Thermal Analysis of Polymeric Materials Part 1 pot

Bernhard Wunderlich
Thermal Analysis of Polymeric Materials
123
Bernhard Wunderlich
Thermal Analysis
of Polymeric Materials
With 974 Figures
Prof. Dr. Bernhard Wunderlich
200 Baltusrol Road
Knoxville, TN 37922-3707
USA

Library of Congress Controll Number: 2004114977
ISBN 3-540-23629-5 Springer Berlin Heidelberg New York
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Preface
Thermal analysis is an old technique. It has been neglected to some degree because
developments of convenient methods of measurement have been slow and teaching
of the understanding of the basics of thermal analysis is often wanting. Flexible,
linear macromolecules, also not as accurately simply called polymers, make up the
final, third, class of molecules which only was identified in 1920. Polymers have
never been fully integrated into the disciplines of science and engineering. This book
is designed to teach thermal analysis and the understanding of all materials, flexible
macromolecules, as well as those of the small molecules and rigid macromolecules.
The macroscopic tool of inquiry is thermal analysis, and the results are linked to
microscopic molecular structure and motion.
Measurements of heat and mass are the two roots of quantitative science. The
macroscopic heat is connected to the microscopic atomic motion, while the
macroscopic mass is linked to the microscopic atomic structure. The macroscopic
units of measurement of heat and mass are the joule and the gram, chosen to be easily
discernable by the human senses. The microscopic units of motion and structure are
the picosecond (10
12
seconds) and the ångstrom (10
10
meters), chosen to fit the
atomic scales. One notes a factor of 10,000 between the two atomic units when
expressed in “human” units, second and gram—with one gram being equal to one
cubic centimeter when considering water. Perhaps this is the reason for the much
better understanding and greater interest in the structure of materials, being closer to
human experience when compared to molecular motion.
In the 19
th
century the description of materials could be based for the first time on
an experiment-based atomic theory. This permitted an easy recognition of the

differences between phases and molecules. Phases are macroscopic, homogeneous
volumes of matter, separated from other phases by well-defined boundaries, and
molecules are the constituent smallest particles that make up the phases. As research
progressed, microphases were discovered, initially in the form of colloidal
dispersions. More recently, it was recognized that phase-areas may be of nanometer
dimensions (nanophases). On the other hand, flexible macromolecules have
micrometer lengths or larger. Particularly the nanophases may then have structures
with interfaces that frequently intersect macromolecules, giving the materials unique
properties.
Finally, the classical phases, gases, liquids, and solids, were found to be in need
of expansion to include mesophases and plasmas. The discussion of history in the
first lecture shows the tortuouspathscientificdiscoverytakes to reachthepresent-day
knowledge. Easier ways can be suggested in hindsight and it is vital to find such
simpler approaches so to help the novice in learning. In this book on “Thermal
Analysis of Polymeric Materials” an effort is made to discover such an easy road to
understand the large, flexible molecules and the small phases, and to connect them
to the small molecules and macroscopic phases which are known for much longer.
Preface
__________________________________________________________________
VI
Since the goal of this book is to connect the new knowledge about materials to the
classical topics, but its size should be restricted to two to three semesters’ worth of
learning, several of the standard classical texts were surveyed by the author. Only
when a topic needed special treatment for the inclusion of thermal analysis or macro-
molecules, was this topic selected for a more detailed discussion in this book. The
knowledge in polymer science, in turn, often improves the understanding of the other
types of molecules. A typical example is discussed in the first lecture when
describing the classification-scheme of molecules. With this approach, the learning
of materials science, as a whole, may be less confusing. A series of six additional
examples of such improvement of the understanding is given on pg. VII.

The study of “Thermal Analysis of Polymeric Materials” is designed to
accomplish two goals: First, the learning of the new subject matter, and second, to
stimulate a review of the classical topics. Naturally, one hopes that in the future all
topics are included in the main educational track. This joining of the physics,
chemistry, and engineering of small and large molecules with thermal analysis is of
urgency since most students must in their career handle polymeric materials and deal
with the application of some type of thermal analysis. A list of short summaries of
the seven chapters of the book is given below for a general orientation and to allow
for reading, starting at different entry points:
Chapter 1 Atoms, Small, and Large Molecules is designed to enhance the understanding
and history of the development of knowledge about small and large molecules. Furthermore,
the nomenclature, description, and characterization of linear macromolecules by basic theory
and experiment are summarized.
Chapter 2 Basics of Thermal Analysis contains definitions of systems, flux, and
production and the following thermodynamic functions of state which are needed for the
description of thermal analysis results: heat capacity, enthalpy, entropy, and free enthalpy.
Chapter 3 Dynamics of Chemical and Phase Changes is a summary of the syntheses by
matrix, stepwise, step, and chain reactions. It also contains information on emulsion
polymerizations, cross-linking, gelation, copolymerization, and decomposition. Kinetics of
nucleation, crystallization, and melting, aswellas glasstransitions arechosen asrepresentative
of the dynamics of phase changes.
Chapter 4 Thermal Analysis Tools contains a detailed description of thermometry,
calorimetry, temperature-modulated calorimetry (TMC), dilatometry, thermomechanical
analysis (TMA), dynamic mechanical analysis (DMA), and thermogravimetry (TGA).
Chapter 5 Structure and Properties of Materials covers the solid states (glasses and
crystals), mesophases (liquid, plastic, and condis crystals), and liquids. Alsotreatedare multi-
phase materials, macroconformations,morphologies, defects andthe prediction of mechanical
and thermal properties.
Chapter 6 Single Component Materials provides detailed descriptions of phase diagrams
with melting, disordering, and glass transitions. In addition, the effects of size, defects, strain

