INTRODUCTION TO PHYSICAL POLYMER SCIENCE

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INTRODUCTION TO PHYSICAL POLYMER SCIENCE

FOURTH EDITION

L.H. Sperling

Lehigh University Bethlehem, Pennsylvania

A JOHN WILEY & SONS, INC. PUBLICATION

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Published by John Wiley & Sons, Inc.,. Hoboken, New Jersey Published simultaneously in Canada

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission.

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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.

p. cm.

Includes index.

ISBN-13 978-0-471-70606-9 (cloth) ISBN-10 0-471-70606-X (cloth)

1. Polymers. 2. Polymerization. I. Title.

QD381.S635 2006 668.9—dc22

2005021351 Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

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This book is dedicated to the many wonderful graduate and undergraduate students, post-doctoral research associates, and visiting scientists who carried out research in my laboratory, and to the very many

more students across America and around the world who studied out of earlier editions of this book. Without them, this edition surely would not have been possible. I take this opportunity to wish all of them continued

good luck and good fortune in their careers.

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Preface to the Fourth Edition xv

Preface to the First Edition xvii

Symbols and Definitions xix

1 Introduction to Polymer Science 1

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 1.8 Molecular Engineering / 21

References / 22 General Reading / 22

Handbooks, Encyclopedias, and Dictionaries / 24 Web Sites / 24

Study Problems / 25

Appendix 1.1 Names for Polymers / 26

2 Chain Structure and Configuration 29

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

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 20th century, but the emphasis is on new materials and applications.

Two of the most important advances are in the fields of nanocomposites and biopolymers. The nanocomposites are of two basic types, carbon nan- otubes and montmorillonite clay exfoliated platelets. The biopolymer aspects can 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 how proteins work in muscles.

Computers are playing increasingly important roles in physical polymer science. 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 plastics 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 as electronics and fire resistance.

All of these topics are covered in this fourth edition. There are, as the reader might 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 in proofreading the manuscript for this book. Many thanks must also be given to the Department of Chemical Engineering and the Department of Ma- terials Science and Engineering, as well as the newly renamed Center for Advanced Materials and Nanotechnology, and the Center for Polymer Science and Engineering at Lehigh University. Special thanks are due to Prof.

Raymond Pearson, who made valuable suggestions for this edition. Special thanks are also due to Ms. Gail Kriebel, Ms. Bess King, and the staff at the E. W. Fairchild-Martindale Library, who helped with literature searching, and provided me with a carrel right in the middle of the stacks.

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

Bethlehem, Pennsylvania L. H. Sperling

February 2005

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PREFACE TO THE FIRST EDITION

Research in polymer science continues to mushroom, producing a plethora of new elastomers, plastics, adhesives, coatings, and fibers. All of this new information is gradually being codified and unified with important new theories abut the interrelationships among polymer structure, physical properties, and useful behavior.Thus the ideas of thermodynamics, kinetics, and polymer chain structure work together to strengthen the field of polymer science.

Following suit, the teaching of polymer science in colleges and universities around the world has continued to evolve. Where once a single introductory course was taught, now several different courses may be offered. The polymer science and engineering courses at Lehigh University include physical polymer science, organic polymer science, and polymer laboratory for interested seniors and first-year graduate students, and graduate courses in emulsion polymerization, polymer blends and composites, and engineering behavior of polymers. There is also a broad-based introductory course at the senior level for students of chemical engineering and chemistry. The students may earn degrees in chemistry, chemical engineering, metallurgy and materials engineering, 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 polymer- interested student would take at Lehigh, and as such there are no special pre- requisites except upper-class or graduate standing in the areas mentioned above. This book was written for such a course.

The present book emphasizes the role of molecular conformation and configuration in determining the physical behavior of polymers. Two relatively new ideas are integrated into the text. Small-angle neutron scattering is doing for polymers in the 1980s what NMR did in the 1970s, by providing an entirely new perspective of molecular structure. Polymer blend science now offers thermodynamics as well as unique morphologies.

Chapter 1 covers most of the important aspects of the rest of the text in a qualitative 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

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polymer chains, and Chapter 3 describes their molecular weight. Chapter 4 shows the interactions between solvent molecules and polymer molecules.

