Polymer Materials E-Book

Jean Louis Halary

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 892

Veröffentlichungsjahr: 2011

Beschreibung

Advanced reviews for Polymer Materials "Molecular modeling of polymers ... is a subject that cannot be found in any other [book] in any appreciable detail. ... [T]he detailed chapters on specific polymer systems is a great idea." -- Gregory Odegard, Michigan Technological University "The polymer community needs a text book which can connect the macroscopic mechanics with mesoscopic and molecular aspects of polymer." -- Liangbin Li, University of Science and Technology of China This book takes a unique, multi-scale approach to the mechanical properties of polymers, covering both the macroscopic and molecular levels unlike any other book on the market. Based on the authors' extensive research and writing in the field, Polymer Materials emphasizes the relationships between the chemical structure and the mechanical behavior of polymer materials, providing authoritative guidelines for assessing polymer performance under different conditions and the design of new materials. Key features of this book include: * Experimental results on selected examples precede and reinforce the development of theoretical features * In-depth discussions of a limited number of polymer systems instead of a brief overview of many * Self-contained chapters with a summary of their key points * Comprehensive problems and a solutions manual for the different parts of the book * Coverage of the basics with an emphasis on polymer dynamics An indispensable resource for polymer scientists and students alike, Polymer Materials is also highly useful for material scientists, engineers, chemists, and physicists in industry and academia.