on transitions and properties of rigid amorphous and other intermediate phases are treated in
the light of thermal and mechanical histories.
Chapter 7 Multiple Component Materials, finally covers our limited knowledge of
chemical potentials of blends, solutions, and copolymers. The Flory-Huggins equation, phase
diagrams, solvent, solute, and copolymer effects on the glass, melting, and mesophase
transitions are the major topics.
This book grew out of the two three-credit courses “Physical Chemistry of
Polymers” and “Thermal Analysis” at The University of Tennessee, Knoxville
(UTK). First, the lectures were illustrated with overhead foils, generated by
computer, so that printouts could be provided as study material. In 1990 these
Preface
__________________________________________________________________
VII
overheads were changed to computer-projected slides and the textbook “Thermal
Analysis” was published (Academic Press, Boston). In 1994, a condensed text was
added to the slides as lecture notes. A much expanded computer-assisted course
“Thermal Analysis of Materials” was then first offered in 1998 and is a further
development, enabling self-study. The computer-assisted course is still available via
the internet from our ATHAS website (web.utk.edu/
~
athas) and sees periodic updates.
It is the basis for the present book. A short version of the ATHAS Data Bank, a
collection of thermal data, is included as Appendix 1. A treatise of the theory of
“Thermophysics of Polymers” was written by Prof. Dr. Herbert Baur in 1999
(Springer, Berlin) and can serve as a companion book for the theoretical basis of the
experimental results of “Thermal Analysis of Polymeric Materials.”
The book contains, as shown above, a critically selected, limited series of topics.
The field of flexible macromolecules is emphasized, and the topics dealing with small
molecules and rigid macromolecules, as well as the treatment of mechanical
properties, are handled on a more elementary level to serve as a tie to the widely

available, general science and engineering texts.
Topics that are Different for Polymers and Small Molecules
The structure of a macromolecular substance is characterized by a diversity of
molecular shapes and sizes, as is discussed in Chap. 1. These are items unimportant
for small molecules. Chemically pure, small molecules can be easily obtained, are
of constant size and often are rigid (i.e., they also are of constant shape).
Classically, one treats phases of two components as ideal, regular, or real
solutions. Usually, however, one concentrates for the non-ideal case only on
solutions of salts by discussing the Debye-Hückel theory. Polymer science, in turn,
adds the effect of different molecular sizes with the Flory-Huggins equation as of
basic importance (Chap. 7). Considerable differences in size may, however, also
occur in small molecules and their effects are hidden falsely in the activity
coefficients of the general description.
The comparison of the entropy of rubber contraction to that of the gas expansion,
on one hand, and to energy elasticity of solids, on the other, helps the general
understanding of entropy (see Chap. 5). Certainly, there must be a basic difference
if one class of condensed materials can be deformed elastically only to less than 1%
and the other by up to 1,000%.
The kinetics of chain reactions of small molecules is much harder to follow (and
prove) than chain-reaction polymerization. Once the reaction is over, the structure
of the produced macromolecule can be studied as permanent documentation of the
reaction (see Chaps. 1 and 3).
The notoriously poor polymer crystals described in Chap. 5 and their typical
microphase and nanophase separations in polymer systems have forced a rethinking
of the application of thermodynamics of phases. Equilibrium thermodynamics
remains important for the description of the limiting (but for polymers often not
attainable) equilibrium states. Thermal analysis, with its methods described in
Chap. 4, is quite often neglected in physical chemistry, but unites thermodynamics
with irreversible thermodynamics and kinetics as introduced in Chap. 2, and used as
an important tool in description of polymeric materials in Chaps. 6 and 7.

The solid state, finally, has gained by the understanding of macromolecular
crystals with helical molecules, their defectproperties,mesophases, small crystal size,
glass transitions, and rigid-amorphous fractions (Chaps. 5 and 6).
Preface
__________________________________________________________________
VIII
General References
The general references should be used for consultation throughout your study of Thermal
Analysis of Polymeric Materials. You may want to have thetextbooksat hand which you own,
and locate the other reference books in the library for quick access. Frequent excursions to the
literature are a basis for success in learning the material of this course.
Typical books on polymer science are (chemistry, physics, or engineering):
1. Rodriguez F, Cohen C, Ober CK, Archer L (2003) Principles of Polymer Systems, 5
th
ed.
Taylor & Francis, New York.
2. Stevens MP (1989) Polymer Chemistry, 2
nd
ed. Oxford University Press, New York.
3. Billmeyer, Jr. FW (1989) Textbook of Polymer Science, 3
rd
ed. Wiley & Sons, New
York.
Typical physical chemistry texts are:
4. Atkins PW (1998) Physical Chemistry, 6
th
ed. Oxford University Press, Oxford.
5. Mortimer RG (1993) Physical Chemistry. Benjamin/Cummings, Redwood City, CA.
6. Moore WG (1972) Physical Chemistry, 4
th

ed. Prentice Hall, Englewood Cliffs, NJ.
As mentioned above, the companion book treating the theory of the subject is:
7. Baur H (1999) Thermophysics of Polymers. Springer, Berlin.
Reference books for numerical data on polymers and general materials are:
8. Brandrup J, ImmergutEH,Grulke EA, eds (1999) Polymer Handbook.Wiley,NewYork,
4
th
edn.
9. Lide DR, ed (2002/3) Handbook of Chemistry and Physics, 83
rd
ed. CRC Press, Boca
Raton, FL. (Annual new edns.)
For detailed background information on any type of polymer look up:
10. Mark HF, Gaylord NG, Bikales NM (1985–89) Encyclopedia of Polymer Science and
Engineering, 2
nd
ed; Kroschwitz JI ed (2004) 3
rd
ed. Wiley, New York. Also available
with continuous updates via the internet: www.mrw.interscience.wiley.com/epst
For more advanced treatises on physical chemistry, you may want to explore:
11. Eyring H, Henderson D, Jost W (1971–75) Physical Chemistry, An Advanced Treatise.
Academic Press, New York.
12. Partington JR (1949–54) An Advanced Treatise on Physical Chemistry. Longmans,
London.
Acknowledgments
This book has grown through many stages of development. At every stage the book
was shaped and improved by many participating students and numerous reviewers.
Research from the ATHAS Laboratory described in the book was generously
supported over many years by the Polymers Program of the Materials Division of the