Chapters 5–7 cover important aspects of the bulk state, both amorphous and crystalline, the glass transition phenomenon, and rubber elasticity. These three chapters offer the greatest depth. Chapter 8 describes creep and stress relaxation, 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 a 50-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. Each chapter is also accompanied by a problem set.

The author thanks the armies of students who studied from this book in manuscript form during its preparation and repeatedly offer suggestions relative to clarity, organization, and grammar. Many researchers from around the world contributed important figures. Dr. J. A. Manson gave much helpful advice 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 University Library provided one of their carrels during much of the actual writing. In particular, the author thanks Sharon Siegler and Victoria Dow and the staff at Mart Library for patient literature searching and photocopying. The author also thanks Andrea Weiss, who carefully photographed many of the figures in this book.

Secretaries Jone Susski, Catherine Hildenberger, and Jeanne Loosbrock each contributed their skills. Lastly, the person who learned the most from the writing of this book was . . .

Bethlehem, Pennsylvania L. H. Sperling

November 1985

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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 6.5.4

diffraction line

Angular amplitude 8.3.3

A_T= reduced variables shift factor 8.6.1.2 Surface area (with various subscripts) 12.2.3

B Bulk modulus 8.1.1.2, 8.1.4

C C* = chiral center, optically active carbon 2.3.2, 2.4.1

C_m= constant 3.3.2

C_N= neutron scatting equivalent of H 5.2.2.1

C_•= characteristic ratio 5.3.1.1

DC_p= change in heat capacity 6.1

CI = crystallinity index 6.5.4

C_p= heat capacity 8.2.9

C₁, C₂= Mooney–Rivlin constants 9.9.1 C₁₀₀, C₀₁₀, C₂₀₀, C₄₀₀, C, C¢, C≤, = generalized strain 9.9.2

energy constants

C₁¢, C₂¢ = WLF constants 10.4.1

C_A= concentration of A A10.1

C_p, C_v= capacitance of polymer and vacuum 14.7.1

SYMBOLS AND DEFINITIONS

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SYMBOL DEFINITION SECTION

D Diffusion coefficient 3.6.6,

4.4.2, 5.4.2.1

Disk diameter 13.9.3

D_e= Deborah number 10.2.4

D¢ = fractal dimension 12.7.3

D2= IPN phase domain size 13.5.4

D = Tensile compliance 8.1.6

E Young’s modulus 1.3, 8.1.1.1

DE = change in energy 2.2.4

Eact= energy of activation 2.8, 8.6.1.2 E* = complex Young’s (tensile) modulus 8.1.8

E¢ = storage modulus 8.1.8

E≤ = loss modulus 8.1.8

E₁, E₂, etc. = spring moduli 10.1.2.1

Elongational compliance 8.1.6

F Helmholtz free energy 9.5

G Gibbs’s free energy 3.2

Group molar attraction constant 3.2.3

DGM= change in free energy on mixing 3.2 G_N⁰= steady-state rubbery shear modulus 5.4.2.1

Radial growth rate of crystal 6.6.2.2

Shear modulus 8.1.1.1

G* = complex shear modulus 8.1.8

G¢ = shear storage modulus 8.2.9

G≤ = shear loss modulus 8.2.9

G = fracture energy 11.1.2

Gc= critical energy of crack growth 11.1.2 Glc= critical energy of crack growth on extension 11.5.2.4

G^s= surface free energy 12.2.1

H H0= magnetic field 2.2.4

Optical constant 3.6

DH_f= enthalpy of fusion 6.1

dH = NMR absorption line width 8.3.4

Heat energy per unit volume per cycle 8.12

Wool’s general function 11.5.3

H^s= surface enthalpy 12.2.1

I I_D= dimer emission intensity 2.10.3.1

I_M= single mer emission intensity 2.10.3.1

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I I₁, I₂, I₃= strain invarients 9.9.2

