2430 carbon atoms were declared to be “polyethylene,” howcould that component having 5280 carbon atoms also be polyethylene? Howcould two sources of the material having different average molecular weightsboth be polyethylene, noting A and B in Figure 1.5?

twen-The answer to these questions lies in defining average molecular weightsand molecular weight distributions (5,6) The two most important molecular

weight averages are the number-average molecular weight, M n,

(1.6)

where N i is the number of molecules of molecular weight M i, and the

weight-average molecular weight, M w,

(1.7)

For single-peaked distributions, M n is usually near the peak The

weight-average molecular weight is always larger For simple distributions, M w may

be 1.5 to 2.0 times M n The ratio M w /M n, sometimes called the polydispersityindex, provides a simple definition of the molecular weight distribution Thusall compositions of are called polyethylene, the molecularweights being specified for each specimen

For many polymers a narrower molecular distribution yields better erties The low end of the distribution may act as a plasticizer, softening thematerial Certainly it does not contribute as much to the tensile strength Thehigh-molecular-weight tail increases processing difficulties, because of its enor-

= Â Â

Figure 1.5 Molecular weight distributions of the same polymer from two different sources,

A and B.

mous contribution to the melt viscosity For these reasons, great emphasis isplaced on characterizing polymer molecular weights.

1.3 MAJOR POLYMER TRANSITIONS

Polymer crystallinity and melting were discussed previously Crystallization is

an example of a first-order transition, in this case liquid to solid Most smallmolecules crystallize, an example being water to ice Thus this transition is veryfamiliar

A less classical transition is the glass–rubber transition in polymers At the

glass transition temperature, T g, the amorphous portions of a polymer soften.The most familiar example is ordinary window glass, which softens and flows

at elevated temperatures Yet glass is not crystalline, but rather it is an phous solid It should be pointed out that many polymers are totally amorphous Carried out under ideal conditions, the glass transition is a type

amor-of second-order transition

The basis for the glass transition is the onset of coordinated molecularmotion is the polymer chain At low temperatures, only vibrational motionsare possible, and the polymer is hard and glassy (Figure 1.6, region 1) (7) Inthe glass transition region, region 2, the polymer softens, the modulus dropsthree orders of magnitude, and the material becomes rubbery Regions 3, 4,and 5 are called the rubbery plateau, the rubbery flow, and the viscous flowregions, respectively Examples of each region are shown in Table 1.2

8 CHAIN STRUCTURE AND CONFIGURATION

Figure 1.6 Idealized modulus–temperature behavior of an amorphous polymer Young’s modulus, stress/strain, is a measure of stiffness.

Depending on the region of viscoelastic behavior, the mechanical ties of polymers differ greatly Model stress–strain behavior is illustrated inFigure 1.7 for regions 1, 2, and 3 Glassy polymers are stiff and often brittle,breaking after only a few percent extension Polymers in the glass transitionregion are more extensible, sometimes exhibiting a yield point (the hump inthe tough plastic stress–strain curve) If the polymer is above its brittle–ductiletransition, Section 11.2.3, rubber-toughened, Chapter 13, or semicrystalline

proper-with its amorphous portions above T g, tough plastic behavior will also beobserved Polymers in the rubbery plateau region are highly elastic, oftenstretching to 500% or more Regions 1, 2, and 3 will be discussed further inChapters 8 and 9 Regions 4 and 5 flow to increasing extents under stress; seeChapter 10

Cross-linked amorphous polymers above their glass transition temperaturebehave rubbery Examples are rubber bands and automotive tire rubber Ingeneral,Young’s modulus of elastomers in the rubbery-plateau region is higherthan the corresponding linear polymers, and is governed by the relation

E = 3nRT, in Figure 1.6 (line not shown); the linear polymer behavior is

illustrated by the line (b) Here, n represents the number of chain segments bound at both ends in a network, per unit volume The quantities R and T are

the gas constant and the absolute temperature, respectively

Polymers may also be partly crystalline The remaining portion of thepolymer, the amorphous material, may be above or below its glass transition

Table 1.2 Typical polymer viscoelastic behavior at room temperature (7a)

a From the latex of Achras sapota, a mixture of cis- and trans-polyisoprene plus polysaccharides.

Figure 1.7 Stress–strain behavior of various polymers While the initial slope yields the modulus, the area under the curve provides the energy to fracture.

temperature, creating four subclasses of materials Table 1.3 gives a commonexample of each While polyethylene and natural rubber need no further intro-duction, common names for processed cellulose are rayon and cellophane.Cotton is nearly pure cellulose, and wood pulp for paper is 80 to 90% cellu-lose A well-known trade name for poly(methyl methacrylate) is Plexiglas®.The modulus–temperature behavior of polymers in either the rubbery-plateauregion or in the semicrystalline region are illustrated further in Figure 8.2,Chapter 8.