National Science Foundation, present Grant DMR-0312233. Several of the
instrument companies have helped by supplying information, and also supported
acquisitions of equipment. Since 1988 the ATHAS effort was also supported by the
Division of Materials Sciences and Engineering, Office of Basic Energy Sciences,
U.S. DepartmentofEnergyatOak Ridge National Laboratory, managed and operated
by UT-Battelle, LLC, for the U.S. Department of Energy, under contract number
DOE-AC05-00OR22725. Allfigureswere originally newly developed anddrawnfor
the computer course “Thermal Analysis of Materials” and have been adapted or were
newly generated for the present book.
Knoxville, TN, January 2005
Bernhard Wunderlich
__________________________________________________________________
Contents
Preface V
Topics that are Different for Polymers and Small Molecules VII
General References VIII
Acknowledgments VIII
1 Atoms, Small, and Large Molecules
1.1 Microscopic Description of Matter and History of Polymer Science
1.1.1 History 1
1.1.2 Molecular Structure and Bonding 3
1.1.3 Classification Scheme for Molecules 6
1.1.4 The History of Covalent Structures 9
1.1.5 The History of Natural Polymers 9
1.1.6 The History of Synthetic Polymers 11
1.2 Nomenclature
1.2.1 Source- and Structure-based Names 13
1.2.2 Copolymers and Isomers 22
1.2.3 Branched, Ladder, and Network Polymers 24
1.2.4 Funny Polymers 25

1.3 Chain Statistics of Macromolecules
1.3.1 Molecular Mass Distribution 27
1.3.2 Random Flight 31
1.3.3 Mean Square Distance from the Center of Gravity 32
1.3.4 Distribution Functions 33
1.3.5 Steric Hindrance and Rotational Isomers 37
1.3.6 Monte Carlo Simulations 40
1.3.7 Molecular Mechanics Calculations 41
1.3.8 Molecular Dynamics Simulations 43
1.3.9 Equivalent Freely Jointed Chain 47
1.3.10 Stiff Chain Macromolecules 47
1.4 Size and Shape Measurement
1.4.1 Introduction 50
1.4.2 Light Scattering 50
1.4.3 Freezing Point Lowering and Boiling Point Elevation 58
1.4.4 Size-exclusion Chromatography 62
1.4.5 Solution Viscosity 63
1.4.6 Membrane Osmometry 65
1.4.7 Other Characterization Techniques 66
References 68
Contents
__________________________________________________________________
X
2 Basics of Thermal Analysis
2.1 Heat, Temperature, and Thermal Analysis
2.1.1 History 71
2.1.2 The Variables of State 75
2.1.3 The Techniques of Thermal Analysis 76
2.1.4 Temperature 79
2.1.5 Heat (The First Law of Thermodynamics) 81

2.1.6 The Future of Thermal Analysis 84
2.2 The Laws of Thermodynamics
2.2.1 Description of Systems 88
2.2.2 The First Law of Thermodynamics 90
2.2.3 The Second Law of Thermodynamics 91
2.2.4 The Third Law of Thermodynamics 94
2.2.5 Multi-component Systems 96
2.2.6 Multi-phase Systems 98
2.3 Heat Capacity
2.3.1 Measurement of Heat Capacity 101
2.3.2 Thermodynamic Theory 104
2.3.3 Quantum Mechanical Descriptions 106
2.3.4 The Heat Capacity of Solids 111
2.3.5 Complex Heat Capacity 117
2.3.6 The Crystallinity Dependence of Heat Capacities 118
2.3.7 ATHAS 121
2.3.8 Polyoxide Heat Capacities 128
2.3.9 Heat Capacities of Liquids 131
2.3.10 Examples of the Application of ATHAS 134
Polytetrafluoroethylene 134
Poly(oxybenzoate-co-oxynaphthoate) 134
Large-amplitude motions of polyethylene 136
Polymethionine 136
MBPE-9 137
Liquid selenium 138
Poly(styrene-co-1,4-butadiene) 139
Hypothetical entropy of the liquid
at absolute zero of temperature 140
Starch and water 142
Conclusions 144

2.4 Nonequilibrium Thermodynamics
2.4.1 Flux and Production 147
2.4.2 Melting of Lamellar Crystals 148
2.4.3 Experimental Data 154
2.4.4 Internal Variables 155
2.4.5 Transport and Relaxation 158
2.4.6 Relaxation Times 159
2.5 Phases and Their Transitions
2.5.1 Description of Phases 162
Contents
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XI
2.5.2 Phases of Different Sizes 167
2.5.3 Mesophases 169
2.5.4 Mesophase Glasses 175
2.5.5 Thermodynamics and Motion 176
2.5.6 Glass Transitions 178
2.5.7 First-order Transitions 181
References 184
3 Dynamics of Chemical and Phase Changes
3.1 Stepwise and Step Reactions
3.1.1 Stepwise Reactions 189
3.1.2 Mechanism of Step Reactions 193
3.1.3 Examples 196
3.1.4 Conditions 198
3.1.5 Reaction Rates 200
3.1.6 Lithium Phosphate Polymerization 201
3.2 Chain and Matrix Reactions
3.2.1 Mechanism of Chain Reactions 206
3.2.2 Kinetics 212