Current 14.7.1

J Flux 4.4.2

J_n= de Gennes defect current 5.4.2.1

Compliance (with various subscripts) 5.4.2.1, 8.1.1.2

Shear compliance 8.1.1, 8.1.6

J* = complex compliance 8.1.6

J¢, J≤ = storage and loss compliance 10.2.4

K K˜ = constant 3.6.1

Wave vector 3.6.1,

5.2.2.1, 12.3.8.1 Equilibrium constant of polymerization 3.7.2.1 Constant in the Mark–Houwink–Sakurada 3.8.3

equation

K_d= distribution coefficient 3.9.2

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

K₁, K₂= measures of free volume 8.6.1.1 K_L, K_H= constants in melt viscosity 10.4.2.1 K = stress intensity factor 11.2.4.1,

11.3.2 K_1c, K_2c, K_3c= critical stress intensity factor in the 11.2.4.1, extension, shear, and tearing modes 11.3.2 DK = stress intensity factor range 11.4.2

L Sample length 9.4

L(x), L(b) = inverse Langevin function 9.10.1 L₁, L₂= transverse lengths 12.3.8.1

2L₀= separation length 12.6.1

M Molecular weight

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

M₁, M₂= mass fractions 8.8.1

M_c= number-average molecular weight between 9.4 cross-links

SYMBOLS AND DEFINITIONS xxi

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SYMBOL DEFINITION SECTION M M_e= molecular weight between entanglements 9.4

M_c¢ = entanglement molecular weight 9.4, 10.4.2.3

Mass 11.1.2

N N_i= number of molecules of molecular weight M_i 1.2.2

Number of cells 3.3.1.2

N_A= Avogadro’s number 3.3.2

N_c= number of molecules in 1 cm³ 4.3.2 N_e= number of mers between entanglements 11.5.2.2 O

P P(q) = single-chain form factor 3.6.1

P_c= critical extent of reaction at the gel point 3.7.4

P˜ = reduced pressure 4.3

P* = characteristic value 4.3

Permeability coefficient 4.4.2

P₁= probability of a chain arm folding back 5.4.3 on itself

Probability of barriers being surmounted 8.6.1.2

P_i= induced polarization 14.8.1

Q Partition function 8.6.3.1

QI, QII= amounts of heat released 9.8.3

R Gas constant 1.3

R• = free radical 1.4.1.2

R = generalized organic group 1.4.1.2

R(q) = Rayleigh’s ratio 3.6

R_e= Reynolds number 14.13.1

Rg= radius of gyration 3.6.1

Ri= rate of initiation 3.7.2.2

Rp= rate of propagation 3.7.2.2

R_t= rate of termination 3.7.2.2

R_e= hydrodynamic sphere equivalent radius 3.8.2 R = ratio of radii of gyration 9.10.6

R¯ = fracture resistance 11.1.2

Resistance in ohms 14.7.1

S Entropy 3.2

DS_M= change in entropy on mixing 3.2

Solubility coefficient 4.4.2

Scaling variable A4.1

S_k= mean separation distance 6.6.2.5

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S Disclination strength 7.6

S^s= surface entropy 12.2.1

S_th= interphase surface thickness 12.3.7.2

T Absolute temperature 1.3

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˜ = reduced temperature 4.3

T* = characteristic temperature 4.3 T = Fraction of light transmitted 5.2.1 T_f* = equilibrium melting temperature of crystals 6.8.5

T_ll= liquid–liquid transition 8.4

T₀= generalized transition temperature 8.6.1.2 T_s= arbitrary WLF temperature 8.6.1.2 T₂= unifying treatment of the second-order glass 8.6.3.4

transition temperature

T_e= fraction of trapped entanglements 9.10.5.1 T_e, T_R, T_d= relaxation times 10.2.5

T_r= reptation time 10.2.5

U U_max= maximum in scattering intensity in the 6.5.1 radial direction

Internal energy 9.5

dU₁, dU₂, dU₃, dU₄, = energies related to fracture 11.1.1

V Molar volume 3.2

V_s= scattering volume 3.6

V_e= hydrodynamic sphere volume 3.8.2

V = reduced volume 4.3

V* = characteristic volume 4.3

V_r= volume of one cell 4.3.2

V₀= occupied volume 8.6.2.1

V_t= specific volume 8.6.2.1

V₁= molar volume of solvent 9.12

Voltage 14.7.1

W Work on elongation 9.7.2

W_a= work of adhesion 12.3.7.2

W_g= Weight fraction gel 9.10.5.1

SYMBOLS AND DEFINITIONS xxiii

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SYMBOL DEFINITION SECTION X Brownian motion average distance traversed 5.2.2.1