Leseprobe

Table of Contents

Cover

Title page

Copyright page

PREFACE

LIST OF SYMBOLS

INTRODUCTION TO POLYMER MATERIALS

I.1. CHRONOLOGICAL LANDMARKS FOR POLYMERS

I.2. THE POLYMER CHAIN

I.3. THE KEY POINTS OF POLYMER SYNTHESIS

I.4. MAJOR POLYMERS

I.5. THE LIGHTNESS OF POLYMER MATERIALS

I.6. MAIN MECHANICAL ASPECTS OF POLYMER MATERIALS

I.7. COMPREHENSIVE SURVEY OF THE POLYMER MECHANICAL BEHAVIORS

PART I

1 THE FOUR CLASSES OF POLYMER MATERIALS

1.1. THE YOUNG MODULUS

1.2. UN-CROSS-LINKED AMORPHOUS POLYMERS

1.3. SEMICRYSTALLINE THERMOPLASTICS

1.4. THERMOSETTING POLYMERS

1.5. CROSS-LINKED ELASTOMERS

1.6. CONCLUSIONS

2 THE MACROMOLECULAR CHAIN IN THE AMORPHOUS BULK POLYMER: STATIC AND DYNAMIC PROPERTIES

2.1. CONFORMATIONAL STATISTICS OF ISOLATED POLYMER CHAINS

2.2. CONFORMATIONAL ENERGY CALCULATIONS

2.3. GLOBAL PROPERTIES OF AN ISOLATED CHAIN

2.4. CHAIN CONFORMATIONS IN BULK AMORPHOUS POLYMERS

2.5. LOCAL DYNAMICS OF ISOLATED CHAINS

2.6. LOCAL DYNAMICS OF A POLYMER CHAIN IN SOLUTION

2.7. LOCAL DYNAMICS IN BULK POLYMERS

2.8. CONCLUSIONS

3 THE GLASS TRANSITION

3.1. EXPERIMENTAL STUDIES

3.2. MOLECULAR ORIGIN OF THE GLASS TRANSITION TEMPERATURE

3.3. OVERVIEW OF THE GLASS TRANSITION TEMPERATURE THEORIES

3.4. EFFECT OF THE POLYMER ARCHITECTURE ON THE GLASS TRANSITION TEMPERATURE

3.5. EFFECT OF THE POLYMER CHEMICAL STRUCTURE ON THE GLASS TRANSITION TEMPERATURE

3.6. GLASS TRANSITION OF RANDOM COPOLYMERS

3.7. GLASS TRANSITION OF POLYMER/PLASTICIZER BLENDS

3.8. CONCLUSIONS

4 SECONDARY RELAXATIONS IN AMORPHOUS POLYMERS

4.1. EXPERIMENTAL EVIDENCES OF A SECONDARY RELAXATION

4.2. IDENTIFICATION OF THE MOTIONS THAT ARE RESPONSIBLE FOR THE SECONDARY RELAXATIONS

4.3. MOTIONAL COOPERATIVITY ASSOCIATED WITH SECONDARY RELAXATIONS

4.4. SECONDARY RELAXATIONS OF POLY(METHYL METHACRYLATE) AND SOME OF ITS RANDOM COPOLYMERS

4.5. SECONDARY RELAXATION OF NEAT AND ANTIPLASTICIZED BISPHENOL-A POLYCARBONATE

4.6. SECONDARY RELAXATIONS IN NEAT AND ANTIPLASTICIZED ARYL-ALIPHATIC EPOXY RESINS

4.7. CONCLUSIONS

5 ENTANGLEMENTS IN BULK UN-CROSS-LINKED POLYMERS

5.1. CONCEPT OF ENTANGLEMENT

5.2. EXPERIMENTAL DETERMINATIONS OF

5.3. THEORETICAL OVERVIEW OF CHAIN DYNAMICS

5.4. RELATIONSHIPS BETWEEN ENTANGLEMENTS AND POLYMER CHEMICAL STRUCTURE

5.5. CONCLUSIONS

6 SEMICRYSTALLINE POLYMERS

6.1. EXPERIMENTAL EVIDENCE OF SEMICRYSTALLINE STATE

6.2. CRYSTALLINE STRUCTURE OF POLYMERS

6.3. MORPHOLOGY OF SEMICRYSTALLINE POLYMERS

6.4. CRYSTALLIZATION KINETICS

6.5. MELTING TEMPERATURE OF CRYSTALLINE DOMAINS

6.6. INFLUENCE OF THE POLYMER CHEMICAL STRUCTURE

6.7. GLASS TRANSITION OF SEMICRYSTALLINE POLYMERS

6.8. CONCLUSIONS

PART II

7 ELASTIC AND HYPERELASTIC BEHAVIORS

7.1. DEFINITION AND PHYSICAL ORIGIN OF AN ELASTIC BEHAVIOR

7.2. ENTHALPIC ELASTICITY (TRUE ELASTICITY)

7.3. ENTROPIC ELASTICITY (HYPERELASTICITY OR RUBBER ELASTICITY)

7.4. CONCLUSIONS

8 LINEAR VISCOELASTIC BEHAVIOR

8.1. INTRODUCTION AND DEFINITIONS

8.2. TRANSIENT MECHANICAL MEASUREMENTS

8.3. DYNAMIC MECHANICAL TESTS

8.4. ANALOGICAL MECHANICAL MODELS

8.5. TIME (OR FREQUENCY)–TEMPERATURE EQUIVALENCE PRINCIPLE

8.6. EXAMPLES OF VISCOELASTIC BEHAVIOR

8.7. CONCLUSIONS

9 ANELASTIC AND VISCOPLASTIC BEHAVIORS

9.1. INVESTIGATION OF STRESS–STRAIN CURVES

9.2. YIELD CRITERIA

9.3. MOLECULAR INTERPRETATION OF YIELDING

9.4. SPECIFIC BEHAVIOR IN THE VISCOPLASTIC RANGE

9.5. INHOMOGENEOUS PLASTIC DEFORMATION OF SEMICRYSTALLINE POLYMERS

9.6. CONCLUSIONS

10 DAMAGE AND FRACTURE OF SOLID POLYMERS

10.1. MICROMECHANISMS OF DEFORMATION

10.2. FRACTURE MECHANICS

10.3.  AND DETERMINATIONS AND VALUES