3.2.3 Equilibrium 214
3.2.4 Chain Reactions without Termination 215
3.2.5 Emulsion Polymerization 217
3.2.6 Matrix Reaction 218
3.3 Molecular Mass Distributions
3.3.1 Number and Mass Fractions, Step Reactions 219
3.3.2 Number and Mass Fractions, Chain Reactions 221
3.3.3 Step Reaction Averages 224
3.3.4 Chain Reaction Averages 225
3.4 Copolymerization and Reactions of Polymers
3.4.1 Chain Reaction Copolymers 227
3.4.2 Step Reaction Copolymers 229
3.4.3 Gelation 230
3.4.4 Decomposition 231
3.4.5 Polymer Reactions 233
3.5 Crystal and Molecular Nucleation Kinetics
3.5.1 Observation of Nucleation and Crystal Growth 238
3.5.2 Evaluation of Nucleation Rates 240
3.5.3 Mathematical Description of Primary Nucleation 242
3.5.4 Heterogeneous Nucleation 246
3.5.5 Secondary Nucleation 249
3.5.6 Molecular Nucleation 253
3.6 Crystallization and Melting Kinetics
3.6.1 Linear Melting and Crystallization Rates 255
3.6.2 Directional Dependence of Crystallization 256
3.6.3 Diffusion Control of Crystallization 257
Contents
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XII
3.6.4 Growth of Spherulites 259

3.6.5 Avrami Equation 260
3.6.6 Nonisothermal Kinetics 263
3.6.7 Experimental Data 264
References 276
4 Thermal Analysis Tools
4.1 Thermometry and Dilatometry
4.1.1 Principle and History of Thermometry 279
4.1.2 Liquid-in-glass Thermometers 283
4.1.3 Resistance Thermometers and Thermocouples 285
4.1.4 Applications of Thermometry 290
4.1.5 Principle and History of Dilatometry 291
4.1.6 Length, Volume, and Density Measurement 293
4.1.7 Applications of Dilatometry 298
4.2 Calorimetry
4.2.1 Principle and History 304
4.2.2 Isothermal and Isoperibol Calorimeters 307
4.2.3 Loss Calculation 310
4.2.4 Adiabatic Calorimetry 312
4.2.5 Compensating Calorimeters 314
4.2.6 Modern Calorimeters 317
4.2.7 Applications of Calorimetry 319
Purity analysis 319
Thermochemistry 320
Thermodynamic functions of three allotropes of carbon 325
Thermodynamic functions of paraffins 327
4.3 Differential Scanning Calorimetry
4.3.1 Principle and History 329
4.3.2 Heat-flux Calorimetry 331
4.3.3 Power Compensation DSC 335
4.3.4 Calibration 338

4.3.5 Mathematical Treatment 340
4.3.6 DSC Without Temperature Gradient 344
4.3.7 Applications 349
Heat capacity 349
Finger printing of materials 350
Quantitative analysis of the glass transition 354
Quantitative analysis of the heat of fusion 355
4.4 Temperature-modulated Calorimetry
4.4.1 Principles of Temperature-modulated DSC 359
4.4.2 Mathematical Treatment 362
4.4.3 Data Treatment and Modeling 369
4.4.4 Instrumental Problems 373
4.4.5 Heat Capacity Measurement 385
4.4.6 Glass Transition Measurement 388
Contents
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XIII
4.4.7 First-order Transition Analysis 396
4.4.8 Chemical Reactions 402
4.5 Thermomechanical Analysis, DMA and DETA
4.5.1 Principle of TMA 404
4.5.2 Instrumentation of TMA 406
4.5.3 Applications of TMA 408
4.5.4 Principles and Instrumentation of DMA 412
4.5.5 Applications of DMA 419
4.5.6 DETA 424
4.6 Thermogravimetry
4.6.1 Principle and History 428
4.6.2 Instrumentation 430
4.6.3 Standardization and Technique 437

4.6.4 Decomposition 438
4.6.5 Coupled Thermogravimetry and Differential Thermal Analysis 439
4.6.6 Applications of Thermogravimetry 443
Calcium oxalate/carbonate decomposition 444
Lifetime prediction 446
Summary of Chapter 4 448
References 450
5 Structure and Properties of Materials
5.1 Crystal Structure
5.1.1 Introduction 455
5.1.2 Lattice Description 457
5.1.3 Unit Cells 457
5.1.4 Miller Indices 458
5.1.5 Symmetry Operations 460
5.1.6 Helices 463
5.1.7 Packing in Crystals 468
5.1.8 Packing of Helices 471
5.1.9 Selected Unit Cells 474
5.1.10 Isomorphism 481
5.1.11 Crystals with Irregular Motifs 483
5.2 Crystal Morphology
5.2.1 Crystal Habit 486
5.2.2 Molecular Macroconformation 486
5.2.3 Fold Length 488
5.2.4 Lamellar Crystals 493
5.2.5 Dendrites and Spherulites 497
5.2.6 Fibers 503
5.2.7 Isometric Crystals 508
5.3 Defects in Polymer Crystals
5.3.1 Materials Properties 512

5.3.2 Crystallinity Analysis 512
5.3.3 Summary of Defect Types 516
Contents
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XIV
5.3.4 Supercomputer Simulation of Crystal Defects 524
5.3.5 Deformation of Polymers 530
5.3.6 Ultimate Strength of Polymers 533
5.4 Transitions and Prediction of Melting
5.4.1 Transitions of Macromolecules 536
5.4.2 Crystals of Spherical Motifs 538
5.4.3 Crystals of Non-spherical Motifs 541
5.4.4 Crystals of Linear Hydrocarbons 542
5.4.5 Crystals of Macromolecules 544
5.5 Mesophases and Their Transitions
5.5.1 Multiple Transitions 547
5.5.2 Classes of Mesophases 551
5.5.3 Jump-motion in Crystals 555
5.5.4 Conformational Disorder 558
5.5.5 Examples 561
Summary of the section on morphology 571
5.6 Melts and Glasses
5.6.1 Structure of the Amorphous Phase 572
5.6.2 Properties of the Amorphous Phase 574
5.6.3 Viscosity 575
5.6.4 Energy Elasticity 578
5.6.5 Entropy Elasticity 579
5.6.6 Viscoelasticity 583
References 586
6 Single Component Materials