X_t= degree of crystallinity 6.6.2.1

X_B= mole fraction of impurity 6.8.1

X₁, X₂= mole fractions 8.8.1

X(t) = average mer interpenetration depth 10.2.6 function of time

X(•) = interpenetration depth constant 10.2.6 Y

Z Avrami constant 6.6.2.1

Constant in cross-link density calculations 8.6.3.2 Number of carbon atoms in a chain’s backbone 10.4.2.1

Zw Backbone atoms per chain 10.4.2

a Exponent in the Mark–Houwink–Sakurada 3.8.3 equation

a_H, a_D= scattering lengths 5.2.2.1

End-to-end distance of a Rouse–Bueche segment 5.4.1

Cell axis distance 6.1.1

van der Wall’s constant 9.6

Half the crack length 11.3.1

Correlation distance 12.3.8.1

b b₁, b₂= polarizabilities 5.2.1

Kuhn segment length 5.3.1.2

Defect stored length 5.4.2.1

van der Wall’s constant 9.6

Statistical segment step length 12.3.7.2

c Solute concentration 3.5.2

d Thickness 5.2.1

Bragg distance 6.2.2

Domain period 13.6.2.1

e

f Functionality of branch units 3.7.4

f₀= frictional coefficient 3.8.2

Function A4.1

f_I= orientation function 5.2.1

Restoring force 5.4.1

Fractional free volume 8.6.1.2

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f f₀= fractional free volume at T_g 8.6.1.2

Retractive force 9.5

f_e= energetic portion of the retractive force 9.5 f_s= entropic portion of the retractive force 9.5

Force on a chain 9.7.1

f* = network functionality 9.10.2

f_xx, f_yy, f_zz= stress components 10.5.2

g Gauche 2.1.2

h Planck’s constant 2.10.2

i i_e= Thomson scattering factor 3.6.1

Square root of minus one 8.1.8

j

k Boltzmann’s constant 2.8

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

k¢ = Huggins’s constant 3.8.4

k≤ = Kraemer’s constant 3.8.4

l Length of a link or mer 5.3.1.1

= crystal thickness 6.4.2.1

m Meso, same side 2.3.3

Mass of a polymer chain 3.10

n Number of mers in the chain 1.1

Number of network chains per unit volume 1.3

Mole fraction 3.3.1.1

Refractive index 3.6, 5.2.1

Any whole number 6.2.2

Avrami constant 6.6.2.1

n_c, n_p= chemical and physical cross-links 9.10.5.1 n_tot= total number of effective cross-links 9.10.5.1

Number of stress cycles 11.4.2

n(t), n_•= number of chains intersecting a unit area 11.5.3 of interface at t and at infinite time

o

p Partial vapor pressure 3.3.1.1

Fractional conversion 3.7.2.3

Persistence length 4.2

SYMBOLS AND DEFINITIONS xxv

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p Number of pitches 6.3.2

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

r Racmic-opposite side 2.3.3

End-to-end distance 3.6.2,

9.7.1, 10.2.7 r˜₀²= root-mean square end-to-end distance of 3.9.7

a chain

Reptation rate 6.6.2.5

r_i

¯², r¯₀²= mean square end-to-end distances of 9.10.4 swollen and relaxed chains

r_y= crack-tip plastic zone radius 11.3.2

Exponent in interface theory 11.5.3

s

t Trans 2.1.2

Time 3.7.2.4

Exponent in interface theory 11.5.3

u Intermolecular excluded volume 3.3.2

u¯ = Stokes terminal velocity 10.5.4

v Volume fraction 3.2

v₂= volume fraction of polymer 4.1.2, 9.10.4

Excluded volume parameter 4.2

v₂* = critical volume concentration 7.5.1

v_f= specific free volume 8.6.1.1

v₀= occupied volume 8.6.1.2

Velocity of chain pullout 11.5.2.2

w Distance from source 3.6

x Mole fraction 4.3.6

General parameter A4.1

Number of mers in chain 3.3.1.2

Axial ratio of liquid crystalline molecule 7.5.1 y

z Charge on the polymer 3.10

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SYMBOL DEFINITION SECTION Greek Alphabet