Actually there are two regions of modulus for semicrystalline polymers If

the amorphous portion is above T g, then the modulus is generally betweenrubbery and glassy If the amorphous portion is glassy, then the polymer will

be actually be a bit stiffer than expected for a 100% glassy polymer

1.4 POLYMER SYNTHESIS AND STRUCTURE

1.4.1 Chain Polymerization

Polymers may be synthesized by two major kinetic schemes, chain and wise polymerization The most important of the chain polymerization methods

step-is called free radical polymerization

acry-late) will be used as an example of free radical polymerization Benzoyl oxide is a common initiator Free radical polymerization has three majorkinetic steps—initiation, propagation, and termination

2DO

10 CHAIN STRUCTURE AND CONFIGURATION

Table 1.3 Examples of polymers at room temperature by transition behavior

group, the free radical can be written R· (It should be pointed out that gen peroxide undergoes the same reaction on a wound, giving a burning sen-sation as the free radicals “kill the germs.”)

hydro-The initiation step usually includes the addition of the first monomer molecule:

(1.9)

In this reaction the free radical attacks the monomer and adds to it Thedouble bond is broken open, and the free radical reappears at the far end

monomer molecules are added rapidly, perhaps in a fraction of a second:

(1.10)

On the addition of each monomer, the free radical moves to the end of thechain

with each other Termination is either by combination,

(1.11)

where R now represents a long-chain portion, or by disproportionation, where

a hydrogen is transferred from one chain to the other This latter result

C

C.2R

O

CH2H

produces in two final chains While the normal mode of addition is a tail reaction (1.10), this termination step is normally head-to-head.

head-to-As a homopolymer, poly(ethyl acrylate) is widely used as an elastomer or

adhesive, being a polymer with a low T g, -22°C As a copolymer with otheracrylics it is used as a latex paint

polymer-izing monomers by the chain kinetic scheme involves the opening of doublebonds to form a linear molecule In a reacting mixture, monomer, fully reactedpolymer, and only a small amount of rapidly reacting species are present Oncethe polymer terminates, it is “dead” and cannot react further by the synthesisscheme outlined previously

Polymers are named by rules laid out by the IUPAC Nomenclature Committee (8,9) For many simple polymers the source-based name uti-lizes the monomer name prefixed by “poly.” If the monomer name has two

or more words, parentheses are placed around the monomer name Thus, inthe above, the monomer ethyl acrylate is polymerized to make poly(ethyl acrylate) Source-based and IUPAC names are compared in Appendix 1.1.Table 1.4 provides a selected list of common chain polymer structures andnames along with comments as to how the polymers are used The “vinyl”monomers are characterized by the general structure CH2=CHR, where Rrepresents any side group One of the best-known vinyl polymers is poly(vinylchloride), where R is —Cl

Polyethylene and polypropylene are the major members of the class of

polymers known as polyolefins; see Section 14.1 The term olefin derives from

the double-bond characteristic of the alkene series

A slight dichotomy exists in the writing of vinyl polymer structures From

a correct nomenclature point of view, the pendant moiety appears on the hand carbon Thus poly(vinyl chloride) should be written However, from a synthesis point of view, the structure is written

left-, because the free radical is borne on the pendant moietycarbon Thus both forms appear in the literature

The diene monomer has the general structure ,where on polymerization one of the double bonds forms the chain bonds,and the other goes to the central position The vinylidenes have two groups

on one carbon Table 1.4 also lists some common copolymers, which areformed by reacting two or more monomers together In general, the polymerstructure most closely resembling the monomer structure will be presentedherein

Today, recycling of plastics has become paramount in preserving the ronment On the bottom of plastic bottles and other plastic items is an iden-tification number and letters; see Table 1.5 This information serves to help inseparation of the plastics prior to recycling Observation of the properties

envi-of the plastic such as modulus, together with the identification, will help

Structure Name Where Used

“Vinyl” class

pipes

X = -H, acrylics

X = -CH 3 , methacrylics

Poly(styrene–stat–butadiene) c

Poly(acrylonitrile–stat–butadiene)

aPolyacrylonitrile is technically a number of the acrylic class because it forms acrylic acid on hydrolysis.

a¢IUPAC recommends

bAlso called polyisobutylene The 2% copolymer with isoprene, after vulcanization, is called butyl rubber.

c The term–stat–means statistical copolymer, as explained in Chapter 2.

d ABS is actually a blend or graft of two random copolymers, poly(acrylonitrile–stat–butadiene) and poly(acrylonitrile–stat–styrene).

n

CH2

CH2CH

C = R

R