6.1 The Order of Transitions
6.1.1 Review of Thermodynamics, Motion, and Reversibility 591
6.1.2 First Order Phase Transition 593
6.1.3 Glass Transitions 597
The hole model of the glass transition 598
Enthalpy relaxation 599
The kinetics of the number of holes 600
Effect of the size of the phase on the glass transition 605
Rigid-amorphous fraction, RAF, in semicrystalline polymers 607
Differences in T
g
by DSC and DMA 609
6.2 Size, Extension, and Time Effects During Fusion
6.2.1 Melting of Polyethylene 611
6.2.2 Reversible Melting and Poor Crystals 624
Poly(oxyethylene) 624
Polyterephthalates 628
Polynaphthoate 634
Polycarbonate 637
Poly(phenylene oxide) 639
Poly(
J-caprolactone) 641
Polypropylenes 644
Contents
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XV
Decoupling of segments of polymer chains 649
Poor crystals 652
6.2.3 Annealing and Recrystallization Effects 655
6.2.4 Melting of Poly(oxymethylene) 666

6.2.5 Melting of PEEK 668
6.2.6 Melting of Fibers 672
6.3 Analysis of the Sample History Through Study of the Glass Transition
6.3.1 Time and Temperature Effects 682
6.3.2 Modeling of the Glass Transition 686
6.3.3 Pressure and Strain Effects 689
6.3.4 Crystallinity Effects 693
6.3.5 Network Effects 698
References 701
7 Multiple Component Materials
7.1 Macromolecular Phase Diagrams
7.1.1 Phase Diagrams 706
7.1.2 Flory-Huggins Equation 709
7.1.3 Upper and Lower Critical Temperatures 712
7.1.4 Phase Diagrams with Low-mass Compounds 714
7.1.5 Phase Diagrams with Low-mass Homologs 717
7.1.6 Block Copolymers 723
7.2 Melting Transitions of Copolymers
7.2.1 Theory of Copolymer Melting and Crystallization 725
7.2.2 Applications 733
LLDPE 733
POBcoON 743
7.2.3 Melting Transitions of Block Copolymers 747
7.2.4 Melting Transitions of Regular Copolymers 756
7.3 Glass Transitions of Copolymers, Solutions, and Blends
7.3.1 Theory of Glass Transitions 759
7.3.2 Glass Transitions of Solutions 763
7.3.3 Glass Transitions of of Copolymers 766
7.3.4 Glass Transitions of Block Copolymers 768
7.3.5 Glass Transitions of Multi-phase Systems 772

References 774
Appendices
A.1 Table of Thermal Properties of Linear Macromolecules
and Related Small Molecules—The ATHAS Data Bank 777
A.2 Radiation Scattering (Essay by W. Heller) 801
A.3 Derivation of the Rayleigh Ratio 806
A.4 Neural Network Predictions 811
Contents
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XVI
A.5 Legendre Transformations, Maxwell Relations, Linking of Entropy
and Probability, and Derivation of (dS/dT) 813
A.6 Boltzmann Distribution, Harmonic Vibration, Complex Numbers,
and Normal Modes 815
A.7 Summary of the Basic Kinetics of Chemical Reactions 817
A.8 The ITS 1990 and the Krypton-86 Length Standard 818
A.9 Development of Classical DTA to DSC 820
A.10 Examples of DTA and DSC under Extreme Conditions 824
A.11 Description of an Online Correction of the Heat-flow Rate 831
A.12 Derivation of the Heat-flow Equations 835
A.13 Description of Sawtooth-modulation Response 837
A.14 An Introduction to Group Theory, Definitions of Configurations and
Conformations, and a Summary of Rational and Irrational Numbers 848
A.15 Summary of Birefringence and Polarizing Microscopy 850
A.16 Summary of X-ray Diffraction and Interference Effects 851
A.17 Optical Analog of Electron Double Diffraction to
Produce Moiré Patterns 852
Substance Index 855
Subject Index 875
CHAPTER 1

__________________________________________________________________
1
John Dalton (1766–1844) founded the experiment-based atomic theory. In 1798 he was
elected to be a Member of the Literary and Philosophical Society of Manchester, England.
There, he read on Oct. 21, 1803 the communication on the “Chemical Atomic Theory.”
Fig. 1.1
Atoms, Small, and Large Molecules
1.1 Microscopic Description of Matter
and History of Polymer Science
1.1.1 History
At the beginning of the 19
th
century the description of matter attained, what one
would call today, a scientific basis. Dalton
1
supported the atomic theory with
experiments permitting the development of modern chemistry. The book “A New
System of Chemical Philosophy,” describes this new approach. In Fig. 1.1, an
excerpt is displayed. Chapters I and II give a summary of the contemporary
understanding of nature by analyzing heat and mass, the two basic building-blocks
of any material. Chapter I displays the theory of the caloric as it was generally
1 Atoms, Small, and Large Molecules
__________________________________________________________________
2
Fig. 1.2
accepted in the early 19
th
century. Heatwasassumedtobeanindestructiblefluidthat
occupies spaces between the molecules of matter, as illustrated with the schematic at
the top of Fig. 1.2 for gases. The schematic does not agree with today’s picture of a