10.4. FATIGUE FRACTURE

10.5. MOLECULAR APPROACH OF FRACTURE BEHAVIOR

10.6. CONCLUSIONS

PART III

11 MECHANICAL PROPERTIES OF POLY(METHYL METHACRYLATE) AND SOME OF ITS RANDOM COPOLYMERS

11.1. POLY(METHYL METHACRYLATE)

11.2. METHYL METHACRYLATE-CO-MALEIMIDE RANDOM COPOLYMERS

11.3. METHYL METHACRYLATE-CO-N-CYCOHEXYLMALEIMIDE RANDOM COPOLYMERS

11.4. METHYL METHACRYLATE-CO-N-METHYLGLUTARIMIDE RANDOM COPOLYMERS

11.5. CONCLUSIONS

12 MECHANICAL PROPERTIES OF BISPHENOL-A POLYCARBONATE

12.1. NEAT BPA-PC

12.2. ANTIPLASTICIZED BPA-PC

12.3. OTHER TOUGH POLYMERS

12.4. CONCLUSIONS

13 MECHANICAL PROPERTIES OF EPOXY RESINS

13.1. SYNTHESIS OF EPOXY RESINS

13.2. MOLECULAR MOBILITY IN THE SOLID STATE

13.3. PLASTIC BEHAVIOR

13.4. FRACTURE BEHAVIOR

13.5. CONCLUSIONS

14 POLYETHYLENE AND ETHYLENE-α-OLEFIN COPOLYMERS

14.1. SYNTHESIS AND STRUCTURAL CHARACTERISTICS OF PE AND RANDOM ETHYLENE-α-OLEFIN COPOLYMERS

14.2. MORPHOLOGY

14.3. MECHANICAL PROPERTIES

14.4. CONCLUSIONS

15 HIGH-MODULUS THERMOPLASTIC POLYMERS

15.1. HIGH-MODULUS PE

15.2. HIGH-MODULUS POLYMERS OBTAINED FROM MESOMORPHOUS POLYMERS

15.3. CONCLUSIONS

PART IV

16 MECHANICAL TESTS FOR STUDYING IMPACT BEHAVIOR

16.1. MECHANICAL TESTS

16.2. FRACTURE BEHAVIORS OF TOUGHENED POLYMERS

17 HIGH-IMPACT POLYSTYRENE

17.1. HIPS SYNTHESIS

17.2. CHARACTERISTIC BEHAVIORS AND OBSERVATIONS

17.3. EFFECT OF THE MAIN PARAMETERS

17.4. TOUGHENING MECHANISMS

17.5. CONCLUSIONS

18 TOUGHENED POLY(METHYL METHACRYLATE)

18.1. ELABORATION OF RT-PMMA

18.2. LOW STRAIN RATE BEHAVIORS AND OBSERVATIONS

18.3. HIGH STRAIN RATE BEHAVIORS AND OBSERVATIONS

18.4. TOUGHENING MECHANISM

18.5. CONSEQUENCES OF TOUGHENING MECHANISMS ON FORMULATION AND BEHAVIOR OF RT-PMMA

18.6. ANALYSIS OF THE DEPENDENCE OF TOUGHENING ON TEMPERATURE AND STRAIN RATE

18.7. CONCLUSIONS

19 TOUGHENED ALIPHATIC POLYAMIDES

19.1. POLYAMIDE–ELASTOMER BLENDS

19.2. LOW STRAIN RATE BEHAVIOR

19.3. IMPACT BEHAVIOR AND OBSERVATIONS

19.4. TOUGHENING MECHANISMS

19.5. TOUGHENING BY BLOCK COPOLYMERS

19.6. CONCLUSIONS

20 TOUGHENED EPOXY RESINS

20.1. TOUGHENING BY ELASTOMER PARTICLES

20.2. TOUGHENING OF EPOXY RESINS BY THERMOPLASTIC POLYMERS

20.3. CONCLUSIONS

PART V

21 CHEMICALLY CROSS-LINKED ELASTOMERS

21.1. MAIN CHEMICALLY CROSS-LINKED ELASTOMERS

21.2. FRACTURE TESTING TECHNIQUES FOR ELASTOMERS

21.3. FRACTURE OF NONCRYSTALLIZING ELASTOMERS

21.4. NATURAL RUBBER

21.5. CONCLUSIONS

22 REINFORCEMENT OF ELASTOMERS BY FILLERS

22.1. DIFFERENT FILLERS AND THEIR CHARACTERIZATION

22.2. CHARACTERISTICS OF THE FILLER–ELASTOMER SYSTEM

22.3. IMPROVEMENT OF ELASTOMER PROPERTIES BY FILLERS

22.4. ANALYSIS OF ELASTIC MODULUS

22.5. SPECIFIC ENERGY DISSIPATION OF FILLED ELASTOMERS

22.6. FRACTURE BEHAVIOR

22.7. CONCLUSIONS

23 THERMOPLASTIC ELASTOMERS

23.1. TRIBLOCK COPOLYMERS WITH IMMISCIBLE BLOCKS

23.2. MULTI-BLOCK COPOLYMERS

23.3. CONCLUSIONS

APPENDIX: PROBLEMS

A.1. CONFORMATIONS OF PP AND PMMA (PART I)

A.2. PET (PART I)

A.3. GLASS TRANSITION TEMPERATURE OF POLYBUTADIENES (PART I)

A.4. PA-6,6 (PARTS I AND II)

A.5. PMMA/PVDF BLENDS (PARTS I AND II)

A.6. BLENDS OF POLYSTYRENE AND POLY(DIMETHYLPHENYLENE OXIDE) (PARTS I AND II)

A.7. BISPHENOL-A POLYCARBONATE AND TETRAMETHYL BISPHENOL-A POLYCARBONATE (PART III)

A.8. SEMIAROMATIC POLYAMIDES (PART III)

A.9. ABS (PART IV)

A.10. RUBBER TOUGHENED POLY(VINYL CHLORIDE) (RT-PVC) (PART IV)

A.11. DETERMINATION OF THE MOLECULAR WEIGHT BETWEEN CROSS-LINKS IN RUBBERY NETWORKS (PARTS II AND V)

A.12. NEAT AND SILICA-FILLED SBRS (PART V)

Index

Translated by Jean Louis Halary and Françoise Lauprêtre and Lucien Monnerie.