A B G

D Logarithmic decrement 8.12

E Z H Q I K L M N X O P R

S dS/dW = scattering cross section 5.2.2.1 T

U

F Universal constant in intrinsic viscosity 3.8.3 C

Y Entropic factor 3.3.2

Y₁= constant 4.1.2

W Number of possible arrangements in space 3.3.1.2

Solid angle 5.2.2.1

Probability of finding all the molecules 9.6

W₁= angular velocity 10.5.4

a a_x= mechanically induced peak frequency shift 2.9 Expansion of a polymer coil in a good solvent 3.8.2

a_A/B= gas selectivity ratio 4.4.6.2

Volumetric coefficient of expansion 8.3 a_R= cubic expansion coefficient in the rubbery 8.6.1.1

state

a_G= cubic expansion coefficient in the glassy state 8.6.1.1

SYMBOLS AND DEFINITIONS xxvii

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SYMBOL DEFINITION SECTION a a_f= expansion coefficient of the free volume 8.6.1.2

Extension ratio 9.4

b b₁= lattice constant 3.3.2

Compressibility 8.1.4

b_f= compressibility free volume 8.11

Gaussian distribution term 9.7.1

g Number of flexible bonds per mer 8.6.3.2

Shear strain 8.1.1.2

g.

= shear rate 10.5.1

g_s= surface tension (intrinsic surface energy) 11.3.1 g_p= plastic deformation energy 11.3.2

Surface tension 12.2.1

g (r) = Debye correlation function 12.3.8.1

g_xx Perpendicular stress 10.5.2

d Solubility parameter 3.2

Measure of internal structure 6.6.2.2

tan d = loss tangent 8.2.9

e Normal strain 8.1.1

e* = van der Waals energy of interaction 4.3.4

Tensile strain 8.1.1.1

e¢, e≤ = dielectric storage and loss constants 8.3.4, 14.7.1 z

h Viscosity of a solution 3.8.1

h₀= viscosity of the solvent 3.8.1

h_rel= relative viscosity 3.8.1

h_sp= specific viscosity 3.8.1

[h] = intrinsic viscosity 3.8.1

Shear viscosity (of a polymer melt) 8.1.1.2

h_g= melt viscosity at T_g 8.6.1.2

h₂, h₃, etc. = dashpot viscosities 10.1.2.2 h¢, h≤ = storage and loss viscosities 10.5.3

h* = complex viscosity 10.5.3

q Flory q-temperature 3.3.2

Angle of scatter 3.6.1

ı k

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SYMBOLS AND DEFINITIONS xxix

l Wavelength 3.6, 6.2.2

l* = chain deformation, phantom network 9.10.6 Volume element in the Takayanagi model 10.1.2.3

Elongational viscosity 8.1.9

m Magnetic moment 2.2.4

Number of network junctions 9.10.2

m_tube= tube mobility of a chain 10.4.2.4

m₁= constant 10.4.2.4

m₀= molecular friction coefficient 11.5.2.2

n Frequency 2.2.4

Kinetic chain length 3.7.2.2

Poisson’s ratio 8.1.1.2

n¯ = kinematic viscosity 10.5.4

x Screening length 4.2

Mesh size 12.7.1

o

p Osmotic pressure 3.5.2, 3.5.3

p₁= 3.1416 3.6

r Density 3.2.2, 6.5.4

r_e= electron density 3.6.1

r = reduced density 4.3

s Stress 5.2.1,

8.1.1.1

Normal stress 8.1.1

s_b= tensile stress to break 1.2.1

Surface free energy of crystals 6.6.2.3 s_R, s_p= stress of the rubber and plastic 10.1.2.3

components of the Takayanagi model

s₁, s₂, s₃= components of triaxial stress 11.2.3

t NMR scale 2.3.4

Turbidity 3.6.1

Relaxation time (various subscripts) 5.4.1, 10.2.1, 11.5.3

Shear stress 8.1.1.2, 10.5

n Poisson’s ratio 8.1.1, 8.1.3

f Volume fraction of polymer 4.2

f¢ = stability parameter 6.8.5

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SYMBOL DEFINITION SECTION f Volume element in the Takayanagi model 10.1.2.3