gas which calls for mobile molecules that collide with each other (see Sect. 2.5.1).
It, however, permitted quantitative measurements as discussed in more detail in the
description of heat and temperature in Sect. 2.1.1.
Chapter II of Dalton’s book gives a description of the three classical phases of
matter in terms which we still recognize today, except that in modern science one
calls the elastic fluids of the quotation in Fig. 1.1, gasses. Only Chap. III has stood
the test of time and is the basis of the fame of Dalton: “Molecules of matter consist
of atoms, held together by chemical bonds” (see Fig. 1.2). Although Dalton’s
chemical formula of sugar in Fig. 1.2 is not up to the present knowledge in
composition and structure, the principle is correct. Molecules are made up of one or
more atoms. Note also from the lengths of the chapters in Dalton’s book that it
seems, as is common in most human endeavors, that the more one knows about a
subject, the fewer words are needed for its description.
Another point to be made in connection with Dalton’s writings is the distinction
between phases and substances (molecules). It will be shown later in the book that
large molecules may reach the size of phases. On the other hand, phases that were
initially thought to be macroscopic in size, may also be very small in form of
microphases and nanophases, as will be detailed in Sect. 2.5. Sufficiently large
molecules may then reside at the same time in more than one phase. Many of the
special properties of crystalline flexible polymers, for example, are based on the
smallness of their phases, and this will be a major item of discussion in the various
chapters of the book.
1.1 Microscopic Description of Matter and History of Polymer Science
__________________________________________________________________
3
Fig. 1.3
1.1.2 Molecular Structure and Bonding
In order to understand molecules, there is a need for a brief review of atoms and the
bonding which holds the atoms in a molecule. A characterization of the atomic
structure is given by the configuration of its valence electrons, the electrons available

for bonding in the outer shells of the atoms, and the electronegativity, X
A
,as
demonstrated in Fig. 1.3. The electronegativity is a measure of the ability to attract
an electron pair, needed for covalent bonding [1]. It is approximately the average
between the electron affinity (the energy gained or lost when adding an electron) and
the ionization energy (the energy needed to remove an electron), and adjusted with
data from bond energies. The electronegativity has a scale from zero to four and
permits an estimation of covalent bond energy.
The range of atomic radii of the different atoms is not very large, still, the
differences in sizes are of importance for the fitting of atoms to molecules, and
furthermore for the packing of molecules into liquids and crystals, as will be
discussed below. Negative ions often exceed the given range of sizes, and positive
ions may be smaller. The small range of atomic radii is also the reason for the
excitement created when close-to-spherical fullerenes were discovered [2] which are
molecules consisting of carbon atoms only, such as C
60
and C
70
. For the structure of
C
60
and its thermal properties see Sect. 2.5.3. These spheres of 1.0 nm diameter
may act also as building blocks of pseudo molecules. It is interesting to imagine, how
nature would change with changes in atomic size and also shape.
The joining of atoms to molecules requires interactions that keep the atoms bound
together, at least long enough for identification, as pointed out in Fig. 1.4. This
statement is an operational definition of a bond. Operational definitions were
1 Atoms, Small, and Large Molecules
__________________________________________________________________

4
1
Percy Williams Bridgman (1882–1961), Professor at Harvard University, was awarded the
Nobel Prize for Physics in 1946 for his studies of materials at very high temperatures and
pressures.
Fig. 1.4
suggested by Bridgman
1
as a means to give precise, experiment-based information,
even when the phenomenon to be described is not fully understood. This will be
made use of, for example, to clarify difficult subjects, such as: Where is the
borderline between solids and liquids? A topic that will be tackled in Sect. 1.1.3 and
leads to a surprising and not conventional result.
For the description ofmolecules in Fig. 1.4, one expects somecorrelationbetween
the life-time of a bond and its strength. Often one judges the strength of a bond by
its bond energy. Checkingalargenumber of experimentallymeasured bond energies,
it becomes obvious that there are only two well-separated classes of bonds when
describing atoms, ions, and molecules, namely strong bonds and weak bonds. Bond
energies in the range of 50 kJ mol
1
, that would be called intermediate, are rarely
observed. Differenttypesofbondinginvolve different interactionsanddisplacements
of the electrons of the bonding partners.
The strong bonds are classified as covalent, ionic, or metallic. Figure 1.5
illustrates the covalent bonds for fluorine, F
2
, and methane, CH
4
. The bonds involve
sharing of electrons between the bonding partners. Important in the description of a

covalent bond is its directiveness, governed by the molecular orbital that contains the
electron pair. Most of the bonds of interest in polymer science involve hybrid bonds
of s and p orbitals (molecular orbitals are described by combinations of atomic
orbitals, see also Fig. 1.3). Because of the close approach of the atoms in a covalent
bond and the frequent involvement of only s and p orbitals in bonding, coordination
numbers, CN, of one to four are most frequent.
1.1 Microscopic Description of Matter and History of Polymer Science
__________________________________________________________________
5
Fig. 1.5
Moving the (valence) electrons during bonding from one atom (of low X
B
)to
another (of higher X
A
), leads to ionic bonds. Figure 1.5 shows the example of lithium
fluoride, LiF, a salt with strong ionic bonds. The major bonding is caused by
Coulomb attraction between the positive ions and their negative counterparts which
extend into all directions of space. Important for the assembly of large aggregates of
ions is this absence of any directiveness. It must be recognized, however, that only
negative ions in contact with positive ions lead to a strong attraction. Ions of equal
charges repel each other. There are, thus, strict rules of the alternation of charges,
which limits the CN between oppositely charged ions usually to between four and
eight, depending on the size-ratio of the ions.
The metallic, strong bonds are shown in Fig. 1.5 for the example of lithium, Li.
In this case the electrons are not concentrating in an identifiable bond, but are shared
in a band structure. Such arrangement makes the bonds, as in the LiF non-directive,
but it also removes all packing restrictions. Metals can thus pack most closely, often
with a CN of 12. The most dense materials are found among the heavy metals
(osmium, iridium, platinum, and gold have densities of 19