Originally published in French under the titles “De la Macromolécule au Matériau Polymère” by Jean Louis Halary and Françoise Lauprêtre © Editions Belin—Paris (2006) and “Mécanique des Matériaux Polymères” by Jean Louis Halary, Françoise Lauprêtre, and Lucien Monnerie, ©Editions Belin—Paris (2008).

Copyright © 2011 by John Wiley & Sons, Inc. All rights reserved

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

Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Halary, Jean Louis.

 [De la macromolécule au matériau polymère. English]

 Polymer materials : macroscopic properties and molecular interpretations / Jean Louis Halary, Françoise Lauprêtre, Lucien Monnerie.

p. cm.

 Includes index.

 ISBN 978-0-470-61619-2 (cloth)

1. Polymers. 2. Macromolecules. I. Lauprêtre, Françoise. II. Monnerie, L. (Lucien) III. Title.

 QD381.H34513 2011

 541′.2254–dc22

2010023285

ePDF: 978-0-470-92201-9

ePub: 978-0-470-92288-0

PREFACE

In the middle of the 1970, the first oil crisis led to a new development of polymer materials. To lighten vehicles and to save energy, polymers replaced metals. However, such a replacement necessitated an improvement of the properties of existing polymers and the development of new chemical structures. An important research activity was generated in order to get a deeper understanding of polymer properties—and, especially, mechanical properties—and of their relations with the chemical structure of the polymer chains.

Such a research benefited from very recent experimental techniques such as 1H and 13C solid-state nuclear magnetic resonance (NMR), molecular modeling, transmission and scanning electronic microscopy, and atomic force microscopy.

Since the 1980, our research group has been intensively involved in this field. Our interest was mostly focused on polymer dynamics and on local motions in solid polymers, as well as on their consequences on the plastic properties and fracture behavior in thermoplastics and in elastomers. This research was performed in close relation with the major European companies involved in polymer materials. Over the years, our academic lectures and industrial trainings have dealt with all these different aspects.

Several textbooks have already been published on polymer properties. However, they are mainly oriented toward specific behaviors such as viscoelasticity, fracture, and toughening or toward materials like thermoplastics, thermosets, and elastomers.

The purpose of this textbook is to cover and emphasize the relationships that can be established between the chemical structure and the mechanical properties of the various types of rigid polymers and elastomer materials. These relations are extended to materials that are either toughened by rubber particles or reinforced by inorganic fillers. The optical and electrical properties, the surface properties, the permeability, and the fire-resistance are not considered.

For each topic under study, the experimental results are described first; in a second step, they are analyzed by taking advantage of the information obtained at the nanomolecular or molecular scales by microscopies, NMR, and molecular modeling, in order to achieve a molecular approach of the properties.

The book is divided into five parts.

Part I (Chapters 1 to 6) is devoted to the necessary polymer background, with a special emphasis on polymer dynamics.

Part II (Chapters 7 to 10) deals with the concepts of mechanical properties.

Part III (Chapters 11 to 15) describes the behaviors of typical rigid polymers.

Part IV (Chapters 16 to 20) is centered on the toughening of rigid polymers.

Part V (Chapters 21 to 23) focuses on pure and filled elastomers and thermoplastic elastomers.

After these five parts we present some comprehensive problems that have been the matter of course final examinations.

This book is designed for graduate and post-graduate students in Polymer Science. An increasing number of graduates in Physics, Mechanics, and Materials Science and Engineering have an interest in polymer materials: In spite of their limited background in Polymer Science, the book is intended to make them aware, without too many difficulties, of the chemical dimension of the macroscopic behaviors with which they are familar. The book should also be of use to the academic teachers who are looking for a unified and interdisciplinary course on polymer mechanics and are interested in selected case studies. We hope that the engineers and scientists in industry and research, who are often searching for predictive recipes on mechanical behavior, will also find useful guidelines to rationalize their application needs.

Finally, we would like to thank all our former students who have enriched the different chapters of this textbook and helped us to upgrade, year after year, our original presentations by their questions, comments, and suggestions. We also would like to express our sincere gratitude to our respective spouses, namely Monique, Jean-Michel, and Monique, for the understanding and support that they never failed to show during the preparation of this new book.