Phase volume fraction 12.3.8.1

c Flory–Huggins heat of mixing term (Sometimes 3.3.2 written c1or c12)

c ¢ = number of cross-links per gram 8.6.3.2 y

w Angular frequency in radians 8.12,

10.2.4

w_g, we= Carnot cycle work 9.8.3

Sample-detector distance 5.2.2.1

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1

INTRODUCTION TO POLYMER SCIENCE

1 Polymer science was born in the great industrial laboratories of the world of the need to make and understand new kinds of plastics, rubber, adhesives, fibers, and coatings. Only much later did polymer science come to academic life. 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 molecular weight, 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 that goes back before the chemical structure of the long chains was understood.

The first polymers used were natural products, especially cotton, starch, proteins, and wool. Beginning early in the twentieth century, synthetic polymers were made. The first polymers of importance, Bakelite and nylon, showed the tremendous possibilities of the new materials. However, the scientists of that day realized that they did not understand many of the relationships between the chemical structures and the physical properties that resulted. The research that ensued forms the basis for physical polymer science.

This book develops the subject of physical polymer science, describing the interrelationships among polymer structure, morphology, and physical and mechanical behavior. Key aspects include molecular weight and molecular weight distribution, and the organization of the atoms down the polymer chain. Many polymers crystallize, and the size, shape, and organization of the

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

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

This chapter provides the student with a brief introduction to the broader field of polymer science. Although physical polymer science does not include polymer synthesis, some knowledge of how polymers are made is helpful in understanding configurational aspects, such as tacticity, which are concerned with how the atoms are organized along the chain. Similarly polymer molecular weights and distributions are controlled by the synthetic detail. This chapter starts at the beginning of polymer science, and it assumes no prior knowledge of the field.

1.1 FROM LITTLE MOLECULES TO BIG MOLECULES

The behavior of polymers represents a continuation of the behavior of smaller molecules 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 commercial gasolines contain many branched-chain materials and aromatics as well as straight-chain alkanes, the viscosity of gasoline is markedly lower than that of kerosene, motor oil, and grease because of its lower average chain length.

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

H CH_{2 n}H C

H H

H

Methane

H

C H

H

Ethane

H C H H

H H C

H

Propane

H C H H

C H H

H

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

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

The polymeric alkanes with no side groups that contain 1000 to 3000 carbon atoms 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, most polyethylenes have initiator residues.

Even at a chain length of thousands of carbons, the melting point of polyethylene is still slightly molecular-weight-dependent, but most linear polyeth- ylenes have melting or fusion temperatures, T_f, near 140°C. The approach to the theoretical asymptote of about 145°C at infinite molecular weight (1) is illustrated schematically in Figure 1.1.

The greatest differences between polyethylene and wax lie in their mechanical behavior, however. While wax is a brittle solid, polyethylene is a tough plastic. Comparing resistance to break of a child’s birthday candle with a wash bottle tip, both of about the same diameter, shows that the wash bottle tip can be repeatedly bent whereas the candle breaks on the first deformation.

CH_{2 n¢}

CH₂ CH₂ _n

1.1 FROM LITTLE MOLECULES TO BIG MOLECULES 3

Table 1.1 Properties of the alkane/polyethylene series Number of Carbons State and Properties of

in Chain Material Applications

1–4 Simple gas Bottled gas for cooking

5–11 Simple liquid Gasoline

9–16 Medium-viscosity liquid Kerosene 16–25 High-viscosity liquid Oil and grease 25–50 Crystalline solid Paraffin wax candles

50–1000 Semicrystalline solid Milk carton adhesives and coatings 1000–5000 Tough plastic solid Polyethylene bottles and containers

3–6 ¥ 10⁵ Fibers Surgical gloves, bullet-proof vests

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Polyethylene is a tough plastic solid because its chains are long enough to connect 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 both within the lamellae and between them. On the other hand, only weak van der Waals forces hold the chains together in wax.