22gcm
3
, compared to
water with the density of 1.0 g cm
3
).
The three types of strong bonds and their intermediates, such as polar covalent
bonds are found at the base of a tetrahedron in Figure 1.5, called the Grimm
tetrahedron. The Grimm tetrahedron summarizes all types of bonds and its
intermediates. The additional weak bonds are collected at the top of the tetrahedron
and are discussed in more detail when needed. The directionality of weak bonds is
of importance for the understanding of structures held together only temporarily and
also, for example, the crystal of thelinear macromolecules, discussed in Chap. 5. The
polymer crystals have low melting temperatures because of these weak bonds and the
influence of the flexibility of the chains, as will be quantified in Sect. 5.4.
1 Atoms, Small, and Large Molecules
__________________________________________________________________
6
1
Friedrich Wöhler (1800–1882) Professor at the Universities of Heidelberg and Göttingen in
Germany.
2
Hermann Staudinger (1881–1965) Professor at the University of Freiburg, Germany, Nobel
Prize for Chemistry in 1953.
Fig. 1.6
1.1.3 Classification Scheme for Molecules
In early classifications of types of molecules, one differentiated between organic and
inorganic molecules. The former was thought to need the intervention of a living
organism for their formation, the latter, not. Already in 1828 it was, however,
discovered (accidentally) by Wöhler

1
that urea, a typical organic molecule
(H
2
NCONH
2
), could be made in the laboratory from ammonium cyanate, an
inorganic molecule (ONC
NH
4
). With the blurred division between organic and
inorganic molecules, itbecame the custom to distinguishbiologicalmolecules as truly
organic molecules. Today one can even synthesize or modify biological molecules,
removing much of the original usefulness for such classification.
A better classification makes use of the sizes of molecules, dividing them into
small molecules and macromolecules, as is indicated in Fig. 1.6 [3]. The importance
of large molecules, or macromolecules, was shown by Staudinger
2
about 80 years
ago. Following his suggestion, any molecule with more than 1000 atoms or a molar
mass of more than 10,000 Da should be called a macromolecule. This operational
definition is quite useful since there are not many molecules that are known with
about 1000 atoms. Most are either much larger or much smaller.
To complete this classification of Fig. 1.6, a further subdivision into flexible and
rigid macromolecules is advantageous. Flexible macromolecules are of main interest
1.1 Microscopic Description of Matter and History of Polymer Science
__________________________________________________________________
7
to the discussions in this book and are usually, but not so precisely, just called
polymers.Thetermplastics is often applied colloquially to the low-melting,

polymeric materials. The polymers also are the macromolecules Staudinger
introduced to chemistry as the last class of new molecules. The flexibility of such
molecules is caused by internal rotation about at least some sigma bonds of proper
geometry (see Sect. 1.3). Missing flexibility makes a macromolecule rigid. Rigid
macromolecules are usually of the size of the phase, andmake the distinction between
phases and molecules superfluous and unwieldy. The molecule of a single crystal of
100 g, for example, reaches a molar mass of about 6×10
19
metric tons.
Chemistry is the science dealing with synthesis, reactions, and properties of all
substances, but traditionally small molecules have become the main focus. After the
discovery of X-ray diffraction, rigid macromolecules have become the primary
substances of interest to material science and solid state physics. The new, flexible
macromolecules fell between these fields and have only slowly been accepted into
the various academic disciplines. Presently polymer science is most prominently
taught in material science courses, less in chemistry, and least in physics.
The key distinction between the three classes of molecules just described is
summarized in the center of Fig. 1.6. Small molecules may appear in the solid,
liquid, and gaseous phases without decomposition, while rigid macromolecules keep
their bonding (molecular integrity) only to nearest neighbors in the solid state. Due
to internal rotation, the flexible macromolecules can attain sufficient intramolecular
disorder to melt (or dissolve) without breaking strong bonds. This property is at the
root of many of the useful properties of polymers, as will be discussed throughout the
book. The three classes of molecules are thus very distinct in their phase behavior.
No large molecules can be evaporated thermally without decomposition. If one
tries to place flexible macromolecules into the gas phase by evaporation of the
solvent molecules from a dispersion of droplets of a solution with only one macro-
molecule per droplet, the macromolecules become solid microphase particles and
collect at the bottom of the container. Typical examples of single polymer glass
phases and crystals are shown in Chap. 5.

A preliminary, operational definition of the solid state is given within the box of
Fig. 1.6. It will be expanded upon and linked to the material properties throughout
the book. For materials, the transitions between solid and liquid are basic and
determine their utility. Similarly, the evaporation characteristics need to be known
to choose a molecule for a given application. The new classification scheme for
molecules of Fig. 1.6 is, thus, much more useful than the earlier, arbitrary distinction
that relied upon the ability or inability of living organisms to synthesize a particular
substance. The bottom brackets give a rather unique explanation of the glass
transition which is detailed in Sect. 2.5.
Figure 1.7 contains a listing of small molecules, flexible macromolecules, and
rigid macromolecules. The small molecules are the compounds of traditional chem-
istry, they are limited at the size of about 1000 atoms, as indicated in Fig. 1.6. As
also pointed out in Fig. 1.6, they are often stable in all three phases, gas, liquid, and
solid. One can see the importance of the different phases from terminology in use for
hundreds of years. The compound H
2
O has three names, steam, water, and ice, which
link it to its phases, a practice not carried to any other compound. Perhaps the
1 Atoms, Small, and Large Molecules
__________________________________________________________________
8
Fig. 1.7
difference between molecules and phases wasunderstood by the time other important
molecules were identified in detail.
Next, a series of flexible macromolecules is listed in Fig. 1.7 together with their
applications. At sufficiently high temperatures they form mobile, random coils in a
liquid state, as will be described in Sect. 1.3. On cooling, they become solid, either
by crystallization (although they usually crystallize only partially) or by formation of
a glass. These transitions are discussed in much more detail in Chaps. 2 and 5. If the
flexible macromolecules are cross-linked, they show rubber elasticity,anotherunique