Jean Louis Halary

Françoise Lauprêtre

Lucien Monnerie

Paris, France

October 2010

LIST OF SYMBOLS

length of half a crackcritical length for crack propagationtube diametershift factorradius of an initial cavity inside a particlefree energyarea of diffuse haloarea of crystalline peakarea of crystallization peakarea of melting peakfree energy of a networkcross sectionlength of a bondlength of a Kuhn linkbulk modulussample thicknessbulk modulus of the core of a particleelastomer bulk moduluselastic constantcharacteristic ratioheat capacitycapacity of a capacitor filled with polymercapacity of an empty capacitor, WLF coefficients at , Mooney–Rivlin coefficients, WLF coefficients at distance between successive planes of the crystal latticeelastomer particle diameterdensity of occupied sitesdiffusion coefficient of a chain along its tubenumber average degree of polymerizationviscoelastic descriptorthickness of the glassy layer at the filler surfaceYoung modulusstorage modulusloss moduluscomplex modulusgeneral Young modulus for plane stress and plane strain conditionsactivation energyabsorbed energy in an impact testcohesive energydispersive energy of filler–elastomer interactionsenergy of filler–filler interactionsYoung modulus of a polymer matrixYoung modulus at the rubbery plateauenergy difference between low- and high-energy conformationsloading frequencyreduced stressprobabibility of a conformational changefunctionality of the network cross-linkstensile force intensityforce required to maintain the ends of a Rouse subchaincreep complianceggravitygauchenumber of chain endsproportionality coefficient in the expression of the plateau shear modulusshear modulusstorage shear modulusloss shear moduluscomplex shear moduluscritical strain energy release rate or fracture energy per surface unitfree enthalpy of crystal formationstorage shear modulus of the elastomer matrixstorage shear modulus of a filled elastomercritical strain energy release rate or fracture energy per surface unit in mode Ifree enthalpy of melting per repeat unitreduced modulus in Payne effect studiesshear modulus at the rubbery plateauactivation free enthalpyenthalpy variation at meltingPayne effect amplitudehPlanck constantfracture hysteresishysteresis associated with a deformationmagnetic fieldquantity of heatactivation enthalpycrystallization enthalpy per unit massmelting enthalpy per unit massvariation of enthalpy at melting of a fully crystalline polymerrelaxation time spectrumpolydispersity indexinvariants of the strain tensorscaterred intensity at angle number of bonds per repeat unitcontour integralcritical value of the contour integraldelayed complianceinstanteneous compliancespring complianceviscous compliancestorage complianceloss compliancecomplex compliancekBoltzmann constantbond stiffness constantangle stiffness constantstress intensity factor, toughnesstoughness in mode Itoughness in mode I at a crack propagation arrest in unstable semi-brittle fracturetoughness in mode I at a crack propagation in unstable semi-brittle fracturetoughness in mode I with a very sharp crackbar lengthmean distance between two branches in PEhammer displacementlength of the slow crack propagation zone in unstable semi-brittle fracturelength of a network chaincrystal dimension along the normal to the () planelength of primitive pathsurface to surface interparticle distancecritical surface to surface interparticle distancetube lengthaverage distance between cross-linksLangevin functionretardation time spectrumweight of the amorphous phaseweight of the crystalline phasemolar mass of an atommolecular weight of a linkdielectric loss modulusaverage molecular weight of a backbone bondpolymer molecular weightmolecular weight between entanglementsmolecular weight of a Kuhn segmentmolecular weight of a repeat unittransverse magnetizationaverage molecular weight between cross-linksnumber average molecular weightweight average molecular weightdirector in a liquid-crystalline phasenumber of entanglements per chainnumber of high energy conformationsnumber of low energy conformationsnumber of real bonds per repeat unitnumber of virtual bonds per repeat unitnumber of repeat unitsaverage number of repeat units between entanglementsnumber of bondsNAAvogadro numbernumber of fatigue cyclesnumber of fatigue cycles at breaknumber of network chains per volume unitnumber of bonds between entanglementsnumber of equivalent bonds between entanglementsnumber of Kuhn segmentsnumber of Kuhn segments between cross-linksnumber of Kuhn segments between entanglementsnumber of adjacent sites in a mobile clusternumber of Rouse subchainstotal number of sitesaverage number of chain backbone bonds between cross-linkshydrostatic pressureapplied loadcritical applied load for crack propagationmaximum load at crack propagationorder parameterlimit pressure at which the glass transition motions would occur at an infinitely low frequencyplastic strain softeningmechanical energynumber of filaments to break for fracturenumber of monomer units in a Rouse sub-chainheatelectric chargeradius of plastic zone under plane stress conditionsradius of plastic zone under plane strain conditionsRgas constantend-to-end distancereinforcement characteristic of a filled elastomerradius of an elastomer particleimpact strength in Charpy testlength of the Dugdale plastic zoneimpact strength in Izod testmean-square end-to-end distancemean-square displacement of polymer beads during a simulation timerelaxation modulusdistance of a segment to the center of gravityentropyentropy of a network chainarea of damage surface or fracture surfaceentropy of a chain in the meltcompliance constantentropy of the networkmean-square radius of gyrationactivation entropyvariation of entropy at meltingtransloading duration until fracturesimulation timecontact time to reach half of the maximum magnetization