In addition a certain portion of polyethylene is amorphous. The chains in this portion are rubbery, imparting flexibility to the entire material. Wax is 100% crystalline, by difference.

The long chain length allows for entanglement (see Figure 1.3). The entanglements 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 polymer chains in the amorphous state. One of the most powerful theories in polymer science (2) states that the conformations of amorphous chains in space are random coils; that is, the directions of the chain portions are statistically determined.

1.2 MOLECULAR WEIGHT AND MOLECULAR WEIGHT DISTRIBUTIONS

While the exact molecular weight required for a substance to be called a polymer is a subject of continued debate, often polymer scientists put the number at about 25,000 g/mol. This is the minimum molecular weight required for 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 during elongation, where stress has the units of Pa, dyn/cm², or lb/in²; see Chapter 11.

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.

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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, s_b, is near zero. As the molecular weight increases, the tensile strength increases rapidly, and then gradually levels off. Since a major point of weakness at the molecular level involves the chain ends, which do not transmit the covalent bond strength, it is predicted that the tensile strength reaches an asymptotic

1.2 MOLECULAR WEIGHT AND MOLECULAR WEIGHT DISTRIBUTIONS 5

Figure 1.2 Comparison of wax and polyethylene structure and morphology.

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value at infinite molecular weight. A large part of the curve in Figure 1.4 can be expressed (3,4)

(1.5)

where M_nis the number-average molecular weight (see below) and A and B are constants. Newer theories by Wool (3) and others suggest that more than 90% of tensile strength and other mechanical properties are attained when the chain reaches eight entanglements in length.

1.2.2 Molecular Weight Averages

The same polymer from different sources may have different molecular weights. Thus polyethylene from source A may have a molecular weight of 150,000 g/mol, whereas polyethylene from source B may have a molecular weight of 400,000 g/mol (see Figure 1.5). To compound the difficulty, all common synthetic polymers and most natural polymers (except proteins) have a distribution in molecular weights. That is, some molecules in a given sample

sb

n

A B

= - M

(a) (b)

Figure 1.3 Entanglement of polymer chains. (a) Low molecular weight, no entanglement.

(b) High molecular weight, chains are entangled. The transition between the two is often at about 600 backbone chain atoms.

Figure 1.4 Effect of polymer molecular weight on tensile strength.

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

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

The answer to these questions lies in defining average molecular weights and molecular weight distributions (5,6). The two most important molecular weight averages are the number-average molecular weight, M_n,

(1.6)

where Niis the number of molecules of molecular weight Mi, and the weight- average molecular weight, Mw,

(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 polydispersity index, provides a simple definition of the molecular weight distribution. Thus all compositions of are called polyethylene, the molecular weights being specified for each specimen.

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

CH₂ CH₂ _n

M N M

w N M

i i i

=

Â Â

2

M N M

n N

i i i

i i

=

Â Â

1.2 MOLECULAR WEIGHT AND MOLECULAR WEIGHT DISTRIBUTIONS 7

Figure 1.5 Molecular weight distributions of the same polymer from two different sources, A and B.

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mous contribution to the melt viscosity. For these reasons, great emphasis is placed 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 small molecules crystallize, an example being water to ice. Thus this transition is very familiar.

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 amorphous solid. It should be pointed out that many polymers are totally amorphous. Carried out under ideal conditions, the glass transition is a type of second-order transition.

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

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

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Depending on the region of viscoelastic behavior, the mechanical properties of polymers differ greatly. Model stress–strain behavior is illustrated in Figure 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 transition region are more extensible, sometimes exhibiting a yield point (the hump in the tough plastic stress–strain curve). If the polymer is above its brittle–ductile transition, Section 11.2.3, rubber-toughened, Chapter 13, or semicrystalline with its amorphous portions above T_g, tough plastic behavior will also be observed. Polymers in the rubbery plateau region are highly elastic, often stretching to 500% or more. Regions 1, 2, and 3 will be discussed further in Chapters 8 and 9. Regions 4 and 5 flow to increasing extents under stress; see Chapter 10.