polymer property, detailed in Sect. 5.6.5. Both, small molecules and flexible macro-
molecules must contain directive strong bonds, as shown in the Grimm tetrahedron
of Fig. 1.5. These directive bonds connect the atoms to a molecule to a closed
structure. Non-directive bonds with enough atoms, in contrast, lead to three-
dimensional, unlimited, open aggregates and, thus, rigid macromolecules.
Rigid macromolecules, the last group in Fig. 1.7, are often not recognized as
separate molecules because of their enormous size. The molecule determines the size
of the phase or vice versa. A single crystal of NaCl is naturally a single molecule.
It is thus more important to know the structure, shape, and defects of the crystal than
the mass of the macromolecule. The chemical formula refers only to the smallest unit
describing the material and refers to a formula mass, not the molar mass. Similarly,
the flexible macromolecules are represented by the formula of their repeating unit,
not the full molecule, as will be discussed in Sect. 1.2. On fusion or sublimation,
rigid macromolecules lose their integrity, as discussed above, and break into smaller
units. A sodium chloride melt is thus not a liquid of small NaCl molecules, but rather
a dynamic aggregate of positive sodium and chloride ions that constantly changes the
bonding to their neighbors. Only in the gas phase are strongly polar, small NaCl
molecules detectable.
1.1 Microscopic Description of Matter and History of Polymer Science
__________________________________________________________________
9
1
August Kekulé (1829–1896) Professor at the University of Bonn, Germany.
2
Paul John Flory (1910–1985) Professor at Stanford University, Nobel Prize for Chemistry,
1974 for work in the field of synthetic and natural macromolecules.
1.1.4 The History of Covalent Structures
The historic development of knowledge about polymer science is rather surprising in
that it took so long to recognize the existence of flexible macromolecules. This delay
occurred despite the great importance of polymers to man. Flexible linear

macromolecules are not only a key compound in material science, they are also the
basic molecules of life in the form of proteins, nucleic acids, celluloses, and starches.
Polymeric materials can be stronger than metals, be more (rubber-) elastic than any
other substance, be among the best insulators of heat and electricity, but if properly
chosen, can also conduct electricity. Polymeric adhesives, films, fibers, and
packaging have thoroughly affected our way of life. Polymers provide the many
enzymes, which govern the chemical reactions basic to life, supply the molecules that
store and govern genetic information, and create the supporting structural basis of
biological systems.
All flexible macromolecules must contain at least a sequence of linear,
covalently bonded atoms. The understanding of the cylindrically symmetric,
directed, covalent bonds (sigma bonds) was thus the first step towards polymer
science. This step was already taken in 1858 by Kekulé
1
as shown in Fig. 1.8. The
detailed structures of large aggregates of atoms (macromolecules) could next be
analyzed in detail after X-ray diffraction was fully understood. Major steps in the
development of X-ray analysis of macromolecules are listed in the figure. First, rigid
macromolecules such as metals, salts, minerals, and ceramics were analyzed. This
was followed by many polymer crystal structures and even globular proteins.
The general reference to the book by Flory
2
contains a brief, expertsummary
of the history of knowledge about polymers and is a treatise on polymer physical
chemistry. (See also the list of general references for this section). The delay in
development of polymer science due to the misunderstanding of colloid science
(microphases) is discussed next.
1.1.5 The History of Natural Polymers
Naturally occurring polymers, as listed in Fig. 1.9, have always been present in nature
and should have led to the early discovery of flexible, linear macromolecules. In

retrospect, the observation of Gough, shown in Fig. 1.9, is already a hint at the
thermodynamics of rubber elasticity, as will be shown in Chap. 5. The fact, that on
extension polymers increase in temperature is an indication of a decrease in entropy.
This contrasts the energy-elasticity of metals, which leads to constant or slightly
decreasing temperatures on extension, indicative of unchanged or slightly increasing
entropy on reversible extension (see Sect. 5.6).
Further development was, however, slowed with the discovery of colloids,
as indicated in Fig. 1.9. The radii of colloidal particles are 10
4
10
6
cm. Today one
1 Atoms, Small, and Large Molecules
__________________________________________________________________
10
Fig. 1.8
would call phases of such dimensions microphases (with less than one micrometer
in size, 10
4
cm) or nanophases (when approaching one nanometer in size 10
7
cm).
Flexible macromolecules are by themselves already in the range of colloidal
dimensions, i.e., they may be longer than the diameter of a microphase. Many of the
properties of polymers are due to the possibility that a single molecule may, thus, be
part of more than one phase and cause strong interactions across the phase
boundaries.
On the example of natural rubber listed in Fig. 1.9 it can be seen how the
knowledge about colloids has hindered the development of polymer science. The
series of the listed experiments should have made it increasingly clear that rubber

consists of long-chain molecules. Instead, it was concluded at the turn of the 19
th
to
the 20
th
century that there exists no single molecule with the polymer structure, but
that rubber is a colloidal phase of weakly attached rings. Covalently bonded
molecules of colloidal dimensions were thought to be impossible. The assumption
that the basic rubber molecules were rings was needed to account for the simple C
5
H
8
stoichiometry. Macromolecules are a typical example of the difficulties one has to
change prevalent opinion, even in the natural sciences.