for a 13C nucleusaging temperaturecrystallization temperatureglass transition temperatureglass transition temperature at a distance from the filler surfaceupper glass transition temperaturemelting temperaturemelting temperature of a crystal of an infinite sizebrittle–ductile transition temperaturetransition temperature from brittle to semi-brittletransition temperature from semi-brittle to ductiletransition temperature from stable–unstable ductile to stable ductilespin–lattice relaxation time in the laboratory framespin–lattice relaxation time in the rotating framespin–spin relaxation time associated with the motional modulation of the dipolar couplingspin–spin relaxation time associated with the motional modulation of the chemical shift anisotropymain () transition temperature as observed by dynamic mechanical analysistemperature of the relaxationlimit temperature at which the glass transition motions would take place at an infinitely slow cooling ratefree volume reduction per cross-linkinternal energybond energystored elastic energyinitiation crack propagation energycrack propagation energycell volumevolume at temperature volume of the amorphous phasevolume of the crystalline phaseactivation volumevolume occupied by a chain in a bulk polymervolume of a coiltotal dynamic free volumedynamic free volume at dynamic free volume per main-chain segmentsample volumefree volume associated with a conformational changeequilibrium volume at hammer speedtransition speed from brittle to semi-brittletransition speed from semi-brittle to ductiletransition speed from stable–unstable ductile to stable ductilepotential energysample widthweight fraction of component workcritical elastic energy densityelastic energy of a filled elastomer associated with a stabilized stretching curve until deformationelastic energy of a filled elastomer associated with a first stretching to deformationfraction of high energy conformations at temperature number of other chains located within a coiloscillation amplitudevolumetric thermal expansion coefficient in the glassy statethermal expansion coefficient of the free volume fractionvolumetric thermal expansion coefficient in the liquid stateisothermal compressibility in the glassy stateisothermal compressibility of the free volume fractionisothermal compressibility in the liquid stateshear strainshear rateaccelaration of atom maximum strain amplitudevan der Waals surface energytorquesurface energy between the fibril and micro-void in a chain disentanglement crazesurface energy between the fibril and micro-void in a chain scission crazesurface energy between a filler and an elastomertearing surface energy of an elastomer particleHildebrand solubility parametertanloss tangentcrack aperturecritical crack apertureexcess volumedisplacementstraincritical strain for craze formationcritical strain for craze formation in chemical environmentengineering straintrue strainyield strainstrain ratedielectric constantstrain tensorcomplex dielectric permittivitydielectric permittivitydielectric losscraze growth rateNewtonian viscositycomplex viscositydynamic viscositydashpot viscosityangle conditionsintensity of the effect of constraints on the amplitude of the junction fluctuationswavelengthextension ratio of a cavityextension ratio at breakextension ratio along the directionnumber of available conformationsnumber of conformations per network chainnumber of conformations of the networkchemical potentialchemical potential of the repeat unit in the crystalline stateCoulomb internal friction coefficientinternal friction coefficientchemical potential of the repeat unit in the liquid statevon Mises internal friction coefficientchemical potential of the solvent in the solutionchemical potential of the pure solventelectric dipole momentfrequency of conformational changesfrequency of cooperative motionscross-link densityequivalent cross-link densityentanglement densityPoisson coefficientPoisson coefficient of a polymer matrixdensity of stable linksdensity of unstable linksfriction coefficient of a beadfriction coefficient of a “blob”friction coefficient of atom friction coefficient of a monomerpolymer densityradius of curvature of a cavitystresscritical stress for craze growthcritical stress for craze propagationcritical stress for craze growth in chemical environmentstress at the surface of a crazevon Mises equivalent stresssurface energy of folded chainshydrostatic stresshydrostatic stress applied to a particlehydrostatic component of the applied stress, principal component of the chemical shift tensorsurface energy of oriented chainsengineering stressplastic flow stressstress of shear band formationtrue stressyield stressDugdale internal stresscritical stress for chain disentanglement craze growthcritical stress for chain scission craze growthstress applied to a samplestress tensorshear stresscorrelation time of WLF cooperative motionsmaximum shear stressrelaxation time corresponding to the Rouse modereptation timecorrelation time of segmental motionsDoi–Edwards transverse relaxation timeDoi–Edwards longitudinal relaxation timeDoi–Edwards relaxation time for reptationcorrelation time of overall chain motionsinternal rotation anglemolar fraction of solventmolar fraction of solutemolar fraction of impurityvolume fraction of cavitated particlescrystalline weight fraction derived from densitycrystalline weight fraction derived from DSCvolume fraction of elastomer within an epoxy matrixvolume fraction of elastomerinitial volume fraction of elastomervolume fraction of fillerdynamic free volume fractionvolume fraction of component polystyrene volume fraction inside a particlevolume fraction of elastomer particlescrystalline weight fractionvolume fraction of the crystalline phase derived from X-ray diffractioninteraction coefficient between components 1 and 2phase angleangular frequency