Cross-linked amorphous polymers above their glass transition temperature behave rubbery. Examples are rubber bands and automotive tire rubber. In general,Young’s modulus of elastomers in the rubbery-plateau region is higher than 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 the polymer, the amorphous material, may be above or below its glass transition

1.3 MAJOR POLYMER TRANSITIONS 9

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

Region Polymer Application

Glassy Poly(methyl methacrylate) Plastic

Glass transition Poly(vinyl acetate) Latex paint

Rubbery plateau Cross-poly(butadiene–stat–styrene) Rubber bands

Rubbery flow Chicle^a Chewing gum

Viscous flow Poly(dimethylsiloxane) Lubricant

aFrom 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.

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temperature, creating four subclasses of materials. Table 1.3 gives a common example of each. While polyethylene and natural rubber need no further introduction, common names for processed cellulose are rayon and cellophane.

Cotton is nearly pure cellulose, and wood pulp for paper is 80 to 90% cellulose. A well-known trade name for poly(methyl methacrylate) is Plexiglas^®. The modulus–temperature behavior of polymers in either the rubbery-plateau region 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 between rubbery 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 step- wise polymerization. The most important of the chain polymerization methods is called free radical polymerization.

1.4.1.1 Free Radical Polymerization The synthesis of poly(ethyl acrylate) will be used as an example of free radical polymerization. Benzoyl peroxide is a common initiator. Free radical polymerization has three major kinetic steps—initiation, propagation, and termination.

1.4.1.2 Initiation On heating, benzoyl peroxide decomposes to give two free radicals:

(1.8)

In this reaction the electrons in the oxygen–oxygen bond are unpaired and become the active site. With R representing a generalized organic chemical

C

Benzoyl peroxide Free radical, R. O

O:O C

O O.

C ^D 2

O

Table 1.3 Examples of polymers at room temperature by transition behavior

Crystalline Amorphous

Above Tg Polyethylene Natural rubber

Below Tg Cellulose Poly(methyl methacrylate)

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

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. The double bond is broken open, and the free radical reappears at the far end.

1.4.1.3 Propagation After initiation reactions (1.8) and (1.9), many 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 the chain.

1.4.1.4 Termination In the termination reaction, two free radicals react 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

O C₂H₅ O C O C₂H₅

CH₂ H

C O

O C₂H₅ C

R CH₂ C CH₂ R

H H

C C. R

O

O C₂H₅

CH₂

R CH₂ H

C + nCH₂ C

O

O C₂H₅

H

C C. CH₂

O

O C₂H₅ H

C CH₂ C

O

O C₂H₅ H₅C₂

H

C C O

O H

n

Free radical Ethyl acrylate Growing chain

C C. R

O

O C₂H₅

CH₂ H

C R. + CH₂ C

O

O C₂H₅

H

1.4 POLYMER SYNTHESIS AND STRUCTURE 11

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

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 other acrylics it is used as a latex paint.

1.4.1.5 Structure and Nomenclature The principal method of polymer- izing monomers by the chain kinetic scheme involves the opening of double bonds to form a linear molecule. In a reacting mixture, monomer, fully reacted polymer, and only a small amount of rapidly reacting species are present. Once the polymer terminates, it is “dead” and cannot react further by the synthesis scheme 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, in the 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 and names along with comments as to how the polymers are used. The “vinyl”

monomers are characterized by the general structure CH₂=CHR, where R represents any side group. One of the best-known vinyl polymers is poly(vinyl chloride), 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 left- hand carbon. Thus poly(vinyl chloride) should be written . However, from a synthesis point of view, the structure is written , because the free radical is borne on the pendant moiety carbon. 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 are formed by reacting two or more monomers together. In general, the polymer structure most closely resembling the monomer structure will be presented herein.

Today, recycling of plastics has become paramount in preserving the envi- ronment. On the bottom of plastic bottles and other plastic items is an identification number and letters; see Table 1.5. This information serves to help in separation of the plastics prior to recycling. Observation of the properties of the plastic such as modulus, together with the identification, will help

CR CH

CH₂ CH₂

CHCl _n CH₂

CHCl CH₂ _n

INTRODUCTION TO PHYSICAL POLYMER SCIENCE