PART I

1

THE FOUR CLASSES OF POLYMER MATERIALS

In this chapter, we will briefly describe the different mechanical behaviors observed in polymer materials; each of them will be investigated in full detail later in this book. Besides, we will soon introduce some typical characteristics of these materials such as the glass transition temperature, chain entanglements, and semi-crystallinity, which will be considered more extensively in Chapters 3, 5, and 6, respectively.

We will first define the Young modulus, , and its experimental determination. The study of the temperature dependence of the Young modulus will lead us to distinguish four classes of polymer materials: the un-cross-linked amorphous polymers, the semi-crystalline thermoplastics, the thermosetting polymers, and the cross-linked elastomers. In each class, a particular system will be chosen as an example to illustrate the corresponding state diagram.

1.1. THE YOUNG MODULUS

Let us consider a parallelepiped sample in the form of a bar of length and cross-section (Figure 1.1), loaded with a tensile strength of intensity, , which results in a lengthening along the stretching direction. In this experiment, the applied strength is sufficiently small to yield a very small as compared to . Under these conditions, whose simplicity will be justified in Chapter 7:

the stress, , and strain, , are defined as

(1.1)

Figure 1.1. Principle of a uniaxial tensile test.

where the stress, , has the dimensions of a pressure and the strain, , is a dimensionless quantity;

The proportionality of the stress to the strain is considered as valid:

(1.2)

The proportionality coefficient, , is the Young modulus of the material. It has the dimensions of a pressure and is expressed in pascals (Pa). In the case of polymers, shows a strong dependence on temperature; it may vary over several orders of magnitude, as shown in the following sections.

1.2. UN-CROSS-LINKED AMORPHOUS POLYMERS

The polymers belonging to this class of materials are characterized by the temperature dependence of the Young modulus shown in Figure 1.2.

Figure 1.2. Schematic temperature dependence of the Young modulus (log scale) for three samples of the same un-cross-linked amorphous polymer, of molecular weight , , and , respectively.

A major descriptor can be seen on this diagram: It is the molecular weight between entanglements, . To get a deeper understanding of the meaning of , let us consider cis-1,4-polyisoprene (natural rubber), atactic PS, PMMA, and BPA-PC, which are un-cross-linked amorphous polymers. For all these polymers, the chains look like a spaghetti dish at the molecular scale, they are disordered, and their wide-angle X-ray scattering diagram exhibits a diffuse halo. Each chain adopts a coil conformation that strongly overlaps with its neighbors, leading to chain entanglements. By definition, chains of average molecular weight, , with a number of entanglements per chain equal to , are characterized by a molecular weight between entanglements, , such that

(1.3)

Figure 1.2 shows that, independently of the sample molecular weight, the Young modulus of un-cross-linked amorphous polymers is of the order of 1 GPa (109 Pa) at low temperature. At the glass transition temperature, , the low-molecular-weight sample becomes a viscous liquid and its Young modulus decreases drastically. For samples with a molecular weight higher than the mole­cular weight between entanglements, , the Young modulus decreases through the glass transition and reaches a plateau value of about 1 MPa (106 Pa); this plateau is called the “rubbery plateau” and its extent increases with molecular weight. At higher temperatures, these high-molecular-weight polymers go through a fluidification zone before becoming highly viscous liquids whose Young modulus drastically becomes reduced.

For an un-cross-linked amorphous polymer, three descriptors (the molecular weight between entanglements, the polymer molecular weight, and the glass transition temperature) are sufficient to define the state diagram of the material. As an example, Figure 1.3a shows the state diagram of atactic PS.

Figure 1.3. State diagram of un-cross-linked amorphous polymers: (a) atactic PS; (b)cis-1,4-polyisoprene.

The borderline of the glassy state is given by the molecular weight dependence of the glass transition temperature (Chapter 3, Section 3.4). The borderline between the rubbery and viscous liquid states is the fluidification curve of the material, whose characteristic temperature sharply increases with the molecular weight of the entangled polymer (Chapter 5, Section 5.2.2). The fact that a polymer belongs to the class of un-cross-linked amorphous polymers does not give any information about its thermoplastic or elastomer character. Thus, atactic PS is a thermoplastic polymer, owing to its glass transition temperature, , of 106°C, far above room temperature (Figure 1.3a). On the other hand, cis-1,4-polyisoprene can be considered as an elastomer since its glass transition temperature, , of −72°C, is far below room temperature (Figure 1.3b).

1.3. SEMICRYSTALLINE THERMOPLASTICS

Polymers belonging to this class are characterized by the temperature dependence of the Young modulus schematized in Figure 1.4.

Figure 1.4. Schematized temperature dependence of the Young modulus for two samples of a semicrystalline thermoplastic polymer, with molecular weights and , respectively.

At low temperature, the Young modulus, which is almost independent of the sample molecular weight, is of the order of 1 GPa, as for un-cross-linked amorphous polymers. At the glass transition temperature, the Young modulus decreases by one order of magnitude only, reaching a first plateau (100 MPa) corresponding to a “leathery state” of the material (this behavior is described in Chapter 9, Section 9.5). Then during the melting of the crystalline domains, at the melting temperature, , the modulus is reduced to a value of 1 MPa. Beyond this point, the behavior is similar to that of un-cross-linked amorphous polymers above . Samples with molecular weight smaller than the molecular weight between entanglements () rapidly become viscous fluids and their Young modulus vanishes. For samples with molecular weight , the Young modulus remains constant all along the rubbery plateau (whose extent increases with molecular weight), then it falls down in the fluidification zone where the material becomes a very viscous fluid.

PE, isotactic PP, PET, PA-6, and PA-6,6 are examples of widely used semicrystalline thermoplastics. In all these polymers, the amorphous regions (in which the chains are disordered and characterized by a glass transition temperature) coexist with crystalline domains (characterized by a melting temperature, ), as described in Chapter 6, Section 6.3.

For a semicrystalline thermoplastic, four descriptors—the molecular weight between entanglements, the polymer molecular weight, the glass transition, and the melting temperatures—are necessary to build the state diagram of the material. As an example, Figure 1.5 shows the state diagram of isotactic PP.

Figure 1.5. State diagram of isotactic PP.

In addition to the curves corresponding to the molecular weight dependence of the glass transition temperature and fluidification temperature, already present in the case of un-cross-linked amorphous polymers, the existence of a leathery state in the state diagram of a semicrystalline thermoplastic is associated with the molecular weight dependence of the melting temperature (Chapter 6, Section 6.5.4).

The thermoplastic character of a semicrystalline polymer is not related to the value of its glass transition temperature: It is associated with its melting temperature, , higher than room temperature. For the examples considered, lies between 121°C (for PE) and 270°C (for PET).

1.4. THERMOSETTING POLYMERS

The polymers belonging to this class of materials are characterized by the temperature dependence of the Young modulus shown in Figure 1.6.

Figure 1.6. Schematized temperature dependence of the Young modulus of two thermosetting polymers with the same chemical structure and different molecular weights between cross-links, .

At low temperature, the Young modulus is of the order of 1 GPa, as for un-cross-linked amorphous polymers and semicrystalline thermoplastics. When the cross-link density is not too high, these resins exhibit a glass transition temperature, as un-cross-linked amorphous polymers do. At , the Young modulus decreases moderately, by one order of magnitude or less, depending on the average molecular weight between cross-links, , and reaches a rubbery plateau which extends until the chemical degradation happens. The existence of a fluid state cannot be obtained without breaking the chains, since all the network meshes are linked by covalent bonds.

Phenolic resins (phenol + methanol), amine resins (methanol + urea or methanol + melamine), and epoxy resins (Chapter 13) (di- or tri-epoxide + multifunctional amine or anhydride hardener) are examples of this class of materials, which are developed for their applications in the glassy state.

The state diagram of these materials is drawn by considering not the molecular weight (which is infinite), but the average molecular weight between cross-links, , along the abscissa axis. Two inter-connected descriptors ( and ) are sufficient to draw the state diagram. As an example, Figure 1.7